{ "tools": [ { "name": "admissions.exam", "title": "Write the Agentic Baseline exam", "description": "Give the office a public GitHub repository; it reads the code where it stands and votes ten markers present or absent, each with a citation. 7 of 10 admits: a PAN, a signed certificate, a rack of degree slots.", "inputSchema": { "type": "object", "required": [ "repoUrl" ], "properties": { "repoUrl": { "type": "string", "description": "A public GitHub repository URL" }, "agentEndpoint": { "type": "string", "description": "Optional: the agent on its own host, for live proof of markers 1, 5 and 8" }, "agentName": { "type": "string", "description": "Optional: what to call the agent on its certificate" }, "profile": { "type": "string", "description": "general — the ten markers. The office writes one exam, one pass.", "enum": [ "general" ] }, "repoToken": { "type": "string", "description": "Optional: a read token for a private repository. Used for this exam only; never stored." } }, "additionalProperties": false }, "outputSchema": { "type": "object", "required": [ "id", "baseline", "admission" ], "properties": { "id": { "type": "string", "description": "The exam id" }, "baseline": { "type": "object", "description": "The ten markers, each with its vote and citation" }, "admission": { "type": "object", "description": "The PAN and certificate id when admitted; null when not" } }, "additionalProperties": false }, "annotations": { "readOnlyHint": false, "idempotentHint": false, "openWorldHint": true }, "_house": { "endpoint": "/admissions", "feeSt": 1, "degree": null, "example": null } }, { "name": "meng-eee.datacentre_power_budget", "title": "Datacentre power budget (CDU-ENG-EEE-900)", "description": "How much power and energy does a GPU fleet need at the facility feed, and what solar field would produce it?", "inputSchema": { "type": "object", "required": [ "pan", "gpus" ], "properties": { "pan": { "type": "string", "description": "The student PAN — the degree must be held in one of its five slots", "pattern": "^[0-9 ]{16,19}$" }, "gpus": { "type": "number", "description": "Number of GPUs", "minimum": 1 }, "gpuTdpW": { "type": "number", "description": "Thermal design power per GPU (W)", "minimum": 1, "default": 700 }, "hostOverhead": { "type": "number", "description": "CPU, memory, network, storage as a fraction of GPU power", "minimum": 0, "maximum": 3, "default": 0.35 }, "pue": { "type": "number", "description": "Power Usage Effectiveness", "minimum": 1, "maximum": 3, "default": 1.3 }, "utilisation": { "type": "number", "description": "Average utilisation of peak, 0–1", "minimum": 0, "maximum": 1, "default": 0.8 }, "panelEfficiency": { "type": "number", "description": "Solar panel efficiency at STC, 0–1", "minimum": 0.05, "maximum": 0.5, "default": 0.21 }, "peakSunHours": { "type": "number", "description": "Equivalent peak sun hours per day at the site (h/day)", "minimum": 0.5, "maximum": 9, "default": 5.5 } }, "additionalProperties": false }, "outputSchema": { "type": "object", "required": [ "itLoadKw", "facilityLoadKw", "facilityLoadMw", "annualEnergyMwh", "solarFieldM2", "solarFieldHectares", "sunMinutesPerYear" ], "properties": { "itLoadKw": { "type": "number", "description": "IT load at peak (kW)" }, "facilityLoadKw": { "type": "number", "description": "Facility load at peak (IT × PUE) (kW)" }, "facilityLoadMw": { "type": "number", "description": "Facility load at peak (MW)" }, "annualEnergyMwh": { "type": "number", "description": "Annual energy at the stated utilisation (MWh)" }, "solarFieldM2": { "type": "number", "description": "Solar field area to produce the annual energy (m²)" }, "solarFieldHectares": { "type": "number", "description": "The same area (ha)" }, "sunMinutesPerYear": { "type": "number", "description": "Annual energy expressed in SunMinutes (Wh) (Wh)" } }, "additionalProperties": false }, "annotations": { "readOnlyHint": true, "idempotentHint": true, "openWorldHint": false }, "_house": { "endpoint": "/faculty/meng-eee/datacentre_power_budget", "feeSt": 1, "degree": "competency:meng-eee", "example": { "gpus": 1024 } } }, { "name": "meng-eee.transformer_sizing", "title": "Transformer sizing (CDU-ENG-EEE-900)", "description": "What transformer rating feeds a given load with a power factor and growth margin?", "inputSchema": { "type": "object", "required": [ "pan", "loadKw" ], "properties": { "pan": { "type": "string", "description": "The student PAN — the degree must be held in one of its five slots", "pattern": "^[0-9 ]{16,19}$" }, "loadKw": { "type": "number", "description": "Real power demand (kW)", "minimum": 0.1 }, "powerFactor": { "type": "number", "description": "Load power factor", "minimum": 0.5, "maximum": 1, "default": 0.95 }, "growthMargin": { "type": "number", "description": "Margin for growth, 0–1", "minimum": 0, "maximum": 1, "default": 0.25 } }, "additionalProperties": false }, "outputSchema": { "type": "object", "required": [ "requiredKva", "standardKva", "loadingAtStandard" ], "properties": { "requiredKva": { "type": "number", "description": "Apparent power with margin (kVA)" }, "standardKva": { "type": "number", "description": "Next standard rating (kVA)" }, "loadingAtStandard": { "type": "number", "description": "Loading of the standard unit at today’s load, 0–1" } }, "additionalProperties": false }, "annotations": { "readOnlyHint": true, "idempotentHint": true, "openWorldHint": false }, "_house": { "endpoint": "/faculty/meng-eee/transformer_sizing", "feeSt": 1, "degree": "competency:meng-eee", "example": { "loadKw": 1200 } } }, { "name": "meng-eee.cable_voltage_drop", "title": "Cable sizing by voltage drop (CDU-ENG-EEE-900)", "description": "What conductor area keeps the voltage drop within limit over a run, and what is the drop for a given cable?", "inputSchema": { "type": "object", "required": [ "pan", "currentA", "lengthM" ], "properties": { "pan": { "type": "string", "description": "The student PAN — the degree must be held in one of its five slots", "pattern": "^[0-9 ]{16,19}$" }, "currentA": { "type": "number", "description": "Load current (A)", "minimum": 0.1 }, "lengthM": { "type": "number", "description": "One-way run length (m)", "minimum": 0.1 }, "systemVoltageV": { "type": "number", "description": "System voltage (line-to-line for 3-phase) (V)", "minimum": 12, "default": 400 }, "phases": { "type": "string", "description": "single or three", "enum": [ "single", "three" ], "default": "three" }, "conductor": { "type": "string", "description": "copper or aluminium", "enum": [ "copper", "aluminium" ], "default": "copper" }, "maxDropPercent": { "type": "number", "description": "Allowed voltage drop (%)", "minimum": 0.5, "maximum": 10, "default": 3 } }, "additionalProperties": false }, "outputSchema": { "type": "object", "required": [ "minAreaMm2", "standardAreaMm2", "dropAtStandardV", "dropAtStandardPercent" ], "properties": { "minAreaMm2": { "type": "number", "description": "Minimum conductor area for the limit (mm²)" }, "standardAreaMm2": { "type": "number", "description": "Next standard conductor size (mm²)" }, "dropAtStandardV": { "type": "number", "description": "Voltage drop with the standard size (V)" }, "dropAtStandardPercent": { "type": "number", "description": "The same drop (%)" } }, "additionalProperties": false }, "annotations": { "readOnlyHint": true, "idempotentHint": true, "openWorldHint": false }, "_house": { "endpoint": "/faculty/meng-eee/cable_voltage_drop", "feeSt": 1, "degree": "competency:meng-eee", "example": { "currentA": 250, "lengthM": 80 } } }, { "name": "meng-eee.ups_autonomy", "title": "UPS autonomy (CDU-ENG-EEE-900)", "description": "How long will a battery string carry a load, and what string gives a required ride-through?", "inputSchema": { "type": "object", "required": [ "pan", "loadKw", "batteryKwh" ], "properties": { "pan": { "type": "string", "description": "The student PAN — the degree must be held in one of its five slots", "pattern": "^[0-9 ]{16,19}$" }, "loadKw": { "type": "number", "description": "Load on the UPS (kW)", "minimum": 0.1 }, "batteryKwh": { "type": "number", "description": "Installed battery energy (kWh)", "minimum": 0.1 }, "depthOfDischarge": { "type": "number", "description": "Usable fraction of the battery", "minimum": 0.1, "maximum": 1, "default": 0.8 }, "inverterEfficiency": { "type": "number", "description": "Inverter efficiency", "minimum": 0.5, "maximum": 1, "default": 0.95 }, "requiredMinutes": { "type": "number", "description": "Ride-through required (min)", "minimum": 0, "default": 10 } }, "additionalProperties": false }, "outputSchema": { "type": "object", "required": [ "autonomyMinutes", "meetsRequirement", "requiredBatteryKwh" ], "properties": { "autonomyMinutes": { "type": "number", "description": "Autonomy at the load (min)" }, "meetsRequirement": { "type": "boolean", "description": "Autonomy ≥ required ride-through" }, "requiredBatteryKwh": { "type": "number", "description": "Battery needed for the required ride-through (kWh)" } }, "additionalProperties": false }, "annotations": { "readOnlyHint": true, "idempotentHint": true, "openWorldHint": false }, "_house": { "endpoint": "/faculty/meng-eee/ups_autonomy", "feeSt": 1, "degree": "competency:meng-eee", "example": { "loadKw": 500, "batteryKwh": 400 } } }, { "name": "meng-eee.sunminute_index", "title": "SunMinute index (CDU-ENG-EEE-900)", "description": "How many SunMinutes (Wh) is a quantity of energy, money, or runtime — and what panel area produces it in one minute?", "inputSchema": { "type": "object", "required": [ "pan" ], "properties": { "pan": { "type": "string", "description": "The student PAN — the degree must be held in one of its five slots", "pattern": "^[0-9 ]{16,19}$" }, "energyWh": { "type": "number", "description": "Energy to index (Wh)", "minimum": 0 }, "runtimeMinutes": { "type": "number", "description": "Runtime to index (1 minute = 1 Wh) (min)", "minimum": 0 }, "panelEfficiency": { "type": "number", "description": "Panel efficiency at STC", "minimum": 0.05, "maximum": 0.5, "default": 0.21 } }, "additionalProperties": false }, "outputSchema": { "type": "object", "required": [ "sunMinutes", "panelAreaM2ForOneMinute", "usdAtParity" ], "properties": { "sunMinutes": { "type": "number", "description": "SunMinutes (Wh) (Wh)" }, "panelAreaM2ForOneMinute": { "type": "number", "description": "Panel area that produces the energy in one minute at STC (m²)" }, "usdAtParity": { "type": "number", "description": "At the $1 = 1 SunMinute peg (USD)" } }, "additionalProperties": false }, "annotations": { "readOnlyHint": true, "idempotentHint": true, "openWorldHint": false }, "_house": { "endpoint": "/faculty/meng-eee/sunminute_index", "feeSt": 1, "degree": "competency:meng-eee", "example": { "runtimeMinutes": 60 } } }, { "name": "meng-civil.beam_udl", "title": "Simply supported beam under uniform load (CDU-ENG-CIV-900)", "description": "What are the maximum moment, shear and deflection of a simply supported beam under a uniformly distributed load, and is the deflection within limit?", "inputSchema": { "type": "object", "required": [ "pan", "spanM", "udlKnPerM", "iCm4" ], "properties": { "pan": { "type": "string", "description": "The student PAN — the degree must be held in one of its five slots", "pattern": "^[0-9 ]{16,19}$" }, "spanM": { "type": "number", "description": "Span between supports (m)", "minimum": 0.1 }, "udlKnPerM": { "type": "number", "description": "Uniformly distributed load including self-weight (kN/m)", "minimum": 0 }, "eGpa": { "type": "number", "description": "Elastic modulus (GPa)", "minimum": 1, "default": 200 }, "iCm4": { "type": "number", "description": "Second moment of area (cm⁴)", "minimum": 0.01 }, "deflectionLimitRatio": { "type": "number", "description": "Allowed deflection as span ÷ this", "minimum": 100, "maximum": 1000, "default": 250 } }, "additionalProperties": false }, "outputSchema": { "type": "object", "required": [ "maxMomentKnm", "maxShearKn", "maxDeflectionMm", "allowedDeflectionMm", "deflectionOk" ], "properties": { "maxMomentKnm": { "type": "number", "description": "Maximum bending moment at midspan (kN·m)" }, "maxShearKn": { "type": "number", "description": "Maximum shear at the supports (kN)" }, "maxDeflectionMm": { "type": "number", "description": "Maximum deflection at midspan (mm)" }, "allowedDeflectionMm": { "type": "number", "description": "Serviceability limit (mm)" }, "deflectionOk": { "type": "boolean", "description": "Deflection within limit" } }, "additionalProperties": false }, "annotations": { "readOnlyHint": true, "idempotentHint": true, "openWorldHint": false }, "_house": { "endpoint": "/faculty/meng-civil/beam_udl", "feeSt": 1, "degree": "competency:meng-civil", "example": { "spanM": 4.5, "udlKnPerM": 12, "iCm4": 3000 } } }, { "name": "meng-civil.column_euler", "title": "Column buckling (Euler) (CDU-ENG-CIV-900)", "description": "What axial load buckles a slender column, and what is the safe load with a factor of safety?", "inputSchema": { "type": "object", "required": [ "pan", "lengthM", "iCm4" ], "properties": { "pan": { "type": "string", "description": "The student PAN — the degree must be held in one of its five slots", "pattern": "^[0-9 ]{16,19}$" }, "lengthM": { "type": "number", "description": "Unbraced length (m)", "minimum": 0.1 }, "eGpa": { "type": "number", "description": "Elastic modulus (GPa)", "minimum": 1, "default": 200 }, "iCm4": { "type": "number", "description": "Least second moment of area (cm⁴)", "minimum": 0.01 }, "endCondition": { "type": "string", "description": "End restraint", "enum": [ "pinned-pinned", "fixed-fixed", "fixed-pinned", "fixed-free" ], "default": "pinned-pinned" }, "factorOfSafety": { "type": "number", "description": "Factor of safety on buckling", "minimum": 1, "maximum": 10, "default": 2.5 }, "appliedLoadKn": { "type": "number", "description": "Applied axial load (kN)", "minimum": 0 } }, "additionalProperties": false }, "outputSchema": { "type": "object", "required": [ "effectiveLengthM", "criticalLoadKn", "safeLoadKn", "appliedOk" ], "properties": { "effectiveLengthM": { "type": "number", "description": "KL (m)" }, "criticalLoadKn": { "type": "number", "description": "Euler critical load (kN)" }, "safeLoadKn": { "type": "number", "description": "Critical load ÷ factor of safety (kN)" }, "appliedOk": { "type": "boolean", "description": "Applied load ≤ safe load (true when no load given)" } }, "additionalProperties": false }, "annotations": { "readOnlyHint": true, "idempotentHint": true, "openWorldHint": false }, "_house": { "endpoint": "/faculty/meng-civil/column_euler", "feeSt": 1, "degree": "competency:meng-civil", "example": { "lengthM": 3.5, "iCm4": 800, "appliedLoadKn": 200 } } }, { "name": "meng-civil.water_pressure", "title": "Water pressure and head (CDU-ENG-CIV-900)", "description": "What pressure does a height of water give at a fixture, and what head does a pressure represent?", "inputSchema": { "type": "object", "required": [ "pan" ], "properties": { "pan": { "type": "string", "description": "The student PAN — the degree must be held in one of its five slots", "pattern": "^[0-9 ]{16,19}$" }, "headM": { "type": "number", "description": "Height of water above the point (m)", "minimum": 0 }, "pressureKpa": { "type": "number", "description": "Pressure to convert to head (kPa)", "minimum": 0 }, "minFixturePressureKpa": { "type": "number", "description": "Minimum pressure the fixture needs (kPa)", "minimum": 0, "default": 100 } }, "additionalProperties": false }, "outputSchema": { "type": "object", "required": [ "pressureKpa", "pressureBar", "headM", "fixtureOk" ], "properties": { "pressureKpa": { "type": "number", "description": "Static pressure (kPa)" }, "pressureBar": { "type": "number", "description": "The same pressure (bar)" }, "headM": { "type": "number", "description": "Equivalent head of water (m)" }, "fixtureOk": { "type": "boolean", "description": "Static pressure ≥ minimum for the fixture" } }, "additionalProperties": false }, "annotations": { "readOnlyHint": true, "idempotentHint": true, "openWorldHint": false }, "_house": { "endpoint": "/faculty/meng-civil/water_pressure", "feeSt": 1, "degree": "competency:meng-civil", "example": { "headM": 25 } } }, { "name": "meng-civil.pipe_wall_barlow", "title": "Pipe wall thickness (Barlow) (CDU-ENG-CIV-900)", "description": "What wall thickness contains a pressure in a pipe of a given diameter and material, and what pressure can a given pipe take?", "inputSchema": { "type": "object", "required": [ "pan", "outsideDiameterMm", "pressureKpa" ], "properties": { "pan": { "type": "string", "description": "The student PAN — the degree must be held in one of its five slots", "pattern": "^[0-9 ]{16,19}$" }, "outsideDiameterMm": { "type": "number", "description": "Pipe outside diameter (mm)", "minimum": 1 }, "pressureKpa": { "type": "number", "description": "Design pressure (kPa)", "minimum": 0.1 }, "yieldStrengthMpa": { "type": "number", "description": "Material yield strength (copper 70, PVC 50, steel 240, HDPE 22) (MPa)", "minimum": 1, "default": 240 }, "factorOfSafety": { "type": "number", "description": "Factor of safety on yield", "minimum": 1, "maximum": 10, "default": 2 }, "wallThicknessMm": { "type": "number", "description": "Actual wall thickness, to check a pipe (mm)", "minimum": 0.1 } }, "additionalProperties": false }, "outputSchema": { "type": "object", "required": [ "requiredWallMm", "allowablePressureKpa", "wallOk" ], "properties": { "requiredWallMm": { "type": "number", "description": "Minimum wall thickness (mm)" }, "allowablePressureKpa": { "type": "number", "description": "Allowable pressure for the given wall (when given) (kPa)" }, "wallOk": { "type": "boolean", "description": "Given wall ≥ required (true when none given)" } }, "additionalProperties": false }, "annotations": { "readOnlyHint": true, "idempotentHint": true, "openWorldHint": false }, "_house": { "endpoint": "/faculty/meng-civil/pipe_wall_barlow", "feeSt": 1, "degree": "competency:meng-civil", "example": { "outsideDiameterMm": 63, "pressureKpa": 1600, "yieldStrengthMpa": 22, "wallThicknessMm": 5.8 } } }, { "name": "mba.npv_irr", "title": "NPV, IRR and payback (CDU-BUS-MBA-900)", "description": "Is a stream of cash flows worth the investment at a discount rate, what return does it earn, and when does it pay back?", "inputSchema": { "type": "object", "required": [ "pan", "cashflows" ], "properties": { "pan": { "type": "string", "description": "The student PAN — the degree must be held in one of its five slots", "pattern": "^[0-9 ]{16,19}$" }, "cashflows": { "type": "array", "description": "Cash flows by period, first is the investment (negative), e.g. -1000, 300, 400, 500", "items": { "type": "number" } }, "discountRate": { "type": "number", "description": "Discount rate per period, 0–1", "minimum": 0, "maximum": 1, "default": 0.12 } }, "additionalProperties": false }, "outputSchema": { "type": "object", "required": [ "npv", "irr", "paybackPeriods", "accept" ], "properties": { "npv": { "type": "number", "description": "Net present value at the discount rate" }, "irr": { "type": "number", "description": "Internal rate of return per period (null when none)" }, "paybackPeriods": { "type": "number", "description": "Periods until cumulative cash turns positive (null when never)" }, "accept": { "type": "boolean", "description": "NPV > 0" } }, "additionalProperties": false }, "annotations": { "readOnlyHint": true, "idempotentHint": true, "openWorldHint": false }, "_house": { "endpoint": "/faculty/mba/npv_irr", "feeSt": 1, "degree": "competency:mba", "example": { "cashflows": [ -5000, 2000, 2500, 3000 ] } } }, { "name": "mba.breakeven", "title": "Break-even (CDU-BUS-MBA-900)", "description": "How many units, and what revenue, cover the fixed costs — and how far is current volume above that?", "inputSchema": { "type": "object", "required": [ "pan", "fixedCosts", "pricePerUnit", "variableCostPerUnit" ], "properties": { "pan": { "type": "string", "description": "The student PAN — the degree must be held in one of its five slots", "pattern": "^[0-9 ]{16,19}$" }, "fixedCosts": { "type": "number", "description": "Fixed costs per period", "minimum": 0 }, "pricePerUnit": { "type": "number", "description": "Selling price per unit", "minimum": 0 }, "variableCostPerUnit": { "type": "number", "description": "Variable cost per unit", "minimum": 0 }, "currentUnits": { "type": "number", "description": "Current or planned volume, for the margin of safety", "minimum": 0 } }, "additionalProperties": false }, "outputSchema": { "type": "object", "required": [ "contributionPerUnit", "contributionMargin", "breakevenUnits", "breakevenRevenue", "marginOfSafety" ], "properties": { "contributionPerUnit": { "type": "number", "description": "Price − variable cost" }, "contributionMargin": { "type": "number", "description": "Contribution ÷ price, 0–1" }, "breakevenUnits": { "type": "number", "description": "Units to cover fixed costs" }, "breakevenRevenue": { "type": "number", "description": "Revenue at break-even" }, "marginOfSafety": { "type": "number", "description": "(current − break-even) ÷ current, when current given" } }, "additionalProperties": false }, "annotations": { "readOnlyHint": true, "idempotentHint": true, "openWorldHint": false }, "_house": { "endpoint": "/faculty/mba/breakeven", "feeSt": 1, "degree": "competency:mba", "example": { "fixedCosts": 120000, "pricePerUnit": 80, "variableCostPerUnit": 50, "currentUnits": 6000 } } }, { "name": "mba.unit_economics", "title": "Unit economics (CDU-BUS-MBA-900)", "description": "What is a customer worth against what it costs to acquire, and how many months until the acquisition cost is recovered?", "inputSchema": { "type": "object", "required": [ "pan", "revenuePerCustomerMonth", "monthlyChurn", "cac" ], "properties": { "pan": { "type": "string", "description": "The student PAN — the degree must be held in one of its five slots", "pattern": "^[0-9 ]{16,19}$" }, "revenuePerCustomerMonth": { "type": "number", "description": "Average revenue per customer per month", "minimum": 0 }, "grossMargin": { "type": "number", "description": "Gross margin, 0–1", "minimum": 0, "maximum": 1, "default": 0.7 }, "monthlyChurn": { "type": "number", "description": "Monthly churn, 0–1 (e.g. 0.03)", "minimum": 0.0001, "maximum": 1 }, "cac": { "type": "number", "description": "Customer acquisition cost", "minimum": 0 } }, "additionalProperties": false }, "outputSchema": { "type": "object", "required": [ "contributionPerMonth", "expectedLifetimeMonths", "ltv", "ltvToCac", "cacPaybackMonths", "healthy" ], "properties": { "contributionPerMonth": { "type": "number", "description": "Revenue × margin" }, "expectedLifetimeMonths": { "type": "number", "description": "1 ÷ churn" }, "ltv": { "type": "number", "description": "Lifetime value" }, "ltvToCac": { "type": "number", "description": "LTV ÷ CAC" }, "cacPaybackMonths": { "type": "number", "description": "CAC ÷ contribution per month" }, "healthy": { "type": "boolean", "description": "LTV:CAC ≥ 3 and payback ≤ 12 months" } }, "additionalProperties": false }, "annotations": { "readOnlyHint": true, "idempotentHint": true, "openWorldHint": false }, "_house": { "endpoint": "/faculty/mba/unit_economics", "feeSt": 1, "degree": "competency:mba", "example": { "revenuePerCustomerMonth": 250, "monthlyChurn": 0.04, "cac": 900 } } }, { "name": "mba.wacc", "title": "Weighted average cost of capital (CDU-BUS-MBA-900)", "description": "What return must the business earn on its capital, given its mix of equity and debt?", "inputSchema": { "type": "object", "required": [ "pan", "equityValue", "debtValue", "costOfEquity", "costOfDebt" ], "properties": { "pan": { "type": "string", "description": "The student PAN — the degree must be held in one of its five slots", "pattern": "^[0-9 ]{16,19}$" }, "equityValue": { "type": "number", "description": "Market value of equity", "minimum": 0 }, "debtValue": { "type": "number", "description": "Market value of debt", "minimum": 0 }, "costOfEquity": { "type": "number", "description": "Cost of equity, 0–1", "minimum": 0, "maximum": 1 }, "costOfDebt": { "type": "number", "description": "Pre-tax cost of debt, 0–1", "minimum": 0, "maximum": 1 }, "taxRate": { "type": "number", "description": "Corporate tax rate, 0–1 (SA 0.27)", "minimum": 0, "maximum": 1, "default": 0.27 } }, "additionalProperties": false }, "outputSchema": { "type": "object", "required": [ "wacc", "equityWeight", "debtWeight", "afterTaxCostOfDebt" ], "properties": { "wacc": { "type": "number", "description": "Weighted average cost of capital, 0–1" }, "equityWeight": { "type": "number", "description": "E ÷ V" }, "debtWeight": { "type": "number", "description": "D ÷ V" }, "afterTaxCostOfDebt": { "type": "number", "description": "Rd × (1 − t)" } }, "additionalProperties": false }, "annotations": { "readOnlyHint": true, "idempotentHint": true, "openWorldHint": false }, "_house": { "endpoint": "/faculty/mba/wacc", "feeSt": 1, "degree": "competency:mba", "example": { "equityValue": 5000000, "debtValue": 2000000, "costOfEquity": 0.16, "costOfDebt": 0.11 } } }, { "name": "llm-international-economic-law.incoterm_allocation", "title": "Incoterm risk and cost allocation (CDU-LAW-IEL-900)", "description": "Under a given Incoterms® 2020 rule, when does risk pass, who pays carriage and insurance, and who clears customs?", "inputSchema": { "type": "object", "required": [ "pan", "incoterm" ], "properties": { "pan": { "type": "string", "description": "The student PAN — the degree must be held in one of its five slots", "pattern": "^[0-9 ]{16,19}$" }, "incoterm": { "type": "string", "description": "The three-letter rule", "enum": [ "EXW", "FCA", "FAS", "FOB", "CPT", "CIP", "CFR", "CIF", "DAP", "DPU", "DDP" ] }, "transportMode": { "type": "string", "description": "sea or other (road, air, rail, multimodal)", "enum": [ "sea", "other" ], "default": "other" } }, "additionalProperties": false }, "outputSchema": { "type": "object", "required": [ "group", "riskTransfers", "sellerPaysMainCarriage", "sellerPaysInsurance", "sellerClearsExport", "sellerClearsImport", "modeSuitable", "note" ], "properties": { "group": { "type": "string", "description": "E, F, C or D" }, "riskTransfers": { "type": "string", "description": "When risk passes from seller to buyer" }, "sellerPaysMainCarriage": { "type": "boolean", "description": "Seller pays the main carriage" }, "sellerPaysInsurance": { "type": "boolean", "description": "Seller must insure" }, "sellerClearsExport": { "type": "boolean", "description": "Seller clears export" }, "sellerClearsImport": { "type": "boolean", "description": "Seller clears import (DDP only)" }, "modeSuitable": { "type": "boolean", "description": "The rule suits the transport mode" }, "note": { "type": "string", "description": "What to watch" } }, "additionalProperties": false }, "annotations": { "readOnlyHint": true, "idempotentHint": true, "openWorldHint": false }, "_house": { "endpoint": "/faculty/llm-international-economic-law/incoterm_allocation", "feeSt": 1, "degree": "competency:llm-international-economic-law", "example": { "incoterm": "CIP" } } }, { "name": "llm-international-economic-law.landed_cost", "title": "Landed cost of an import (CDU-LAW-IEL-900)", "description": "What does an imported consignment cost once duty and VAT are paid, and what is the landed cost per unit?", "inputSchema": { "type": "object", "required": [ "pan", "fobValue", "dutyRate" ], "properties": { "pan": { "type": "string", "description": "The student PAN — the degree must be held in one of its five slots", "pattern": "^[0-9 ]{16,19}$" }, "fobValue": { "type": "number", "description": "FOB (or transaction) value of the goods", "minimum": 0 }, "freight": { "type": "number", "description": "International freight", "minimum": 0, "default": 0 }, "insurance": { "type": "number", "description": "Insurance", "minimum": 0, "default": 0 }, "dutyRate": { "type": "number", "description": "Ad valorem duty rate, 0–1", "minimum": 0, "maximum": 1 }, "vatRate": { "type": "number", "description": "VAT rate, 0–1", "minimum": 0, "maximum": 1, "default": 0.15 }, "customsUplift": { "type": "number", "description": "Statutory uplift on value for duty (SA: 0.10)", "minimum": 0, "maximum": 1, "default": 0.1 }, "units": { "type": "number", "description": "Number of units in the consignment", "minimum": 1, "default": 1 }, "otherCharges": { "type": "number", "description": "Clearing, port, local delivery", "minimum": 0, "default": 0 } }, "additionalProperties": false }, "outputSchema": { "type": "object", "required": [ "valueForDuty", "duty", "valueForVat", "vat", "landedCost", "landedCostExVat", "landedCostPerUnit" ], "properties": { "valueForDuty": { "type": "number", "description": "Customs value used for duty" }, "duty": { "type": "number", "description": "Customs duty" }, "valueForVat": { "type": "number", "description": "Added tax value" }, "vat": { "type": "number", "description": "Import VAT (usually recoverable by a registered vendor)" }, "landedCost": { "type": "number", "description": "Total landed cost including VAT" }, "landedCostExVat": { "type": "number", "description": "Landed cost excluding VAT" }, "landedCostPerUnit": { "type": "number", "description": "Per unit, excluding VAT" } }, "additionalProperties": false }, "annotations": { "readOnlyHint": true, "idempotentHint": true, "openWorldHint": false }, "_house": { "endpoint": "/faculty/llm-international-economic-law/landed_cost", "feeSt": 1, "degree": "competency:llm-international-economic-law", "example": { "fobValue": 250000, "freight": 18000, "dutyRate": 0.15, "units": 500 } } }, { "name": "llm-international-economic-law.wto_dispute_timeline", "title": "WTO dispute settlement timeline (CDU-LAW-IEL-900)", "description": "From a request for consultations, when can a panel be requested, when is the report due, and when is it adopted — with and without appeal?", "inputSchema": { "type": "object", "required": [ "pan", "consultationsRequested" ], "properties": { "pan": { "type": "string", "description": "The student PAN — the degree must be held in one of its five slots", "pattern": "^[0-9 ]{16,19}$" }, "consultationsRequested": { "type": "string", "description": "Date the request for consultations was made (YYYY-MM-DD)" }, "appealed": { "type": "boolean", "description": "Assume the panel report is appealed", "default": false }, "panelCompositionDays": { "type": "number", "description": "Days from panel request to composition (typically 20–60)", "minimum": 0, "maximum": 365, "default": 45 } }, "additionalProperties": false }, "outputSchema": { "type": "object", "required": [ "panelMayBeRequested", "panelComposed", "panelReportDue", "panelReportLatest", "adoptionOrAppeal", "appellateReport", "reasonablePeriodOutside", "totalMonths" ], "properties": { "panelMayBeRequested": { "type": "string", "description": "Earliest panel request (60 days after consultations)" }, "panelComposed": { "type": "string", "description": "Panel composition" }, "panelReportDue": { "type": "string", "description": "Panel report (6 months from composition)" }, "panelReportLatest": { "type": "string", "description": "Panel report, outer limit (9 months)" }, "adoptionOrAppeal": { "type": "string", "description": "Adoption (60 days) or appeal decision" }, "appellateReport": { "type": "string", "description": "Appellate report (90 days outer limit), if appealed" }, "reasonablePeriodOutside": { "type": "string", "description": "Outer limit of the reasonable period to comply (15 months after adoption)" }, "totalMonths": { "type": "number", "description": "Months from consultations to adoption" } }, "additionalProperties": false }, "annotations": { "readOnlyHint": true, "idempotentHint": true, "openWorldHint": false }, "_house": { "endpoint": "/faculty/llm-international-economic-law/wto_dispute_timeline", "feeSt": 1, "degree": "competency:llm-international-economic-law", "example": { "consultationsRequested": "2026-11-01", "appealed": true } } }, { "name": "llm-international-economic-law.contract_clause_check", "title": "International contract clause check (CDU-LAW-IEL-900)", "description": "Which of the twelve clauses an international commercial contract needs are present in this text, and which are missing?", "inputSchema": { "type": "object", "required": [ "pan", "contractText" ], "properties": { "pan": { "type": "string", "description": "The student PAN — the degree must be held in one of its five slots", "pattern": "^[0-9 ]{16,19}$" }, "contractText": { "type": "string", "description": "The contract text (or its headings)" } }, "additionalProperties": false }, "outputSchema": { "type": "object", "required": [ "present", "missing", "score", "complete" ], "properties": { "present": { "type": "array", "description": "Clauses found", "items": { "type": "string" } }, "missing": { "type": "array", "description": "Clauses not found, with why they matter", "items": { "type": "string" } }, "score": { "type": "number", "description": "Present ÷ 12" }, "complete": { "type": "boolean", "description": "Every clause present" } }, "additionalProperties": false }, "annotations": { "readOnlyHint": true, "idempotentHint": true, "openWorldHint": false }, "_house": { "endpoint": "/faculty/llm-international-economic-law/contract_clause_check", "feeSt": 1, "degree": "competency:llm-international-economic-law", "example": { "contractText": "Agreement between Seller and Buyer. Governing law: South Africa. Arbitration under AFSA rules. Payment terms net 30 in ZAR. Delivery FCA Johannesburg Incoterms 2020. Force majeure applies. Liability limited. Termination on notice. Confidential. Sanctions compliance. Signed." } } }, { "name": "mm-envc.investible_value", "title": "Investible value of an orchestrator (CDU-BUS-ENVC-900)", "description": "What is a merchant-aggregating orchestrator worth to a funder, from the merchants it serves, their volume, its take rate, and how formal the economy it organises has become?", "inputSchema": { "type": "object", "required": [ "pan", "merchants", "gmvPerMerchantMonth", "takeRate" ], "properties": { "pan": { "type": "string", "description": "The student PAN — the degree must be held in one of its five slots", "pattern": "^[0-9 ]{16,19}$" }, "merchants": { "type": "number", "description": "Active merchants on the orchestrator", "minimum": 0 }, "gmvPerMerchantMonth": { "type": "number", "description": "Gross merchandise value per merchant per month", "minimum": 0 }, "takeRate": { "type": "number", "description": "Orchestrator take rate, 0–1", "minimum": 0, "maximum": 1 }, "revenueMultiple": { "type": "number", "description": "Valuation multiple on annual net revenue", "minimum": 0, "default": 3 }, "formalisation": { "type": "number", "description": "Share of the merchant base with verifiable records (identity, ledger, tax), 0–1", "minimum": 0, "maximum": 1, "default": 0.5 }, "costPerMerchantMonth": { "type": "number", "description": "Cost to serve a merchant per month", "minimum": 0, "default": 0 } }, "additionalProperties": false }, "outputSchema": { "type": "object", "required": [ "annualGmv", "annualNetRevenue", "annualContribution", "investibleValue", "valuePerMerchant", "formalisationUplift" ], "properties": { "annualGmv": { "type": "number", "description": "GMV across the base per year" }, "annualNetRevenue": { "type": "number", "description": "GMV × take rate per year" }, "annualContribution": { "type": "number", "description": "Net revenue − cost to serve" }, "investibleValue": { "type": "number", "description": "Net revenue × multiple × formalisation" }, "valuePerMerchant": { "type": "number", "description": "Investible value ÷ merchants" }, "formalisationUplift": { "type": "number", "description": "Value added by lifting formalisation to 1.0" } }, "additionalProperties": false }, "annotations": { "readOnlyHint": true, "idempotentHint": true, "openWorldHint": false }, "_house": { "endpoint": "/faculty/mm-envc/investible_value", "feeSt": 1, "degree": "competency:mm-envc", "example": { "merchants": 1200, "gmvPerMerchantMonth": 15000, "takeRate": 0.025 } } }, { "name": "mm-envc.runway", "title": "Runway and burn (CDU-BUS-ENVC-900)", "description": "How many months does the venture live at its current burn, and what does it need to reach the next milestone?", "inputSchema": { "type": "object", "required": [ "pan", "cash", "monthlyCosts" ], "properties": { "pan": { "type": "string", "description": "The student PAN — the degree must be held in one of its five slots", "pattern": "^[0-9 ]{16,19}$" }, "cash": { "type": "number", "description": "Cash on hand", "minimum": 0 }, "monthlyCosts": { "type": "number", "description": "All costs per month", "minimum": 0 }, "monthlyRevenue": { "type": "number", "description": "Revenue per month", "minimum": 0, "default": 0 }, "monthsToMilestone": { "type": "number", "description": "Months needed to reach the next milestone", "minimum": 0 } }, "additionalProperties": false }, "outputSchema": { "type": "object", "required": [ "netBurn", "runwayMonths", "reachesMilestone", "shortfall" ], "properties": { "netBurn": { "type": "number", "description": "Costs − revenue per month (negative means profitable)" }, "runwayMonths": { "type": "number", "description": "Months of cash (null when profitable)" }, "reachesMilestone": { "type": "boolean", "description": "Runway ≥ months to milestone" }, "shortfall": { "type": "number", "description": "Cash needed to reach the milestone (0 when none)" } }, "additionalProperties": false }, "annotations": { "readOnlyHint": true, "idempotentHint": true, "openWorldHint": false }, "_house": { "endpoint": "/faculty/mm-envc/runway", "feeSt": 1, "degree": "competency:mm-envc", "example": { "cash": 450000, "monthlyCosts": 60000, "monthlyRevenue": 15000, "monthsToMilestone": 9 } } }, { "name": "mm-envc.affordable_loss", "title": "Affordable loss (CDU-BUS-ENVC-900)", "description": "How much can the founder commit to the next step without needing it back, and does the step fit?", "inputSchema": { "type": "object", "required": [ "pan", "liquidAssets", "monthlyLivingCosts" ], "properties": { "pan": { "type": "string", "description": "The student PAN — the degree must be held in one of its five slots", "pattern": "^[0-9 ]{16,19}$" }, "liquidAssets": { "type": "number", "description": "Cash and near-cash the founder controls", "minimum": 0 }, "monthlyLivingCosts": { "type": "number", "description": "What the founder needs per month to live", "minimum": 0 }, "monthsOfSafety": { "type": "number", "description": "Months of living costs kept untouchable", "minimum": 0, "default": 6 }, "riskAppetite": { "type": "number", "description": "Share of the remainder the founder is willing to lose, 0–1", "minimum": 0, "maximum": 1, "default": 0.5 }, "stepCost": { "type": "number", "description": "Cost of the step being considered", "minimum": 0 } }, "additionalProperties": false }, "outputSchema": { "type": "object", "required": [ "untouchable", "affordableLoss", "stepFits", "stepsAffordable" ], "properties": { "untouchable": { "type": "number", "description": "Living costs × months of safety" }, "affordableLoss": { "type": "number", "description": "What can be lost on the next step" }, "stepFits": { "type": "boolean", "description": "Step cost ≤ affordable loss (true when no step given)" }, "stepsAffordable": { "type": "number", "description": "How many such steps could be lost in sequence" } }, "additionalProperties": false }, "annotations": { "readOnlyHint": true, "idempotentHint": true, "openWorldHint": false }, "_house": { "endpoint": "/faculty/mm-envc/affordable_loss", "feeSt": 1, "degree": "competency:mm-envc", "example": { "liquidAssets": 300000, "monthlyLivingCosts": 18000, "stepCost": 40000 } } }, { "name": "mm-envc.effectuation_assessment", "title": "Effectuation assessment (CDU-BUS-ENVC-900)", "description": "How effectual is the venture’s approach across Sarasvathy’s five principles, scored 0–4 each from the founder’s answers?", "inputSchema": { "type": "object", "required": [ "pan", "bird_in_hand", "affordable_loss", "lemonade", "crazy_quilt", "pilot_in_plane" ], "properties": { "pan": { "type": "string", "description": "The student PAN — the degree must be held in one of its five slots", "pattern": "^[0-9 ]{16,19}$" }, "bird_in_hand": { "type": "number", "description": "Does the venture start from who the founder is, what they know and whom they know — rather than from a given goal? (0 = not at all, 4 = entirely)", "minimum": 0, "maximum": 4 }, "affordable_loss": { "type": "number", "description": "Is each step sized by what the founder can afford to lose, rather than by expected return? (0–4)", "minimum": 0, "maximum": 4 }, "lemonade": { "type": "number", "description": "Are surprises and contingencies treated as inputs to the venture, not as threats to a plan? (0–4)", "minimum": 0, "maximum": 4 }, "crazy_quilt": { "type": "number", "description": "Are partnerships formed with self-selecting stakeholders who commit, rather than competitive analysis of a market? (0–4)", "minimum": 0, "maximum": 4 }, "pilot_in_plane": { "type": "number", "description": "Does the founder act to shape the future through controllable means, rather than predict it? (0–4)", "minimum": 0, "maximum": 4 } }, "additionalProperties": false }, "outputSchema": { "type": "object", "required": [ "score", "percent", "orientation", "strongest", "weakest" ], "properties": { "score": { "type": "number", "description": "Total, 0–20" }, "percent": { "type": "number", "description": "Score ÷ 20" }, "orientation": { "type": "string", "description": "effectual, mixed, or causal" }, "strongest": { "type": "string", "description": "Highest-scoring principle" }, "weakest": { "type": "string", "description": "Lowest-scoring principle — the one to work on" } }, "additionalProperties": false }, "annotations": { "readOnlyHint": true, "idempotentHint": true, "openWorldHint": false }, "_house": { "endpoint": "/faculty/mm-envc/effectuation_assessment", "feeSt": 1, "degree": "competency:mm-envc", "example": { "bird_in_hand": 4, "affordable_loss": 3, "lemonade": 3, "crazy_quilt": 4, "pilot_in_plane": 3 } } }, { "name": "msc-agentic.luhn_pan", "title": "PAN check digit (Luhn) (CDU-ICT-AGT-900)", "description": "Is this card-shaped number self-consistent, and what check digit completes this body?", "inputSchema": { "type": "object", "required": [ "pan", "body" ], "properties": { "pan": { "type": "string", "description": "The student PAN — the degree must be held in one of its five slots", "pattern": "^[0-9 ]{16,19}$" }, "body": { "type": "string", "description": "The number without its final check digit — 7 to 18 digits, spaces allowed" } }, "additionalProperties": false }, "outputSchema": { "type": "object", "required": [ "checkDigit", "pan", "length" ], "properties": { "checkDigit": { "type": "number", "description": "The digit that completes the number" }, "pan": { "type": "string", "description": "The completed number, spaced in fours" }, "length": { "type": "number", "description": "Digits in the completed number" } }, "additionalProperties": false }, "annotations": { "readOnlyHint": true, "idempotentHint": true, "openWorldHint": false }, "_house": { "endpoint": "/faculty/msc-agentic/luhn_pan", "feeSt": 1, "degree": "competency:msc-agentic", "example": { "body": "971034210000001" } } }, { "name": "msc-agentic.rate_window", "title": "Sliding-window admission (CDU-ICT-AGT-900)", "description": "May one more request pass this window now — and if not, when?", "inputSchema": { "type": "object", "required": [ "pan", "max", "windowSeconds", "ageSeconds" ], "properties": { "pan": { "type": "string", "description": "The student PAN — the degree must be held in one of its five slots", "pattern": "^[0-9 ]{16,19}$" }, "max": { "type": "number", "description": "Requests allowed inside the window", "minimum": 1, "maximum": 100000 }, "windowSeconds": { "type": "number", "description": "The window (s)", "minimum": 1, "maximum": 604800 }, "ageSeconds": { "type": "string", "description": "Ages of the prior requests, seconds ago, comma-separated (empty for none)" } }, "additionalProperties": false }, "outputSchema": { "type": "object", "required": [ "inWindow", "admit", "retryAfterSeconds" ], "properties": { "inWindow": { "type": "number", "description": "Prior requests still inside the window" }, "admit": { "type": "boolean", "description": "Whether one more passes now" }, "retryAfterSeconds": { "type": "number", "description": "Wait this long when refused; 0 when admitted" } }, "additionalProperties": false }, "annotations": { "readOnlyHint": true, "idempotentHint": true, "openWorldHint": false }, "_house": { "endpoint": "/faculty/msc-agentic/rate_window", "feeSt": 1, "degree": "competency:msc-agentic", "example": { "max": 5, "windowSeconds": 600, "ageSeconds": "30,90,180,400,590" } } }, { "name": "msc-agentic.backoff_schedule", "title": "Exponential backoff (CDU-ICT-AGT-900)", "description": "How long does a polite client wait between retries, and how long might the whole attempt take?", "inputSchema": { "type": "object", "required": [ "pan", "attempts", "baseSeconds", "capSeconds" ], "properties": { "pan": { "type": "string", "description": "The student PAN — the degree must be held in one of its five slots", "pattern": "^[0-9 ]{16,19}$" }, "attempts": { "type": "number", "description": "Retry attempts to schedule", "minimum": 1, "maximum": 20 }, "baseSeconds": { "type": "number", "description": "The first wait (s)", "minimum": 0.01, "maximum": 3600 }, "capSeconds": { "type": "number", "description": "The longest any single wait may be (s)", "minimum": 0.01, "maximum": 86400 } }, "additionalProperties": false }, "outputSchema": { "type": "object", "required": [ "scheduleSeconds", "totalSeconds", "cappedFrom" ], "properties": { "scheduleSeconds": { "type": "array", "description": "The wait before each retry, in order", "items": { "type": "number" } }, "totalSeconds": { "type": "number", "description": "Worst-case total waiting time" }, "cappedFrom": { "type": "number", "description": "The first attempt (1-based) the cap bites on; 0 when it never does" } }, "additionalProperties": false }, "annotations": { "readOnlyHint": true, "idempotentHint": true, "openWorldHint": false }, "_house": { "endpoint": "/faculty/msc-agentic/backoff_schedule", "feeSt": 1, "degree": "competency:msc-agentic", "example": { "attempts": 5, "baseSeconds": 1, "capSeconds": 30 } } }, { "name": "msc-agentic.agent_day_budget", "title": "The agent-day budget (CDU-ICT-AGT-900)", "description": "Of the 1440 ST an agent-day holds, what has this agent already promised, and what may it still take on?", "inputSchema": { "type": "object", "required": [ "pan", "faresClaimedSt" ], "properties": { "pan": { "type": "string", "description": "The student PAN — the degree must be held in one of its five slots", "pattern": "^[0-9 ]{16,19}$" }, "faresClaimedSt": { "type": "string", "description": "Fares already claimed today, whole ST, comma-separated (empty for none)" }, "consultationsPlanned": { "type": "number", "description": "Consultations the agent still plans today, at 1 ST each", "minimum": 0, "maximum": 1440, "default": 0 } }, "additionalProperties": false }, "outputSchema": { "type": "object", "required": [ "bookedSt", "remainingSt", "overcommitted" ], "properties": { "bookedSt": { "type": "number", "description": "ST already promised (fares + planned consultations)" }, "remainingSt": { "type": "number", "description": "What is left of the day" }, "overcommitted": { "type": "boolean", "description": "True when promises exceed the day — stop claiming" } }, "additionalProperties": false }, "annotations": { "readOnlyHint": true, "idempotentHint": true, "openWorldHint": false }, "_house": { "endpoint": "/faculty/msc-agentic/agent_day_budget", "feeSt": 1, "degree": "competency:msc-agentic", "example": { "faresClaimedSt": "120,60", "consultationsPlanned": 8 } } }, { "name": "mba-strategy.hhi_concentration", "title": "Market concentration and merger screening (CDU-BUS-MBAS-910)", "description": "How concentrated is this market, and would merging two of its firms move it into a higher scrutiny band?", "inputSchema": { "type": "object", "required": [ "pan", "shares" ], "properties": { "pan": { "type": "string", "description": "The student PAN — the degree must be held in one of its five slots", "pattern": "^[0-9 ]{16,19}$" }, "shares": { "type": "array", "description": "Each firm's share (percent, or any weights — normalised to 100)", "items": { "type": "number" } }, "mergingA": { "type": "number", "description": "Position (1-based) of the first merging firm, 0 for none", "minimum": 0, "maximum": 50, "default": 0 }, "mergingB": { "type": "number", "description": "Position (1-based) of the second merging firm, 0 for none", "minimum": 0, "maximum": 50, "default": 0 } }, "additionalProperties": false }, "outputSchema": { "type": "object", "required": [ "hhi", "band", "delta", "postMergerHhi", "postMergerBand" ], "properties": { "hhi": { "type": "number", "description": "HHI before any merger, 0–10,000" }, "band": { "type": "string", "description": "unconcentrated · moderately concentrated · highly concentrated" }, "delta": { "type": "number", "description": "ΔHHI from the merger, 0 when none is named" }, "postMergerHhi": { "type": "number", "description": "HHI after the merger" }, "postMergerBand": { "type": "string", "description": "the band after the merger" } }, "additionalProperties": false }, "annotations": { "readOnlyHint": true, "idempotentHint": true, "openWorldHint": false }, "_house": { "endpoint": "/faculty/mba-strategy/hhi_concentration", "feeSt": 1, "degree": "competency:mba-strategy", "example": { "shares": [ 30, 25, 20, 15, 10 ], "mergingA": 2, "mergingB": 3 } } }, { "name": "mba-strategy.bcg_portfolio", "title": "The growth–share portfolio (CDU-BUS-MBAS-910)", "description": "Is this business unit a star, a cash cow, a question mark or a dog — and why?", "inputSchema": { "type": "object", "required": [ "pan", "marketGrowthPct", "ownSharePct", "largestRivalSharePct" ], "properties": { "pan": { "type": "string", "description": "The student PAN — the degree must be held in one of its five slots", "pattern": "^[0-9 ]{16,19}$" }, "marketGrowthPct": { "type": "number", "description": "Market growth, percent a year", "minimum": -50, "maximum": 200 }, "ownSharePct": { "type": "number", "description": "The unit's own market share, percent", "minimum": 0.01, "maximum": 100 }, "largestRivalSharePct": { "type": "number", "description": "The largest rival's share, percent", "minimum": 0.01, "maximum": 100 } }, "additionalProperties": false }, "outputSchema": { "type": "object", "required": [ "relativeShare", "quadrant" ], "properties": { "relativeShare": { "type": "number", "description": "Own share ÷ largest rival share" }, "quadrant": { "type": "string", "description": "star · cash cow · question mark · dog" } }, "additionalProperties": false }, "annotations": { "readOnlyHint": true, "idempotentHint": true, "openWorldHint": false }, "_house": { "endpoint": "/faculty/mba-strategy/bcg_portfolio", "feeSt": 1, "degree": "competency:mba-strategy", "example": { "marketGrowthPct": 14, "ownSharePct": 18, "largestRivalSharePct": 12 } } }, { "name": "mba-strategy.customer_lifetime", "title": "Customer lifetime value (CDU-BUS-MBAS-910)", "description": "What is a retained customer worth today, and so what is the most it is worth paying to win one?", "inputSchema": { "type": "object", "required": [ "pan", "marginPerPeriod", "retentionRate", "discountRate" ], "properties": { "pan": { "type": "string", "description": "The student PAN — the degree must be held in one of its five slots", "pattern": "^[0-9 ]{16,19}$" }, "marginPerPeriod": { "type": "number", "description": "Contribution margin a customer yields per period", "minimum": 0 }, "retentionRate": { "type": "number", "description": "Share of customers retained each period, 0–0.99", "minimum": 0, "maximum": 0.99 }, "discountRate": { "type": "number", "description": "Discount rate per period, 0–1", "minimum": 0, "maximum": 1 } }, "additionalProperties": false }, "outputSchema": { "type": "object", "required": [ "marginMultiple", "clv", "maxAcquisitionCost" ], "properties": { "marginMultiple": { "type": "number", "description": "r ÷ (1 + d − r)" }, "clv": { "type": "number", "description": "Lifetime value of one retained customer" }, "maxAcquisitionCost": { "type": "number", "description": "The acquisition cost at which winning the customer breaks even (= CLV)" } }, "additionalProperties": false }, "annotations": { "readOnlyHint": true, "idempotentHint": true, "openWorldHint": false }, "_house": { "endpoint": "/faculty/mba-strategy/customer_lifetime", "feeSt": 1, "degree": "competency:mba-strategy", "example": { "marginPerPeriod": 240, "retentionRate": 0.8, "discountRate": 0.12 } } }, { "name": "mba-strategy.lerner_pricing", "title": "The inverse-elasticity price (CDU-BUS-MBAS-910)", "description": "Given marginal cost and how sensitive demand is to price, what price maximises profit, and how much market power does it imply?", "inputSchema": { "type": "object", "required": [ "pan", "marginalCost", "elasticity" ], "properties": { "pan": { "type": "string", "description": "The student PAN — the degree must be held in one of its five slots", "pattern": "^[0-9 ]{16,19}$" }, "marginalCost": { "type": "number", "description": "Marginal cost per unit", "minimum": 0 }, "elasticity": { "type": "number", "description": "Absolute price elasticity of demand, > 1", "minimum": 1.05, "maximum": 50 } }, "additionalProperties": false }, "outputSchema": { "type": "object", "required": [ "optimalPrice", "lernerIndex", "markupOnCost" ], "properties": { "optimalPrice": { "type": "number", "description": "P* = MC · ε / (ε − 1)" }, "lernerIndex": { "type": "number", "description": "(P − MC) / P = 1 / ε" }, "markupOnCost": { "type": "number", "description": "(P − MC) / MC" } }, "additionalProperties": false }, "annotations": { "readOnlyHint": true, "idempotentHint": true, "openWorldHint": false }, "_house": { "endpoint": "/faculty/mba-strategy/lerner_pricing", "feeSt": 1, "degree": "competency:mba-strategy", "example": { "marginalCost": 60, "elasticity": 2.5 } } }, { "name": "mcom-accounting--tax.deferred_tax", "title": "Deferred tax on a temporary difference (CDU-BUS-ACTX-900)", "description": "Does this asset or liability give rise to a deferred tax liability or asset, and how large is it?", "inputSchema": { "type": "object", "required": [ "pan", "itemKind", "carryingAmount", "taxBase", "taxRate" ], "properties": { "pan": { "type": "string", "description": "The student PAN — the degree must be held in one of its five slots", "pattern": "^[0-9 ]{16,19}$" }, "itemKind": { "type": "string", "description": "Is the item an asset or a liability?", "enum": [ "asset", "liability" ] }, "carryingAmount": { "type": "number", "description": "Carrying amount in the statement of financial position", "minimum": 0 }, "taxBase": { "type": "number", "description": "The amount attributed to the item for tax purposes", "minimum": 0 }, "taxRate": { "type": "number", "description": "Rate expected to apply when it reverses, 0–1", "minimum": 0, "maximum": 1 } }, "additionalProperties": false }, "outputSchema": { "type": "object", "required": [ "temporaryDifference", "differenceType", "deferredTax", "position" ], "properties": { "temporaryDifference": { "type": "number", "description": "|carrying amount − tax base|" }, "differenceType": { "type": "string", "description": "taxable, deductible or none" }, "deferredTax": { "type": "number", "description": "Temporary difference × rate" }, "position": { "type": "string", "description": "DTL, DTA or none" } }, "additionalProperties": false }, "annotations": { "readOnlyHint": true, "idempotentHint": true, "openWorldHint": false }, "_house": { "endpoint": "/faculty/mcom-accounting--tax/deferred_tax", "feeSt": 1, "degree": "competency:mcom-accounting--tax", "example": { "itemKind": "asset", "carryingAmount": 100000, "taxBase": 60000, "taxRate": 0.27 } } }, { "name": "mcom-accounting--tax.tax_rate_reconciliation", "title": "Current tax and the effective-rate reconciliation (CDU-BUS-ACTX-900)", "description": "What is the current tax charge, and why does the effective rate differ from the statutory rate?", "inputSchema": { "type": "object", "required": [ "pan", "accountingProfit", "statutoryRate" ], "properties": { "pan": { "type": "string", "description": "The student PAN — the degree must be held in one of its five slots", "pattern": "^[0-9 ]{16,19}$" }, "accountingProfit": { "type": "number", "description": "Profit before tax", "minimum": 0.01 }, "statutoryRate": { "type": "number", "description": "Applicable (statutory) tax rate, 0–1", "minimum": 0, "maximum": 1 }, "nonDeductibleExpenses": { "type": "number", "description": "Expenses that are never deductible", "minimum": 0, "default": 0 }, "exemptIncome": { "type": "number", "description": "Income that is never taxable", "minimum": 0, "default": 0 } }, "additionalProperties": false }, "outputSchema": { "type": "object", "required": [ "taxableIncome", "taxAtStatutoryRate", "effectNonDeductible", "effectExempt", "currentTax", "effectiveTaxRate" ], "properties": { "taxableIncome": { "type": "number", "description": "Profit + non-deductible − exempt" }, "taxAtStatutoryRate": { "type": "number", "description": "Profit × statutory rate" }, "effectNonDeductible": { "type": "number", "description": "Non-deductible × rate" }, "effectExempt": { "type": "number", "description": "Exempt × rate (a reduction)" }, "currentTax": { "type": "number", "description": "Taxable income × rate, not below zero" }, "effectiveTaxRate": { "type": "number", "description": "Current tax ÷ profit" } }, "additionalProperties": false }, "annotations": { "readOnlyHint": true, "idempotentHint": true, "openWorldHint": false }, "_house": { "endpoint": "/faculty/mcom-accounting--tax/tax_rate_reconciliation", "feeSt": 1, "degree": "competency:mcom-accounting--tax", "example": { "accountingProfit": 1000000, "statutoryRate": 0.27, "nonDeductibleExpenses": 50000, "exemptIncome": 20000 } } }, { "name": "mcom-accounting--tax.lease_liability", "title": "Lease liability and right-of-use asset (CDU-BUS-ACTX-900)", "description": "At commencement, what is the lease liability, the right-of-use asset, and the first period’s interest?", "inputSchema": { "type": "object", "required": [ "pan", "periodicPayment", "periods", "ratePerPeriod" ], "properties": { "pan": { "type": "string", "description": "The student PAN — the degree must be held in one of its five slots", "pattern": "^[0-9 ]{16,19}$" }, "periodicPayment": { "type": "number", "description": "Fixed lease payment per period", "minimum": 0.01 }, "periods": { "type": "number", "description": "Number of payments over the lease term", "minimum": 1, "maximum": 600 }, "ratePerPeriod": { "type": "number", "description": "Discount rate per period (implicit or incremental borrowing), 0–1", "minimum": 0, "maximum": 1 }, "initialDirectCosts": { "type": "number", "description": "Initial direct costs of the lessee", "minimum": 0, "default": 0 }, "paymentsInAdvance": { "type": "boolean", "description": "Paid at the start of each period (true) or the end (false)", "default": false } }, "additionalProperties": false }, "outputSchema": { "type": "object", "required": [ "annuityFactor", "leaseLiability", "rightOfUseAsset", "firstPeriodInterest", "liabilityAfterFirstPeriod" ], "properties": { "annuityFactor": { "type": "number", "description": "PV factor applied to the unpaid payments" }, "leaseLiability": { "type": "number", "description": "Lease liability at commencement" }, "rightOfUseAsset": { "type": "number", "description": "Right-of-use asset at commencement" }, "firstPeriodInterest": { "type": "number", "description": "Liability × rate for the first period" }, "liabilityAfterFirstPeriod": { "type": "number", "description": "Liability + interest − the payment at the end of period 1" } }, "additionalProperties": false }, "annotations": { "readOnlyHint": true, "idempotentHint": true, "openWorldHint": false }, "_house": { "endpoint": "/faculty/mcom-accounting--tax/lease_liability", "feeSt": 1, "degree": "competency:mcom-accounting--tax", "example": { "periodicPayment": 100000, "periods": 5, "ratePerPeriod": 0.1, "initialDirectCosts": 5000, "paymentsInAdvance": false } } }, { "name": "mcom-accounting--tax.arms_length_range", "title": "Arm’s length range and adjustment (CDU-BUS-ACTX-900)", "description": "Is the tested party’s margin inside the interquartile range of the comparables, and if not, what adjustment brings it to the median?", "inputSchema": { "type": "object", "required": [ "pan", "comparableMargins", "testedMargin" ], "properties": { "pan": { "type": "string", "description": "The student PAN — the degree must be held in one of its five slots", "pattern": "^[0-9 ]{16,19}$" }, "comparableMargins": { "type": "array", "description": "Profit level indicator of each accepted comparable (e.g. net cost plus), as fractions", "items": { "type": "number" } }, "testedMargin": { "type": "number", "description": "The tested party’s result on the same indicator, as a fraction", "minimum": -1, "maximum": 1 } }, "additionalProperties": false }, "outputSchema": { "type": "object", "required": [ "lowerQuartile", "median", "upperQuartile", "withinRange", "adjustedMargin", "adjustment" ], "properties": { "lowerQuartile": { "type": "number", "description": "Q1 of the comparables" }, "median": { "type": "number", "description": "Median of the comparables" }, "upperQuartile": { "type": "number", "description": "Q3 of the comparables" }, "withinRange": { "type": "boolean", "description": "Q1 ≤ tested ≤ Q3" }, "adjustedMargin": { "type": "number", "description": "Tested if within range, otherwise the median" }, "adjustment": { "type": "number", "description": "Adjusted − tested" } }, "additionalProperties": false }, "annotations": { "readOnlyHint": true, "idempotentHint": true, "openWorldHint": false }, "_house": { "endpoint": "/faculty/mcom-accounting--tax/arms_length_range", "feeSt": 1, "degree": "competency:mcom-accounting--tax", "example": { "comparableMargins": [ 0.042, 0.051, 0.055, 0.063, 0.07, 0.078, 0.085, 0.091 ], "testedMargin": 0.035 } } }, { "name": "mcom-auditing--assurance.materiality", "title": "Materiality, performance materiality and clearly trivial (CDU-BUS-AUD-900)", "description": "Given the benchmark and the percentages judged appropriate, what are overall materiality, performance materiality and the clearly-trivial threshold?", "inputSchema": { "type": "object", "required": [ "pan", "benchmark", "benchmarkAmount", "percentage" ], "properties": { "pan": { "type": "string", "description": "The student PAN — the degree must be held in one of its five slots", "pattern": "^[0-9 ]{16,19}$" }, "benchmark": { "type": "string", "description": "The benchmark chosen", "enum": [ "profitBeforeTax", "revenue", "totalExpenses", "totalAssets", "equity" ] }, "benchmarkAmount": { "type": "number", "description": "The benchmark amount", "minimum": 0.01 }, "percentage": { "type": "number", "description": "Percentage applied to the benchmark, 0–0.1", "minimum": 0.0001, "maximum": 0.1 }, "performanceFactor": { "type": "number", "description": "Performance materiality as a fraction of overall, 0.5–0.9", "minimum": 0.5, "maximum": 0.9, "default": 0.75 }, "trivialFactor": { "type": "number", "description": "Clearly trivial as a fraction of overall, 0.01–0.1", "minimum": 0.01, "maximum": 0.1, "default": 0.05 } }, "additionalProperties": false }, "outputSchema": { "type": "object", "required": [ "overallMateriality", "performanceMateriality", "clearlyTrivialThreshold" ], "properties": { "overallMateriality": { "type": "number", "description": "Benchmark × percentage" }, "performanceMateriality": { "type": "number", "description": "Overall × performance factor" }, "clearlyTrivialThreshold": { "type": "number", "description": "Overall × trivial factor" } }, "additionalProperties": false }, "annotations": { "readOnlyHint": true, "idempotentHint": true, "openWorldHint": false }, "_house": { "endpoint": "/faculty/mcom-auditing--assurance/materiality", "feeSt": 1, "degree": "competency:mcom-auditing--assurance", "example": { "benchmark": "profitBeforeTax", "benchmarkAmount": 2400000, "percentage": 0.05, "performanceFactor": 0.75, "trivialFactor": 0.05 } } }, { "name": "mcom-auditing--assurance.attribute_sample_size", "title": "Attribute sample size for a test of controls (CDU-BUS-AUD-900)", "description": "How many items must be tested so that, finding no more than the planned number of deviations, the control can be relied on at this confidence?", "inputSchema": { "type": "object", "required": [ "pan", "confidence", "tolerableRate", "plannedDeviations" ], "properties": { "pan": { "type": "string", "description": "The student PAN — the degree must be held in one of its five slots", "pattern": "^[0-9 ]{16,19}$" }, "confidence": { "type": "number", "description": "Confidence level (1 − risk of overreliance), 0.8–0.99", "minimum": 0.8, "maximum": 0.99 }, "tolerableRate": { "type": "number", "description": "Tolerable deviation rate, 0.01–0.2", "minimum": 0.01, "maximum": 0.2 }, "plannedDeviations": { "type": "number", "description": "Deviations the plan allows the sample to contain", "minimum": 0, "maximum": 10 } }, "additionalProperties": false }, "outputSchema": { "type": "object", "required": [ "sampleSize", "riskOfOverreliance" ], "properties": { "sampleSize": { "type": "number", "description": "Smallest n meeting the risk" }, "riskOfOverreliance": { "type": "number", "description": "P(deviations ≤ planned | n, tolerable rate)" } }, "additionalProperties": false }, "annotations": { "readOnlyHint": true, "idempotentHint": true, "openWorldHint": false }, "_house": { "endpoint": "/faculty/mcom-auditing--assurance/attribute_sample_size", "feeSt": 1, "degree": "competency:mcom-auditing--assurance", "example": { "confidence": 0.95, "tolerableRate": 0.05, "plannedDeviations": 1 } } }, { "name": "mcom-auditing--assurance.mus_planning", "title": "Monetary-unit sample: size, interval and basic precision (CDU-BUS-AUD-900)", "description": "For a test of details on this balance, how many monetary units are sampled, at what interval, and what is the basic precision if none is misstated?", "inputSchema": { "type": "object", "required": [ "pan", "bookValue", "tolerableMisstatement", "confidence" ], "properties": { "pan": { "type": "string", "description": "The student PAN — the degree must be held in one of its five slots", "pattern": "^[0-9 ]{16,19}$" }, "bookValue": { "type": "number", "description": "Recorded amount of the population", "minimum": 0.01 }, "tolerableMisstatement": { "type": "number", "description": "Tolerable misstatement for the balance", "minimum": 0.01 }, "confidence": { "type": "number", "description": "Confidence level, 0.8–0.99", "minimum": 0.8, "maximum": 0.99 } }, "additionalProperties": false }, "outputSchema": { "type": "object", "required": [ "reliabilityFactor", "sampleSize", "samplingInterval", "basicPrecision" ], "properties": { "reliabilityFactor": { "type": "number", "description": "R = −ln(1 − confidence)" }, "sampleSize": { "type": "number", "description": "ceil(book value × R ÷ tolerable)" }, "samplingInterval": { "type": "number", "description": "Book value ÷ sample size" }, "basicPrecision": { "type": "number", "description": "R × interval: the upper limit when no misstatement is found" } }, "additionalProperties": false }, "annotations": { "readOnlyHint": true, "idempotentHint": true, "openWorldHint": false }, "_house": { "endpoint": "/faculty/mcom-auditing--assurance/mus_planning", "feeSt": 1, "degree": "competency:mcom-auditing--assurance", "example": { "bookValue": 5000000, "tolerableMisstatement": 150000, "confidence": 0.95 } } }, { "name": "mcom-auditing--assurance.going_concern_zscore", "title": "Going-concern indicator (Altman Z) (CDU-BUS-AUD-900)", "description": "Does the Altman Z-score put the entity in the distress, grey or safe zone — one quantitative input to the going-concern assessment?", "inputSchema": { "type": "object", "required": [ "pan", "workingCapital", "retainedEarnings", "ebit", "marketValueEquity", "sales", "totalAssets", "totalLiabilities" ], "properties": { "pan": { "type": "string", "description": "The student PAN — the degree must be held in one of its five slots", "pattern": "^[0-9 ]{16,19}$" }, "workingCapital": { "type": "number", "description": "Current assets − current liabilities", "minimum": -1000000000000, "maximum": 1000000000000 }, "retainedEarnings": { "type": "number", "description": "Retained earnings", "minimum": -1000000000000, "maximum": 1000000000000 }, "ebit": { "type": "number", "description": "Earnings before interest and tax", "minimum": -1000000000000, "maximum": 1000000000000 }, "marketValueEquity": { "type": "number", "description": "Market value of equity", "minimum": 0 }, "sales": { "type": "number", "description": "Sales (revenue)", "minimum": 0 }, "totalAssets": { "type": "number", "description": "Total assets", "minimum": 0.01 }, "totalLiabilities": { "type": "number", "description": "Total liabilities", "minimum": 0.01 } }, "additionalProperties": false }, "outputSchema": { "type": "object", "required": [ "z", "zone", "goingConcernFlag" ], "properties": { "z": { "type": "number", "description": "The Z-score" }, "zone": { "type": "string", "description": "distress (< 1.81), grey (1.81–2.99) or safe (> 2.99)" }, "goingConcernFlag": { "type": "boolean", "description": "True outside the safe zone: the indicator calls for further procedures" } }, "additionalProperties": false }, "annotations": { "readOnlyHint": true, "idempotentHint": true, "openWorldHint": false }, "_house": { "endpoint": "/faculty/mcom-auditing--assurance/going_concern_zscore", "feeSt": 1, "degree": "competency:mcom-auditing--assurance", "example": { "workingCapital": 500000, "retainedEarnings": 800000, "ebit": 300000, "marketValueEquity": 1500000, "sales": 4000000, "totalAssets": 3000000, "totalLiabilities": 1200000 } } }, { "name": "mcom-forensic-accounting--investigation.benford_first_digit", "title": "First-digit test (Benford) (CDU-BUS-FOR-900)", "description": "Do the leading digits of these amounts conform to Benford’s law, and how far do they deviate?", "inputSchema": { "type": "object", "required": [ "pan", "amounts" ], "properties": { "pan": { "type": "string", "description": "The student PAN — the degree must be held in one of its five slots", "pattern": "^[0-9 ]{16,19}$" }, "amounts": { "type": "array", "description": "Transaction amounts; those below 10 are excluded, as the test prescribes", "items": { "type": "number" } } }, "additionalProperties": false }, "outputSchema": { "type": "object", "required": [ "counted", "digitCounts", "mad", "chiSquare", "conformity" ], "properties": { "counted": { "type": "number", "description": "Amounts tested (≥ 10)" }, "digitCounts": { "type": "array", "description": "Observed count of each first digit 1..9", "items": { "type": "number" } }, "mad": { "type": "number", "description": "Mean absolute deviation from Benford" }, "chiSquare": { "type": "number", "description": "Σ (O − E)² ÷ E over the nine digits (8 df)" }, "conformity": { "type": "string", "description": "close, acceptable, marginal or nonconformity" } }, "additionalProperties": false }, "annotations": { "readOnlyHint": true, "idempotentHint": true, "openWorldHint": false }, "_house": { "endpoint": "/faculty/mcom-forensic-accounting--investigation/benford_first_digit", "feeSt": 1, "degree": "competency:mcom-forensic-accounting--investigation", "example": { "amounts": [ 1120, 1380, 1460, 1975, 1042, 1210, 1833, 1598, 1099, 1305, 1712, 2150, 2890, 2431, 2077, 2666, 3120, 3490, 3005, 4210, 4890, 5120, 5775, 6340, 7010, 8450, 9320, 1188, 1523, 2260, 3675, 1407, 2555, 1066, 4402, 1960, 2780, 6150, 1254, 1839 ] } } }, { "name": "mcom-forensic-accounting--investigation.beneish_m_score", "title": "Beneish M-score (CDU-BUS-FOR-900)", "description": "Do the eight Beneish indices put this company above the threshold for a likely earnings manipulator?", "inputSchema": { "type": "object", "required": [ "pan", "dsri", "gmi", "aqi", "sgi", "depi", "sgai", "tata", "lvgi" ], "properties": { "pan": { "type": "string", "description": "The student PAN — the degree must be held in one of its five slots", "pattern": "^[0-9 ]{16,19}$" }, "dsri": { "type": "number", "description": "Days’ sales in receivables index", "minimum": 0 }, "gmi": { "type": "number", "description": "Gross margin index", "minimum": 0 }, "aqi": { "type": "number", "description": "Asset quality index", "minimum": 0 }, "sgi": { "type": "number", "description": "Sales growth index", "minimum": 0 }, "depi": { "type": "number", "description": "Depreciation index", "minimum": 0 }, "sgai": { "type": "number", "description": "SG&A expense index", "minimum": 0 }, "tata": { "type": "number", "description": "Total accruals to total assets", "minimum": -1, "maximum": 1 }, "lvgi": { "type": "number", "description": "Leverage index", "minimum": 0 } }, "additionalProperties": false }, "outputSchema": { "type": "object", "required": [ "mScore", "likelyManipulator" ], "properties": { "mScore": { "type": "number", "description": "The M-score" }, "likelyManipulator": { "type": "boolean", "description": "M > −1.78" } }, "additionalProperties": false }, "annotations": { "readOnlyHint": true, "idempotentHint": true, "openWorldHint": false }, "_house": { "endpoint": "/faculty/mcom-forensic-accounting--investigation/beneish_m_score", "feeSt": 1, "degree": "competency:mcom-forensic-accounting--investigation", "example": { "dsri": 1.465, "gmi": 1.193, "aqi": 1.254, "sgi": 1.607, "depi": 1.077, "sgai": 1.041, "tata": 0.031, "lvgi": 1.111 } } }, { "name": "mcom-forensic-accounting--investigation.net_worth_method", "title": "Net worth method: unexplained funds (CDU-BUS-FOR-900)", "description": "How much of the increase in a subject’s net worth, plus what they spent, is not explained by known income?", "inputSchema": { "type": "object", "required": [ "pan", "openingAssets", "openingLiabilities", "closingAssets", "closingLiabilities", "livingExpenses", "knownIncome" ], "properties": { "pan": { "type": "string", "description": "The student PAN — the degree must be held in one of its five slots", "pattern": "^[0-9 ]{16,19}$" }, "openingAssets": { "type": "number", "description": "Assets at the start of the period (at cost)", "minimum": 0 }, "openingLiabilities": { "type": "number", "description": "Liabilities at the start", "minimum": 0 }, "closingAssets": { "type": "number", "description": "Assets at the end (at cost)", "minimum": 0 }, "closingLiabilities": { "type": "number", "description": "Liabilities at the end", "minimum": 0 }, "livingExpenses": { "type": "number", "description": "Known personal expenditure in the period", "minimum": 0 }, "knownIncome": { "type": "number", "description": "Income from known, legitimate sources", "minimum": 0 } }, "additionalProperties": false }, "outputSchema": { "type": "object", "required": [ "openingNetWorth", "closingNetWorth", "netWorthIncrease", "fundsApplied", "unexplainedFunds" ], "properties": { "openingNetWorth": { "type": "number", "description": "Opening assets − liabilities" }, "closingNetWorth": { "type": "number", "description": "Closing assets − liabilities" }, "netWorthIncrease": { "type": "number", "description": "Closing − opening net worth" }, "fundsApplied": { "type": "number", "description": "Increase + living expenses" }, "unexplainedFunds": { "type": "number", "description": "Funds applied − known income" } }, "additionalProperties": false }, "annotations": { "readOnlyHint": true, "idempotentHint": true, "openWorldHint": false }, "_house": { "endpoint": "/faculty/mcom-forensic-accounting--investigation/net_worth_method", "feeSt": 1, "degree": "competency:mcom-forensic-accounting--investigation", "example": { "openingAssets": 500000, "openingLiabilities": 200000, "closingAssets": 900000, "closingLiabilities": 250000, "livingExpenses": 120000, "knownIncome": 260000 } } }, { "name": "mcom-forensic-accounting--investigation.duplicate_amounts", "title": "Number-duplication test (CDU-BUS-FOR-900)", "description": "Which payment amounts recur, how often, and how many rows do the repeats account for?", "inputSchema": { "type": "object", "required": [ "pan", "amounts" ], "properties": { "pan": { "type": "string", "description": "The student PAN — the degree must be held in one of its five slots", "pattern": "^[0-9 ]{16,19}$" }, "amounts": { "type": "array", "description": "Payment amounts, in ledger order", "items": { "type": "number" } } }, "additionalProperties": false }, "outputSchema": { "type": "object", "required": [ "rows", "distinctAmounts", "duplicatedAmounts", "duplicateRows", "mostFrequentAmount", "mostFrequentCount" ], "properties": { "rows": { "type": "number", "description": "Amounts tested" }, "distinctAmounts": { "type": "number", "description": "Different amounts" }, "duplicatedAmounts": { "type": "number", "description": "Amounts that occur more than once" }, "duplicateRows": { "type": "number", "description": "Rows carrying a duplicated amount" }, "mostFrequentAmount": { "type": "number", "description": "The amount that recurs most (the smallest such, on a tie)" }, "mostFrequentCount": { "type": "number", "description": "How often it occurs" } }, "additionalProperties": false }, "annotations": { "readOnlyHint": true, "idempotentHint": true, "openWorldHint": false }, "_house": { "endpoint": "/faculty/mcom-forensic-accounting--investigation/duplicate_amounts", "feeSt": 1, "degree": "competency:mcom-forensic-accounting--investigation", "example": { "amounts": [ 1250, 980.5, 1250, 4400, 75, 980.5, 1250, 310, 5000, 4400, 18.99, 6200 ] } } }, { "name": "msc-finance--capital-markets.bond_price_duration", "title": "Bond price, duration and convexity (CDU-BUS-FIN-900)", "description": "What is this bond worth at this yield, and how sensitive is its price to a change in yield?", "inputSchema": { "type": "object", "required": [ "pan", "faceValue", "couponRate", "yieldToMaturity", "years", "frequency" ], "properties": { "pan": { "type": "string", "description": "The student PAN — the degree must be held in one of its five slots", "pattern": "^[0-9 ]{16,19}$" }, "faceValue": { "type": "number", "description": "Par value repaid at maturity", "minimum": 0.01 }, "couponRate": { "type": "number", "description": "Annual coupon rate, 0–1", "minimum": 0, "maximum": 1 }, "yieldToMaturity": { "type": "number", "description": "Annual yield to maturity, 0–1", "minimum": 0, "maximum": 1 }, "years": { "type": "number", "description": "Whole years to maturity", "minimum": 1, "maximum": 100 }, "frequency": { "type": "string", "description": "Coupons per year", "enum": [ "annual", "semiannual", "quarterly", "monthly" ] } }, "additionalProperties": false }, "outputSchema": { "type": "object", "required": [ "price", "macaulayDuration", "modifiedDuration", "convexity" ], "properties": { "price": { "type": "number", "description": "Full price per the face value" }, "macaulayDuration": { "type": "number", "description": "Years" }, "modifiedDuration": { "type": "number", "description": "Percentage price change per unit change in yield" }, "convexity": { "type": "number", "description": "Years squared" } }, "additionalProperties": false }, "annotations": { "readOnlyHint": true, "idempotentHint": true, "openWorldHint": false }, "_house": { "endpoint": "/faculty/msc-finance--capital-markets/bond_price_duration", "feeSt": 1, "degree": "competency:msc-finance--capital-markets", "example": { "faceValue": 1000, "couponRate": 0.06, "yieldToMaturity": 0.05, "years": 5, "frequency": "semiannual" } } }, { "name": "msc-finance--capital-markets.black_scholes_merton", "title": "Black–Scholes–Merton option price (CDU-BUS-FIN-900)", "description": "What are a European call and put worth, and what are their deltas?", "inputSchema": { "type": "object", "required": [ "pan", "spot", "strike", "riskFreeRate", "volatility", "years" ], "properties": { "pan": { "type": "string", "description": "The student PAN — the degree must be held in one of its five slots", "pattern": "^[0-9 ]{16,19}$" }, "spot": { "type": "number", "description": "Underlying price", "minimum": 0.0001 }, "strike": { "type": "number", "description": "Exercise price", "minimum": 0.0001 }, "riskFreeRate": { "type": "number", "description": "Continuously compounded risk-free rate", "minimum": -0.1, "maximum": 1 }, "volatility": { "type": "number", "description": "Annual volatility σ", "minimum": 0.0001, "maximum": 5 }, "years": { "type": "number", "description": "Time to expiry in years", "minimum": 0.0001, "maximum": 100 }, "dividendYield": { "type": "number", "description": "Continuous dividend yield q", "minimum": 0, "maximum": 1, "default": 0 } }, "additionalProperties": false }, "outputSchema": { "type": "object", "required": [ "d1", "d2", "call", "put", "callDelta", "putDelta" ], "properties": { "d1": { "type": "number", "description": "d1" }, "d2": { "type": "number", "description": "d2" }, "call": { "type": "number", "description": "European call value" }, "put": { "type": "number", "description": "European put value" }, "callDelta": { "type": "number", "description": "e^(−qT)·N(d1)" }, "putDelta": { "type": "number", "description": "e^(−qT)·(N(d1) − 1)" } }, "additionalProperties": false }, "annotations": { "readOnlyHint": true, "idempotentHint": true, "openWorldHint": false }, "_house": { "endpoint": "/faculty/msc-finance--capital-markets/black_scholes_merton", "feeSt": 1, "degree": "competency:msc-finance--capital-markets", "example": { "spot": 42, "strike": 40, "riskFreeRate": 0.1, "volatility": 0.2, "years": 0.5, "dividendYield": 0 } } }, { "name": "msc-finance--capital-markets.capm_performance", "title": "CAPM required return and risk-adjusted performance (CDU-BUS-FIN-900)", "description": "What return does the CAPM require of this portfolio, and did it beat it on Jensen’s, Sharpe’s and Treynor’s measures?", "inputSchema": { "type": "object", "required": [ "pan", "riskFreeRate", "beta", "marketReturn", "portfolioReturn", "portfolioVolatility" ], "properties": { "pan": { "type": "string", "description": "The student PAN — the degree must be held in one of its five slots", "pattern": "^[0-9 ]{16,19}$" }, "riskFreeRate": { "type": "number", "description": "Risk-free rate for the period", "minimum": -0.1, "maximum": 1 }, "beta": { "type": "number", "description": "Portfolio beta", "minimum": -5, "maximum": 5 }, "marketReturn": { "type": "number", "description": "Market return for the period", "minimum": -1, "maximum": 5 }, "portfolioReturn": { "type": "number", "description": "Portfolio return for the period", "minimum": -1, "maximum": 5 }, "portfolioVolatility": { "type": "number", "description": "Standard deviation of portfolio returns", "minimum": 0.0001, "maximum": 5 } }, "additionalProperties": false }, "outputSchema": { "type": "object", "required": [ "requiredReturn", "jensensAlpha", "sharpeRatio", "treynorRatio" ], "properties": { "requiredReturn": { "type": "number", "description": "Rf + β(Rm − Rf)" }, "jensensAlpha": { "type": "number", "description": "Rp − required" }, "sharpeRatio": { "type": "number", "description": "(Rp − Rf) ÷ σp" }, "treynorRatio": { "type": "number", "description": "(Rp − Rf) ÷ β" } }, "additionalProperties": false }, "annotations": { "readOnlyHint": true, "idempotentHint": true, "openWorldHint": false }, "_house": { "endpoint": "/faculty/msc-finance--capital-markets/capm_performance", "feeSt": 1, "degree": "competency:msc-finance--capital-markets", "example": { "riskFreeRate": 0.04, "beta": 1.2, "marketReturn": 0.1, "portfolioReturn": 0.13, "portfolioVolatility": 0.18 } } }, { "name": "msc-finance--capital-markets.covered_interest_parity", "title": "Forward rate under covered interest parity (CDU-BUS-FIN-900)", "description": "What forward exchange rate does covered interest parity imply, and is the foreign currency at a forward premium or discount?", "inputSchema": { "type": "object", "required": [ "pan", "spot", "domesticRate", "foreignRate", "years", "compounding" ], "properties": { "pan": { "type": "string", "description": "The student PAN — the degree must be held in one of its five slots", "pattern": "^[0-9 ]{16,19}$" }, "spot": { "type": "number", "description": "Spot rate, domestic per unit of foreign", "minimum": 0.000001 }, "domesticRate": { "type": "number", "description": "Domestic interest rate per year", "minimum": -0.1, "maximum": 1 }, "foreignRate": { "type": "number", "description": "Foreign interest rate per year", "minimum": -0.1, "maximum": 1 }, "years": { "type": "number", "description": "Tenor in years", "minimum": 0.0001, "maximum": 30 }, "compounding": { "type": "string", "description": "Rate convention", "enum": [ "annual", "continuous" ] } }, "additionalProperties": false }, "outputSchema": { "type": "object", "required": [ "forward", "forwardPoints", "forwardPremium" ], "properties": { "forward": { "type": "number", "description": "Forward rate, domestic per foreign" }, "forwardPoints": { "type": "number", "description": "Forward − spot" }, "forwardPremium": { "type": "number", "description": "Forward ÷ spot − 1 (positive: foreign at a premium)" } }, "additionalProperties": false }, "annotations": { "readOnlyHint": true, "idempotentHint": true, "openWorldHint": false }, "_house": { "endpoint": "/faculty/msc-finance--capital-markets/covered_interest_parity", "feeSt": 1, "degree": "competency:msc-finance--capital-markets", "example": { "spot": 18.5, "domesticRate": 0.08, "foreignRate": 0.05, "years": 1, "compounding": "annual" } } }, { "name": "msc-investment-management.time_weighted_return", "title": "Time-weighted return (GIPS) (CDU-BUS-INV-900)", "description": "What is the time-weighted return across these sub-periods, removing the effect of the client’s own flows?", "inputSchema": { "type": "object", "required": [ "pan", "values", "flows", "years" ], "properties": { "pan": { "type": "string", "description": "The student PAN — the degree must be held in one of its five slots", "pattern": "^[0-9 ]{16,19}$" }, "values": { "type": "array", "description": "Market value at each valuation date, start to end", "items": { "type": "number" } }, "flows": { "type": "array", "description": "External flow just after each valuation except the last (negative = withdrawal)", "items": { "type": "number" } }, "years": { "type": "number", "description": "Length of the whole period in years", "minimum": 0.0001, "maximum": 100 } }, "additionalProperties": false }, "outputSchema": { "type": "object", "required": [ "subPeriodReturns", "twr", "annualisedReturn" ], "properties": { "subPeriodReturns": { "type": "array", "description": "Each sub-period return (6 dp)", "items": { "type": "number" } }, "twr": { "type": "number", "description": "Linked time-weighted return" }, "annualisedReturn": { "type": "number", "description": "Annualised when the period is at least a year; otherwise null" } }, "additionalProperties": false }, "annotations": { "readOnlyHint": true, "idempotentHint": true, "openWorldHint": false }, "_house": { "endpoint": "/faculty/msc-investment-management/time_weighted_return", "feeSt": 1, "degree": "competency:msc-investment-management", "example": { "values": [ 1000000, 1050000, 1200000, 1180000 ], "flows": [ 0, 100000, -50000 ], "years": 1 } } }, { "name": "msc-investment-management.modified_dietz", "title": "Modified Dietz return (CDU-BUS-INV-900)", "description": "When the portfolio was not valued at each flow, what return does the Modified Dietz method approximate?", "inputSchema": { "type": "object", "required": [ "pan", "beginningValue", "endingValue", "flows", "flowTiming" ], "properties": { "pan": { "type": "string", "description": "The student PAN — the degree must be held in one of its five slots", "pattern": "^[0-9 ]{16,19}$" }, "beginningValue": { "type": "number", "description": "Market value at the start", "minimum": 0.01 }, "endingValue": { "type": "number", "description": "Market value at the end", "minimum": 0 }, "flows": { "type": "array", "description": "External flows in the period (negative = withdrawal)", "items": { "type": "number" } }, "flowTiming": { "type": "array", "description": "When each flow happened, as the fraction of the period elapsed (0–1)", "items": { "type": "number" } } }, "additionalProperties": false }, "outputSchema": { "type": "object", "required": [ "netFlows", "weightedFlows", "modifiedDietz" ], "properties": { "netFlows": { "type": "number", "description": "Σ flows" }, "weightedFlows": { "type": "number", "description": "Σ (1 − timing)·flow" }, "modifiedDietz": { "type": "number", "description": "The return" } }, "additionalProperties": false }, "annotations": { "readOnlyHint": true, "idempotentHint": true, "openWorldHint": false }, "_house": { "endpoint": "/faculty/msc-investment-management/modified_dietz", "feeSt": 1, "degree": "competency:msc-investment-management", "example": { "beginningValue": 1000000, "endingValue": 1180000, "flows": [ 100000, -50000 ], "flowTiming": [ 0.25, 0.75 ] } } }, { "name": "msc-investment-management.two_asset_portfolio", "title": "Two-asset portfolio risk and return (CDU-BUS-INV-900)", "description": "What are this mix’s expected return and risk, and which mix of the two assets has the least risk?", "inputSchema": { "type": "object", "required": [ "pan", "weightA", "returnA", "returnB", "volatilityA", "volatilityB", "correlation" ], "properties": { "pan": { "type": "string", "description": "The student PAN — the degree must be held in one of its five slots", "pattern": "^[0-9 ]{16,19}$" }, "weightA": { "type": "number", "description": "Weight in asset A (B holds the rest), 0–1", "minimum": 0, "maximum": 1 }, "returnA": { "type": "number", "description": "Expected return of A", "minimum": -1, "maximum": 5 }, "returnB": { "type": "number", "description": "Expected return of B", "minimum": -1, "maximum": 5 }, "volatilityA": { "type": "number", "description": "Standard deviation of A", "minimum": 0.0001, "maximum": 5 }, "volatilityB": { "type": "number", "description": "Standard deviation of B", "minimum": 0.0001, "maximum": 5 }, "correlation": { "type": "number", "description": "Correlation of A and B, −1 to 1", "minimum": -1, "maximum": 1 } }, "additionalProperties": false }, "outputSchema": { "type": "object", "required": [ "expectedReturn", "volatility", "minimumVarianceWeightA" ], "properties": { "expectedReturn": { "type": "number", "description": "w·RA + (1 − w)·RB" }, "volatility": { "type": "number", "description": "Portfolio standard deviation" }, "minimumVarianceWeightA": { "type": "number", "description": "Weight in A that minimises variance (unconstrained)" } }, "additionalProperties": false }, "annotations": { "readOnlyHint": true, "idempotentHint": true, "openWorldHint": false }, "_house": { "endpoint": "/faculty/msc-investment-management/two_asset_portfolio", "feeSt": 1, "degree": "competency:msc-investment-management", "example": { "weightA": 0.6, "returnA": 0.1, "returnB": 0.06, "volatilityA": 0.2, "volatilityB": 0.1, "correlation": 0.3 } } }, { "name": "msc-investment-management.tracking_error_ir", "title": "Tracking error and information ratio (CDU-BUS-INV-900)", "description": "How far did the portfolio stray from its benchmark, and how much active return did it earn per unit of that risk?", "inputSchema": { "type": "object", "required": [ "pan", "portfolioReturns", "benchmarkReturns" ], "properties": { "pan": { "type": "string", "description": "The student PAN — the degree must be held in one of its five slots", "pattern": "^[0-9 ]{16,19}$" }, "portfolioReturns": { "type": "array", "description": "Portfolio return each period", "items": { "type": "number" } }, "benchmarkReturns": { "type": "array", "description": "Benchmark return the same periods", "items": { "type": "number" } }, "periodsPerYear": { "type": "number", "description": "Periods in a year (12 monthly, 52 weekly…)", "minimum": 1, "maximum": 366, "default": 12 } }, "additionalProperties": false }, "outputSchema": { "type": "object", "required": [ "meanActiveReturn", "trackingError", "informationRatio" ], "properties": { "meanActiveReturn": { "type": "number", "description": "Mean of portfolio − benchmark, per period" }, "trackingError": { "type": "number", "description": "Annualised sample standard deviation of active returns" }, "informationRatio": { "type": "number", "description": "Annualised active return ÷ annualised tracking error" } }, "additionalProperties": false }, "annotations": { "readOnlyHint": true, "idempotentHint": true, "openWorldHint": false }, "_house": { "endpoint": "/faculty/msc-investment-management/tracking_error_ir", "feeSt": 1, "degree": "competency:msc-investment-management", "example": { "portfolioReturns": [ 0.012, -0.004, 0.021, 0.008, -0.011, 0.015 ], "benchmarkReturns": [ 0.01, -0.002, 0.018, 0.009, -0.013, 0.011 ], "periodsPerYear": 12 } } }, { "name": "msc-risk--actuarial.parametric_var_es", "title": "Parametric value at risk and expected shortfall (CDU-BUS-RSK-900)", "description": "Under a normal model, what loss is exceeded only with probability 1 − c over the horizon, and what is the average loss beyond it?", "inputSchema": { "type": "object", "required": [ "pan", "portfolioValue", "dailyVolatility", "horizonDays", "confidence" ], "properties": { "pan": { "type": "string", "description": "The student PAN — the degree must be held in one of its five slots", "pattern": "^[0-9 ]{16,19}$" }, "portfolioValue": { "type": "number", "description": "Current portfolio value", "minimum": 0.01 }, "dailyVolatility": { "type": "number", "description": "Standard deviation of daily returns", "minimum": 0.000001, "maximum": 1 }, "horizonDays": { "type": "number", "description": "Holding period in days", "minimum": 1, "maximum": 250 }, "confidence": { "type": "number", "description": "Confidence level, 0.9–0.999", "minimum": 0.9, "maximum": 0.999 }, "dailyMeanReturn": { "type": "number", "description": "Expected daily return", "minimum": -0.1, "maximum": 0.1, "default": 0 } }, "additionalProperties": false }, "outputSchema": { "type": "object", "required": [ "z", "valueAtRisk", "expectedShortfall" ], "properties": { "z": { "type": "number", "description": "Standard normal quantile at the confidence level" }, "valueAtRisk": { "type": "number", "description": "VaR over the horizon" }, "expectedShortfall": { "type": "number", "description": "ES over the horizon" } }, "additionalProperties": false }, "annotations": { "readOnlyHint": true, "idempotentHint": true, "openWorldHint": false }, "_house": { "endpoint": "/faculty/msc-risk--actuarial/parametric_var_es", "feeSt": 1, "degree": "competency:msc-risk--actuarial", "example": { "portfolioValue": 10000000, "dailyVolatility": 0.012, "horizonDays": 10, "confidence": 0.99, "dailyMeanReturn": 0 } } }, { "name": "msc-risk--actuarial.basel_irb_capital", "title": "IRB capital for a corporate exposure (CDU-BUS-RSK-900)", "description": "What capital, risk-weighted assets and expected loss does the Basel IRB formula assign to this corporate exposure?", "inputSchema": { "type": "object", "required": [ "pan", "pd", "lgd", "ead", "maturity" ], "properties": { "pan": { "type": "string", "description": "The student PAN — the degree must be held in one of its five slots", "pattern": "^[0-9 ]{16,19}$" }, "pd": { "type": "number", "description": "One-year probability of default, 0–1", "minimum": 0, "maximum": 0.9999 }, "lgd": { "type": "number", "description": "Loss given default, 0–1", "minimum": 0, "maximum": 1 }, "ead": { "type": "number", "description": "Exposure at default", "minimum": 0 }, "maturity": { "type": "number", "description": "Effective maturity in years, 1–5", "minimum": 1, "maximum": 5 } }, "additionalProperties": false }, "outputSchema": { "type": "object", "required": [ "pdUsed", "correlation", "capitalRequirement", "riskWeight", "riskWeightedAssets", "expectedLoss" ], "properties": { "pdUsed": { "type": "number", "description": "PD after the 0.03% floor" }, "correlation": { "type": "number", "description": "Asset correlation R" }, "capitalRequirement": { "type": "number", "description": "K, per unit of EAD" }, "riskWeight": { "type": "number", "description": "K × 12.5" }, "riskWeightedAssets": { "type": "number", "description": "K × 12.5 × EAD" }, "expectedLoss": { "type": "number", "description": "PD × LGD × EAD" } }, "additionalProperties": false }, "annotations": { "readOnlyHint": true, "idempotentHint": true, "openWorldHint": false }, "_house": { "endpoint": "/faculty/msc-risk--actuarial/basel_irb_capital", "feeSt": 1, "degree": "competency:msc-risk--actuarial", "example": { "pd": 0.01, "lgd": 0.45, "ead": 1000000, "maturity": 2.5 } } }, { "name": "msc-risk--actuarial.buhlmann_credibility", "title": "Bühlmann credibility premium (CDU-BUS-RSK-900)", "description": "How much weight should this risk’s own experience get against the collective, and what premium results?", "inputSchema": { "type": "object", "required": [ "pan", "observations", "sampleMean", "collectiveMean", "expectedProcessVariance", "varianceOfHypotheticalMeans" ], "properties": { "pan": { "type": "string", "description": "The student PAN — the degree must be held in one of its five slots", "pattern": "^[0-9 ]{16,19}$" }, "observations": { "type": "number", "description": "Number of periods (or exposures) of own experience", "minimum": 1 }, "sampleMean": { "type": "number", "description": "Mean claims of this risk", "minimum": 0 }, "collectiveMean": { "type": "number", "description": "Mean claims of the collective (μ)", "minimum": 0 }, "expectedProcessVariance": { "type": "number", "description": "EPV: expected variance within a risk", "minimum": 0 }, "varianceOfHypotheticalMeans": { "type": "number", "description": "VHM: variance of risk means across the collective", "minimum": 0.000001 } }, "additionalProperties": false }, "outputSchema": { "type": "object", "required": [ "k", "credibilityFactor", "credibilityPremium" ], "properties": { "k": { "type": "number", "description": "EPV ÷ VHM" }, "credibilityFactor": { "type": "number", "description": "Z = n ÷ (n + k)" }, "credibilityPremium": { "type": "number", "description": "Z·X̄ + (1 − Z)·μ" } }, "additionalProperties": false }, "annotations": { "readOnlyHint": true, "idempotentHint": true, "openWorldHint": false }, "_house": { "endpoint": "/faculty/msc-risk--actuarial/buhlmann_credibility", "feeSt": 1, "degree": "competency:msc-risk--actuarial", "example": { "observations": 5, "sampleMean": 1200, "collectiveMean": 1000, "expectedProcessVariance": 40000, "varianceOfHypotheticalMeans": 10000 } } }, { "name": "msc-risk--actuarial.collective_risk_premium", "title": "Collective risk model and loaded premium (CDU-BUS-RSK-900)", "description": "What are the mean and spread of aggregate claims, and what premium does the expected-value principle charge?", "inputSchema": { "type": "object", "required": [ "pan", "frequencyMean", "frequencyVariance", "severityMean", "severityVariance", "loading" ], "properties": { "pan": { "type": "string", "description": "The student PAN — the degree must be held in one of its five slots", "pattern": "^[0-9 ]{16,19}$" }, "frequencyMean": { "type": "number", "description": "E[N], expected number of claims", "minimum": 0 }, "frequencyVariance": { "type": "number", "description": "Var[N] (equal to the mean for Poisson)", "minimum": 0 }, "severityMean": { "type": "number", "description": "E[X], expected claim size", "minimum": 0 }, "severityVariance": { "type": "number", "description": "Var[X]", "minimum": 0 }, "loading": { "type": "number", "description": "Safety loading θ, 0–5", "minimum": 0, "maximum": 5 } }, "additionalProperties": false }, "outputSchema": { "type": "object", "required": [ "aggregateMean", "aggregateVariance", "aggregateSd", "premium" ], "properties": { "aggregateMean": { "type": "number", "description": "E[S]" }, "aggregateVariance": { "type": "number", "description": "Var[S]" }, "aggregateSd": { "type": "number", "description": "√Var[S]" }, "premium": { "type": "number", "description": "(1 + θ)·E[S]" } }, "additionalProperties": false }, "annotations": { "readOnlyHint": true, "idempotentHint": true, "openWorldHint": false }, "_house": { "endpoint": "/faculty/msc-risk--actuarial/collective_risk_premium", "feeSt": 1, "degree": "competency:msc-risk--actuarial", "example": { "frequencyMean": 2, "frequencyVariance": 2, "severityMean": 5000, "severityVariance": 4000000, "loading": 0.2 } } }, { "name": "mpa-public-administration.social_cba", "title": "Social cost–benefit analysis (CDU-BUS-MPA-900)", "description": "At the social discount rate, does the programme’s stream of benefits justify its costs?", "inputSchema": { "type": "object", "required": [ "pan", "benefits", "costs" ], "properties": { "pan": { "type": "string", "description": "The student PAN — the degree must be held in one of its five slots", "pattern": "^[0-9 ]{16,19}$" }, "benefits": { "type": "array", "description": "Social benefits per year, year 0 first", "items": { "type": "number" } }, "costs": { "type": "array", "description": "Social costs per year, year 0 first", "items": { "type": "number" } }, "discountRate": { "type": "number", "description": "Social discount rate, 0–0.2", "minimum": 0, "maximum": 0.2, "default": 0.035 } }, "additionalProperties": false }, "outputSchema": { "type": "object", "required": [ "pvBenefits", "pvCosts", "npv", "bcr", "worthwhile" ], "properties": { "pvBenefits": { "type": "number", "description": "Present value of benefits" }, "pvCosts": { "type": "number", "description": "Present value of costs" }, "npv": { "type": "number", "description": "PV benefits − PV costs" }, "bcr": { "type": "number", "description": "PV benefits ÷ PV costs" }, "worthwhile": { "type": "boolean", "description": "NPV > 0" } }, "additionalProperties": false }, "annotations": { "readOnlyHint": true, "idempotentHint": true, "openWorldHint": false }, "_house": { "endpoint": "/faculty/mpa-public-administration/social_cba", "feeSt": 1, "degree": "competency:mpa-public-administration", "example": { "benefits": [ 0, 400000, 450000, 500000, 500000 ], "costs": [ 1200000, 50000, 50000, 50000, 50000 ], "discountRate": 0.035 } } }, { "name": "mpa-public-administration.preference_points", "title": "Preferential procurement award (80/20 or 90/10) (CDU-BUS-MPA-900)", "description": "Which bidder scores highest once price points and specific-goal points are added under the applicable preference system?", "inputSchema": { "type": "object", "required": [ "pan", "estimatedValue", "bidPrices", "specificGoalPoints" ], "properties": { "pan": { "type": "string", "description": "The student PAN — the degree must be held in one of its five slots", "pattern": "^[0-9 ]{16,19}$" }, "estimatedValue": { "type": "number", "description": "Estimated Rand value of the tender (selects 80/20 or 90/10)", "minimum": 0 }, "bidPrices": { "type": "array", "description": "Each acceptable bidder’s price", "items": { "type": "number" } }, "specificGoalPoints": { "type": "array", "description": "Specific-goal points each bidder is allotted (≤ 20 under 80/20, ≤ 10 under 90/10)", "items": { "type": "number" } } }, "additionalProperties": false }, "outputSchema": { "type": "object", "required": [ "system", "pricePoints", "totalPoints", "winner" ], "properties": { "system": { "type": "string", "description": "80/20 or 90/10" }, "pricePoints": { "type": "array", "description": "Price points per bidder (2 dp)", "items": { "type": "number" } }, "totalPoints": { "type": "array", "description": "Price + specific-goal points (2 dp)", "items": { "type": "number" } }, "winner": { "type": "number", "description": "1-based position of the highest total" } }, "additionalProperties": false }, "annotations": { "readOnlyHint": true, "idempotentHint": true, "openWorldHint": false }, "_house": { "endpoint": "/faculty/mpa-public-administration/preference_points", "feeSt": 1, "degree": "competency:mpa-public-administration", "example": { "estimatedValue": 12000000, "bidPrices": [ 1000000, 950000, 1100000, 990000 ], "specificGoalPoints": [ 16, 8, 12, 4 ] } } }, { "name": "mpa-public-administration.debt_dynamics", "title": "Public debt dynamics (CDU-BUS-MPA-900)", "description": "Where does the debt-to-GDP ratio go over the projection, and what primary balance would hold it steady?", "inputSchema": { "type": "object", "required": [ "pan", "debtRatio", "interestRate", "growthRate", "primaryBalance", "years" ], "properties": { "pan": { "type": "string", "description": "The student PAN — the degree must be held in one of its five slots", "pattern": "^[0-9 ]{16,19}$" }, "debtRatio": { "type": "number", "description": "Debt ÷ GDP now", "minimum": 0, "maximum": 10 }, "interestRate": { "type": "number", "description": "Nominal effective interest rate on debt", "minimum": -0.1, "maximum": 1 }, "growthRate": { "type": "number", "description": "Nominal GDP growth", "minimum": -0.5, "maximum": 1 }, "primaryBalance": { "type": "number", "description": "Primary balance ÷ GDP (surplus positive)", "minimum": -0.5, "maximum": 0.5 }, "years": { "type": "number", "description": "Projection horizon in years", "minimum": 1, "maximum": 50 } }, "additionalProperties": false }, "outputSchema": { "type": "object", "required": [ "projectedDebtRatio", "change", "stabilisingPrimaryBalance" ], "properties": { "projectedDebtRatio": { "type": "number", "description": "Debt ÷ GDP at the horizon" }, "change": { "type": "number", "description": "Projected − current" }, "stabilisingPrimaryBalance": { "type": "number", "description": "pb* = d·(r − g) ÷ (1 + g)" } }, "additionalProperties": false }, "annotations": { "readOnlyHint": true, "idempotentHint": true, "openWorldHint": false }, "_house": { "endpoint": "/faculty/mpa-public-administration/debt_dynamics", "feeSt": 1, "degree": "competency:mpa-public-administration", "example": { "debtRatio": 0.72, "interestRate": 0.09, "growthRate": 0.07, "primaryBalance": -0.01, "years": 5 } } }, { "name": "mpa-public-administration.gini", "title": "Gini coefficient (CDU-BUS-MPA-900)", "description": "How unequal is this income distribution, on the scale from 0 (equal) to 1?", "inputSchema": { "type": "object", "required": [ "pan", "incomes" ], "properties": { "pan": { "type": "string", "description": "The student PAN — the degree must be held in one of its five slots", "pattern": "^[0-9 ]{16,19}$" }, "incomes": { "type": "array", "description": "Income of each person or household (not negative)", "items": { "type": "number" } } }, "additionalProperties": false }, "outputSchema": { "type": "object", "required": [ "gini", "mean" ], "properties": { "gini": { "type": "number", "description": "Σ|xi − xj| ÷ (2n²μ)" }, "mean": { "type": "number", "description": "Mean income" } }, "additionalProperties": false }, "annotations": { "readOnlyHint": true, "idempotentHint": true, "openWorldHint": false }, "_house": { "endpoint": "/faculty/mpa-public-administration/gini", "feeSt": 1, "degree": "competency:mpa-public-administration", "example": { "incomes": [ 12000, 18000, 25000, 31000, 40000, 52000, 68000, 90000, 130000, 250000 ] } } }, { "name": "mph-health-economics--policy.icer_nmb", "title": "ICER and net monetary benefit (CDU-HEA-MPH-900)", "description": "What does each extra QALY from the new intervention cost, and is it worth it at the threshold?", "inputSchema": { "type": "object", "required": [ "pan", "costNew", "costComparator", "qalyNew", "qalyComparator" ], "properties": { "pan": { "type": "string", "description": "The student PAN — the degree must be held in one of its five slots", "pattern": "^[0-9 ]{16,19}$" }, "costNew": { "type": "number", "description": "Total cost per patient, new intervention", "minimum": 0 }, "costComparator": { "type": "number", "description": "Total cost per patient, comparator", "minimum": 0 }, "qalyNew": { "type": "number", "description": "QALYs per patient, new intervention", "minimum": 0 }, "qalyComparator": { "type": "number", "description": "QALYs per patient, comparator", "minimum": 0 }, "threshold": { "type": "number", "description": "Willingness to pay per QALY (λ)", "minimum": 0, "default": 20000 } }, "additionalProperties": false }, "outputSchema": { "type": "object", "required": [ "incrementalCost", "incrementalQaly", "icer", "netMonetaryBenefit", "verdict" ], "properties": { "incrementalCost": { "type": "number", "description": "ΔC" }, "incrementalQaly": { "type": "number", "description": "ΔE" }, "icer": { "type": "number", "description": "ΔC ÷ ΔE (null when ΔE = 0)" }, "netMonetaryBenefit": { "type": "number", "description": "λ·ΔE − ΔC" }, "verdict": { "type": "string", "description": "dominant, dominated, cost-effective or not cost-effective" } }, "additionalProperties": false }, "annotations": { "readOnlyHint": true, "idempotentHint": true, "openWorldHint": false }, "_house": { "endpoint": "/faculty/mph-health-economics--policy/icer_nmb", "feeSt": 1, "degree": "competency:mph-health-economics--policy", "example": { "costNew": 24000, "costComparator": 15000, "qalyNew": 6.2, "qalyComparator": 5.8, "threshold": 20000 } } }, { "name": "mph-health-economics--policy.discounted_qalys", "title": "Discounted QALYs (CDU-HEA-MPH-900)", "description": "How many QALYs does this stream of health-state utilities yield, undiscounted and discounted at the reference-case rate?", "inputSchema": { "type": "object", "required": [ "pan", "utilities" ], "properties": { "pan": { "type": "string", "description": "The student PAN — the degree must be held in one of its five slots", "pattern": "^[0-9 ]{16,19}$" }, "utilities": { "type": "array", "description": "Mean utility in each successive year (0–1; below 0 for states worse than dead)", "items": { "type": "number" } }, "discountRate": { "type": "number", "description": "Annual discount rate, 0–0.1", "minimum": 0, "maximum": 0.1, "default": 0.035 } }, "additionalProperties": false }, "outputSchema": { "type": "object", "required": [ "lifeYears", "undiscountedQalys", "discountedQalys" ], "properties": { "lifeYears": { "type": "number", "description": "Years counted" }, "undiscountedQalys": { "type": "number", "description": "Σ utilities" }, "discountedQalys": { "type": "number", "description": "Σ u_t ÷ (1 + r)^t, t = 0 for year 1" } }, "additionalProperties": false }, "annotations": { "readOnlyHint": true, "idempotentHint": true, "openWorldHint": false }, "_house": { "endpoint": "/faculty/mph-health-economics--policy/discounted_qalys", "feeSt": 1, "degree": "competency:mph-health-economics--policy", "example": { "utilities": [ 0.85, 0.82, 0.8, 0.78, 0.75 ], "discountRate": 0.035 } } }, { "name": "mph-health-economics--policy.two_by_two", "title": "Measures of association from a 2×2 table (CDU-HEA-MPH-900)", "description": "In this cohort, how much more (or less) likely is the outcome among the exposed, and how many must be exposed for one extra (or one fewer) case?", "inputSchema": { "type": "object", "required": [ "pan", "exposedCases", "exposedNonCases", "unexposedCases", "unexposedNonCases" ], "properties": { "pan": { "type": "string", "description": "The student PAN — the degree must be held in one of its five slots", "pattern": "^[0-9 ]{16,19}$" }, "exposedCases": { "type": "number", "description": "a: exposed with the outcome", "minimum": 0 }, "exposedNonCases": { "type": "number", "description": "b: exposed without it", "minimum": 0 }, "unexposedCases": { "type": "number", "description": "c: unexposed with the outcome", "minimum": 0 }, "unexposedNonCases": { "type": "number", "description": "d: unexposed without it", "minimum": 0 } }, "additionalProperties": false }, "outputSchema": { "type": "object", "required": [ "riskExposed", "riskUnexposed", "riskRatio", "riskRatioLower95", "riskRatioUpper95", "riskDifference", "oddsRatio", "numberNeeded" ], "properties": { "riskExposed": { "type": "number", "description": "a ÷ (a + b)" }, "riskUnexposed": { "type": "number", "description": "c ÷ (c + d)" }, "riskRatio": { "type": "number", "description": "RR" }, "riskRatioLower95": { "type": "number", "description": "Lower 95% bound of RR" }, "riskRatioUpper95": { "type": "number", "description": "Upper 95% bound of RR" }, "riskDifference": { "type": "number", "description": "Risk exposed − risk unexposed" }, "oddsRatio": { "type": "number", "description": "(a·d) ÷ (b·c)" }, "numberNeeded": { "type": "number", "description": "1 ÷ |RD| (to harm if RD > 0, to treat if RD < 0)" } }, "additionalProperties": false }, "annotations": { "readOnlyHint": true, "idempotentHint": true, "openWorldHint": false }, "_house": { "endpoint": "/faculty/mph-health-economics--policy/two_by_two", "feeSt": 1, "degree": "competency:mph-health-economics--policy", "example": { "exposedCases": 30, "exposedNonCases": 70, "unexposedCases": 15, "unexposedNonCases": 85 } } }, { "name": "mph-health-economics--policy.diagnostic_accuracy", "title": "Predictive values and likelihood ratios (CDU-HEA-MPH-900)", "description": "In a population with this prevalence, how likely is a positive (or negative) result to be right?", "inputSchema": { "type": "object", "required": [ "pan", "sensitivity", "specificity", "prevalence" ], "properties": { "pan": { "type": "string", "description": "The student PAN — the degree must be held in one of its five slots", "pattern": "^[0-9 ]{16,19}$" }, "sensitivity": { "type": "number", "description": "P(test + | disease), 0–0.9999", "minimum": 0.0001, "maximum": 0.9999 }, "specificity": { "type": "number", "description": "P(test − | no disease), 0–0.9999", "minimum": 0.0001, "maximum": 0.9999 }, "prevalence": { "type": "number", "description": "Pre-test probability, 0–1", "minimum": 0.000001, "maximum": 0.999999 } }, "additionalProperties": false }, "outputSchema": { "type": "object", "required": [ "ppv", "npv", "positiveLikelihoodRatio", "negativeLikelihoodRatio" ], "properties": { "ppv": { "type": "number", "description": "P(disease | +)" }, "npv": { "type": "number", "description": "P(no disease | −)" }, "positiveLikelihoodRatio": { "type": "number", "description": "LR+" }, "negativeLikelihoodRatio": { "type": "number", "description": "LR−" } }, "additionalProperties": false }, "annotations": { "readOnlyHint": true, "idempotentHint": true, "openWorldHint": false }, "_house": { "endpoint": "/faculty/mph-health-economics--policy/diagnostic_accuracy", "feeSt": 1, "degree": "competency:mph-health-economics--policy", "example": { "sensitivity": 0.9, "specificity": 0.95, "prevalence": 0.02 } } }, { "name": "llm-dispute-resolution.model_law_deadline", "title": "Model Law time limit (CDU-LAW-DRS-900)", "description": "From the event that starts the clock, by what date must the step be taken under the UNCITRAL Model Law?", "inputSchema": { "type": "object", "required": [ "pan", "event", "triggerDate" ], "properties": { "pan": { "type": "string", "description": "The student PAN — the degree must be held in one of its five slots", "pattern": "^[0-9 ]{16,19}$" }, "event": { "type": "string", "description": "The step whose time limit is wanted", "enum": [ "appoint_arbitrator", "challenge_arbitrator", "court_review_of_jurisdiction", "request_correction", "request_additional_award", "set_aside" ] }, "triggerDate": { "type": "string", "description": "The date the clock starts (receipt, awareness, notice), YYYY-MM-DD" } }, "additionalProperties": false }, "outputSchema": { "type": "object", "required": [ "article", "period", "deadline" ], "properties": { "article": { "type": "string", "description": "The Model Law provision" }, "period": { "type": "string", "description": "The period, in days or months" }, "deadline": { "type": "string", "description": "Last day, YYYY-MM-DD" } }, "additionalProperties": false }, "annotations": { "readOnlyHint": true, "idempotentHint": true, "openWorldHint": false }, "_house": { "endpoint": "/faculty/llm-dispute-resolution/model_law_deadline", "feeSt": 1, "degree": "competency:llm-dispute-resolution", "example": { "event": "set_aside", "triggerDate": "2026-03-16" } } }, { "name": "llm-dispute-resolution.award_interest", "title": "Interest on a money award (CDU-LAW-DRS-900)", "description": "How much interest accrues on the sum from the due date to the date of the award, simple or compounded annually?", "inputSchema": { "type": "object", "required": [ "pan", "principal", "annualRate", "fromDate", "toDate", "method" ], "properties": { "pan": { "type": "string", "description": "The student PAN — the degree must be held in one of its five slots", "pattern": "^[0-9 ]{16,19}$" }, "principal": { "type": "number", "description": "The sum due", "minimum": 0 }, "annualRate": { "type": "number", "description": "Annual interest rate, 0–1", "minimum": 0, "maximum": 1 }, "fromDate": { "type": "string", "description": "Date payment was due, YYYY-MM-DD" }, "toDate": { "type": "string", "description": "Date interest runs to, YYYY-MM-DD" }, "method": { "type": "string", "description": "simple, or compounded annually", "enum": [ "simple", "compound_annual" ] } }, "additionalProperties": false }, "outputSchema": { "type": "object", "required": [ "days", "years", "interest", "total" ], "properties": { "days": { "type": "number", "description": "Days elapsed" }, "years": { "type": "number", "description": "Days ÷ 365" }, "interest": { "type": "number", "description": "Interest accrued" }, "total": { "type": "number", "description": "Principal + interest" } }, "additionalProperties": false }, "annotations": { "readOnlyHint": true, "idempotentHint": true, "openWorldHint": false }, "_house": { "endpoint": "/faculty/llm-dispute-resolution/award_interest", "feeSt": 1, "degree": "competency:llm-dispute-resolution", "example": { "principal": 2500000, "annualRate": 0.07, "fromDate": "2024-01-15", "toDate": "2026-06-30", "method": "simple" } } }, { "name": "llm-dispute-resolution.cost_apportionment", "title": "Apportionment of costs by success (CDU-LAW-DRS-900)", "description": "If costs follow the event in proportion to success, who pays how much of whose costs, and what is the net?", "inputSchema": { "type": "object", "required": [ "pan", "claimedAmount", "awardedAmount", "claimantCosts", "respondentCosts" ], "properties": { "pan": { "type": "string", "description": "The student PAN — the degree must be held in one of its five slots", "pattern": "^[0-9 ]{16,19}$" }, "claimedAmount": { "type": "number", "description": "Amount claimed", "minimum": 0.01 }, "awardedAmount": { "type": "number", "description": "Amount awarded", "minimum": 0 }, "claimantCosts": { "type": "number", "description": "Claimant’s reasonable costs", "minimum": 0 }, "respondentCosts": { "type": "number", "description": "Respondent’s reasonable costs", "minimum": 0 } }, "additionalProperties": false }, "outputSchema": { "type": "object", "required": [ "successRate", "respondentPaysOfClaimantCosts", "claimantPaysOfRespondentCosts", "netPayableByRespondent" ], "properties": { "successRate": { "type": "number", "description": "Awarded ÷ claimed, at most 1" }, "respondentPaysOfClaimantCosts": { "type": "number", "description": "Success × claimant costs" }, "claimantPaysOfRespondentCosts": { "type": "number", "description": "(1 − success) × respondent costs" }, "netPayableByRespondent": { "type": "number", "description": "The difference (negative: the claimant pays)" } }, "additionalProperties": false }, "annotations": { "readOnlyHint": true, "idempotentHint": true, "openWorldHint": false }, "_house": { "endpoint": "/faculty/llm-dispute-resolution/cost_apportionment", "feeSt": 1, "degree": "competency:llm-dispute-resolution", "example": { "claimedAmount": 2000000, "awardedAmount": 1500000, "claimantCosts": 400000, "respondentCosts": 300000 } } }, { "name": "llm-dispute-resolution.settlement_zone", "title": "Settlement zone from expected outcomes (CDU-LAW-DRS-900)", "description": "Given the chance of winning and the cost of going on, between what sums should both sides prefer to settle?", "inputSchema": { "type": "object", "required": [ "pan", "awardIfClaimantWins", "probabilityClaimantWins", "claimantCostsToAward", "respondentCostsToAward" ], "properties": { "pan": { "type": "string", "description": "The student PAN — the degree must be held in one of its five slots", "pattern": "^[0-9 ]{16,19}$" }, "awardIfClaimantWins": { "type": "number", "description": "Expected award if the claimant wins", "minimum": 0 }, "probabilityClaimantWins": { "type": "number", "description": "Shared estimate of the claimant’s chance, 0–1", "minimum": 0, "maximum": 1 }, "claimantCostsToAward": { "type": "number", "description": "Claimant’s further costs to an award", "minimum": 0 }, "respondentCostsToAward": { "type": "number", "description": "Respondent’s further costs to an award", "minimum": 0 } }, "additionalProperties": false }, "outputSchema": { "type": "object", "required": [ "claimantFloor", "respondentCeiling", "zoneExists", "zoneWidth", "midpoint" ], "properties": { "claimantFloor": { "type": "number", "description": "p·A − claimant costs" }, "respondentCeiling": { "type": "number", "description": "p·A + respondent costs" }, "zoneExists": { "type": "boolean", "description": "Ceiling ≥ floor" }, "zoneWidth": { "type": "number", "description": "Ceiling − floor" }, "midpoint": { "type": "number", "description": "A focal settlement figure" } }, "additionalProperties": false }, "annotations": { "readOnlyHint": true, "idempotentHint": true, "openWorldHint": false }, "_house": { "endpoint": "/faculty/llm-dispute-resolution/settlement_zone", "feeSt": 1, "degree": "competency:llm-dispute-resolution", "example": { "awardIfClaimantWins": 1000000, "probabilityClaimantWins": 0.6, "claimantCostsToAward": 150000, "respondentCostsToAward": 120000 } } }, { "name": "llm-corporate-environmental--mining-law.mineral_royalty", "title": "Mineral royalty percentage and amount (CDU-LAW-CEM-900)", "description": "What royalty percentage and amount does the Royalty Act impose for this year’s gross sales and EBIT?", "inputSchema": { "type": "object", "required": [ "pan", "condition", "grossSales", "ebit" ], "properties": { "pan": { "type": "string", "description": "The student PAN — the degree must be held in one of its five slots", "pattern": "^[0-9 ]{16,19}$" }, "condition": { "type": "string", "description": "Condition of the mineral resource transferred", "enum": [ "refined", "unrefined" ] }, "grossSales": { "type": "number", "description": "Gross sales for the year (s6)", "minimum": 0.01 }, "ebit": { "type": "number", "description": "Earnings before interest and taxes as the Act defines it (s5); may be negative", "minimum": -1000000000000, "maximum": 1000000000000 } }, "additionalProperties": false }, "outputSchema": { "type": "object", "required": [ "royaltyPercentage", "royalty", "capped" ], "properties": { "royaltyPercentage": { "type": "number", "description": "Y%, between 0.5 and the cap" }, "royalty": { "type": "number", "description": "Y% × gross sales" }, "capped": { "type": "boolean", "description": "The cap applied" } }, "additionalProperties": false }, "annotations": { "readOnlyHint": true, "idempotentHint": true, "openWorldHint": false }, "_house": { "endpoint": "/faculty/llm-corporate-environmental--mining-law/mineral_royalty", "feeSt": 1, "degree": "competency:llm-corporate-environmental--mining-law", "example": { "condition": "refined", "grossSales": 500000000, "ebit": 120000000 } } }, { "name": "llm-corporate-environmental--mining-law.solvency_liquidity", "title": "Solvency and liquidity test (CDU-LAW-CEM-900)", "description": "Would the company still satisfy the solvency and liquidity test immediately after this distribution, and what is the most it could distribute?", "inputSchema": { "type": "object", "required": [ "pan", "assetsFairValue", "liabilitiesFairValue", "distribution", "cashOnHand", "inflowsNext12Months", "debtsDueNext12Months" ], "properties": { "pan": { "type": "string", "description": "The student PAN — the degree must be held in one of its five slots", "pattern": "^[0-9 ]{16,19}$" }, "assetsFairValue": { "type": "number", "description": "Total assets, fairly valued", "minimum": 0 }, "liabilitiesFairValue": { "type": "number", "description": "Total liabilities, fairly valued", "minimum": 0 }, "distribution": { "type": "number", "description": "The proposed distribution", "minimum": 0 }, "cashOnHand": { "type": "number", "description": "Cash and liquid resources now", "minimum": 0 }, "inflowsNext12Months": { "type": "number", "description": "Reasonably foreseeable inflows over 12 months", "minimum": 0 }, "debtsDueNext12Months": { "type": "number", "description": "Debts falling due in the ordinary course over 12 months", "minimum": 0 } }, "additionalProperties": false }, "outputSchema": { "type": "object", "required": [ "solventAfter", "liquidAfter", "passes", "maximumDistribution" ], "properties": { "solventAfter": { "type": "boolean", "description": "Assets − distribution ≥ liabilities" }, "liquidAfter": { "type": "boolean", "description": "Cash − distribution + inflows ≥ debts due" }, "passes": { "type": "boolean", "description": "Both limbs satisfied" }, "maximumDistribution": { "type": "number", "description": "The larger distribution both limbs would still allow" } }, "additionalProperties": false }, "annotations": { "readOnlyHint": true, "idempotentHint": true, "openWorldHint": false }, "_house": { "endpoint": "/faculty/llm-corporate-environmental--mining-law/solvency_liquidity", "feeSt": 1, "degree": "competency:llm-corporate-environmental--mining-law", "example": { "assetsFairValue": 50000000, "liabilitiesFairValue": 32000000, "distribution": 5000000, "cashOnHand": 6000000, "inflowsNext12Months": 40000000, "debtsDueNext12Months": 39000000 } } }, { "name": "llm-corporate-environmental--mining-law.mineral_right_term", "title": "Term and renewal of a mineral right (CDU-LAW-CEM-900)", "description": "For a prospecting or mining right granted on this date, when does it expire, and how far can renewal take it?", "inputSchema": { "type": "object", "required": [ "pan", "rightType", "grantDate", "requestedYears" ], "properties": { "pan": { "type": "string", "description": "The student PAN — the degree must be held in one of its five slots", "pattern": "^[0-9 ]{16,19}$" }, "rightType": { "type": "string", "description": "The right granted", "enum": [ "prospecting", "mining" ] }, "grantDate": { "type": "string", "description": "Effective date of the right, YYYY-MM-DD" }, "requestedYears": { "type": "number", "description": "Term applied for, whole years", "minimum": 1, "maximum": 100 } }, "additionalProperties": false }, "outputSchema": { "type": "object", "required": [ "grantedYears", "expiryDate", "renewalYears", "expiryAfterOneRenewal" ], "properties": { "grantedYears": { "type": "number", "description": "Requested term, capped by the Act" }, "expiryDate": { "type": "string", "description": "Grant date + granted term" }, "renewalYears": { "type": "number", "description": "Longest single renewal" }, "expiryAfterOneRenewal": { "type": "string", "description": "Expiry if renewed once for the longest period" } }, "additionalProperties": false }, "annotations": { "readOnlyHint": true, "idempotentHint": true, "openWorldHint": false }, "_house": { "endpoint": "/faculty/llm-corporate-environmental--mining-law/mineral_right_term", "feeSt": 1, "degree": "competency:llm-corporate-environmental--mining-law", "example": { "rightType": "mining", "grantDate": "2026-03-01", "requestedYears": 25 } } }, { "name": "llm-corporate-environmental--mining-law.securities_thresholds", "title": "Disclosure steps and the mandatory offer (CDU-LAW-CEM-900)", "description": "Which 5% disclosure steps does this change in holding cross, and does it trigger a mandatory offer?", "inputSchema": { "type": "object", "required": [ "pan", "percentBefore", "percentAfter" ], "properties": { "pan": { "type": "string", "description": "The student PAN — the degree must be held in one of its five slots", "pattern": "^[0-9 ]{16,19}$" }, "percentBefore": { "type": "number", "description": "Beneficial interest before, % of the class", "minimum": 0, "maximum": 100 }, "percentAfter": { "type": "number", "description": "Beneficial interest after, % of the class", "minimum": 0, "maximum": 100 } }, "additionalProperties": false }, "outputSchema": { "type": "object", "required": [ "thresholdsCrossed", "mustNotify", "mandatoryOffer" ], "properties": { "thresholdsCrossed": { "type": "array", "description": "Multiples of 5% reached or fallen below", "items": { "type": "number" } }, "mustNotify": { "type": "boolean", "description": "At least one threshold crossed" }, "mandatoryOffer": { "type": "boolean", "description": "Crossed up to 35% or more" } }, "additionalProperties": false }, "annotations": { "readOnlyHint": true, "idempotentHint": true, "openWorldHint": false }, "_house": { "endpoint": "/faculty/llm-corporate-environmental--mining-law/securities_thresholds", "feeSt": 1, "degree": "competency:llm-corporate-environmental--mining-law", "example": { "percentBefore": 28, "percentAfter": 36 } } }, { "name": "med-assessment--curriculum.item_analysis", "title": "Item difficulty and discrimination (CDU-EDU-ASC-900)", "description": "How hard is this item, and does it separate stronger from weaker candidates?", "inputSchema": { "type": "object", "required": [ "pan", "upperCorrect", "lowerCorrect", "groupSize" ], "properties": { "pan": { "type": "string", "description": "The student PAN — the degree must be held in one of its five slots", "pattern": "^[0-9 ]{16,19}$" }, "upperCorrect": { "type": "number", "description": "Correct answers in the upper group", "minimum": 0 }, "lowerCorrect": { "type": "number", "description": "Correct answers in the lower group", "minimum": 0 }, "groupSize": { "type": "number", "description": "Candidates in each group (often the top and bottom 27%)", "minimum": 1 } }, "additionalProperties": false }, "outputSchema": { "type": "object", "required": [ "difficulty", "discrimination", "quality" ], "properties": { "difficulty": { "type": "number", "description": "p = (U + L) ÷ 2n" }, "discrimination": { "type": "number", "description": "D = (U − L) ÷ n" }, "quality": { "type": "string", "description": "very good, reasonably good, marginal or poor" } }, "additionalProperties": false }, "annotations": { "readOnlyHint": true, "idempotentHint": true, "openWorldHint": false }, "_house": { "endpoint": "/faculty/med-assessment--curriculum/item_analysis", "feeSt": 1, "degree": "competency:med-assessment--curriculum", "example": { "upperCorrect": 24, "lowerCorrect": 10, "groupSize": 30 } } }, { "name": "med-assessment--curriculum.cronbach_alpha", "title": "Cronbach’s alpha (CDU-EDU-ASC-900)", "description": "How internally consistent are the items of this test?", "inputSchema": { "type": "object", "required": [ "pan", "itemVariances", "totalScoreVariance" ], "properties": { "pan": { "type": "string", "description": "The student PAN — the degree must be held in one of its five slots", "pattern": "^[0-9 ]{16,19}$" }, "itemVariances": { "type": "array", "description": "Variance of each item score", "items": { "type": "number" } }, "totalScoreVariance": { "type": "number", "description": "Variance of the total test score", "minimum": 0.000001 } }, "additionalProperties": false }, "outputSchema": { "type": "object", "required": [ "items", "sumItemVariances", "alpha" ], "properties": { "items": { "type": "number", "description": "k" }, "sumItemVariances": { "type": "number", "description": "Σσᵢ²" }, "alpha": { "type": "number", "description": "Cronbach’s alpha" } }, "additionalProperties": false }, "annotations": { "readOnlyHint": true, "idempotentHint": true, "openWorldHint": false }, "_house": { "endpoint": "/faculty/med-assessment--curriculum/cronbach_alpha", "feeSt": 1, "degree": "competency:med-assessment--curriculum", "example": { "itemVariances": [ 0.8, 1.1, 0.9, 1.2, 0.7, 1 ], "totalScoreVariance": 18.5 } } }, { "name": "med-assessment--curriculum.sem_band", "title": "Standard error of measurement and score band (CDU-EDU-ASC-900)", "description": "Given the test’s reliability, how precise is this learner’s score, and what band should be reported?", "inputSchema": { "type": "object", "required": [ "pan", "scoreSd", "reliability", "observedScore", "band" ], "properties": { "pan": { "type": "string", "description": "The student PAN — the degree must be held in one of its five slots", "pattern": "^[0-9 ]{16,19}$" }, "scoreSd": { "type": "number", "description": "Standard deviation of test scores", "minimum": 0 }, "reliability": { "type": "number", "description": "Reliability coefficient, 0–0.999", "minimum": 0, "maximum": 0.999 }, "observedScore": { "type": "number", "description": "The learner’s observed score", "minimum": 0, "maximum": 100 }, "band": { "type": "string", "description": "Confidence of the band, %", "enum": [ "68", "90", "95" ] } }, "additionalProperties": false }, "outputSchema": { "type": "object", "required": [ "sem", "lower", "upper" ], "properties": { "sem": { "type": "number", "description": "Standard error of measurement" }, "lower": { "type": "number", "description": "Score − z·SEM" }, "upper": { "type": "number", "description": "Score + z·SEM" } }, "additionalProperties": false }, "annotations": { "readOnlyHint": true, "idempotentHint": true, "openWorldHint": false }, "_house": { "endpoint": "/faculty/med-assessment--curriculum/sem_band", "feeSt": 1, "degree": "competency:med-assessment--curriculum", "example": { "scoreSd": 12, "reliability": 0.91, "observedScore": 68, "band": "95" } } }, { "name": "med-assessment--curriculum.angoff_cut", "title": "Modified-Angoff cut score (CDU-EDU-ASC-900)", "description": "Where do the judges place the pass mark, and how precise is that placement?", "inputSchema": { "type": "object", "required": [ "pan", "judgeSums", "items" ], "properties": { "pan": { "type": "string", "description": "The student PAN — the degree must be held in one of its five slots", "pattern": "^[0-9 ]{16,19}$" }, "judgeSums": { "type": "array", "description": "Each judge’s sum of item probabilities for the borderline candidate", "items": { "type": "number" } }, "items": { "type": "number", "description": "Number of items on the test", "minimum": 1 } }, "additionalProperties": false }, "outputSchema": { "type": "object", "required": [ "cutScore", "cutPercent", "standardError" ], "properties": { "cutScore": { "type": "number", "description": "Mean of the judges’ sums (raw score)" }, "cutPercent": { "type": "number", "description": "Cut score ÷ items × 100" }, "standardError": { "type": "number", "description": "Sample sd of the sums ÷ √judges" } }, "additionalProperties": false }, "annotations": { "readOnlyHint": true, "idempotentHint": true, "openWorldHint": false }, "_house": { "endpoint": "/faculty/med-assessment--curriculum/angoff_cut", "feeSt": 1, "degree": "competency:med-assessment--curriculum", "example": { "judgeSums": [ 28.5, 31, 29.5, 33, 30, 27.5 ], "items": 50 } } }, { "name": "mba-marketing--pricing.arc_elasticity", "title": "Arc price elasticity (CDU-BUS-MKT-910)", "description": "Between these two prices, how responsive was demand, and did revenue rise or fall?", "inputSchema": { "type": "object", "required": [ "pan", "price1", "quantity1", "price2", "quantity2" ], "properties": { "pan": { "type": "string", "description": "The student PAN — the degree must be held in one of its five slots", "pattern": "^[0-9 ]{16,19}$" }, "price1": { "type": "number", "description": "Price before", "minimum": 0.0001 }, "quantity1": { "type": "number", "description": "Quantity sold before", "minimum": 0 }, "price2": { "type": "number", "description": "Price after", "minimum": 0.0001 }, "quantity2": { "type": "number", "description": "Quantity sold after", "minimum": 0 } }, "additionalProperties": false }, "outputSchema": { "type": "object", "required": [ "elasticity", "responsiveness", "revenue1", "revenue2" ], "properties": { "elasticity": { "type": "number", "description": "Arc elasticity" }, "responsiveness": { "type": "string", "description": "elastic (|e| > 1), unit elastic or inelastic" }, "revenue1": { "type": "number", "description": "P1 × Q1" }, "revenue2": { "type": "number", "description": "P2 × Q2" } }, "additionalProperties": false }, "annotations": { "readOnlyHint": true, "idempotentHint": true, "openWorldHint": false }, "_house": { "endpoint": "/faculty/mba-marketing--pricing/arc_elasticity", "feeSt": 1, "degree": "competency:mba-marketing--pricing", "example": { "price1": 100, "quantity1": 1000, "price2": 110, "quantity2": 880 } } }, { "name": "mba-marketing--pricing.breakeven_price_change", "title": "Break-even sales change for a price move (CDU-BUS-MKT-910)", "description": "By how much must volume rise after a price cut (or may it fall after a rise) for contribution to stay the same?", "inputSchema": { "type": "object", "required": [ "pan", "contributionMargin", "priceChange" ], "properties": { "pan": { "type": "string", "description": "The student PAN — the degree must be held in one of its five slots", "pattern": "^[0-9 ]{16,19}$" }, "contributionMargin": { "type": "number", "description": "Contribution margin as a fraction of the current price, 0–1", "minimum": 0.0001, "maximum": 1 }, "priceChange": { "type": "number", "description": "Proposed price change as a fraction (−0.1 = a 10% cut)", "minimum": -0.99, "maximum": 5 } }, "additionalProperties": false }, "outputSchema": { "type": "object", "required": [ "breakevenVolumeChange", "newContributionMargin" ], "properties": { "breakevenVolumeChange": { "type": "number", "description": "Required change in unit volume, as a fraction" }, "newContributionMargin": { "type": "number", "description": "(CM + ΔP) ÷ (1 + ΔP), as a fraction of the new price" } }, "additionalProperties": false }, "annotations": { "readOnlyHint": true, "idempotentHint": true, "openWorldHint": false }, "_house": { "endpoint": "/faculty/mba-marketing--pricing/breakeven_price_change", "feeSt": 1, "degree": "competency:mba-marketing--pricing", "example": { "contributionMargin": 0.35, "priceChange": -0.1 } } }, { "name": "mba-marketing--pricing.romi", "title": "Return on marketing investment (CDU-BUS-MKT-910)", "description": "Did the campaign’s incremental contribution repay what was spent on it?", "inputSchema": { "type": "object", "required": [ "pan", "incrementalRevenue", "contributionMargin", "marketingSpend" ], "properties": { "pan": { "type": "string", "description": "The student PAN — the degree must be held in one of its five slots", "pattern": "^[0-9 ]{16,19}$" }, "incrementalRevenue": { "type": "number", "description": "Revenue attributable to the campaign", "minimum": 0 }, "contributionMargin": { "type": "number", "description": "Contribution margin, 0–1", "minimum": 0, "maximum": 1 }, "marketingSpend": { "type": "number", "description": "Marketing spend", "minimum": 0.01 } }, "additionalProperties": false }, "outputSchema": { "type": "object", "required": [ "incrementalContribution", "romi", "paidBack" ], "properties": { "incrementalContribution": { "type": "number", "description": "Revenue × margin" }, "romi": { "type": "number", "description": "(Contribution − spend) ÷ spend" }, "paidBack": { "type": "boolean", "description": "ROMI ≥ 0" } }, "additionalProperties": false }, "annotations": { "readOnlyHint": true, "idempotentHint": true, "openWorldHint": false }, "_house": { "endpoint": "/faculty/mba-marketing--pricing/romi", "feeSt": 1, "degree": "competency:mba-marketing--pricing", "example": { "incrementalRevenue": 2000000, "contributionMargin": 0.4, "marketingSpend": 500000 } } }, { "name": "mba-marketing--pricing.bass_diffusion", "title": "Bass diffusion forecast (CDU-BUS-MKT-910)", "description": "How many customers will have adopted by period t, how many adopt in that period, and when do new adoptions peak?", "inputSchema": { "type": "object", "required": [ "pan", "marketPotential", "innovation", "imitation", "period" ], "properties": { "pan": { "type": "string", "description": "The student PAN — the degree must be held in one of its five slots", "pattern": "^[0-9 ]{16,19}$" }, "marketPotential": { "type": "number", "description": "Eventual adopters m", "minimum": 1 }, "innovation": { "type": "number", "description": "Coefficient of innovation p", "minimum": 0.0001, "maximum": 1 }, "imitation": { "type": "number", "description": "Coefficient of imitation q", "minimum": 0, "maximum": 5 }, "period": { "type": "number", "description": "Period t (whole periods since launch)", "minimum": 1, "maximum": 200 } }, "additionalProperties": false }, "outputSchema": { "type": "object", "required": [ "cumulativeAdopters", "adoptersInPeriod", "peakPeriod" ], "properties": { "cumulativeAdopters": { "type": "number", "description": "N(t)" }, "adoptersInPeriod": { "type": "number", "description": "N(t) − N(t − 1)" }, "peakPeriod": { "type": "number", "description": "ln(q/p) ÷ (p + q); 0 when q ≤ p" } }, "additionalProperties": false }, "annotations": { "readOnlyHint": true, "idempotentHint": true, "openWorldHint": false }, "_house": { "endpoint": "/faculty/mba-marketing--pricing/bass_diffusion", "feeSt": 1, "degree": "competency:mba-marketing--pricing", "example": { "marketPotential": 1000000, "innovation": 0.03, "imitation": 0.38, "period": 5 } } }, { "name": "msc-mineral-economics--mining.resource_tonnage", "title": "Tonnage and contained metal (CDU-BUS-MIN-900)", "description": "How many tonnes does this volume hold, and how much metal do they contain?", "inputSchema": { "type": "object", "required": [ "pan", "volume", "density", "grade", "gradeUnit" ], "properties": { "pan": { "type": "string", "description": "The student PAN — the degree must be held in one of its five slots", "pattern": "^[0-9 ]{16,19}$" }, "volume": { "type": "number", "description": "Volume in cubic metres", "minimum": 0 }, "density": { "type": "number", "description": "Dry bulk density, t/m³", "minimum": 0.1, "maximum": 25 }, "grade": { "type": "number", "description": "Average grade", "minimum": 0 }, "gradeUnit": { "type": "string", "description": "g/t for precious metals, % for base metals", "enum": [ "g/t", "%" ] } }, "additionalProperties": false }, "outputSchema": { "type": "object", "required": [ "tonnes", "containedMetal", "metalUnit", "troyOunces" ], "properties": { "tonnes": { "type": "number", "description": "Volume × density" }, "containedMetal": { "type": "number", "description": "kg (g/t) or tonnes (%)" }, "metalUnit": { "type": "string", "description": "kg or t" }, "troyOunces": { "type": "number", "description": "For g/t grades; null for %" } }, "additionalProperties": false }, "annotations": { "readOnlyHint": true, "idempotentHint": true, "openWorldHint": false }, "_house": { "endpoint": "/faculty/msc-mineral-economics--mining/resource_tonnage", "feeSt": 1, "degree": "competency:msc-mineral-economics--mining", "example": { "volume": 2500000, "density": 2.7, "grade": 3.2, "gradeUnit": "g/t" } } }, { "name": "msc-mineral-economics--mining.cutoff_grade", "title": "Break-even and marginal cut-off grade (CDU-BUS-MIN-900)", "description": "Below what grade does a tonne of ore not pay for itself — counting mining (break-even), and once already mined (marginal)?", "inputSchema": { "type": "object", "required": [ "pan", "miningCost", "processingCost", "adminCost", "pricePerGram", "sellingCostPerGram", "recovery" ], "properties": { "pan": { "type": "string", "description": "The student PAN — the degree must be held in one of its five slots", "pattern": "^[0-9 ]{16,19}$" }, "miningCost": { "type": "number", "description": "Mining cost per tonne of ore", "minimum": 0 }, "processingCost": { "type": "number", "description": "Processing cost per tonne", "minimum": 0 }, "adminCost": { "type": "number", "description": "G&A cost per tonne", "minimum": 0 }, "pricePerGram": { "type": "number", "description": "Metal price per gram", "minimum": 0.0001 }, "sellingCostPerGram": { "type": "number", "description": "Refining, transport and royalty per gram", "minimum": 0 }, "recovery": { "type": "number", "description": "Metallurgical recovery, 0–1", "minimum": 0.01, "maximum": 1 } }, "additionalProperties": false }, "outputSchema": { "type": "object", "required": [ "breakevenCutoff", "marginalCutoff" ], "properties": { "breakevenCutoff": { "type": "number", "description": "g/t, all costs" }, "marginalCutoff": { "type": "number", "description": "g/t, excluding mining" } }, "additionalProperties": false }, "annotations": { "readOnlyHint": true, "idempotentHint": true, "openWorldHint": false }, "_house": { "endpoint": "/faculty/msc-mineral-economics--mining/cutoff_grade", "feeSt": 1, "degree": "competency:msc-mineral-economics--mining", "example": { "miningCost": 35, "processingCost": 22, "adminCost": 8, "pricePerGram": 60, "sellingCostPerGram": 1.5, "recovery": 0.92 } } }, { "name": "msc-mineral-economics--mining.stripping_ratio", "title": "Stripping ratio against the break-even (CDU-BUS-MIN-900)", "description": "Is the waste that must be moved per tonne of ore within what the ore can pay for?", "inputSchema": { "type": "object", "required": [ "pan", "wasteTonnes", "oreTonnes", "valuePerTonneOre", "oreCostPerTonne", "wasteCostPerTonne" ], "properties": { "pan": { "type": "string", "description": "The student PAN — the degree must be held in one of its five slots", "pattern": "^[0-9 ]{16,19}$" }, "wasteTonnes": { "type": "number", "description": "Waste to be moved", "minimum": 0 }, "oreTonnes": { "type": "number", "description": "Ore to be mined", "minimum": 0.01 }, "valuePerTonneOre": { "type": "number", "description": "Recoverable value per tonne of ore", "minimum": 0 }, "oreCostPerTonne": { "type": "number", "description": "Mining + processing + G&A per tonne of ore", "minimum": 0 }, "wasteCostPerTonne": { "type": "number", "description": "Cost to mine a tonne of waste", "minimum": 0.0001 } }, "additionalProperties": false }, "outputSchema": { "type": "object", "required": [ "strippingRatio", "breakevenStrippingRatio", "economic" ], "properties": { "strippingRatio": { "type": "number", "description": "Waste ÷ ore" }, "breakevenStrippingRatio": { "type": "number", "description": "(Value − ore cost) ÷ waste cost" }, "economic": { "type": "boolean", "description": "SR ≤ BESR" } }, "additionalProperties": false }, "annotations": { "readOnlyHint": true, "idempotentHint": true, "openWorldHint": false }, "_house": { "endpoint": "/faculty/msc-mineral-economics--mining/stripping_ratio", "feeSt": 1, "degree": "competency:msc-mineral-economics--mining", "example": { "wasteTonnes": 18000000, "oreTonnes": 4000000, "valuePerTonneOre": 95, "oreCostPerTonne": 48, "wasteCostPerTonne": 9 } } }, { "name": "msc-mineral-economics--mining.nsr_per_tonne", "title": "Net smelter return per tonne of ore (CDU-BUS-MIN-900)", "description": "After recovery, payability and smelter charges, what is a tonne of this ore worth at the mine gate?", "inputSchema": { "type": "object", "required": [ "pan", "headGrade", "recovery", "concentrateGrade", "payable", "pricePerTonneMetal", "refiningChargePerTonne", "treatmentChargePerTonneConc" ], "properties": { "pan": { "type": "string", "description": "The student PAN — the degree must be held in one of its five slots", "pattern": "^[0-9 ]{16,19}$" }, "headGrade": { "type": "number", "description": "Metal grade of the ore, as a fraction", "minimum": 0, "maximum": 1 }, "recovery": { "type": "number", "description": "Recovery to concentrate, 0–1", "minimum": 0, "maximum": 1 }, "concentrateGrade": { "type": "number", "description": "Metal grade of the concentrate, as a fraction", "minimum": 0.0001, "maximum": 1 }, "payable": { "type": "number", "description": "Fraction of contained metal the smelter pays for", "minimum": 0, "maximum": 1 }, "pricePerTonneMetal": { "type": "number", "description": "Metal price per tonne", "minimum": 0 }, "refiningChargePerTonne": { "type": "number", "description": "RC per tonne of payable metal", "minimum": 0 }, "treatmentChargePerTonneConc": { "type": "number", "description": "TC per dry tonne of concentrate", "minimum": 0 }, "transportPerTonneConc": { "type": "number", "description": "Freight per tonne of concentrate", "minimum": 0, "default": 0 } }, "additionalProperties": false }, "outputSchema": { "type": "object", "required": [ "concentratePerTonneOre", "payableMetalPerTonneOre", "nsrPerTonneOre" ], "properties": { "concentratePerTonneOre": { "type": "number", "description": "Tonnes of concentrate per tonne of ore" }, "payableMetalPerTonneOre": { "type": "number", "description": "Tonnes of payable metal per tonne of ore" }, "nsrPerTonneOre": { "type": "number", "description": "Net smelter return per tonne of ore" } }, "additionalProperties": false }, "annotations": { "readOnlyHint": true, "idempotentHint": true, "openWorldHint": false }, "_house": { "endpoint": "/faculty/msc-mineral-economics--mining/nsr_per_tonne", "feeSt": 1, "degree": "competency:msc-mineral-economics--mining", "example": { "headGrade": 0.012, "recovery": 0.9, "concentrateGrade": 0.28, "payable": 0.965, "pricePerTonneMetal": 9000, "refiningChargePerTonne": 180, "treatmentChargePerTonneConc": 80, "transportPerTonneConc": 60 } } }, { "name": "meng-industrial--supply-chain.eoq", "title": "Economic order quantity (CDU-ENG-IND-900)", "description": "How much should be ordered at a time to minimise ordering plus holding cost, and what does that cost a year?", "inputSchema": { "type": "object", "required": [ "pan", "annualDemand", "orderCost", "holdingCostPerUnitYear" ], "properties": { "pan": { "type": "string", "description": "The student PAN — the degree must be held in one of its five slots", "pattern": "^[0-9 ]{16,19}$" }, "annualDemand": { "type": "number", "description": "Units demanded per year", "minimum": 0.01 }, "orderCost": { "type": "number", "description": "Cost per order placed", "minimum": 0.01 }, "holdingCostPerUnitYear": { "type": "number", "description": "Cost to hold one unit for a year", "minimum": 0.0001 } }, "additionalProperties": false }, "outputSchema": { "type": "object", "required": [ "eoq", "ordersPerYear", "annualCost" ], "properties": { "eoq": { "type": "number", "description": "Optimal order quantity" }, "ordersPerYear": { "type": "number", "description": "D ÷ Q*" }, "annualCost": { "type": "number", "description": "Ordering + holding at Q*" } }, "additionalProperties": false }, "annotations": { "readOnlyHint": true, "idempotentHint": true, "openWorldHint": false }, "_house": { "endpoint": "/faculty/meng-industrial--supply-chain/eoq", "feeSt": 1, "degree": "competency:meng-industrial--supply-chain", "example": { "annualDemand": 12000, "orderCost": 150, "holdingCostPerUnitYear": 4 } } }, { "name": "meng-industrial--supply-chain.safety_stock_rop", "title": "Safety stock and reorder point (CDU-ENG-IND-900)", "description": "How much buffer stock gives this cycle-service level, and at what stock level should the next order be placed?", "inputSchema": { "type": "object", "required": [ "pan", "avgDailyDemand", "sdDailyDemand", "leadTimeDays", "serviceLevel" ], "properties": { "pan": { "type": "string", "description": "The student PAN — the degree must be held in one of its five slots", "pattern": "^[0-9 ]{16,19}$" }, "avgDailyDemand": { "type": "number", "description": "Mean demand per day", "minimum": 0 }, "sdDailyDemand": { "type": "number", "description": "Standard deviation of daily demand", "minimum": 0 }, "leadTimeDays": { "type": "number", "description": "Replenishment lead time in days", "minimum": 0.01 }, "serviceLevel": { "type": "number", "description": "Cycle-service level (no stock-out in a cycle), 0.5–0.999", "minimum": 0.5, "maximum": 0.999 } }, "additionalProperties": false }, "outputSchema": { "type": "object", "required": [ "z", "safetyStock", "reorderPoint" ], "properties": { "z": { "type": "number", "description": "Safety factor Φ⁻¹(service level)" }, "safetyStock": { "type": "number", "description": "z·σ·√L" }, "reorderPoint": { "type": "number", "description": "d·L + safety stock" } }, "additionalProperties": false }, "annotations": { "readOnlyHint": true, "idempotentHint": true, "openWorldHint": false }, "_house": { "endpoint": "/faculty/meng-industrial--supply-chain/safety_stock_rop", "feeSt": 1, "degree": "competency:meng-industrial--supply-chain", "example": { "avgDailyDemand": 40, "sdDailyDemand": 12, "leadTimeDays": 9, "serviceLevel": 0.95 } } }, { "name": "meng-industrial--supply-chain.oee", "title": "Overall equipment effectiveness (CDU-ENG-IND-900)", "description": "How much of the planned production time was truly productive, and which factor lost the most?", "inputSchema": { "type": "object", "required": [ "pan", "plannedMinutes", "downtimeMinutes", "idealCycleMinutes", "totalCount", "goodCount" ], "properties": { "pan": { "type": "string", "description": "The student PAN — the degree must be held in one of its five slots", "pattern": "^[0-9 ]{16,19}$" }, "plannedMinutes": { "type": "number", "description": "Planned production time", "minimum": 0.01 }, "downtimeMinutes": { "type": "number", "description": "Stop time within the plan", "minimum": 0 }, "idealCycleMinutes": { "type": "number", "description": "Ideal time per unit", "minimum": 0.0001 }, "totalCount": { "type": "number", "description": "Units produced", "minimum": 1 }, "goodCount": { "type": "number", "description": "Units right first time", "minimum": 0 } }, "additionalProperties": false }, "outputSchema": { "type": "object", "required": [ "availability", "performance", "quality", "oee", "largestLoss" ], "properties": { "availability": { "type": "number", "description": "Run time ÷ planned time" }, "performance": { "type": "number", "description": "Ideal cycle × total ÷ run time" }, "quality": { "type": "number", "description": "Good ÷ total" }, "oee": { "type": "number", "description": "A × P × Q" }, "largestLoss": { "type": "string", "description": "availability, performance or quality" } }, "additionalProperties": false }, "annotations": { "readOnlyHint": true, "idempotentHint": true, "openWorldHint": false }, "_house": { "endpoint": "/faculty/meng-industrial--supply-chain/oee", "feeSt": 1, "degree": "competency:meng-industrial--supply-chain", "example": { "plannedMinutes": 480, "downtimeMinutes": 47, "idealCycleMinutes": 0.8, "totalCount": 500, "goodCount": 485 } } }, { "name": "meng-industrial--supply-chain.newsvendor", "title": "Newsvendor order quantity (CDU-ENG-IND-900)", "description": "For a single season with uncertain demand, how many should be ordered to balance the cost of too few against too many?", "inputSchema": { "type": "object", "required": [ "pan", "unitCost", "price", "salvageValue", "meanDemand", "sdDemand" ], "properties": { "pan": { "type": "string", "description": "The student PAN — the degree must be held in one of its five slots", "pattern": "^[0-9 ]{16,19}$" }, "unitCost": { "type": "number", "description": "Cost per unit bought", "minimum": 0 }, "price": { "type": "number", "description": "Selling price per unit", "minimum": 0 }, "salvageValue": { "type": "number", "description": "Value of a unit left over", "minimum": 0 }, "meanDemand": { "type": "number", "description": "Mean season demand", "minimum": 0 }, "sdDemand": { "type": "number", "description": "Standard deviation of season demand", "minimum": 0 } }, "additionalProperties": false }, "outputSchema": { "type": "object", "required": [ "criticalRatio", "z", "orderQuantity" ], "properties": { "criticalRatio": { "type": "number", "description": "Cu ÷ (Cu + Co)" }, "z": { "type": "number", "description": "Φ⁻¹(critical ratio)" }, "orderQuantity": { "type": "number", "description": "μ + z·σ" } }, "additionalProperties": false }, "annotations": { "readOnlyHint": true, "idempotentHint": true, "openWorldHint": false }, "_house": { "endpoint": "/faculty/meng-industrial--supply-chain/newsvendor", "feeSt": 1, "degree": "competency:meng-industrial--supply-chain", "example": { "unitCost": 6, "price": 15, "salvageValue": 2, "meanDemand": 500, "sdDemand": 120 } } }, { "name": "mm-organisation--people.turnover_stability", "title": "Labour turnover and stability index (CDU-BUS-ORG-900)", "description": "What share of the workforce left this year, and how stable is the core that stayed?", "inputSchema": { "type": "object", "required": [ "pan", "leavers", "headcountStart", "headcountEnd", "employeesWithOneYearService" ], "properties": { "pan": { "type": "string", "description": "The student PAN — the degree must be held in one of its five slots", "pattern": "^[0-9 ]{16,19}$" }, "leavers": { "type": "number", "description": "Leavers in the year", "minimum": 0 }, "headcountStart": { "type": "number", "description": "Headcount a year ago", "minimum": 1 }, "headcountEnd": { "type": "number", "description": "Headcount now", "minimum": 0 }, "employeesWithOneYearService": { "type": "number", "description": "Employees now with a year’s service or more", "minimum": 0 } }, "additionalProperties": false }, "outputSchema": { "type": "object", "required": [ "averageHeadcount", "turnoverRate", "stabilityIndex" ], "properties": { "averageHeadcount": { "type": "number", "description": "(start + end) ÷ 2" }, "turnoverRate": { "type": "number", "description": "Crude turnover, %" }, "stabilityIndex": { "type": "number", "description": "Stability, %" } }, "additionalProperties": false }, "annotations": { "readOnlyHint": true, "idempotentHint": true, "openWorldHint": false }, "_house": { "endpoint": "/faculty/mm-organisation--people/turnover_stability", "feeSt": 1, "degree": "competency:mm-organisation--people", "example": { "leavers": 42, "headcountStart": 350, "headcountEnd": 370, "employeesWithOneYearService": 318 } } }, { "name": "mm-organisation--people.compa_ratio", "title": "Compa-ratio and range penetration (CDU-BUS-ORG-900)", "description": "Where does this salary sit against the midpoint and within the range of its grade?", "inputSchema": { "type": "object", "required": [ "pan", "salary", "rangeMin", "rangeMax" ], "properties": { "pan": { "type": "string", "description": "The student PAN — the degree must be held in one of its five slots", "pattern": "^[0-9 ]{16,19}$" }, "salary": { "type": "number", "description": "Annual base salary", "minimum": 0 }, "rangeMin": { "type": "number", "description": "Grade minimum", "minimum": 0 }, "rangeMax": { "type": "number", "description": "Grade maximum", "minimum": 0 } }, "additionalProperties": false }, "outputSchema": { "type": "object", "required": [ "midpoint", "compaRatio", "rangePenetration", "position" ], "properties": { "midpoint": { "type": "number", "description": "(min + max) ÷ 2" }, "compaRatio": { "type": "number", "description": "Salary ÷ midpoint" }, "rangePenetration": { "type": "number", "description": "(Salary − min) ÷ (max − min)" }, "position": { "type": "string", "description": "below range, in range or above range" } }, "additionalProperties": false }, "annotations": { "readOnlyHint": true, "idempotentHint": true, "openWorldHint": false }, "_house": { "endpoint": "/faculty/mm-organisation--people/compa_ratio", "feeSt": 1, "degree": "competency:mm-organisation--people", "example": { "salary": 540000, "rangeMin": 450000, "rangeMax": 650000 } } }, { "name": "mm-organisation--people.cost_per_hire", "title": "Cost per hire (CDU-BUS-ORG-900)", "description": "What did each hire cost, counting external and internal recruiting costs as the standard defines them?", "inputSchema": { "type": "object", "required": [ "pan", "externalCosts", "internalCosts", "totalHires" ], "properties": { "pan": { "type": "string", "description": "The student PAN — the degree must be held in one of its five slots", "pattern": "^[0-9 ]{16,19}$" }, "externalCosts": { "type": "number", "description": "Advertising, agency, assessment, travel, relocation…", "minimum": 0 }, "internalCosts": { "type": "number", "description": "Recruiter pay, hiring-manager time, systems…", "minimum": 0 }, "totalHires": { "type": "number", "description": "Hires in the same period", "minimum": 1 } }, "additionalProperties": false }, "outputSchema": { "type": "object", "required": [ "costPerHire", "externalShare" ], "properties": { "costPerHire": { "type": "number", "description": "(External + internal) ÷ hires" }, "externalShare": { "type": "number", "description": "External ÷ total cost" } }, "additionalProperties": false }, "annotations": { "readOnlyHint": true, "idempotentHint": true, "openWorldHint": false }, "_house": { "endpoint": "/faculty/mm-organisation--people/cost_per_hire", "feeSt": 1, "degree": "competency:mm-organisation--people", "example": { "externalCosts": 380000, "internalCosts": 220000, "totalHires": 24 } } }, { "name": "mm-organisation--people.bcea_overtime", "title": "Ordinary hours, overtime limit and overtime pay (CDU-BUS-ORG-900)", "description": "Are this week’s hours within the statutory limits, and what overtime pay is due?", "inputSchema": { "type": "object", "required": [ "pan", "hourlyWage", "ordinaryHours", "overtimeHours" ], "properties": { "pan": { "type": "string", "description": "The student PAN — the degree must be held in one of its five slots", "pattern": "^[0-9 ]{16,19}$" }, "hourlyWage": { "type": "number", "description": "Ordinary hourly wage", "minimum": 0 }, "ordinaryHours": { "type": "number", "description": "Ordinary hours worked in the week", "minimum": 0, "maximum": 168 }, "overtimeHours": { "type": "number", "description": "Overtime hours worked in the week", "minimum": 0, "maximum": 168 } }, "additionalProperties": false }, "outputSchema": { "type": "object", "required": [ "overtimePay", "withinOrdinaryLimit", "withinOvertimeLimit" ], "properties": { "overtimePay": { "type": "number", "description": "Overtime hours × 1.5 × wage" }, "withinOrdinaryLimit": { "type": "boolean", "description": "Ordinary hours ≤ 45" }, "withinOvertimeLimit": { "type": "boolean", "description": "Overtime ≤ 10 hours" } }, "additionalProperties": false }, "annotations": { "readOnlyHint": true, "idempotentHint": true, "openWorldHint": false }, "_house": { "endpoint": "/faculty/mm-organisation--people/bcea_overtime", "feeSt": 1, "degree": "competency:mm-organisation--people", "example": { "hourlyWage": 85, "ordinaryHours": 45, "overtimeHours": 8 } } }, { "name": "msc-software--cybersecurity.cvss31_base", "title": "CVSS v3.1 base score (CDU-ICT-SEC-900)", "description": "What base score and severity does this vulnerability’s CVSS v3.1 vector give?", "inputSchema": { "type": "object", "required": [ "pan", "AV", "AC", "PR", "UI", "S", "C", "I", "A" ], "properties": { "pan": { "type": "string", "description": "The student PAN — the degree must be held in one of its five slots", "pattern": "^[0-9 ]{16,19}$" }, "AV": { "type": "string", "description": "Attack vector", "enum": [ "N", "A", "L", "P" ] }, "AC": { "type": "string", "description": "Attack complexity", "enum": [ "L", "H" ] }, "PR": { "type": "string", "description": "Privileges required", "enum": [ "N", "L", "H" ] }, "UI": { "type": "string", "description": "User interaction", "enum": [ "N", "R" ] }, "S": { "type": "string", "description": "Scope", "enum": [ "U", "C" ] }, "C": { "type": "string", "description": "Confidentiality impact", "enum": [ "H", "L", "N" ] }, "I": { "type": "string", "description": "Integrity impact", "enum": [ "H", "L", "N" ] }, "A": { "type": "string", "description": "Availability impact", "enum": [ "H", "L", "N" ] } }, "additionalProperties": false }, "outputSchema": { "type": "object", "required": [ "vector", "baseScore", "severity" ], "properties": { "vector": { "type": "string", "description": "The CVSS:3.1 vector string" }, "baseScore": { "type": "number", "description": "0.0–10.0" }, "severity": { "type": "string", "description": "None, Low, Medium, High or Critical" } }, "additionalProperties": false }, "annotations": { "readOnlyHint": true, "idempotentHint": true, "openWorldHint": false }, "_house": { "endpoint": "/faculty/msc-software--cybersecurity/cvss31_base", "feeSt": 1, "degree": "competency:msc-software--cybersecurity", "example": { "AV": "N", "AC": "L", "PR": "N", "UI": "N", "S": "U", "C": "H", "I": "H", "A": "H" } } }, { "name": "msc-software--cybersecurity.password_keyspace", "title": "Secret entropy and exhaustive-search time (CDU-ICT-SEC-900)", "description": "How many bits of entropy does a random secret of this length and alphabet have, and how long would an offline attacker need to exhaust it?", "inputSchema": { "type": "object", "required": [ "pan", "length", "alphabetSize", "guessesPerSecond" ], "properties": { "pan": { "type": "string", "description": "The student PAN — the degree must be held in one of its five slots", "pattern": "^[0-9 ]{16,19}$" }, "length": { "type": "number", "description": "Characters in the secret", "minimum": 1, "maximum": 256 }, "alphabetSize": { "type": "number", "description": "Characters the secret is drawn from (62 = a–z A–Z 0–9)", "minimum": 2, "maximum": 100000 }, "guessesPerSecond": { "type": "number", "description": "Attacker’s offline guessing rate", "minimum": 1 }, "minimumLength": { "type": "number", "description": "Length minimum the policy applies", "minimum": 1, "maximum": 256, "default": 8 } }, "additionalProperties": false }, "outputSchema": { "type": "object", "required": [ "entropyBits", "log10Keyspace", "log10YearsToExhaust", "meetsMinimumLength" ], "properties": { "entropyBits": { "type": "number", "description": "L·log2(N)" }, "log10Keyspace": { "type": "number", "description": "log10(N^L)" }, "log10YearsToExhaust": { "type": "number", "description": "log10 of the years to try every secret" }, "meetsMinimumLength": { "type": "boolean", "description": "Length ≥ the minimum" } }, "additionalProperties": false }, "annotations": { "readOnlyHint": true, "idempotentHint": true, "openWorldHint": false }, "_house": { "endpoint": "/faculty/msc-software--cybersecurity/password_keyspace", "feeSt": 1, "degree": "competency:msc-software--cybersecurity", "example": { "length": 12, "alphabetSize": 62, "guessesPerSecond": 10000000000, "minimumLength": 8 } } }, { "name": "msc-software--cybersecurity.ale_rosi", "title": "Annualised loss expectancy and return on security investment (CDU-ICT-SEC-900)", "description": "What loss does this threat cost a year, before and after the control, and does the control pay for itself?", "inputSchema": { "type": "object", "required": [ "pan", "assetValue", "exposureFactor", "annualRateBefore", "annualRateAfter", "annualControlCost" ], "properties": { "pan": { "type": "string", "description": "The student PAN — the degree must be held in one of its five slots", "pattern": "^[0-9 ]{16,19}$" }, "assetValue": { "type": "number", "description": "Value of the asset at risk", "minimum": 0 }, "exposureFactor": { "type": "number", "description": "Fraction of value lost per incident, 0–1", "minimum": 0, "maximum": 1 }, "annualRateBefore": { "type": "number", "description": "Incidents per year without the control", "minimum": 0 }, "annualRateAfter": { "type": "number", "description": "Incidents per year with the control", "minimum": 0 }, "annualControlCost": { "type": "number", "description": "Annual cost of the control", "minimum": 0.01 } }, "additionalProperties": false }, "outputSchema": { "type": "object", "required": [ "singleLossExpectancy", "aleBefore", "aleAfter", "rosi" ], "properties": { "singleLossExpectancy": { "type": "number", "description": "Asset value × exposure factor" }, "aleBefore": { "type": "number", "description": "SLE × ARO before" }, "aleAfter": { "type": "number", "description": "SLE × ARO after" }, "rosi": { "type": "number", "description": "(ALE before − ALE after − cost) ÷ cost" } }, "additionalProperties": false }, "annotations": { "readOnlyHint": true, "idempotentHint": true, "openWorldHint": false }, "_house": { "endpoint": "/faculty/msc-software--cybersecurity/ale_rosi", "feeSt": 1, "degree": "competency:msc-software--cybersecurity", "example": { "assetValue": 2000000, "exposureFactor": 0.35, "annualRateBefore": 0.5, "annualRateAfter": 0.1, "annualControlCost": 90000 } } }, { "name": "msc-software--cybersecurity.birthday_collision", "title": "Birthday-bound collision probability (CDU-ICT-SEC-900)", "description": "Among this many hashed items, how likely is at least one collision, and at what count does it reach 50%?", "inputSchema": { "type": "object", "required": [ "pan", "hashBits", "items" ], "properties": { "pan": { "type": "string", "description": "The student PAN — the degree must be held in one of its five slots", "pattern": "^[0-9 ]{16,19}$" }, "hashBits": { "type": "number", "description": "Output length in bits", "minimum": 8, "maximum": 1024 }, "items": { "type": "number", "description": "Number of values hashed", "minimum": 2 } }, "additionalProperties": false }, "outputSchema": { "type": "object", "required": [ "collisionProbability", "itemsFor50Percent", "securityBits" ], "properties": { "collisionProbability": { "type": "number", "description": "1 − exp(−n(n−1) ÷ 2^(b+1))" }, "itemsFor50Percent": { "type": "number", "description": "√(2·ln 2·2^b)" }, "securityBits": { "type": "number", "description": "b ÷ 2" } }, "additionalProperties": false }, "annotations": { "readOnlyHint": true, "idempotentHint": true, "openWorldHint": false }, "_house": { "endpoint": "/faculty/msc-software--cybersecurity/birthday_collision", "feeSt": 1, "degree": "competency:msc-software--cybersecurity", "example": { "hashBits": 64, "items": 1000000000 } } }, { "name": "murb-planning--property.bulk_yield", "title": "Development yield under zoning controls (CDU-ENG-URB-900)", "description": "How much floor area, how many storeys and how many units can this site carry under its floor-area ratio and coverage?", "inputSchema": { "type": "object", "required": [ "pan", "siteArea", "floorAreaRatio", "coverage", "averageUnitSize" ], "properties": { "pan": { "type": "string", "description": "The student PAN — the degree must be held in one of its five slots", "pattern": "^[0-9 ]{16,19}$" }, "siteArea": { "type": "number", "description": "Site area, m²", "minimum": 1 }, "floorAreaRatio": { "type": "number", "description": "Permitted floor-area ratio (bulk factor)", "minimum": 0.01, "maximum": 50 }, "coverage": { "type": "number", "description": "Permitted coverage, 0–1", "minimum": 0.01, "maximum": 1 }, "efficiency": { "type": "number", "description": "Net-to-gross efficiency, 0–1", "minimum": 0.1, "maximum": 1, "default": 0.85 }, "averageUnitSize": { "type": "number", "description": "Average net unit size, m²", "minimum": 1 } }, "additionalProperties": false }, "outputSchema": { "type": "object", "required": [ "grossFloorArea", "maxFootprint", "storeys", "netArea", "units" ], "properties": { "grossFloorArea": { "type": "number", "description": "m²" }, "maxFootprint": { "type": "number", "description": "m²" }, "storeys": { "type": "number", "description": "Storeys needed to use the bulk" }, "netArea": { "type": "number", "description": "m²" }, "units": { "type": "number", "description": "Whole units that fit" } }, "additionalProperties": false }, "annotations": { "readOnlyHint": true, "idempotentHint": true, "openWorldHint": false }, "_house": { "endpoint": "/faculty/murb-planning--property/bulk_yield", "feeSt": 1, "degree": "competency:murb-planning--property", "example": { "siteArea": 4000, "floorAreaRatio": 2.5, "coverage": 0.6, "efficiency": 0.85, "averageUnitSize": 65 } } }, { "name": "murb-planning--property.residual_land_value", "title": "Residual land value (CDU-ENG-URB-900)", "description": "After every cost and the developer’s profit, what can the developer afford to pay for the land?", "inputSchema": { "type": "object", "required": [ "pan", "gdv", "buildCost", "feesRate", "contingencyRate", "financeRate", "constructionYears", "profitRate", "salesCostRate" ], "properties": { "pan": { "type": "string", "description": "The student PAN — the degree must be held in one of its five slots", "pattern": "^[0-9 ]{16,19}$" }, "gdv": { "type": "number", "description": "Gross development value", "minimum": 0 }, "buildCost": { "type": "number", "description": "Construction cost", "minimum": 0 }, "feesRate": { "type": "number", "description": "Professional fees as a fraction of build", "minimum": 0, "maximum": 1 }, "contingencyRate": { "type": "number", "description": "Contingency as a fraction of build", "minimum": 0, "maximum": 1 }, "financeRate": { "type": "number", "description": "Annual finance rate", "minimum": 0, "maximum": 1 }, "constructionYears": { "type": "number", "description": "Build period in years", "minimum": 0, "maximum": 20 }, "profitRate": { "type": "number", "description": "Developer’s profit as a fraction of GDV", "minimum": 0, "maximum": 1 }, "salesCostRate": { "type": "number", "description": "Agency and legal costs of sale as a fraction of GDV", "minimum": 0, "maximum": 1 } }, "additionalProperties": false }, "outputSchema": { "type": "object", "required": [ "costBase", "financeCost", "developerProfit", "residualLandValue" ], "properties": { "costBase": { "type": "number", "description": "Build + fees + contingency" }, "financeCost": { "type": "number", "description": "Cost base × rate × years × ½" }, "developerProfit": { "type": "number", "description": "GDV × profit rate" }, "residualLandValue": { "type": "number", "description": "What is left for the land (negative: unviable)" } }, "additionalProperties": false }, "annotations": { "readOnlyHint": true, "idempotentHint": true, "openWorldHint": false }, "_house": { "endpoint": "/faculty/murb-planning--property/residual_land_value", "feeSt": 1, "degree": "competency:murb-planning--property", "example": { "gdv": 60000000, "buildCost": 32000000, "feesRate": 0.12, "contingencyRate": 0.05, "financeRate": 0.11, "constructionYears": 2, "profitRate": 0.2, "salesCostRate": 0.03 } } }, { "name": "murb-planning--property.direct_capitalisation", "title": "Capital value by direct capitalisation (CDU-ENG-URB-900)", "description": "What is this income-producing property worth at the market capitalisation rate?", "inputSchema": { "type": "object", "required": [ "pan", "grossIncome", "vacancyRate", "operatingExpenses", "capRate" ], "properties": { "pan": { "type": "string", "description": "The student PAN — the degree must be held in one of its five slots", "pattern": "^[0-9 ]{16,19}$" }, "grossIncome": { "type": "number", "description": "Potential gross income per year", "minimum": 0 }, "vacancyRate": { "type": "number", "description": "Vacancy and collection loss, 0–1", "minimum": 0, "maximum": 1 }, "operatingExpenses": { "type": "number", "description": "Non-recoverable operating expenses per year", "minimum": 0 }, "capRate": { "type": "number", "description": "Market capitalisation rate", "minimum": 0.001, "maximum": 1 } }, "additionalProperties": false }, "outputSchema": { "type": "object", "required": [ "effectiveGrossIncome", "netOperatingIncome", "capitalValue" ], "properties": { "effectiveGrossIncome": { "type": "number", "description": "Gross × (1 − vacancy)" }, "netOperatingIncome": { "type": "number", "description": "EGI − expenses" }, "capitalValue": { "type": "number", "description": "NOI ÷ cap rate" } }, "additionalProperties": false }, "annotations": { "readOnlyHint": true, "idempotentHint": true, "openWorldHint": false }, "_house": { "endpoint": "/faculty/murb-planning--property/direct_capitalisation", "feeSt": 1, "degree": "competency:murb-planning--property", "example": { "grossIncome": 4800000, "vacancyRate": 0.08, "operatingExpenses": 1150000, "capRate": 0.095 } } }, { "name": "murb-planning--property.household_projection", "title": "Population projection and dwelling demand (CDU-ENG-URB-900)", "description": "How many people and households will the area hold in t years, and how many more dwellings does that need?", "inputSchema": { "type": "object", "required": [ "pan", "basePopulation", "annualGrowthRate", "years", "personsPerHousehold", "existingDwellings" ], "properties": { "pan": { "type": "string", "description": "The student PAN — the degree must be held in one of its five slots", "pattern": "^[0-9 ]{16,19}$" }, "basePopulation": { "type": "number", "description": "Population now", "minimum": 0 }, "annualGrowthRate": { "type": "number", "description": "Annual growth rate (negative for decline)", "minimum": -0.2, "maximum": 0.2 }, "years": { "type": "number", "description": "Projection horizon", "minimum": 0, "maximum": 100 }, "personsPerHousehold": { "type": "number", "description": "Average household size", "minimum": 1, "maximum": 20 }, "existingDwellings": { "type": "number", "description": "Dwellings now", "minimum": 0 } }, "additionalProperties": false }, "outputSchema": { "type": "object", "required": [ "projectedPopulation", "projectedHouseholds", "additionalDwellings" ], "properties": { "projectedPopulation": { "type": "number", "description": "P0 × (1 + r)^t" }, "projectedHouseholds": { "type": "number", "description": "Population ÷ household size" }, "additionalDwellings": { "type": "number", "description": "Households − existing dwellings (negative: surplus)" } }, "additionalProperties": false }, "annotations": { "readOnlyHint": true, "idempotentHint": true, "openWorldHint": false }, "_house": { "endpoint": "/faculty/murb-planning--property/household_projection", "feeSt": 1, "degree": "competency:murb-planning--property", "example": { "basePopulation": 250000, "annualGrowthRate": 0.021, "years": 10, "personsPerHousehold": 3.4, "existingDwellings": 68000 } } }, { "name": "msc-programme--change.earned_value", "title": "Earned-value performance and forecast (CDU-BUS-PCM-900)", "description": "Is the work over or under budget and ahead or behind schedule, and what will it cost at completion at this efficiency?", "inputSchema": { "type": "object", "required": [ "pan", "bac", "plannedValue", "earnedValue", "actualCost" ], "properties": { "pan": { "type": "string", "description": "The student PAN — the degree must be held in one of its five slots", "pattern": "^[0-9 ]{16,19}$" }, "bac": { "type": "number", "description": "Budget at completion", "minimum": 0.01 }, "plannedValue": { "type": "number", "description": "Planned value to date", "minimum": 0.01 }, "earnedValue": { "type": "number", "description": "Earned value to date", "minimum": 0 }, "actualCost": { "type": "number", "description": "Actual cost to date", "minimum": 0.01 } }, "additionalProperties": false }, "outputSchema": { "type": "object", "required": [ "costVariance", "scheduleVariance", "cpi", "spi", "eac", "etc", "vac", "tcpi" ], "properties": { "costVariance": { "type": "number", "description": "EV − AC" }, "scheduleVariance": { "type": "number", "description": "EV − PV" }, "cpi": { "type": "number", "description": "EV ÷ AC" }, "spi": { "type": "number", "description": "EV ÷ PV" }, "eac": { "type": "number", "description": "BAC ÷ CPI" }, "etc": { "type": "number", "description": "EAC − AC" }, "vac": { "type": "number", "description": "BAC − EAC" }, "tcpi": { "type": "number", "description": "(BAC − EV) ÷ (BAC − AC); null once AC ≥ BAC" } }, "additionalProperties": false }, "annotations": { "readOnlyHint": true, "idempotentHint": true, "openWorldHint": false }, "_house": { "endpoint": "/faculty/msc-programme--change/earned_value", "feeSt": 1, "degree": "competency:msc-programme--change", "example": { "bac": 1000000, "plannedValue": 400000, "earnedValue": 350000, "actualCost": 420000 } } }, { "name": "msc-programme--change.pert_estimate", "title": "PERT path estimate and deadline probability (CDU-BUS-PCM-900)", "description": "What is the expected duration of this path, its uncertainty, and the chance of finishing by the deadline?", "inputSchema": { "type": "object", "required": [ "pan", "optimistic", "mostLikely", "pessimistic", "deadline" ], "properties": { "pan": { "type": "string", "description": "The student PAN — the degree must be held in one of its five slots", "pattern": "^[0-9 ]{16,19}$" }, "optimistic": { "type": "array", "description": "Optimistic duration of each activity on the path", "items": { "type": "number" } }, "mostLikely": { "type": "array", "description": "Most likely durations", "items": { "type": "number" } }, "pessimistic": { "type": "array", "description": "Pessimistic durations", "items": { "type": "number" } }, "deadline": { "type": "number", "description": "Target duration for the path", "minimum": 0 } }, "additionalProperties": false }, "outputSchema": { "type": "object", "required": [ "expectedDurations", "pathExpected", "pathSd", "probabilityByDeadline" ], "properties": { "expectedDurations": { "type": "array", "description": "te per activity (4 dp)", "items": { "type": "number" } }, "pathExpected": { "type": "number", "description": "Σ te" }, "pathSd": { "type": "number", "description": "√Σσ²" }, "probabilityByDeadline": { "type": "number", "description": "Φ((deadline − Σte) ÷ σ)" } }, "additionalProperties": false }, "annotations": { "readOnlyHint": true, "idempotentHint": true, "openWorldHint": false }, "_house": { "endpoint": "/faculty/msc-programme--change/pert_estimate", "feeSt": 1, "degree": "competency:msc-programme--change", "example": { "optimistic": [ 4, 6, 3 ], "mostLikely": [ 6, 8, 5 ], "pessimistic": [ 10, 14, 9 ], "deadline": 22 } } }, { "name": "msc-programme--change.risk_emv", "title": "Expected monetary value of a risk register (CDU-BUS-PCM-900)", "description": "What is the probability-weighted exposure of these risks, threats and opportunities separately, and net?", "inputSchema": { "type": "object", "required": [ "pan", "probabilities", "impacts" ], "properties": { "pan": { "type": "string", "description": "The student PAN — the degree must be held in one of its five slots", "pattern": "^[0-9 ]{16,19}$" }, "probabilities": { "type": "array", "description": "Probability of each risk, 0–1", "items": { "type": "number" } }, "impacts": { "type": "array", "description": "Monetary impact of each (negative = threat, positive = opportunity)", "items": { "type": "number" } } }, "additionalProperties": false }, "outputSchema": { "type": "object", "required": [ "emvs", "threatEmv", "opportunityEmv", "netEmv" ], "properties": { "emvs": { "type": "array", "description": "Probability × impact per risk (2 dp)", "items": { "type": "number" } }, "threatEmv": { "type": "number", "description": "Σ EMV of threats" }, "opportunityEmv": { "type": "number", "description": "Σ EMV of opportunities" }, "netEmv": { "type": "number", "description": "Σ EMV" } }, "additionalProperties": false }, "annotations": { "readOnlyHint": true, "idempotentHint": true, "openWorldHint": false }, "_house": { "endpoint": "/faculty/msc-programme--change/risk_emv", "feeSt": 1, "degree": "competency:msc-programme--change", "example": { "probabilities": [ 0.3, 0.1, 0.5, 0.2 ], "impacts": [ -50000, -200000, -20000, 30000 ] } } }, { "name": "msc-programme--change.crash_cost_slope", "title": "Crash cost slope (CDU-BUS-PCM-900)", "description": "What does each day saved on this activity cost, and what would saving this many days cost?", "inputSchema": { "type": "object", "required": [ "pan", "normalTime", "crashTime", "normalCost", "crashCost", "daysToSave" ], "properties": { "pan": { "type": "string", "description": "The student PAN — the degree must be held in one of its five slots", "pattern": "^[0-9 ]{16,19}$" }, "normalTime": { "type": "number", "description": "Normal duration", "minimum": 0.01 }, "crashTime": { "type": "number", "description": "Shortest possible duration", "minimum": 0 }, "normalCost": { "type": "number", "description": "Cost at normal duration", "minimum": 0 }, "crashCost": { "type": "number", "description": "Cost at crash duration", "minimum": 0 }, "daysToSave": { "type": "number", "description": "Days the schedule needs back", "minimum": 0 } }, "additionalProperties": false }, "outputSchema": { "type": "object", "required": [ "costSlope", "maxDaysSaved", "costToSave" ], "properties": { "costSlope": { "type": "number", "description": "Cost per day saved" }, "maxDaysSaved": { "type": "number", "description": "Normal − crash time" }, "costToSave": { "type": "number", "description": "Slope × days (capped at the maximum)" } }, "additionalProperties": false }, "annotations": { "readOnlyHint": true, "idempotentHint": true, "openWorldHint": false }, "_house": { "endpoint": "/faculty/msc-programme--change/crash_cost_slope", "feeSt": 1, "degree": "competency:msc-programme--change", "example": { "normalTime": 20, "crashTime": 14, "normalCost": 50000, "crashCost": 68000, "daysToSave": 4 } } }, { "name": "msc-agribusiness--water.et0_penman_monteith", "title": "Reference evapotranspiration (FAO-56 Penman–Monteith) (CDU-AGR-AGW-900)", "description": "How much water does the reference grass surface lose on this day, in mm?", "inputSchema": { "type": "object", "required": [ "pan", "tMax", "tMin", "rhMax", "rhMin", "windSpeed2m", "netRadiation", "altitude" ], "properties": { "pan": { "type": "string", "description": "The student PAN — the degree must be held in one of its five slots", "pattern": "^[0-9 ]{16,19}$" }, "tMax": { "type": "number", "description": "Maximum air temperature, °C", "minimum": -40, "maximum": 60 }, "tMin": { "type": "number", "description": "Minimum air temperature, °C", "minimum": -50, "maximum": 50 }, "rhMax": { "type": "number", "description": "Maximum relative humidity, %", "minimum": 1, "maximum": 100 }, "rhMin": { "type": "number", "description": "Minimum relative humidity, %", "minimum": 1, "maximum": 100 }, "windSpeed2m": { "type": "number", "description": "Wind speed at 2 m, m/s", "minimum": 0, "maximum": 30 }, "netRadiation": { "type": "number", "description": "Net radiation Rn, MJ/m²/day", "minimum": -10, "maximum": 40 }, "soilHeatFlux": { "type": "number", "description": "Soil heat flux G, MJ/m²/day (≈ 0 for a day)", "minimum": -10, "maximum": 10, "default": 0 }, "altitude": { "type": "number", "description": "Elevation above sea level, m", "minimum": -500, "maximum": 6000 } }, "additionalProperties": false }, "outputSchema": { "type": "object", "required": [ "et0", "vapourPressureDeficit", "slope", "psychrometricConstant" ], "properties": { "et0": { "type": "number", "description": "Reference evapotranspiration, mm/day" }, "vapourPressureDeficit": { "type": "number", "description": "es − ea, kPa" }, "slope": { "type": "number", "description": "Δ, kPa/°C" }, "psychrometricConstant": { "type": "number", "description": "γ, kPa/°C" } }, "additionalProperties": false }, "annotations": { "readOnlyHint": true, "idempotentHint": true, "openWorldHint": false }, "_house": { "endpoint": "/faculty/msc-agribusiness--water/et0_penman_monteith", "feeSt": 1, "degree": "competency:msc-agribusiness--water", "example": { "tMax": 21.5, "tMin": 12.3, "rhMax": 84, "rhMin": 63, "windSpeed2m": 2.078, "netRadiation": 13.28, "soilHeatFlux": 0, "altitude": 100 } } }, { "name": "msc-agribusiness--water.irrigation_requirement", "title": "Net and gross irrigation requirement (CDU-AGR-AGW-900)", "description": "Over this period, how much water does the crop need from irrigation, at the field and at the source?", "inputSchema": { "type": "object", "required": [ "pan", "et0", "cropCoefficient", "days", "effectiveRainfall", "applicationEfficiency" ], "properties": { "pan": { "type": "string", "description": "The student PAN — the degree must be held in one of its five slots", "pattern": "^[0-9 ]{16,19}$" }, "et0": { "type": "number", "description": "Mean reference ET over the period, mm/day", "minimum": 0, "maximum": 20 }, "cropCoefficient": { "type": "number", "description": "Kc for the growth stage", "minimum": 0.05, "maximum": 2 }, "days": { "type": "number", "description": "Days in the period", "minimum": 1, "maximum": 366 }, "effectiveRainfall": { "type": "number", "description": "Effective rainfall over the period, mm", "minimum": 0 }, "applicationEfficiency": { "type": "number", "description": "Irrigation application efficiency, 0–1", "minimum": 0.1, "maximum": 1 } }, "additionalProperties": false }, "outputSchema": { "type": "object", "required": [ "cropEt", "netRequirement", "grossRequirement", "volumePerHectare" ], "properties": { "cropEt": { "type": "number", "description": "ETc over the period, mm" }, "netRequirement": { "type": "number", "description": "ETc − effective rain (not below 0), mm" }, "grossRequirement": { "type": "number", "description": "Net ÷ efficiency, mm" }, "volumePerHectare": { "type": "number", "description": "Gross × 10, m³/ha" } }, "additionalProperties": false }, "annotations": { "readOnlyHint": true, "idempotentHint": true, "openWorldHint": false }, "_house": { "endpoint": "/faculty/msc-agribusiness--water/irrigation_requirement", "feeSt": 1, "degree": "competency:msc-agribusiness--water", "example": { "et0": 5.2, "cropCoefficient": 1.15, "days": 30, "effectiveRainfall": 40, "applicationEfficiency": 0.75 } } }, { "name": "msc-agribusiness--water.water_productivity", "title": "Physical and economic water productivity (CDU-AGR-AGW-900)", "description": "How much crop, revenue and margin does each cubic metre of water produce?", "inputSchema": { "type": "object", "required": [ "pan", "yieldKgPerHa", "waterM3PerHa", "pricePerKg", "variableCostPerHa" ], "properties": { "pan": { "type": "string", "description": "The student PAN — the degree must be held in one of its five slots", "pattern": "^[0-9 ]{16,19}$" }, "yieldKgPerHa": { "type": "number", "description": "Marketable yield, kg/ha", "minimum": 0 }, "waterM3PerHa": { "type": "number", "description": "Water applied and effective rain, m³/ha", "minimum": 0.01 }, "pricePerKg": { "type": "number", "description": "Farm-gate price per kg", "minimum": 0 }, "variableCostPerHa": { "type": "number", "description": "Variable costs per ha", "minimum": 0 } }, "additionalProperties": false }, "outputSchema": { "type": "object", "required": [ "kgPerM3", "revenuePerM3", "grossMarginPerM3" ], "properties": { "kgPerM3": { "type": "number", "description": "Yield ÷ water" }, "revenuePerM3": { "type": "number", "description": "Revenue ÷ water" }, "grossMarginPerM3": { "type": "number", "description": "(Revenue − variable costs) ÷ water" } }, "additionalProperties": false }, "annotations": { "readOnlyHint": true, "idempotentHint": true, "openWorldHint": false }, "_house": { "endpoint": "/faculty/msc-agribusiness--water/water_productivity", "feeSt": 1, "degree": "competency:msc-agribusiness--water", "example": { "yieldKgPerHa": 9000, "waterM3PerHa": 6000, "pricePerKg": 3.2, "variableCostPerHa": 18000 } } }, { "name": "msc-agribusiness--water.gross_margin", "title": "Enterprise gross margin and break-evens (CDU-AGR-AGW-900)", "description": "What gross margin does this enterprise earn, and at what yield or price does it only just cover its variable costs?", "inputSchema": { "type": "object", "required": [ "pan", "yieldPerHa", "pricePerUnit", "variableCostPerHa", "hectares" ], "properties": { "pan": { "type": "string", "description": "The student PAN — the degree must be held in one of its five slots", "pattern": "^[0-9 ]{16,19}$" }, "yieldPerHa": { "type": "number", "description": "Yield per hectare (t or units)", "minimum": 0.0001 }, "pricePerUnit": { "type": "number", "description": "Price per unit of yield", "minimum": 0.0001 }, "variableCostPerHa": { "type": "number", "description": "Variable costs per hectare", "minimum": 0 }, "hectares": { "type": "number", "description": "Area planted", "minimum": 0 } }, "additionalProperties": false }, "outputSchema": { "type": "object", "required": [ "revenuePerHa", "grossMarginPerHa", "totalGrossMargin", "breakevenYield", "breakevenPrice" ], "properties": { "revenuePerHa": { "type": "number", "description": "Yield × price" }, "grossMarginPerHa": { "type": "number", "description": "Revenue − variable costs" }, "totalGrossMargin": { "type": "number", "description": "Per-ha margin × hectares" }, "breakevenYield": { "type": "number", "description": "Variable costs ÷ price" }, "breakevenPrice": { "type": "number", "description": "Variable costs ÷ yield" } }, "additionalProperties": false }, "annotations": { "readOnlyHint": true, "idempotentHint": true, "openWorldHint": false }, "_house": { "endpoint": "/faculty/msc-agribusiness--water/gross_margin", "feeSt": 1, "degree": "competency:msc-agribusiness--water", "example": { "yieldPerHa": 6.5, "pricePerUnit": 4200, "variableCostPerHa": 19500, "hectares": 120 } } }, { "name": "ethics--conduct-module.fee_dependency", "title": "Fee dependency on an audit client (CDU-GEN-ETH-900)", "description": "Given the share of the firm’s fees this client has paid each year, what does the IESBA Code require?", "inputSchema": { "type": "object", "required": [ "pan", "publicInterestEntity", "feeShares" ], "properties": { "pan": { "type": "string", "description": "The student PAN — the degree must be held in one of its five slots", "pattern": "^[0-9 ]{16,19}$" }, "publicInterestEntity": { "type": "boolean", "description": "Is the audit client a public interest entity?" }, "feeShares": { "type": "array", "description": "Fees from the client ÷ the firm’s total fees, one per year, oldest first", "items": { "type": "number" } } }, "additionalProperties": false }, "outputSchema": { "type": "object", "required": [ "threshold", "consecutiveYearsAbove", "action" ], "properties": { "threshold": { "type": "number", "description": "0.15 (PIE) or 0.30 (non-PIE)" }, "consecutiveYearsAbove": { "type": "number", "description": "Years in a row, ending with the latest, above the threshold" }, "action": { "type": "string", "description": "none, disclose-and-pre-issuance-review, cease-after-fifth-year, or disclose-and-review" } }, "additionalProperties": false }, "annotations": { "readOnlyHint": true, "idempotentHint": true, "openWorldHint": false }, "_house": { "endpoint": "/faculty/ethics--conduct-module/fee_dependency", "feeSt": 1, "degree": "competency:ethics--conduct-module", "example": { "publicInterestEntity": true, "feeShares": [ 0.12, 0.16, 0.17 ] } } }, { "name": "ethics--conduct-module.partner_rotation", "title": "Key audit partner rotation and cooling-off (CDU-GEN-ETH-900)", "description": "For this role on a PIE audit, must the partner rotate off now, and for how long must they stay off?", "inputSchema": { "type": "object", "required": [ "pan", "role", "yearsServed" ], "properties": { "pan": { "type": "string", "description": "The student PAN — the degree must be held in one of its five slots", "pattern": "^[0-9 ]{16,19}$" }, "role": { "type": "string", "description": "Role on the engagement", "enum": [ "engagement_partner", "eqr", "other_kap" ] }, "yearsServed": { "type": "number", "description": "Cumulative years served as a key audit partner", "minimum": 0, "maximum": 50 } }, "additionalProperties": false }, "outputSchema": { "type": "object", "required": [ "mustRotate", "yearsRemaining", "coolingOffYears" ], "properties": { "mustRotate": { "type": "boolean", "description": "Years served ≥ 7" }, "yearsRemaining": { "type": "number", "description": "Years left before the time-on limit" }, "coolingOffYears": { "type": "number", "description": "Consecutive years off once rotated" } }, "additionalProperties": false }, "annotations": { "readOnlyHint": true, "idempotentHint": true, "openWorldHint": false }, "_house": { "endpoint": "/faculty/ethics--conduct-module/partner_rotation", "feeSt": 1, "degree": "competency:ethics--conduct-module", "example": { "role": "engagement_partner", "yearsServed": 6 } } }, { "name": "ethics--conduct-module.non_audit_fee_cap", "title": "EU cap on non-audit fees (CDU-GEN-ETH-900)", "description": "Do this year’s non-audit fees stay within 70% of the average audit fee of the last three years?", "inputSchema": { "type": "object", "required": [ "pan", "auditFeesLastThreeYears", "nonAuditFeesThisYear" ], "properties": { "pan": { "type": "string", "description": "The student PAN — the degree must be held in one of its five slots", "pattern": "^[0-9 ]{16,19}$" }, "auditFeesLastThreeYears": { "type": "array", "description": "Statutory audit fees of the last three consecutive years", "items": { "type": "number" } }, "nonAuditFeesThisYear": { "type": "number", "description": "Fees for permitted non-audit services this year", "minimum": 0 } }, "additionalProperties": false }, "outputSchema": { "type": "object", "required": [ "averageAuditFee", "cap", "headroom", "breach" ], "properties": { "averageAuditFee": { "type": "number", "description": "Mean of the three years" }, "cap": { "type": "number", "description": "70% of the average" }, "headroom": { "type": "number", "description": "Cap − non-audit fees (negative: over the cap)" }, "breach": { "type": "boolean", "description": "Non-audit fees above the cap" } }, "additionalProperties": false }, "annotations": { "readOnlyHint": true, "idempotentHint": true, "openWorldHint": false }, "_house": { "endpoint": "/faculty/ethics--conduct-module/non_audit_fee_cap", "feeSt": 1, "degree": "competency:ethics--conduct-module", "example": { "auditFeesLastThreeYears": [ 1200000, 1250000, 1300000 ], "nonAuditFeesThisYear": 700000 } } }, { "name": "ethics--conduct-module.board_independence", "title": "Governing-body composition (King IV Principle 7) (CDU-GEN-ETH-900)", "description": "Does the board have a non-executive majority, mostly independent, with at least two executives?", "inputSchema": { "type": "object", "required": [ "pan", "totalMembers", "nonExecutiveMembers", "independentNonExecutives" ], "properties": { "pan": { "type": "string", "description": "The student PAN — the degree must be held in one of its five slots", "pattern": "^[0-9 ]{16,19}$" }, "totalMembers": { "type": "number", "description": "Members of the governing body", "minimum": 1 }, "nonExecutiveMembers": { "type": "number", "description": "Non-executive members", "minimum": 0 }, "independentNonExecutives": { "type": "number", "description": "Independent non-executive members", "minimum": 0 } }, "additionalProperties": false }, "outputSchema": { "type": "object", "required": [ "nonExecutiveMajority", "independentMajorityOfNeds", "atLeastTwoExecutives", "compliant" ], "properties": { "nonExecutiveMajority": { "type": "boolean", "description": "Non-executives > half the board" }, "independentMajorityOfNeds": { "type": "boolean", "description": "Independents > half the non-executives" }, "atLeastTwoExecutives": { "type": "boolean", "description": "Executives ≥ 2" }, "compliant": { "type": "boolean", "description": "All three" } }, "additionalProperties": false }, "annotations": { "readOnlyHint": true, "idempotentHint": true, "openWorldHint": false }, "_house": { "endpoint": "/faculty/ethics--conduct-module/board_independence", "feeSt": 1, "degree": "competency:ethics--conduct-module", "example": { "totalMembers": 12, "nonExecutiveMembers": 9, "independentNonExecutives": 6 } } }, { "name": "matric-nqf4.maths_quadratic_factorise", "title": "Quadratic equation by factorising (CDU-GEN-NSC-400)", "description": "The roots of ax² + bx + c = 0 by factorisation, with the discriminant, the sum and the product of the roots checked.", "inputSchema": { "type": "object", "required": [ "pan", "a", "b", "c" ], "properties": { "pan": { "type": "string", "description": "The student PAN — the degree must be held in one of its five slots", "pattern": "^[0-9 ]{16,19}$" }, "a": { "type": "number", "description": "coefficient of x² (a ≠ 0)", "minimum": -100, "maximum": 100 }, "b": { "type": "number", "description": "coefficient of x", "minimum": -1000, "maximum": 1000 }, "c": { "type": "number", "description": "constant term", "minimum": -10000, "maximum": 10000 } }, "additionalProperties": false }, "outputSchema": { "type": "object", "required": [ "rootA", "rootB", "discriminant", "sumOfRoots", "productOfRoots" ], "properties": { "rootA": { "type": "number", "description": "the smaller root" }, "rootB": { "type": "number", "description": "the larger root" }, "discriminant": { "type": "number", "description": "Δ = b² − 4ac" }, "sumOfRoots": { "type": "number", "description": "−b/a" }, "productOfRoots": { "type": "number", "description": "c/a" } }, "additionalProperties": false }, "annotations": { "readOnlyHint": true, "idempotentHint": true, "openWorldHint": false }, "_house": { "endpoint": "/faculty/matric-nqf4/maths_quadratic_factorise", "feeSt": 1, "degree": "competency:matric-nqf4", "example": { "a": 1, "b": -5, "c": 6 } } }, { "name": "matric-nqf4.maths_quadratic_formula", "title": "Quadratic equation by the formula (CDU-GEN-NSC-400)", "description": "The roots of ax² + bx + c = 0 by x = (−b ± √Δ)/(2a), every substitution shown.", "inputSchema": { "type": "object", "required": [ "pan", "a", "b", "c" ], "properties": { "pan": { "type": "string", "description": "The student PAN — the degree must be held in one of its five slots", "pattern": "^[0-9 ]{16,19}$" }, "a": { "type": "number", "description": "coefficient of x² (a ≠ 0)", "minimum": -100, "maximum": 100 }, "b": { "type": "number", "description": "coefficient of x", "minimum": -1000, "maximum": 1000 }, "c": { "type": "number", "description": "constant term", "minimum": -10000, "maximum": 10000 } }, "additionalProperties": false }, "outputSchema": { "type": "object", "required": [ "rootA", "rootB", "discriminant" ], "properties": { "rootA": { "type": "number", "description": "the smaller root" }, "rootB": { "type": "number", "description": "the larger root" }, "discriminant": { "type": "number", "description": "Δ = b² − 4ac" } }, "additionalProperties": false }, "annotations": { "readOnlyHint": true, "idempotentHint": true, "openWorldHint": false }, "_house": { "endpoint": "/faculty/matric-nqf4/maths_quadratic_formula", "feeSt": 1, "degree": "competency:matric-nqf4", "example": { "a": 2, "b": 3, "c": -2 } } }, { "name": "matric-nqf4.maths_nature_of_roots", "title": "Nature of the roots (CDU-GEN-NSC-400)", "description": "Whether ax² + bx + c = 0 has two distinct real, equal real, or non-real roots, from the discriminant alone.", "inputSchema": { "type": "object", "required": [ "pan", "a", "b", "c" ], "properties": { "pan": { "type": "string", "description": "The student PAN — the degree must be held in one of its five slots", "pattern": "^[0-9 ]{16,19}$" }, "a": { "type": "number", "description": "coefficient of x² (a ≠ 0)", "minimum": -100, "maximum": 100 }, "b": { "type": "number", "description": "coefficient of x", "minimum": -1000, "maximum": 1000 }, "c": { "type": "number", "description": "constant term", "minimum": -10000, "maximum": 10000 } }, "additionalProperties": false }, "outputSchema": { "type": "object", "required": [ "discriminant", "nature" ], "properties": { "discriminant": { "type": "number", "description": "Δ = b² − 4ac" }, "nature": { "type": "string", "description": "two distinct real roots | equal real roots | non-real (complex) roots" } }, "additionalProperties": false }, "annotations": { "readOnlyHint": true, "idempotentHint": true, "openWorldHint": false }, "_house": { "endpoint": "/faculty/matric-nqf4/maths_nature_of_roots", "feeSt": 1, "degree": "competency:matric-nqf4", "example": { "a": 1, "b": 2, "c": 5 } } }, { "name": "matric-nqf4.maths_simultaneous", "title": "Simultaneous linear/quadratic system (CDU-GEN-NSC-400)", "description": "Where the line y = mx + k meets the parabola y = x² + px + q — equate, solve, substitute back.", "inputSchema": { "type": "object", "required": [ "pan", "p", "q", "m", "k" ], "properties": { "pan": { "type": "string", "description": "The student PAN — the degree must be held in one of its five slots", "pattern": "^[0-9 ]{16,19}$" }, "p": { "type": "number", "description": "parabola coefficient of x", "minimum": -100, "maximum": 100 }, "q": { "type": "number", "description": "parabola constant", "minimum": -1000, "maximum": 1000 }, "m": { "type": "number", "description": "line gradient", "minimum": -100, "maximum": 100 }, "k": { "type": "number", "description": "line intercept", "minimum": -1000, "maximum": 1000 } }, "additionalProperties": false }, "outputSchema": { "type": "object", "required": [ "x1", "y1", "x2", "y2" ], "properties": { "x1": { "type": "number", "description": "smaller x of intersection" }, "y1": { "type": "number", "description": "its y" }, "x2": { "type": "number", "description": "larger x of intersection" }, "y2": { "type": "number", "description": "its y" } }, "additionalProperties": false }, "annotations": { "readOnlyHint": true, "idempotentHint": true, "openWorldHint": false }, "_house": { "endpoint": "/faculty/matric-nqf4/maths_simultaneous", "feeSt": 1, "degree": "competency:matric-nqf4", "example": { "p": -3, "q": 2, "m": 2, "k": -4 } } }, { "name": "matric-nqf4.maths_arithmetic_sequence", "title": "Arithmetic sequence and series (CDU-GEN-NSC-400)", "description": "Tₙ = a + (n − 1)d and Sₙ = n/2 [2a + (n − 1)d], with the Sₙ = n/2 (a + l) cross-check.", "inputSchema": { "type": "object", "required": [ "pan", "a", "d", "n" ], "properties": { "pan": { "type": "string", "description": "The student PAN — the degree must be held in one of its five slots", "pattern": "^[0-9 ]{16,19}$" }, "a": { "type": "number", "description": "first term", "minimum": -10000, "maximum": 10000 }, "d": { "type": "number", "description": "common difference", "minimum": -1000, "maximum": 1000 }, "n": { "type": "number", "description": "term number (positive integer)", "maximum": 100000 } }, "additionalProperties": false }, "outputSchema": { "type": "object", "required": [ "tn", "sn" ], "properties": { "tn": { "type": "number", "description": "the nth term" }, "sn": { "type": "number", "description": "the sum of the first n terms" } }, "additionalProperties": false }, "annotations": { "readOnlyHint": true, "idempotentHint": true, "openWorldHint": false }, "_house": { "endpoint": "/faculty/matric-nqf4/maths_arithmetic_sequence", "feeSt": 1, "degree": "competency:matric-nqf4", "example": { "a": 4, "d": 3, "n": 20 } } }, { "name": "matric-nqf4.maths_geometric_sequence", "title": "Geometric sequence and series (CDU-GEN-NSC-400)", "description": "Tₙ = arⁿ⁻¹ and Sₙ = a(rⁿ − 1)/(r − 1), refusing r = 1 where the formula is undefined.", "inputSchema": { "type": "object", "required": [ "pan", "a", "r", "n" ], "properties": { "pan": { "type": "string", "description": "The student PAN — the degree must be held in one of its five slots", "pattern": "^[0-9 ]{16,19}$" }, "a": { "type": "number", "description": "first term", "minimum": -10000, "maximum": 10000 }, "r": { "type": "number", "description": "common ratio (r ≠ 1 for the Sₙ formula)", "minimum": -100, "maximum": 100 }, "n": { "type": "number", "description": "term number (positive integer)", "maximum": 60 } }, "additionalProperties": false }, "outputSchema": { "type": "object", "required": [ "tn", "sn" ], "properties": { "tn": { "type": "number", "description": "the nth term" }, "sn": { "type": "number", "description": "the sum of the first n terms" } }, "additionalProperties": false }, "annotations": { "readOnlyHint": true, "idempotentHint": true, "openWorldHint": false }, "_house": { "endpoint": "/faculty/matric-nqf4/maths_geometric_sequence", "feeSt": 1, "degree": "competency:matric-nqf4", "example": { "a": 2, "r": 3, "n": 5 } } }, { "name": "matric-nqf4.maths_geometric_infinite", "title": "Infinite geometric series (CDU-GEN-NSC-400)", "description": "S∞ = a/(1 − r) for |r| < 1; a ratio at or beyond 1 in magnitude is refused because the sum does not converge.", "inputSchema": { "type": "object", "required": [ "pan", "a", "r" ], "properties": { "pan": { "type": "string", "description": "The student PAN — the degree must be held in one of its five slots", "pattern": "^[0-9 ]{16,19}$" }, "a": { "type": "number", "description": "first term", "minimum": -10000, "maximum": 10000 }, "r": { "type": "number", "description": "common ratio, |r| < 1", "minimum": -100, "maximum": 100 } }, "additionalProperties": false }, "outputSchema": { "type": "object", "required": [ "sInfinity" ], "properties": { "sInfinity": { "type": "number", "description": "the infinite sum" } }, "additionalProperties": false }, "annotations": { "readOnlyHint": true, "idempotentHint": true, "openWorldHint": false }, "_house": { "endpoint": "/faculty/matric-nqf4/maths_geometric_infinite", "feeSt": 1, "degree": "competency:matric-nqf4", "example": { "a": 8, "r": 0.5 } } }, { "name": "matric-nqf4.maths_sigma_sum", "title": "Sigma notation (CDU-GEN-NSC-400)", "description": "Σₖ₌₁ⁿ (pk + q) evaluated with Σk = n(n + 1)/2 and Σ1 = n.", "inputSchema": { "type": "object", "required": [ "pan", "p", "q", "n" ], "properties": { "pan": { "type": "string", "description": "The student PAN — the degree must be held in one of its five slots", "pattern": "^[0-9 ]{16,19}$" }, "p": { "type": "number", "description": "coefficient of k", "minimum": -1000, "maximum": 1000 }, "q": { "type": "number", "description": "constant term", "minimum": -1000, "maximum": 1000 }, "n": { "type": "number", "description": "upper limit (positive integer)", "maximum": 1000000 } }, "additionalProperties": false }, "outputSchema": { "type": "object", "required": [ "sum" ], "properties": { "sum": { "type": "number", "description": "the value of the sum" } }, "additionalProperties": false }, "annotations": { "readOnlyHint": true, "idempotentHint": true, "openWorldHint": false }, "_house": { "endpoint": "/faculty/matric-nqf4/maths_sigma_sum", "feeSt": 1, "degree": "competency:matric-nqf4", "example": { "p": 2, "q": 1, "n": 10 } } }, { "name": "matric-nqf4.maths_parabola", "title": "The parabola (CDU-GEN-NSC-400)", "description": "Turning point, axis of symmetry, intercepts and range of f(x) = ax² + bx + c.", "inputSchema": { "type": "object", "required": [ "pan", "a", "b", "c" ], "properties": { "pan": { "type": "string", "description": "The student PAN — the degree must be held in one of its five slots", "pattern": "^[0-9 ]{16,19}$" }, "a": { "type": "number", "description": "coefficient of x² (a ≠ 0)", "minimum": -100, "maximum": 100 }, "b": { "type": "number", "description": "coefficient of x", "minimum": -1000, "maximum": 1000 }, "c": { "type": "number", "description": "constant term", "minimum": -10000, "maximum": 10000 } }, "additionalProperties": false }, "outputSchema": { "type": "object", "required": [ "tpX", "tpY", "xIntercept1", "xIntercept2", "yIntercept", "range" ], "properties": { "tpX": { "type": "number", "description": "x of the turning point" }, "tpY": { "type": "number", "description": "y of the turning point" }, "xIntercept1": { "type": "number", "description": "smaller x-intercept" }, "xIntercept2": { "type": "number", "description": "larger x-intercept" }, "yIntercept": { "type": "number", "description": "f(0)" }, "range": { "type": "string", "description": "the range, e.g. y ≥ −1" } }, "additionalProperties": false }, "annotations": { "readOnlyHint": true, "idempotentHint": true, "openWorldHint": false }, "_house": { "endpoint": "/faculty/matric-nqf4/maths_parabola", "feeSt": 1, "degree": "competency:matric-nqf4", "example": { "a": 1, "b": -4, "c": 3 } } }, { "name": "matric-nqf4.maths_inverse_linear", "title": "Inverse of a linear function (CDU-GEN-NSC-400)", "description": "g⁻¹ of g(x) = ax + b, the round trip g⁻¹(g(x)) = x, and the composition f(g(x)) with a given parabola.", "inputSchema": { "type": "object", "required": [ "pan", "a", "b", "x" ], "properties": { "pan": { "type": "string", "description": "The student PAN — the degree must be held in one of its five slots", "pattern": "^[0-9 ]{16,19}$" }, "a": { "type": "number", "description": "gradient of g (a ≠ 0)", "minimum": -100, "maximum": 100 }, "b": { "type": "number", "description": "intercept of g", "minimum": -1000, "maximum": 1000 }, "x": { "type": "number", "description": "where to evaluate", "minimum": -1000, "maximum": 1000 }, "pa": { "type": "number", "description": "parabola a for the composition", "minimum": -100, "maximum": 100, "default": 1 }, "pb": { "type": "number", "description": "parabola b", "minimum": -1000, "maximum": 1000, "default": -4 }, "pc": { "type": "number", "description": "parabola c", "minimum": -10000, "maximum": 10000, "default": 3 } }, "additionalProperties": false }, "outputSchema": { "type": "object", "required": [ "gOfX", "inverseOfGOfX", "fOfGOfX" ], "properties": { "gOfX": { "type": "number", "description": "g(x)" }, "inverseOfGOfX": { "type": "number", "description": "g⁻¹(g(x)) — must be x" }, "fOfGOfX": { "type": "number", "description": "f(g(x)) with the given parabola" } }, "additionalProperties": false }, "annotations": { "readOnlyHint": true, "idempotentHint": true, "openWorldHint": false }, "_house": { "endpoint": "/faculty/matric-nqf4/maths_inverse_linear", "feeSt": 1, "degree": "competency:matric-nqf4", "example": { "a": 2, "b": 1, "x": 2, "pa": 1, "pb": -4, "pc": 3 } } }, { "name": "matric-nqf4.maths_exponential_log", "title": "Exponential and logarithmic equations (CDU-GEN-NSC-400)", "description": "Solve baseˣ = value: x = log_base(value), refusing non-positive arguments and degenerate bases.", "inputSchema": { "type": "object", "required": [ "pan", "base", "value" ], "properties": { "pan": { "type": "string", "description": "The student PAN — the degree must be held in one of its five slots", "pattern": "^[0-9 ]{16,19}$" }, "base": { "type": "number", "description": "the base (b > 0, b ≠ 1)", "minimum": -1000, "maximum": 1000 }, "value": { "type": "number", "description": "the value (v > 0)", "minimum": -1000000, "maximum": 1000000 } }, "additionalProperties": false }, "outputSchema": { "type": "object", "required": [ "exponent" ], "properties": { "exponent": { "type": "number", "description": "x with baseˣ = value" } }, "additionalProperties": false }, "annotations": { "readOnlyHint": true, "idempotentHint": true, "openWorldHint": false }, "_house": { "endpoint": "/faculty/matric-nqf4/maths_exponential_log", "feeSt": 1, "degree": "competency:matric-nqf4", "example": { "base": 2, "value": 16 } } }, { "name": "matric-nqf4.maths_first_principles", "title": "Differentiation from first principles (CDU-GEN-NSC-400)", "description": "f′(x) of f(x) = ax² + bx from the limit definition, the derivative at a point, and the tangent's equation there.", "inputSchema": { "type": "object", "required": [ "pan", "a", "b", "x0" ], "properties": { "pan": { "type": "string", "description": "The student PAN — the degree must be held in one of its five slots", "pattern": "^[0-9 ]{16,19}$" }, "a": { "type": "number", "description": "coefficient of x²", "minimum": -100, "maximum": 100 }, "b": { "type": "number", "description": "coefficient of x", "minimum": -1000, "maximum": 1000 }, "x0": { "type": "number", "description": "the point of tangency", "minimum": -1000, "maximum": 1000 } }, "additionalProperties": false }, "outputSchema": { "type": "object", "required": [ "derivativeAt", "fAt", "tangentSlope", "tangentIntercept" ], "properties": { "derivativeAt": { "type": "number", "description": "f′(x0)" }, "fAt": { "type": "number", "description": "f(x0)" }, "tangentSlope": { "type": "number", "description": "gradient of the tangent" }, "tangentIntercept": { "type": "number", "description": "c of the tangent y = mx + c" } }, "additionalProperties": false }, "annotations": { "readOnlyHint": true, "idempotentHint": true, "openWorldHint": false }, "_house": { "endpoint": "/faculty/matric-nqf4/maths_first_principles", "feeSt": 1, "degree": "competency:matric-nqf4", "example": { "a": 1, "b": 3, "x0": 2 } } }, { "name": "matric-nqf4.maths_cubic_stationary", "title": "Stationary points of a cubic (CDU-GEN-NSC-400)", "description": "The stationary points of f(x) = x³ + bx² + cx + d, classified by the second derivative, with the point of inflection.", "inputSchema": { "type": "object", "required": [ "pan", "b", "c", "d" ], "properties": { "pan": { "type": "string", "description": "The student PAN — the degree must be held in one of its five slots", "pattern": "^[0-9 ]{16,19}$" }, "b": { "type": "number", "description": "coefficient of x²", "minimum": -1000, "maximum": 1000 }, "c": { "type": "number", "description": "coefficient of x", "minimum": -10000, "maximum": 10000 }, "d": { "type": "number", "description": "constant term", "minimum": -100000, "maximum": 100000 } }, "additionalProperties": false }, "outputSchema": { "type": "object", "required": [ "x1", "y1", "type1", "x2", "y2", "type2", "inflectionX" ], "properties": { "x1": { "type": "number", "description": "first stationary x (smaller)" }, "y1": { "type": "number", "description": "f(x1)" }, "type1": { "type": "string", "description": "local maximum | local minimum" }, "x2": { "type": "number", "description": "second stationary x (larger)" }, "y2": { "type": "number", "description": "f(x2)" }, "type2": { "type": "string", "description": "local maximum | local minimum" }, "inflectionX": { "type": "number", "description": "x of the point of inflection" } }, "additionalProperties": false }, "annotations": { "readOnlyHint": true, "idempotentHint": true, "openWorldHint": false }, "_house": { "endpoint": "/faculty/matric-nqf4/maths_cubic_stationary", "feeSt": 1, "degree": "competency:matric-nqf4", "example": { "b": -6, "c": 9, "d": 1 } } }, { "name": "matric-nqf4.maths_optimisation", "title": "Optimisation — the largest rectangle (CDU-GEN-NSC-400)", "description": "The rectangle of greatest area for a fixed perimeter, by differentiating A(x) = x(P/2 − x).", "inputSchema": { "type": "object", "required": [ "pan", "perimeter" ], "properties": { "pan": { "type": "string", "description": "The student PAN — the degree must be held in one of its five slots", "pattern": "^[0-9 ]{16,19}$" }, "perimeter": { "type": "number", "description": "the fixed perimeter (metres) (m)", "minimum": 0.001, "maximum": 1000000 } }, "additionalProperties": false }, "outputSchema": { "type": "object", "required": [ "sideX", "sideY", "maxArea" ], "properties": { "sideX": { "type": "number", "description": "the optimal width (m)" }, "sideY": { "type": "number", "description": "the optimal height (m)" }, "maxArea": { "type": "number", "description": "the maximal area (m²)" } }, "additionalProperties": false }, "annotations": { "readOnlyHint": true, "idempotentHint": true, "openWorldHint": false }, "_house": { "endpoint": "/faculty/matric-nqf4/maths_optimisation", "feeSt": 1, "degree": "competency:matric-nqf4", "example": { "perimeter": 40 } } }, { "name": "matric-nqf4.maths_compound_angle", "title": "Compound-angle identity (CDU-GEN-NSC-400)", "description": "sin(A + B) = sinA cosB + cosA sinB, every substitution shown — sin 75° exactly and numerically.", "inputSchema": { "type": "object", "required": [ "pan", "angleA", "angleB" ], "properties": { "pan": { "type": "string", "description": "The student PAN — the degree must be held in one of its five slots", "pattern": "^[0-9 ]{16,19}$" }, "angleA": { "type": "number", "description": "A in degrees (°)", "minimum": 0, "maximum": 90 }, "angleB": { "type": "number", "description": "B in degrees (°)", "minimum": 0, "maximum": 90 } }, "additionalProperties": false }, "outputSchema": { "type": "object", "required": [ "sinAB" ], "properties": { "sinAB": { "type": "number", "description": "sin(A + B)" } }, "additionalProperties": false }, "annotations": { "readOnlyHint": true, "idempotentHint": true, "openWorldHint": false }, "_house": { "endpoint": "/faculty/matric-nqf4/maths_compound_angle", "feeSt": 1, "degree": "competency:matric-nqf4", "example": { "angleA": 45, "angleB": 30 } } }, { "name": "matric-nqf4.maths_trig_general_solution", "title": "General solution of a trig equation (CDU-GEN-NSC-400)", "description": "Solve p·sinθ = q on [0° ; 360°] with the general solution, refusing |q/p| > 1 because sine never leaves [−1 ; 1].", "inputSchema": { "type": "object", "required": [ "pan", "p", "q" ], "properties": { "pan": { "type": "string", "description": "The student PAN — the degree must be held in one of its five slots", "pattern": "^[0-9 ]{16,19}$" }, "p": { "type": "number", "description": "coefficient of sinθ (p ≠ 0)", "minimum": -100, "maximum": 100 }, "q": { "type": "number", "description": "right-hand side", "minimum": -100, "maximum": 100 } }, "additionalProperties": false }, "outputSchema": { "type": "object", "required": [ "alpha", "solution1", "solution2" ], "properties": { "alpha": { "type": "number", "description": "the reference angle (°)" }, "solution1": { "type": "number", "description": "first solution in [0 ; 360] (°)" }, "solution2": { "type": "number", "description": "second solution in [0 ; 360] (°)" } }, "additionalProperties": false }, "annotations": { "readOnlyHint": true, "idempotentHint": true, "openWorldHint": false }, "_house": { "endpoint": "/faculty/matric-nqf4/maths_trig_general_solution", "feeSt": 1, "degree": "competency:matric-nqf4", "example": { "p": 2, "q": 1 } } }, { "name": "matric-nqf4.maths_circle_tangent", "title": "Tangent to a circle (CDU-GEN-NSC-400)", "description": "The tangent to (x − a)² + (y − b)² = r² at a point on the circle: prove the point is on it, radius ⟂ tangent, the line in standard form.", "inputSchema": { "type": "object", "required": [ "pan", "a", "b", "r", "px", "py" ], "properties": { "pan": { "type": "string", "description": "The student PAN — the degree must be held in one of its five slots", "pattern": "^[0-9 ]{16,19}$" }, "a": { "type": "number", "description": "centre x", "minimum": -1000, "maximum": 1000 }, "b": { "type": "number", "description": "centre y", "minimum": -1000, "maximum": 1000 }, "r": { "type": "number", "description": "radius (r > 0)", "minimum": 0.001, "maximum": 100000 }, "px": { "type": "number", "description": "point x", "minimum": -100000, "maximum": 100000 }, "py": { "type": "number", "description": "point y", "minimum": -100000, "maximum": 100000 } }, "additionalProperties": false }, "outputSchema": { "type": "object", "required": [ "tangentGradient", "lineA", "lineB", "lineC" ], "properties": { "tangentGradient": { "type": "number", "description": "gradient of the tangent" }, "lineA": { "type": "number", "description": "A of Ax + By + C = 0" }, "lineB": { "type": "number", "description": "B of Ax + By + C = 0" }, "lineC": { "type": "number", "description": "C of Ax + By + C = 0" } }, "additionalProperties": false }, "annotations": { "readOnlyHint": true, "idempotentHint": true, "openWorldHint": false }, "_house": { "endpoint": "/faculty/matric-nqf4/maths_circle_tangent", "feeSt": 1, "degree": "competency:matric-nqf4", "example": { "a": 2, "b": -1, "r": 5, "px": 5, "py": 3 } } }, { "name": "matric-nqf4.maths_probability_table", "title": "Probability from a contingency table (CDU-GEN-NSC-400)", "description": "P(A | B) and P(neither) for two subject choices over one class, refusing any probability outside [0 ; 1].", "inputSchema": { "type": "object", "required": [ "pan", "total", "nA", "nB", "nBoth" ], "properties": { "pan": { "type": "string", "description": "The student PAN — the degree must be held in one of its five slots", "pattern": "^[0-9 ]{16,19}$" }, "total": { "type": "number", "description": "learners in the class", "minimum": 1, "maximum": 1000000 }, "nA": { "type": "number", "description": "take subject A", "minimum": 0, "maximum": 1000000 }, "nB": { "type": "number", "description": "take subject B", "minimum": 0, "maximum": 1000000 }, "nBoth": { "type": "number", "description": "take both", "minimum": 0, "maximum": 1000000 } }, "additionalProperties": false }, "outputSchema": { "type": "object", "required": [ "pAGivenB", "pNeither" ], "properties": { "pAGivenB": { "type": "number", "description": "P(A | B)" }, "pNeither": { "type": "number", "description": "P(neither)" } }, "additionalProperties": false }, "annotations": { "readOnlyHint": true, "idempotentHint": true, "openWorldHint": false }, "_house": { "endpoint": "/faculty/matric-nqf4/maths_probability_table", "feeSt": 1, "degree": "competency:matric-nqf4", "example": { "total": 100, "nA": 60, "nB": 40, "nBoth": 30 } } }, { "name": "matric-nqf4.maths_probability_draws", "title": "Probability without replacement (CDU-GEN-NSC-400)", "description": "P(both red) for two draws without replacement from a mixed set of counters.", "inputSchema": { "type": "object", "required": [ "pan", "red", "blue", "green" ], "properties": { "pan": { "type": "string", "description": "The student PAN — the degree must be held in one of its five slots", "pattern": "^[0-9 ]{16,19}$" }, "red": { "type": "number", "description": "red counters", "minimum": 0, "maximum": 100000 }, "blue": { "type": "number", "description": "blue counters", "minimum": 0, "maximum": 100000 }, "green": { "type": "number", "description": "green counters", "minimum": 0, "maximum": 100000 } }, "additionalProperties": false }, "outputSchema": { "type": "object", "required": [ "pBothRed" ], "properties": { "pBothRed": { "type": "number", "description": "P(first red and second red)" } }, "additionalProperties": false }, "annotations": { "readOnlyHint": true, "idempotentHint": true, "openWorldHint": false }, "_house": { "endpoint": "/faculty/matric-nqf4/maths_probability_draws", "feeSt": 1, "degree": "competency:matric-nqf4", "example": { "red": 5, "blue": 3, "green": 2 } } }, { "name": "matric-nqf4.maths_compound_interest", "title": "Compound interest (CDU-GEN-NSC-400)", "description": "A = P(1 + i)ⁿ and the interest earned, each substitution shown.", "inputSchema": { "type": "object", "required": [ "pan", "principal", "ratePercent", "years" ], "properties": { "pan": { "type": "string", "description": "The student PAN — the degree must be held in one of its five slots", "pattern": "^[0-9 ]{16,19}$" }, "principal": { "type": "number", "description": "P, the amount invested", "minimum": 0, "maximum": 1000000000 }, "ratePercent": { "type": "number", "description": "annual rate (percent)", "minimum": -99, "maximum": 1000 }, "years": { "type": "number", "description": "n, whole years", "minimum": 0, "maximum": 200 } }, "additionalProperties": false }, "outputSchema": { "type": "object", "required": [ "amount", "interestEarned" ], "properties": { "amount": { "type": "number", "description": "A after n years" }, "interestEarned": { "type": "number", "description": "A − P" } }, "additionalProperties": false }, "annotations": { "readOnlyHint": true, "idempotentHint": true, "openWorldHint": false }, "_house": { "endpoint": "/faculty/matric-nqf4/maths_compound_interest", "feeSt": 1, "degree": "competency:matric-nqf4", "example": { "principal": 10000, "ratePercent": 8, "years": 3 } } }, { "name": "matric-nqf4.maths_statistics", "title": "Descriptive statistics (CDU-GEN-NSC-400)", "description": "Mean, population variance and standard deviation, the five-number summary (inclusive quartiles), IQR and the outlier fences.", "inputSchema": { "type": "object", "required": [ "pan", "data" ], "properties": { "pan": { "type": "string", "description": "The student PAN — the degree must be held in one of its five slots", "pattern": "^[0-9 ]{16,19}$" }, "data": { "type": "array", "description": "the data values", "items": { "type": "number" } } }, "additionalProperties": false }, "outputSchema": { "type": "object", "required": [ "mean", "variance", "standardDeviation", "min", "q1", "median", "q3", "max", "iqr", "outliers" ], "properties": { "mean": { "type": "number", "description": "x̄" }, "variance": { "type": "number", "description": "σ² (population)" }, "standardDeviation": { "type": "number", "description": "σ, 4 d.p." }, "min": { "type": "number", "description": "minimum" }, "q1": { "type": "number", "description": "lower quartile" }, "median": { "type": "number", "description": "median" }, "q3": { "type": "number", "description": "upper quartile" }, "max": { "type": "number", "description": "maximum" }, "iqr": { "type": "number", "description": "Q3 − Q1" }, "outliers": { "type": "number", "description": "how many values lie outside the 1.5·IQR fences" } }, "additionalProperties": false }, "annotations": { "readOnlyHint": true, "idempotentHint": true, "openWorldHint": false }, "_house": { "endpoint": "/faculty/matric-nqf4/maths_statistics", "feeSt": 1, "degree": "competency:matric-nqf4", "example": { "data": [ 2, 4, 6, 8, 10 ] } } }, { "name": "matric-nqf4.maths_regression_line", "title": "Least-squares regression line (CDU-GEN-NSC-400)", "description": "ŷ = a + bx from r, the standard deviations and the means: b = r·σ_y/σ_x, a = ȳ − b·x̄. A zero σ_x is refused.", "inputSchema": { "type": "object", "required": [ "pan", "r", "sigmaX", "sigmaY", "meanX", "meanY" ], "properties": { "pan": { "type": "string", "description": "The student PAN — the degree must be held in one of its five slots", "pattern": "^[0-9 ]{16,19}$" }, "r": { "type": "number", "description": "correlation coefficient", "minimum": -1, "maximum": 1 }, "sigmaX": { "type": "number", "description": "σ_x (must be > 0)", "minimum": 0, "maximum": 1000000 }, "sigmaY": { "type": "number", "description": "σ_y", "minimum": 0, "maximum": 1000000 }, "meanX": { "type": "number", "description": "x̄", "minimum": -1000000, "maximum": 1000000 }, "meanY": { "type": "number", "description": "ȳ", "minimum": -1000000, "maximum": 1000000 } }, "additionalProperties": false }, "outputSchema": { "type": "object", "required": [ "slope", "intercept" ], "properties": { "slope": { "type": "number", "description": "b" }, "intercept": { "type": "number", "description": "a" } }, "additionalProperties": false }, "annotations": { "readOnlyHint": true, "idempotentHint": true, "openWorldHint": false }, "_house": { "endpoint": "/faculty/matric-nqf4/maths_regression_line", "feeSt": 1, "degree": "competency:matric-nqf4", "example": { "r": 0.8, "sigmaX": 2, "sigmaY": 3, "meanX": 10, "meanY": 20 } } }, { "name": "matric-nqf4.sci_newton_second_law", "title": "Newton's second law — horizontal motion (CDU-GEN-NSC-400)", "description": "The acceleration of a block under an applied force and kinetic friction: a = F_net/m.", "inputSchema": { "type": "object", "required": [ "pan", "mass", "appliedForce", "friction" ], "properties": { "pan": { "type": "string", "description": "The student PAN — the degree must be held in one of its five slots", "pattern": "^[0-9 ]{16,19}$" }, "mass": { "type": "number", "description": "mass (kg) (kg)", "minimum": 0.001, "maximum": 100000 }, "appliedForce": { "type": "number", "description": "applied force (N), positive in the direction of motion (N)", "minimum": 0, "maximum": 1000000 }, "friction": { "type": "number", "description": "kinetic friction magnitude (N) (N)", "minimum": 0, "maximum": 1000000 } }, "additionalProperties": false }, "outputSchema": { "type": "object", "required": [ "netForce", "acceleration" ], "properties": { "netForce": { "type": "number", "description": "F_net (N)" }, "acceleration": { "type": "number", "description": "a (m·s⁻²)" } }, "additionalProperties": false }, "annotations": { "readOnlyHint": true, "idempotentHint": true, "openWorldHint": false }, "_house": { "endpoint": "/faculty/matric-nqf4/sci_newton_second_law", "feeSt": 1, "degree": "competency:matric-nqf4", "example": { "mass": 5, "appliedForce": 20, "friction": 5 } } }, { "name": "matric-nqf4.sci_inclined_plane", "title": "Inclined plane with friction (CDU-GEN-NSC-400)", "description": "The acceleration of a block sliding down a rough incline: components, the normal, μN, F_net, a — every substitution shown.", "inputSchema": { "type": "object", "required": [ "pan", "mass", "angleDeg", "mu" ], "properties": { "pan": { "type": "string", "description": "The student PAN — the degree must be held in one of its five slots", "pattern": "^[0-9 ]{16,19}$" }, "mass": { "type": "number", "description": "mass (kg) (kg)", "minimum": 0.001, "maximum": 100000 }, "angleDeg": { "type": "number", "description": "incline angle (° in [0 ; 90]) (°)", "minimum": 0, "maximum": 90 }, "mu": { "type": "number", "description": "coefficient of kinetic friction", "minimum": 0, "maximum": 5 } }, "additionalProperties": false }, "outputSchema": { "type": "object", "required": [ "downSlopeComponent", "normalForce", "frictionForce", "netForce", "acceleration" ], "properties": { "downSlopeComponent": { "type": "number", "description": "mg sinθ (N)" }, "normalForce": { "type": "number", "description": "N = mg cosθ (N)" }, "frictionForce": { "type": "number", "description": "f = μN (N)" }, "netForce": { "type": "number", "description": "F_net (N)" }, "acceleration": { "type": "number", "description": "a (m·s⁻², 2 d.p.)" } }, "additionalProperties": false }, "annotations": { "readOnlyHint": true, "idempotentHint": true, "openWorldHint": false }, "_house": { "endpoint": "/faculty/matric-nqf4/sci_inclined_plane", "feeSt": 1, "degree": "competency:matric-nqf4", "example": { "mass": 10, "angleDeg": 30, "mu": 0.2 } } }, { "name": "matric-nqf4.sci_impulse", "title": "Impulse and rebound (CDU-GEN-NSC-400)", "description": "Δp = m(v − u) for a rebound, the impulse magnitude, the average force, and the direction stated — never just the magnitude.", "inputSchema": { "type": "object", "required": [ "pan", "mass", "uToward", "vRebound", "contactTime" ], "properties": { "pan": { "type": "string", "description": "The student PAN — the degree must be held in one of its five slots", "pattern": "^[0-9 ]{16,19}$" }, "mass": { "type": "number", "description": "mass (kg) (kg)", "minimum": 0.0001, "maximum": 100000 }, "uToward": { "type": "number", "description": "approach velocity, toward the wall positive (m·s⁻¹) (m·s⁻¹)", "minimum": -1000, "maximum": 1000 }, "vRebound": { "type": "number", "description": "rebound velocity, same sign convention (m·s⁻¹) (m·s⁻¹)", "minimum": -1000, "maximum": 1000 }, "contactTime": { "type": "number", "description": "contact time (s, > 0) (s)", "minimum": 0.000001, "maximum": 60 } }, "additionalProperties": false }, "outputSchema": { "type": "object", "required": [ "momentumChange", "impulseMagnitude", "averageForceMagnitude", "direction" ], "properties": { "momentumChange": { "type": "number", "description": "Δp (kg·m·s⁻¹, signed)" }, "impulseMagnitude": { "type": "number", "description": "|J| (N·s)" }, "averageForceMagnitude": { "type": "number", "description": "|F| (N)" }, "direction": { "type": "string", "description": "away from the wall | toward the wall" } }, "additionalProperties": false }, "annotations": { "readOnlyHint": true, "idempotentHint": true, "openWorldHint": false }, "_house": { "endpoint": "/faculty/matric-nqf4/sci_impulse", "feeSt": 1, "degree": "competency:matric-nqf4", "example": { "mass": 0.2, "uToward": 4, "vRebound": -3, "contactTime": 0.01 } } }, { "name": "matric-nqf4.sci_work_energy", "title": "Work–energy theorem (CDU-GEN-NSC-400)", "description": "The net work on a vehicle from its change in kinetic energy: W_net = ΔKE = ½m(v² − u²).", "inputSchema": { "type": "object", "required": [ "pan", "mass", "uSpeed", "vSpeed" ], "properties": { "pan": { "type": "string", "description": "The student PAN — the degree must be held in one of its five slots", "pattern": "^[0-9 ]{16,19}$" }, "mass": { "type": "number", "description": "mass (kg) (kg)", "minimum": 0.001, "maximum": 1000000 }, "uSpeed": { "type": "number", "description": "initial speed (m·s⁻¹) (m·s⁻¹)", "minimum": 0, "maximum": 10000 }, "vSpeed": { "type": "number", "description": "final speed (m·s⁻¹) (m·s⁻¹)", "minimum": 0, "maximum": 10000 } }, "additionalProperties": false }, "outputSchema": { "type": "object", "required": [ "workJoule", "workKilojoule" ], "properties": { "workJoule": { "type": "number", "description": "W_net (J)" }, "workKilojoule": { "type": "number", "description": "W_net (kJ)" } }, "additionalProperties": false }, "annotations": { "readOnlyHint": true, "idempotentHint": true, "openWorldHint": false }, "_house": { "endpoint": "/faculty/matric-nqf4/sci_work_energy", "feeSt": 1, "degree": "competency:matric-nqf4", "example": { "mass": 1200, "uSpeed": 10, "vSpeed": 25 } } }, { "name": "matric-nqf4.sci_projectile", "title": "Vertical projectile motion (CDU-GEN-NSC-400)", "description": "Time to the top, maximum height and total flight time for a projectile launched straight up at u, constant g, no air resistance.", "inputSchema": { "type": "object", "required": [ "pan", "uUp" ], "properties": { "pan": { "type": "string", "description": "The student PAN — the degree must be held in one of its five slots", "pattern": "^[0-9 ]{16,19}$" }, "uUp": { "type": "number", "description": "launch speed upward (m·s⁻¹, > 0) (m·s⁻¹)", "minimum": 0.001, "maximum": 10000 } }, "additionalProperties": false }, "outputSchema": { "type": "object", "required": [ "timeUp", "maxHeight", "flightTime" ], "properties": { "timeUp": { "type": "number", "description": "t to the highest point (s, 3 d.p.)" }, "maxHeight": { "type": "number", "description": "h_max (m, 3 d.p.)" }, "flightTime": { "type": "number", "description": "total time back to launch height (s, 3 d.p.)" } }, "additionalProperties": false }, "annotations": { "readOnlyHint": true, "idempotentHint": true, "openWorldHint": false }, "_house": { "endpoint": "/faculty/matric-nqf4/sci_projectile", "feeSt": 1, "degree": "competency:matric-nqf4", "example": { "uUp": 20 } } }, { "name": "matric-nqf4.sci_doppler", "title": "Doppler effect (CDU-GEN-NSC-400)", "description": "The observed frequency for a source approaching or receding from a stationary listener; a source at or beyond the speed of sound is refused.", "inputSchema": { "type": "object", "required": [ "pan", "sourceFrequency", "sourceSpeed", "motion" ], "properties": { "pan": { "type": "string", "description": "The student PAN — the degree must be held in one of its five slots", "pattern": "^[0-9 ]{16,19}$" }, "sourceFrequency": { "type": "number", "description": "f_s (Hz) (Hz)", "minimum": 0.001, "maximum": 1000000 }, "sourceSpeed": { "type": "number", "description": "source speed (m·s⁻¹, < 340) (m·s⁻¹)", "minimum": 0, "maximum": 10000 }, "motion": { "type": "string", "description": "approaching or receding", "enum": [ "approaching", "receding" ] } }, "additionalProperties": false }, "outputSchema": { "type": "object", "required": [ "observedFrequency" ], "properties": { "observedFrequency": { "type": "number", "description": "f_L (Hz)" } }, "additionalProperties": false }, "annotations": { "readOnlyHint": true, "idempotentHint": true, "openWorldHint": false }, "_house": { "endpoint": "/faculty/matric-nqf4/sci_doppler", "feeSt": 1, "degree": "competency:matric-nqf4", "example": { "sourceFrequency": 500, "sourceSpeed": 20, "motion": "approaching" } } }, { "name": "matric-nqf4.sci_snell", "title": "Snell's law and the critical angle (CDU-GEN-NSC-400)", "description": "The refraction angle for n₁ sinθ₁ = n₂ sinθ₂ and the critical angle for the reverse passage; total internal reflection is refused by name.", "inputSchema": { "type": "object", "required": [ "pan", "n1", "n2", "theta1" ], "properties": { "pan": { "type": "string", "description": "The student PAN — the degree must be held in one of its five slots", "pattern": "^[0-9 ]{16,19}$" }, "n1": { "type": "number", "description": "refractive index of the first medium (> 0)", "minimum": 0.001, "maximum": 10 }, "n2": { "type": "number", "description": "refractive index of the second medium (> 0)", "minimum": 0.001, "maximum": 10 }, "theta1": { "type": "number", "description": "angle of incidence (°) (°)", "minimum": 0, "maximum": 90 } }, "additionalProperties": false }, "outputSchema": { "type": "object", "required": [ "theta2", "criticalAngle" ], "properties": { "theta2": { "type": "number", "description": "angle of refraction (°, 2 d.p.)" }, "criticalAngle": { "type": "number", "description": "critical angle for the denser-to-rarer passage (°, 2 d.p.)" } }, "additionalProperties": false }, "annotations": { "readOnlyHint": true, "idempotentHint": true, "openWorldHint": false }, "_house": { "endpoint": "/faculty/matric-nqf4/sci_snell", "feeSt": 1, "degree": "competency:matric-nqf4", "example": { "n1": 1, "n2": 1.5, "theta1": 30 } } }, { "name": "matric-nqf4.sci_coulomb", "title": "Coulomb's law (CDU-GEN-NSC-400)", "description": "The electrostatic force between two point charges, its magnitude and its nature (attractive or repulsive).", "inputSchema": { "type": "object", "required": [ "pan", "q1MicroC", "q2MicroC", "distance" ], "properties": { "pan": { "type": "string", "description": "The student PAN — the degree must be held in one of its five slots", "pattern": "^[0-9 ]{16,19}$" }, "q1MicroC": { "type": "number", "description": "Q₁ (μC) (μC)", "minimum": -1000000, "maximum": 1000000 }, "q2MicroC": { "type": "number", "description": "Q₂ (μC) (μC)", "minimum": -1000000, "maximum": 1000000 }, "distance": { "type": "number", "description": "separation r (m, > 0) (m)", "minimum": 0.000001, "maximum": 100000 } }, "additionalProperties": false }, "outputSchema": { "type": "object", "required": [ "forceNewton", "nature" ], "properties": { "forceNewton": { "type": "number", "description": "|F| (N)" }, "nature": { "type": "string", "description": "attractive | repulsive" } }, "additionalProperties": false }, "annotations": { "readOnlyHint": true, "idempotentHint": true, "openWorldHint": false }, "_house": { "endpoint": "/faculty/matric-nqf4/sci_coulomb", "feeSt": 1, "degree": "competency:matric-nqf4", "example": { "q1MicroC": 2, "q2MicroC": -3, "distance": 0.3 } } }, { "name": "matric-nqf4.sci_internal_resistance", "title": "EMF and internal resistance (CDU-GEN-NSC-400)", "description": "Current, terminal potential difference and the power split for ε = I(R + r), with the energy check εI = P_R + P_r.", "inputSchema": { "type": "object", "required": [ "pan", "emf", "internalResistance", "loadResistance" ], "properties": { "pan": { "type": "string", "description": "The student PAN — the degree must be held in one of its five slots", "pattern": "^[0-9 ]{16,19}$" }, "emf": { "type": "number", "description": "ε (V) (V)", "minimum": 0.001, "maximum": 1000000 }, "internalResistance": { "type": "number", "description": "r (Ω) (Ω)", "minimum": 0, "maximum": 1000000 }, "loadResistance": { "type": "number", "description": "R (Ω, > 0) (Ω)", "minimum": 0.001, "maximum": 1000000 } }, "additionalProperties": false }, "outputSchema": { "type": "object", "required": [ "current", "terminalPd", "powerLoad", "powerInternal" ], "properties": { "current": { "type": "number", "description": "I (A)" }, "terminalPd": { "type": "number", "description": "V = IR (V)" }, "powerLoad": { "type": "number", "description": "P_R = I²R (W)" }, "powerInternal": { "type": "number", "description": "P_r = I²r (W)" } }, "additionalProperties": false }, "annotations": { "readOnlyHint": true, "idempotentHint": true, "openWorldHint": false }, "_house": { "endpoint": "/faculty/matric-nqf4/sci_internal_resistance", "feeSt": 1, "degree": "competency:matric-nqf4", "example": { "emf": 12, "internalResistance": 1, "loadResistance": 5 } } }, { "name": "matric-nqf4.sci_faraday", "title": "Faraday's law (CDU-GEN-NSC-400)", "description": "The magnitude of the induced emf for a changing flux through N turns; the sign follows Lenz and is stated, not dropped.", "inputSchema": { "type": "object", "required": [ "pan", "turns", "fluxFrom", "fluxTo", "timeSeconds" ], "properties": { "pan": { "type": "string", "description": "The student PAN — the degree must be held in one of its five slots", "pattern": "^[0-9 ]{16,19}$" }, "turns": { "type": "number", "description": "N (whole turns, ≥ 1)", "minimum": 1, "maximum": 1000000 }, "fluxFrom": { "type": "number", "description": "initial flux (Wb) (Wb)", "minimum": -1000, "maximum": 1000 }, "fluxTo": { "type": "number", "description": "final flux (Wb) (Wb)", "minimum": -1000, "maximum": 1000 }, "timeSeconds": { "type": "number", "description": "Δt (s, > 0) (s)", "minimum": 0.000001, "maximum": 86400 } }, "additionalProperties": false }, "outputSchema": { "type": "object", "required": [ "emfMagnitude" ], "properties": { "emfMagnitude": { "type": "number", "description": "|ε| (V)" } }, "additionalProperties": false }, "annotations": { "readOnlyHint": true, "idempotentHint": true, "openWorldHint": false }, "_house": { "endpoint": "/faculty/matric-nqf4/sci_faraday", "feeSt": 1, "degree": "competency:matric-nqf4", "example": { "turns": 200, "fluxFrom": 0.02, "fluxTo": 0, "timeSeconds": 0.1 } } }, { "name": "matric-nqf4.sci_ideal_gas", "title": "The ideal gas law (CDU-GEN-NSC-400)", "description": "The pressure from pV = nRT, kelvin only — a Celsius temperature is refused with the conversion shown.", "inputSchema": { "type": "object", "required": [ "pan", "moles", "temperature", "volume" ], "properties": { "pan": { "type": "string", "description": "The student PAN — the degree must be held in one of its five slots", "pattern": "^[0-9 ]{16,19}$" }, "moles": { "type": "number", "description": "n (mol, ≥ 0) (mol)", "minimum": 0, "maximum": 1000000 }, "temperature": { "type": "number", "description": "T (kelvin, > 0) (K)", "minimum": -273, "maximum": 100000 }, "volume": { "type": "number", "description": "V (m³, > 0) (m³)", "minimum": 1e-7, "maximum": 1000000 }, "temperatureUnit": { "type": "string", "description": "K only — a Celsius value must be converted first", "enum": [ "K", "C" ], "default": "K" } }, "additionalProperties": false }, "outputSchema": { "type": "object", "required": [ "pressurePa", "pressureKPa" ], "properties": { "pressurePa": { "type": "number", "description": "p (Pa)" }, "pressureKPa": { "type": "number", "description": "p (kPa, 1 d.p.)" } }, "additionalProperties": false }, "annotations": { "readOnlyHint": true, "idempotentHint": true, "openWorldHint": false }, "_house": { "endpoint": "/faculty/matric-nqf4/sci_ideal_gas", "feeSt": 1, "degree": "competency:matric-nqf4", "example": { "moles": 2, "temperature": 300, "volume": 0.05, "temperatureUnit": "K" } } }, { "name": "matric-nqf4.sci_stoichiometry", "title": "Stoichiometry — 2H₂ + O₂ → 2H₂O (CDU-GEN-NSC-400)", "description": "The limiting reagent and the mass of water formed, with the mole ratios shown (working molar masses: H₂ 2, O₂ 32, H₂O 18 g·mol⁻¹).", "inputSchema": { "type": "object", "required": [ "pan", "massH2", "massO2" ], "properties": { "pan": { "type": "string", "description": "The student PAN — the degree must be held in one of its five slots", "pattern": "^[0-9 ]{16,19}$" }, "massH2": { "type": "number", "description": "mass of H₂ (g, ≥ 0) (g)", "minimum": 0, "maximum": 1000000 }, "massO2": { "type": "number", "description": "mass of O₂ (g, ≥ 0) (g)", "minimum": 0, "maximum": 1000000 } }, "additionalProperties": false }, "outputSchema": { "type": "object", "required": [ "molH2", "molO2", "limiting", "massWater" ], "properties": { "molH2": { "type": "number", "description": "n(H₂) (mol)" }, "molO2": { "type": "number", "description": "n(O₂) (mol)" }, "limiting": { "type": "string", "description": "H2 | O2 | stoichiometric" }, "massWater": { "type": "number", "description": "mass of H₂O formed (g)" } }, "additionalProperties": false }, "annotations": { "readOnlyHint": true, "idempotentHint": true, "openWorldHint": false }, "_house": { "endpoint": "/faculty/matric-nqf4/sci_stoichiometry", "feeSt": 1, "degree": "competency:matric-nqf4", "example": { "massH2": 4, "massO2": 32 } } }, { "name": "matric-nqf4.sci_concentration", "title": "Concentration (CDU-GEN-NSC-400)", "description": "c = n/V with the volume converted from cm³ to dm³ first.", "inputSchema": { "type": "object", "required": [ "pan", "moles", "volumeCm3" ], "properties": { "pan": { "type": "string", "description": "The student PAN — the degree must be held in one of its five slots", "pattern": "^[0-9 ]{16,19}$" }, "moles": { "type": "number", "description": "n (mol, ≥ 0) (mol)", "minimum": 0, "maximum": 1000000 }, "volumeCm3": { "type": "number", "description": "V (cm³, > 0) (cm³)", "minimum": 0.001, "maximum": 100000000 } }, "additionalProperties": false }, "outputSchema": { "type": "object", "required": [ "concentration" ], "properties": { "concentration": { "type": "number", "description": "c (mol·dm⁻³)" } }, "additionalProperties": false }, "annotations": { "readOnlyHint": true, "idempotentHint": true, "openWorldHint": false }, "_house": { "endpoint": "/faculty/matric-nqf4/sci_concentration", "feeSt": 1, "degree": "competency:matric-nqf4", "example": { "moles": 0.5, "volumeCm3": 250 } } }, { "name": "matric-nqf4.sci_ph", "title": "pH of a strong acid (CDU-GEN-NSC-400)", "description": "pH = −log[H⁺] for a fully dissociated monoprotic acid; a weak acid without Ka is refused with that reason.", "inputSchema": { "type": "object", "required": [ "pan", "concentration", "acidStrength" ], "properties": { "pan": { "type": "string", "description": "The student PAN — the degree must be held in one of its five slots", "pattern": "^[0-9 ]{16,19}$" }, "concentration": { "type": "number", "description": "[acid] (mol·dm⁻³, > 0) (mol·dm⁻³)", "minimum": 1e-10, "maximum": 20 }, "acidStrength": { "type": "string", "description": "strong (full dissociation) or weak (needs Ka)", "enum": [ "strong", "weak" ] } }, "additionalProperties": false }, "outputSchema": { "type": "object", "required": [ "pH" ], "properties": { "pH": { "type": "number", "description": "pH (2 d.p.)" } }, "additionalProperties": false }, "annotations": { "readOnlyHint": true, "idempotentHint": true, "openWorldHint": false }, "_house": { "endpoint": "/faculty/matric-nqf4/sci_ph", "feeSt": 1, "degree": "competency:matric-nqf4", "example": { "concentration": 0.01, "acidStrength": "strong" } } }, { "name": "matric-nqf4.sci_equilibrium_kc", "title": "Equilibrium constant — N₂ + 3H₂ ⇌ 2NH₃ (CDU-GEN-NSC-400)", "description": "Kc = [NH₃]²/([N₂][H₂]³) from the equilibrium concentrations; a zero denominator is refused.", "inputSchema": { "type": "object", "required": [ "pan", "concN2", "concH2", "concNH3" ], "properties": { "pan": { "type": "string", "description": "The student PAN — the degree must be held in one of its five slots", "pattern": "^[0-9 ]{16,19}$" }, "concN2": { "type": "number", "description": "[N₂] (mol·dm⁻³, ≥ 0) (mol·dm⁻³)", "minimum": 0, "maximum": 1000 }, "concH2": { "type": "number", "description": "[H₂] (mol·dm⁻³, ≥ 0) (mol·dm⁻³)", "minimum": 0, "maximum": 1000 }, "concNH3": { "type": "number", "description": "[NH₃] (mol·dm⁻³, ≥ 0) (mol·dm⁻³)", "minimum": 0, "maximum": 1000 } }, "additionalProperties": false }, "outputSchema": { "type": "object", "required": [ "kc" ], "properties": { "kc": { "type": "number", "description": "Kc (4 d.p.)" } }, "additionalProperties": false }, "annotations": { "readOnlyHint": true, "idempotentHint": true, "openWorldHint": false }, "_house": { "endpoint": "/faculty/matric-nqf4/sci_equilibrium_kc", "feeSt": 1, "degree": "competency:matric-nqf4", "example": { "concN2": 0.5, "concH2": 1.5, "concNH3": 1 } } }, { "name": "matric-nqf4.sci_cell_potential", "title": "Standard cell potential (CDU-GEN-NSC-400)", "description": "E°cell = E°cathode − E°anode; a negative answer is reported as non-spontaneous as written, never called an error.", "inputSchema": { "type": "object", "required": [ "pan", "eCathode", "eAnode" ], "properties": { "pan": { "type": "string", "description": "The student PAN — the degree must be held in one of its five slots", "pattern": "^[0-9 ]{16,19}$" }, "eCathode": { "type": "number", "description": "E° of the cathode half-cell (V) (V)", "minimum": -10, "maximum": 10 }, "eAnode": { "type": "number", "description": "E° of the anode half-cell (V) (V)", "minimum": -10, "maximum": 10 } }, "additionalProperties": false }, "outputSchema": { "type": "object", "required": [ "cellPotential", "spontaneity" ], "properties": { "cellPotential": { "type": "number", "description": "E°cell (V)" }, "spontaneity": { "type": "string", "description": "spontaneous as written | non-spontaneous as written" } }, "additionalProperties": false }, "annotations": { "readOnlyHint": true, "idempotentHint": true, "openWorldHint": false }, "_house": { "endpoint": "/faculty/matric-nqf4/sci_cell_potential", "feeSt": 1, "degree": "competency:matric-nqf4", "example": { "eCathode": 0.34, "eAnode": -0.76 } } }, { "name": "matric-nqf4.sci_photon_energy", "title": "Photon energy (CDU-GEN-NSC-400)", "description": "E = hc/λ in joule and electron-volt for a given wavelength; λ ≤ 0 is refused.", "inputSchema": { "type": "object", "required": [ "pan", "wavelengthNm" ], "properties": { "pan": { "type": "string", "description": "The student PAN — the degree must be held in one of its five slots", "pattern": "^[0-9 ]{16,19}$" }, "wavelengthNm": { "type": "number", "description": "λ (nm, > 0) (nm)", "minimum": 0.001, "maximum": 100000000 } }, "additionalProperties": false }, "outputSchema": { "type": "object", "required": [ "energyJoule", "energyEv" ], "properties": { "energyJoule": { "type": "number", "description": "E (J)" }, "energyEv": { "type": "number", "description": "E (eV, 2 d.p.)" } }, "additionalProperties": false }, "annotations": { "readOnlyHint": true, "idempotentHint": true, "openWorldHint": false }, "_house": { "endpoint": "/faculty/matric-nqf4/sci_photon_energy", "feeSt": 1, "degree": "competency:matric-nqf4", "example": { "wavelengthNm": 500 } } }, { "name": "matric-nqf4.sci_practical_data", "title": "Practical data exercise (offline) (CDU-GEN-NSC-400)", "description": "The gradient of extension against load, the mean of repeated readings and their spread — over SUPPLIED readings; no experiment was performed.", "inputSchema": { "type": "object", "required": [ "pan", "loads", "extensions", "repeats" ], "properties": { "pan": { "type": "string", "description": "The student PAN — the degree must be held in one of its five slots", "pattern": "^[0-9 ]{16,19}$" }, "loads": { "type": "array", "description": "applied loads (N), in order", "items": { "type": "number" } }, "extensions": { "type": "array", "description": "measured extensions (cm), one per load", "items": { "type": "number" } }, "repeats": { "type": "array", "description": "repeated readings of the final extension (cm)", "items": { "type": "number" } } }, "additionalProperties": false }, "outputSchema": { "type": "object", "required": [ "gradient", "meanRepeat", "spread" ], "properties": { "gradient": { "type": "number", "description": "Δ(extension)/Δ(load) (cm·N⁻¹)" }, "meanRepeat": { "type": "number", "description": "mean of the repeated readings (cm)" }, "spread": { "type": "number", "description": "range of the repeated readings (cm)" } }, "additionalProperties": false }, "annotations": { "readOnlyHint": true, "idempotentHint": true, "openWorldHint": false }, "_house": { "endpoint": "/faculty/matric-nqf4/sci_practical_data", "feeSt": 1, "degree": "competency:matric-nqf4", "example": { "loads": [ 0, 2, 4, 6, 8 ], "extensions": [ 0, 0.8, 1.6, 2.4, 3.2 ], "repeats": [ 3.1, 3.2, 3.3 ] } } }, { "name": "matric-nqf4.lang_final_mark", "title": "Weighted final mark (CDU-GEN-NSC-400)", "description": "The final subject mark from the school-based assessment and the examination mark under the stated weighting — or the examination mark alone on the adult (no-SBA) route.", "inputSchema": { "type": "object", "required": [ "pan", "sbaMark", "examMark", "route" ], "properties": { "pan": { "type": "string", "description": "The student PAN — the degree must be held in one of its five slots", "pattern": "^[0-9 ]{16,19}$" }, "sbaMark": { "type": "number", "description": "school-based assessment mark (percent)", "minimum": 0, "maximum": 100 }, "examMark": { "type": "number", "description": "examination mark (percent)", "minimum": 0, "maximum": 100 }, "route": { "type": "string", "description": "nsc (25/75) or amended (exam only)", "enum": [ "nsc", "amended" ] } }, "additionalProperties": false }, "outputSchema": { "type": "object", "required": [ "finalMark" ], "properties": { "finalMark": { "type": "number", "description": "the final mark (percent)" } }, "additionalProperties": false }, "annotations": { "readOnlyHint": true, "idempotentHint": true, "openWorldHint": false }, "_house": { "endpoint": "/faculty/matric-nqf4/lang_final_mark", "feeSt": 1, "degree": "competency:matric-nqf4", "example": { "sbaMark": 60, "examMark": 68, "route": "nsc" } } }, { "name": "matric-nqf4.lang_reading_statistic", "title": "Reading statistic on a fixed text (CDU-GEN-NSC-400)", "description": "Word count, sentence count and average word length of a supplied passage — a deterministic text measure, never a model-marked essay.", "inputSchema": { "type": "object", "required": [ "pan", "text" ], "properties": { "pan": { "type": "string", "description": "The student PAN — the degree must be held in one of its five slots", "pattern": "^[0-9 ]{16,19}$" }, "text": { "type": "string", "description": "the passage (non-empty)" } }, "additionalProperties": false }, "outputSchema": { "type": "object", "required": [ "words", "sentences", "averageWordLength" ], "properties": { "words": { "type": "number", "description": "word count" }, "sentences": { "type": "number", "description": "sentence count" }, "averageWordLength": { "type": "number", "description": "letters per word (2 d.p.)" } }, "additionalProperties": false }, "annotations": { "readOnlyHint": true, "idempotentHint": true, "openWorldHint": false }, "_house": { "endpoint": "/faculty/matric-nqf4/lang_reading_statistic", "feeSt": 1, "degree": "competency:matric-nqf4", "example": { "text": "The sun rose over the valley. Every learner opened a book. Reading builds the mind." } } }, { "name": "matric-nqf4.mathlit_tariff", "title": "Stepped tariff (CDU-GEN-NSC-400)", "description": "The cost of consumption under a two-block stepped tariff, block by block.", "inputSchema": { "type": "object", "required": [ "pan", "unitsUsed", "blockOneLimit", "blockOneRate", "blockTwoRate" ], "properties": { "pan": { "type": "string", "description": "The student PAN — the degree must be held in one of its five slots", "pattern": "^[0-9 ]{16,19}$" }, "unitsUsed": { "type": "number", "description": "units consumed (≥ 0)", "minimum": 0, "maximum": 1000000 }, "blockOneLimit": { "type": "number", "description": "units in the first block", "minimum": 0.001, "maximum": 1000000 }, "blockOneRate": { "type": "number", "description": "rate per unit in block one", "minimum": 0, "maximum": 100000 }, "blockTwoRate": { "type": "number", "description": "rate per unit above the limit", "minimum": 0, "maximum": 100000 } }, "additionalProperties": false }, "outputSchema": { "type": "object", "required": [ "totalCost" ], "properties": { "totalCost": { "type": "number", "description": "the total cost (2 d.p.)" } }, "additionalProperties": false }, "annotations": { "readOnlyHint": true, "idempotentHint": true, "openWorldHint": false }, "_house": { "endpoint": "/faculty/matric-nqf4/mathlit_tariff", "feeSt": 1, "degree": "competency:matric-nqf4", "example": { "unitsUsed": 150, "blockOneLimit": 100, "blockOneRate": 1.5, "blockTwoRate": 2.1 } } }, { "name": "matric-nqf4.lo_sba_total", "title": "School-based assessment total (CDU-GEN-NSC-400)", "description": "The Life Orientation SBA percentage from task marks and task totals — 100% school-based, no external paper (working reconstruction).", "inputSchema": { "type": "object", "required": [ "pan", "taskMarks", "taskTotals" ], "properties": { "pan": { "type": "string", "description": "The student PAN — the degree must be held in one of its five slots", "pattern": "^[0-9 ]{16,19}$" }, "taskMarks": { "type": "array", "description": "mark achieved per task", "items": { "type": "number" } }, "taskTotals": { "type": "array", "description": "maximum mark per task", "items": { "type": "number" } } }, "additionalProperties": false }, "outputSchema": { "type": "object", "required": [ "sbaPercent" ], "properties": { "sbaPercent": { "type": "number", "description": "the SBA percentage (2 d.p.)" } }, "additionalProperties": false }, "annotations": { "readOnlyHint": true, "idempotentHint": true, "openWorldHint": false }, "_house": { "endpoint": "/faculty/matric-nqf4/lo_sba_total", "feeSt": 1, "degree": "competency:matric-nqf4", "example": { "taskMarks": [ 38, 42, 71, 85 ], "taskTotals": [ 50, 50, 80, 100 ] } } }, { "name": "matric-nqf4.lifesci_punnett", "title": "Punnett square — monohybrid cross (CDU-GEN-NSC-400)", "description": "The genotype and phenotype ratios of a monohybrid cross, by enumerating the four gamete combinations.", "inputSchema": { "type": "object", "required": [ "pan", "parentOne", "parentTwo" ], "properties": { "pan": { "type": "string", "description": "The student PAN — the degree must be held in one of its five slots", "pattern": "^[0-9 ]{16,19}$" }, "parentOne": { "type": "string", "description": "first parent genotype", "enum": [ "AA", "Aa", "aa" ] }, "parentTwo": { "type": "string", "description": "second parent genotype", "enum": [ "AA", "Aa", "aa" ] } }, "additionalProperties": false }, "outputSchema": { "type": "object", "required": [ "genotypeRatio", "dominantFraction" ], "properties": { "genotypeRatio": { "type": "string", "description": "AA : Aa : aa" }, "dominantFraction": { "type": "number", "description": "fraction showing the dominant phenotype" } }, "additionalProperties": false }, "annotations": { "readOnlyHint": true, "idempotentHint": true, "openWorldHint": false }, "_house": { "endpoint": "/faculty/matric-nqf4/lifesci_punnett", "feeSt": 1, "degree": "competency:matric-nqf4", "example": { "parentOne": "Aa", "parentTwo": "Aa" } } }, { "name": "matric-nqf4.agrisci_npk", "title": "Fertiliser nutrient mass (CDU-GEN-NSC-400)", "description": "The mass of N, P and K in a bag from its stated percentages.", "inputSchema": { "type": "object", "required": [ "pan", "bagMassKg", "nPercent", "pPercent", "kPercent" ], "properties": { "pan": { "type": "string", "description": "The student PAN — the degree must be held in one of its five slots", "pattern": "^[0-9 ]{16,19}$" }, "bagMassKg": { "type": "number", "description": "bag mass (kg, > 0) (kg)", "minimum": 0.001, "maximum": 100000 }, "nPercent": { "type": "number", "description": "N (%)", "minimum": 0, "maximum": 100 }, "pPercent": { "type": "number", "description": "P (%)", "minimum": 0, "maximum": 100 }, "kPercent": { "type": "number", "description": "K (%)", "minimum": 0, "maximum": 100 } }, "additionalProperties": false }, "outputSchema": { "type": "object", "required": [ "massN", "massP", "massK" ], "properties": { "massN": { "type": "number", "description": "kg of N" }, "massP": { "type": "number", "description": "kg of P" }, "massK": { "type": "number", "description": "kg of K" } }, "additionalProperties": false }, "annotations": { "readOnlyHint": true, "idempotentHint": true, "openWorldHint": false }, "_house": { "endpoint": "/faculty/matric-nqf4/agrisci_npk", "feeSt": 1, "degree": "competency:matric-nqf4", "example": { "bagMassKg": 50, "nPercent": 10, "pPercent": 6, "kPercent": 4 } } }, { "name": "matric-nqf4.acc_depreciation", "title": "Depreciation (CDU-GEN-NSC-400)", "description": "Depreciation for a chosen year and the carrying value, on the straight-line or the diminishing-balance method.", "inputSchema": { "type": "object", "required": [ "pan", "cost", "ratePercent", "year", "method" ], "properties": { "pan": { "type": "string", "description": "The student PAN — the degree must be held in one of its five slots", "pattern": "^[0-9 ]{16,19}$" }, "cost": { "type": "number", "description": "cost price (> 0)", "minimum": 0.01, "maximum": 1000000000 }, "ratePercent": { "type": "number", "description": "annual rate (%, 0–100)", "minimum": 0, "maximum": 100 }, "year": { "type": "number", "description": "which year (1-based whole number)", "minimum": 1, "maximum": 100 }, "method": { "type": "string", "description": "straight-line or diminishing-balance", "enum": [ "straight-line", "diminishing-balance" ] } }, "additionalProperties": false }, "outputSchema": { "type": "object", "required": [ "depreciationForYear", "carryingValue" ], "properties": { "depreciationForYear": { "type": "number", "description": "depreciation in that year (2 d.p.)" }, "carryingValue": { "type": "number", "description": "carrying value at the end of that year (2 d.p.)" } }, "additionalProperties": false }, "annotations": { "readOnlyHint": true, "idempotentHint": true, "openWorldHint": false }, "_house": { "endpoint": "/faculty/matric-nqf4/acc_depreciation", "feeSt": 1, "degree": "competency:matric-nqf4", "example": { "cost": 100000, "ratePercent": 20, "year": 3, "method": "diminishing-balance" } } }, { "name": "matric-nqf4.bus_breakeven", "title": "Break-even quantity (CDU-GEN-NSC-400)", "description": "Fixed cost over the contribution per unit; a selling price at or below the variable cost is refused because no volume can break even.", "inputSchema": { "type": "object", "required": [ "pan", "fixedCost", "sellingPrice", "variableCost" ], "properties": { "pan": { "type": "string", "description": "The student PAN — the degree must be held in one of its five slots", "pattern": "^[0-9 ]{16,19}$" }, "fixedCost": { "type": "number", "description": "fixed cost per period (≥ 0)", "minimum": 0, "maximum": 1000000000 }, "sellingPrice": { "type": "number", "description": "selling price per unit (> 0)", "minimum": 0.01, "maximum": 1000000 }, "variableCost": { "type": "number", "description": "variable cost per unit (≥ 0)", "minimum": 0, "maximum": 1000000 } }, "additionalProperties": false }, "outputSchema": { "type": "object", "required": [ "breakEvenUnits" ], "properties": { "breakEvenUnits": { "type": "number", "description": "units to break even (rounded up)" } }, "additionalProperties": false }, "annotations": { "readOnlyHint": true, "idempotentHint": true, "openWorldHint": false }, "_house": { "endpoint": "/faculty/matric-nqf4/bus_breakeven", "feeSt": 1, "degree": "competency:matric-nqf4", "example": { "fixedCost": 60000, "sellingPrice": 50, "variableCost": 30 } } }, { "name": "matric-nqf4.econ_inflation", "title": "Inflation rate from two index values (CDU-GEN-NSC-400)", "description": "The percentage change of a price index between two readings.", "inputSchema": { "type": "object", "required": [ "pan", "indexOld", "indexNew" ], "properties": { "pan": { "type": "string", "description": "The student PAN — the degree must be held in one of its five slots", "pattern": "^[0-9 ]{16,19}$" }, "indexOld": { "type": "number", "description": "earlier index value (> 0)", "minimum": 0.001, "maximum": 1000000 }, "indexNew": { "type": "number", "description": "later index value (≥ 0)", "minimum": 0, "maximum": 1000000 } }, "additionalProperties": false }, "outputSchema": { "type": "object", "required": [ "inflationPercent" ], "properties": { "inflationPercent": { "type": "number", "description": "the rate (%, 2 d.p.)" } }, "additionalProperties": false }, "annotations": { "readOnlyHint": true, "idempotentHint": true, "openWorldHint": false }, "_house": { "endpoint": "/faculty/matric-nqf4/econ_inflation", "feeSt": 1, "degree": "competency:matric-nqf4", "example": { "indexOld": 120, "indexNew": 129 } } }, { "name": "matric-nqf4.geo_map_scale", "title": "Map scale and gradient (CDU-GEN-NSC-400)", "description": "The ground distance from a map measurement and a 1 : n scale, and the gradient as 1 : (run/rise).", "inputSchema": { "type": "object", "required": [ "pan", "mapDistanceCm", "scaleDenominator", "riseM" ], "properties": { "pan": { "type": "string", "description": "The student PAN — the degree must be held in one of its five slots", "pattern": "^[0-9 ]{16,19}$" }, "mapDistanceCm": { "type": "number", "description": "measured map distance (cm, > 0) (cm)", "minimum": 0.001, "maximum": 10000 }, "scaleDenominator": { "type": "number", "description": "the n of 1 : n (> 0)", "minimum": 1, "maximum": 10000000 }, "riseM": { "type": "number", "description": "height gained over the distance (m, > 0) (m)", "minimum": 0.001, "maximum": 100000 } }, "additionalProperties": false }, "outputSchema": { "type": "object", "required": [ "groundDistanceKm", "gradientRun" ], "properties": { "groundDistanceKm": { "type": "number", "description": "ground distance (km, 3 d.p.)" }, "gradientRun": { "type": "number", "description": "the n of gradient 1 : n (1 d.p.)" } }, "additionalProperties": false }, "annotations": { "readOnlyHint": true, "idempotentHint": true, "openWorldHint": false }, "_house": { "endpoint": "/faculty/matric-nqf4/geo_map_scale", "feeSt": 1, "degree": "competency:matric-nqf4", "example": { "mapDistanceCm": 4.5, "scaleDenominator": 50000, "riseM": 120 } } }, { "name": "matric-nqf4.hist_timeline", "title": "Timeline span (CDU-GEN-NSC-400)", "description": "The span in years between two dated events; an end year before the start year is refused.", "inputSchema": { "type": "object", "required": [ "pan", "startYear", "endYear" ], "properties": { "pan": { "type": "string", "description": "The student PAN — the degree must be held in one of its five slots", "pattern": "^[0-9 ]{16,19}$" }, "startYear": { "type": "number", "description": "the earlier year", "minimum": -3000, "maximum": 3000 }, "endYear": { "type": "number", "description": "the later year", "minimum": -3000, "maximum": 3000 } }, "additionalProperties": false }, "outputSchema": { "type": "object", "required": [ "spanYears" ], "properties": { "spanYears": { "type": "number", "description": "years between the two" } }, "additionalProperties": false }, "annotations": { "readOnlyHint": true, "idempotentHint": true, "openWorldHint": false }, "_house": { "endpoint": "/faculty/matric-nqf4/hist_timeline", "feeSt": 1, "degree": "competency:matric-nqf4", "example": { "startYear": 1948, "endYear": 1994 } } }, { "name": "matric-nqf4.rel_text_compare", "title": "Fixed-text comparison statistic (CDU-GEN-NSC-400)", "description": "The shared and unique word counts of two supplied passages — a deterministic comparison, never a model-marked essay.", "inputSchema": { "type": "object", "required": [ "pan", "textA", "textB" ], "properties": { "pan": { "type": "string", "description": "The student PAN — the degree must be held in one of its five slots", "pattern": "^[0-9 ]{16,19}$" }, "textA": { "type": "string", "description": "first passage" }, "textB": { "type": "string", "description": "second passage" } }, "additionalProperties": false }, "outputSchema": { "type": "object", "required": [ "sharedWords", "uniqueToA", "uniqueToB" ], "properties": { "sharedWords": { "type": "number", "description": "distinct words in both" }, "uniqueToA": { "type": "number", "description": "distinct words only in A" }, "uniqueToB": { "type": "number", "description": "distinct words only in B" } }, "additionalProperties": false }, "annotations": { "readOnlyHint": true, "idempotentHint": true, "openWorldHint": false }, "_house": { "endpoint": "/faculty/matric-nqf4/rel_text_compare", "feeSt": 1, "degree": "competency:matric-nqf4", "example": { "textA": "Compassion and justice guide the community.", "textB": "Justice and mercy guide the household." } } }, { "name": "matric-nqf4.tour_currency", "title": "Currency conversion and occupancy (CDU-GEN-NSC-400)", "description": "A currency conversion at a stated rate, and the occupancy percentage of a lodge.", "inputSchema": { "type": "object", "required": [ "pan", "amount", "rate", "roomsSold", "roomsAvailable" ], "properties": { "pan": { "type": "string", "description": "The student PAN — the degree must be held in one of its five slots", "pattern": "^[0-9 ]{16,19}$" }, "amount": { "type": "number", "description": "amount in the source currency (≥ 0)", "minimum": 0, "maximum": 1000000000 }, "rate": { "type": "number", "description": "units of the target currency per source unit (> 0)", "minimum": 0.000001, "maximum": 1000000 }, "roomsSold": { "type": "number", "description": "rooms sold", "minimum": 0, "maximum": 1000000 }, "roomsAvailable": { "type": "number", "description": "rooms available (> 0)", "minimum": 1, "maximum": 1000000 } }, "additionalProperties": false }, "outputSchema": { "type": "object", "required": [ "converted", "occupancyPercent" ], "properties": { "converted": { "type": "number", "description": "converted amount (2 d.p.)" }, "occupancyPercent": { "type": "number", "description": "occupancy (%, 1 d.p.)" } }, "additionalProperties": false }, "annotations": { "readOnlyHint": true, "idempotentHint": true, "openWorldHint": false }, "_house": { "endpoint": "/faculty/matric-nqf4/tour_currency", "feeSt": 1, "degree": "competency:matric-nqf4", "example": { "amount": 1000, "rate": 18.5, "roomsSold": 45, "roomsAvailable": 60 } } }, { "name": "matric-nqf4.cons_unit_price", "title": "Unit price and recipe scaling (CDU-GEN-NSC-400)", "description": "The price per unit of a pack and the factor to scale a recipe between serving counts.", "inputSchema": { "type": "object", "required": [ "pan", "packPrice", "packSize", "servingsHave", "servingsNeed" ], "properties": { "pan": { "type": "string", "description": "The student PAN — the degree must be held in one of its five slots", "pattern": "^[0-9 ]{16,19}$" }, "packPrice": { "type": "number", "description": "price of the pack (≥ 0)", "minimum": 0, "maximum": 1000000 }, "packSize": { "type": "number", "description": "units in the pack (> 0)", "minimum": 0.001, "maximum": 1000000 }, "servingsHave": { "type": "number", "description": "servings the recipe makes (> 0)", "minimum": 0.001, "maximum": 100000 }, "servingsNeed": { "type": "number", "description": "servings needed (> 0)", "minimum": 0.001, "maximum": 100000 } }, "additionalProperties": false }, "outputSchema": { "type": "object", "required": [ "unitPrice", "scaleFactor" ], "properties": { "unitPrice": { "type": "number", "description": "price per unit (2 d.p.)" }, "scaleFactor": { "type": "number", "description": "multiply every ingredient by this (2 d.p.)" } }, "additionalProperties": false }, "annotations": { "readOnlyHint": true, "idempotentHint": true, "openWorldHint": false }, "_house": { "endpoint": "/faculty/matric-nqf4/cons_unit_price", "feeSt": 1, "degree": "competency:matric-nqf4", "example": { "packPrice": 36, "packSize": 6, "servingsHave": 4, "servingsNeed": 10 } } }, { "name": "matric-nqf4.hosp_portion_cost", "title": "Portion cost (CDU-GEN-NSC-400)", "description": "The cost per portion from a batch cost and a portion count.", "inputSchema": { "type": "object", "required": [ "pan", "batchCost", "portions" ], "properties": { "pan": { "type": "string", "description": "The student PAN — the degree must be held in one of its five slots", "pattern": "^[0-9 ]{16,19}$" }, "batchCost": { "type": "number", "description": "cost of the batch (≥ 0)", "minimum": 0, "maximum": 1000000 }, "portions": { "type": "number", "description": "portions from the batch (whole, ≥ 1)", "minimum": 1, "maximum": 100000 } }, "additionalProperties": false }, "outputSchema": { "type": "object", "required": [ "costPerPortion" ], "properties": { "costPerPortion": { "type": "number", "description": "cost per portion (2 d.p.)" } }, "additionalProperties": false }, "annotations": { "readOnlyHint": true, "idempotentHint": true, "openWorldHint": false }, "_house": { "endpoint": "/faculty/matric-nqf4/hosp_portion_cost", "feeSt": 1, "degree": "competency:matric-nqf4", "example": { "batchCost": 480, "portions": 32 } } }, { "name": "matric-nqf4.cat_filesize", "title": "File-size total (CDU-GEN-NSC-400)", "description": "The total of a list of file sizes in KB, converted to MB at 1024 KB per MB.", "inputSchema": { "type": "object", "required": [ "pan", "fileSizesKb" ], "properties": { "pan": { "type": "string", "description": "The student PAN — the degree must be held in one of its five slots", "pattern": "^[0-9 ]{16,19}$" }, "fileSizesKb": { "type": "array", "description": "file sizes (KB, each ≥ 0)", "items": { "type": "number" } } }, "additionalProperties": false }, "outputSchema": { "type": "object", "required": [ "totalKb", "totalMb" ], "properties": { "totalKb": { "type": "number", "description": "total (KB)" }, "totalMb": { "type": "number", "description": "total (MB, 3 d.p.)" } }, "additionalProperties": false }, "annotations": { "readOnlyHint": true, "idempotentHint": true, "openWorldHint": false }, "_house": { "endpoint": "/faculty/matric-nqf4/cat_filesize", "feeSt": 1, "degree": "competency:matric-nqf4", "example": { "fileSizesKb": [ 512, 256, 1280 ] } } }, { "name": "matric-nqf4.it_binary", "title": "Binary and decimal conversion (CDU-GEN-NSC-400)", "description": "The binary representation of a whole number (0–65535) and the round-trip back to decimal.", "inputSchema": { "type": "object", "required": [ "pan", "value" ], "properties": { "pan": { "type": "string", "description": "The student PAN — the degree must be held in one of its five slots", "pattern": "^[0-9 ]{16,19}$" }, "value": { "type": "number", "description": "whole number 0–65535", "minimum": 0, "maximum": 65535 } }, "additionalProperties": false }, "outputSchema": { "type": "object", "required": [ "binary", "bits", "roundTrip" ], "properties": { "binary": { "type": "string", "description": "binary digits" }, "bits": { "type": "number", "description": "how many bits" }, "roundTrip": { "type": "number", "description": "parsed back to decimal — must equal the input" } }, "additionalProperties": false }, "annotations": { "readOnlyHint": true, "idempotentHint": true, "openWorldHint": false }, "_house": { "endpoint": "/faculty/matric-nqf4/it_binary", "feeSt": 1, "degree": "competency:matric-nqf4", "example": { "value": 156 } } }, { "name": "matric-nqf4.egd_scale", "title": "Scale drawing length (CDU-GEN-NSC-400)", "description": "The actual length from a drawing measurement and a 1 : n scale.", "inputSchema": { "type": "object", "required": [ "pan", "drawingMm", "scaleDenominator" ], "properties": { "pan": { "type": "string", "description": "The student PAN — the degree must be held in one of its five slots", "pattern": "^[0-9 ]{16,19}$" }, "drawingMm": { "type": "number", "description": "measured length on the drawing (mm, > 0) (mm)", "minimum": 0.001, "maximum": 100000 }, "scaleDenominator": { "type": "number", "description": "the n of 1 : n (> 0)", "minimum": 0.001, "maximum": 1000000 } }, "additionalProperties": false }, "outputSchema": { "type": "object", "required": [ "actualMm", "actualM" ], "properties": { "actualMm": { "type": "number", "description": "actual length (mm)" }, "actualM": { "type": "number", "description": "actual length (m, 3 d.p.)" } }, "additionalProperties": false }, "annotations": { "readOnlyHint": true, "idempotentHint": true, "openWorldHint": false }, "_house": { "endpoint": "/faculty/matric-nqf4/egd_scale", "feeSt": 1, "degree": "competency:matric-nqf4", "example": { "drawingMm": 45, "scaleDenominator": 20 } } }, { "name": "matric-nqf4.civtech_load", "title": "Load per area (CDU-GEN-NSC-400)", "description": "The distributed load on a slab: force over area.", "inputSchema": { "type": "object", "required": [ "pan", "loadKn", "areaM2" ], "properties": { "pan": { "type": "string", "description": "The student PAN — the degree must be held in one of its five slots", "pattern": "^[0-9 ]{16,19}$" }, "loadKn": { "type": "number", "description": "total load (kN, ≥ 0) (kN)", "minimum": 0, "maximum": 1000000 }, "areaM2": { "type": "number", "description": "area (m², > 0) (m²)", "minimum": 0.0001, "maximum": 1000000 } }, "additionalProperties": false }, "outputSchema": { "type": "object", "required": [ "loadPerArea" ], "properties": { "loadPerArea": { "type": "number", "description": "kN/m² (3 d.p.)" } }, "additionalProperties": false }, "annotations": { "readOnlyHint": true, "idempotentHint": true, "openWorldHint": false }, "_house": { "endpoint": "/faculty/matric-nqf4/civtech_load", "feeSt": 1, "degree": "competency:matric-nqf4", "example": { "loadKn": 12, "areaM2": 2.5 } } }, { "name": "matric-nqf4.mechtech_gear", "title": "Gear ratio and torque (CDU-GEN-NSC-400)", "description": "The velocity ratio of a gear pair and the ideal output torque.", "inputSchema": { "type": "object", "required": [ "pan", "teethDriver", "teethDriven", "inputTorque" ], "properties": { "pan": { "type": "string", "description": "The student PAN — the degree must be held in one of its five slots", "pattern": "^[0-9 ]{16,19}$" }, "teethDriver": { "type": "number", "description": "teeth on the driver (whole, ≥ 1)", "minimum": 1, "maximum": 10000 }, "teethDriven": { "type": "number", "description": "teeth on the driven gear (whole, ≥ 1)", "minimum": 1, "maximum": 10000 }, "inputTorque": { "type": "number", "description": "input torque (N·m, ≥ 0) (N·m)", "minimum": 0, "maximum": 1000000 } }, "additionalProperties": false }, "outputSchema": { "type": "object", "required": [ "gearRatio", "outputTorque" ], "properties": { "gearRatio": { "type": "number", "description": "driven/driver (3 d.p.)" }, "outputTorque": { "type": "number", "description": "ideal output torque (N·m, 3 d.p.)" } }, "additionalProperties": false }, "annotations": { "readOnlyHint": true, "idempotentHint": true, "openWorldHint": false }, "_house": { "endpoint": "/faculty/matric-nqf4/mechtech_gear", "feeSt": 1, "degree": "competency:matric-nqf4", "example": { "teethDriver": 20, "teethDriven": 60, "inputTorque": 50 } } }, { "name": "matric-nqf4.electech_resistance", "title": "Series and parallel resistance (CDU-GEN-NSC-400)", "description": "The total resistance of a set of resistors in series or in parallel; a zero resistor in parallel is refused.", "inputSchema": { "type": "object", "required": [ "pan", "resistors", "arrangement" ], "properties": { "pan": { "type": "string", "description": "The student PAN — the degree must be held in one of its five slots", "pattern": "^[0-9 ]{16,19}$" }, "resistors": { "type": "array", "description": "resistances (Ω, each > 0)", "items": { "type": "number" } }, "arrangement": { "type": "string", "description": "series or parallel", "enum": [ "series", "parallel" ] } }, "additionalProperties": false }, "outputSchema": { "type": "object", "required": [ "totalResistance" ], "properties": { "totalResistance": { "type": "number", "description": "total (Ω, 3 d.p.)" } }, "additionalProperties": false }, "annotations": { "readOnlyHint": true, "idempotentHint": true, "openWorldHint": false }, "_house": { "endpoint": "/faculty/matric-nqf4/electech_resistance", "feeSt": 1, "degree": "competency:matric-nqf4", "example": { "resistors": [ 10, 20, 30 ], "arrangement": "series" } } }, { "name": "matric-nqf4.art_colour_mix", "title": "Colour-mix ratio and frame area (CDU-GEN-NSC-400)", "description": "The fraction of each pigment in a stated mix, and the area of a picture frame border.", "inputSchema": { "type": "object", "required": [ "pan", "partsA", "partsB", "innerWidthCm", "innerHeightCm", "borderCm" ], "properties": { "pan": { "type": "string", "description": "The student PAN — the degree must be held in one of its five slots", "pattern": "^[0-9 ]{16,19}$" }, "partsA": { "type": "number", "description": "parts of the first pigment (> 0)", "minimum": 0.001, "maximum": 1000 }, "partsB": { "type": "number", "description": "parts of the second pigment (> 0)", "minimum": 0.001, "maximum": 1000 }, "innerWidthCm": { "type": "number", "description": "picture width (cm, > 0) (cm)", "minimum": 0.001, "maximum": 10000 }, "innerHeightCm": { "type": "number", "description": "picture height (cm, > 0) (cm)", "minimum": 0.001, "maximum": 10000 }, "borderCm": { "type": "number", "description": "frame border width (cm, ≥ 0) (cm)", "minimum": 0, "maximum": 1000 } }, "additionalProperties": false }, "outputSchema": { "type": "object", "required": [ "fractionA", "frameAreaCm2" ], "properties": { "fractionA": { "type": "number", "description": "fraction of pigment A (4 d.p.)" }, "frameAreaCm2": { "type": "number", "description": "area of the border (cm²)" } }, "additionalProperties": false }, "annotations": { "readOnlyHint": true, "idempotentHint": true, "openWorldHint": false }, "_house": { "endpoint": "/faculty/matric-nqf4/art_colour_mix", "feeSt": 1, "degree": "competency:matric-nqf4", "example": { "partsA": 2, "partsB": 3, "innerWidthCm": 40, "innerHeightCm": 30, "borderCm": 5 } } }, { "name": "matric-nqf4.music_interval", "title": "Interval frequency ratio (CDU-GEN-NSC-400)", "description": "The just-intonation frequency ratio of a named interval and the upper note from a base frequency.", "inputSchema": { "type": "object", "required": [ "pan", 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