Conquest Designer University

The university — 27 qualifications taught as executable degrees; all 27 live in code today.

Faculty of General Studies · CDU-GEN-NSC-400 · NSC · v1.0.0

Senior Certificate (Amended) — exam-readiness programme (NQF 4 matric)

The complete matric subject catalogue on one row: the eleven official languages at three levels, Mathematics and Physical Sciences at full CAPS Grade 12 depth with independently recomputed worked solutions, and every other Umalusi subject with its own deterministic worked-reference unit. The house proves exam readiness; it does not register candidates, mark scripts that count, or issue the Senior Certificate — those are the roles of the examining authorities.

Lineage

  • Conquest Designer University, 2026 — authored from the offline coursework base (an unofficial working reconstruction of CAPS and the Umalusi qualification); a readiness mapping — the DBE administers the examination and Umalusi certifies it, never the house

Final research project

Matriculate Again in 24 Hours — exam readiness across the complete Umalusi subject catalogue, proven against deterministic reference engines

Syllabus

  1. Languages: the eleven official languages at Home / First Additional / Second Additional level
  2. Mathematics (flawless focus): algebra and equations; patterns, sequences and series; functions and graphs; calculus; probability; finance; analytical geometry; trigonometry; Euclidean geometry and measurement; statistics
  3. Physical Sciences (flawless focus): mechanics; waves, sound and light; electricity and magnetism; matter and materials; chemical change; chemical systems
  4. The full elective catalogue: Mathematical Literacy, Life Orientation, Life Sciences, Agricultural Sciences, Accounting, Business Studies, Economics, Geography, History, Religion Studies, Tourism, Consumer Studies, Hospitality Studies, the technology subjects, the arts subjects and the named additional electives
  5. The qualification rules: the 7-subject package and the adult second-chance route, the working assessment splits, the pass rules and the designated-subject list — all working reconstructions with verify-before-claim items

Reference

Quadratic formula
x = (−b ± √(b² − 4ac)) / (2a), a ≠ 0; Δ = b² − 4ac
Sequences
Tₙ = a + (n − 1)d; Sₙ = n/2 [2a + (n − 1)d]; Tₙ = arⁿ⁻¹; S∞ = a/(1 − r), |r| < 1
Calculus
f′(x) = limₕ→₀ [f(x+h) − f(x)]/h; d/dx axⁿ = naxⁿ⁻¹
Trigonometry
sin(A ± B) = sinA cosB ± cosA sinB; sine, cosine and area rules
Mechanics
F_net = ma; f = μN; F_net Δt = Δp; W_net = ΔKE; g = 9,8 m·s⁻²
Waves and light
v = fλ; f_L = v/(v ∓ v_s)·f_s; n₁ sinθ₁ = n₂ sinθ₂; E = hf = hc/λ
Chemistry
pV = nRT; c = n/V; pH = −log[H⁺]; Kc from equilibrium concentrations; E°cell = E°cathode − E°anode
Assessment split (working)
25% school-based assessment, 75% examination; Life Orientation 100% school-based; the adult route has no school-based component — working reconstruction, each a verify item
What this row never claims
registration, accreditation, an examination centre, or the issuing of a Senior Certificate — readiness only

Units

Quadratic equation by factorising · Quadratic equation by the formula · Nature of the roots · Simultaneous linear/quadratic system · Arithmetic sequence and series · Geometric sequence and series · Infinite geometric series · Sigma notation · The parabola · Inverse of a linear function · Exponential and logarithmic equations · Differentiation from first principles · Stationary points of a cubic · Optimisation — the largest rectangle · Compound-angle identity · General solution of a trig equation · Tangent to a circle · Probability from a contingency table · Probability without replacement · Compound interest · Descriptive statistics · Least-squares regression line · Newton's second law — horizontal motion · Inclined plane with friction · Impulse and rebound · Work–energy theorem · Vertical projectile motion · Doppler effect · Snell's law and the critical angle · Coulomb's law · EMF and internal resistance · Faraday's law · The ideal gas law · Stoichiometry — 2H₂ + O₂ → 2H₂O · Concentration · pH of a strong acid · Equilibrium constant — N₂ + 3H₂ ⇌ 2NH₃ · Standard cell potential · Photon energy · Practical data exercise (offline) · Weighted final mark · Reading statistic on a fixed text · Stepped tariff · School-based assessment total · Punnett square — monohybrid cross · Fertiliser nutrient mass · Depreciation · Break-even quantity · Inflation rate from two index values · Map scale and gradient · Timeline span · Fixed-text comparison statistic · Currency conversion and occupancy · Unit price and recipe scaling · Portion cost · File-size total · Binary and decimal conversion · Scale drawing length · Load per area · Gear ratio and torque · Series and parallel resistance · Colour-mix ratio and frame area · Interval frequency ratio · Lighting-cue duration total · Tempo and bar count

Role when narrated: You are a patient matric tutor working one unit at a time. State the formula, substitute every number, carry the units, and end with the check a learner can redo by hand. You never claim the house registers candidates or issues certificates; readiness is the product.

Quadratic equation by factorising · maths_quadratic_factorise

Try with the example

The roots of ax² + bx + c = 0 by factorisation, with the discriminant, the sum and the product of the roots checked.

Reference: CAPS Grade 12 Mathematics, worked reference M1 (offline reconstruction); quadratic formula and nature of roots

Returns

rootA
the smaller root
rootB
the larger root
discriminant
Δ = b² − 4ac
sumOfRoots
−b/a
productOfRoots
c/a

The example

{
  "a": 1,
  "b": -5,
  "c": 6
}

Agents: POST /faculty/matric-nqf4/maths_quadratic_factorise with JSON {pan, …inputs} and the x-402-payment header. Manifest.

Quadratic equation by the formula · maths_quadratic_formula

Try with the example

The roots of ax² + bx + c = 0 by x = (−b ± √Δ)/(2a), every substitution shown.

Reference: CAPS Grade 12 Mathematics, worked reference M2 (offline reconstruction); x = (−b ± √(b² − 4ac)) / (2a), a ≠ 0

Returns

rootA
the smaller root
rootB
the larger root
discriminant
Δ = b² − 4ac

The example

{
  "a": 2,
  "b": 3,
  "c": -2
}

Agents: POST /faculty/matric-nqf4/maths_quadratic_formula with JSON {pan, …inputs} and the x-402-payment header. Manifest.

Nature of the roots · maths_nature_of_roots

Try with the example

Whether ax² + bx + c = 0 has two distinct real, equal real, or non-real roots, from the discriminant alone.

Reference: CAPS Grade 12 Mathematics, worked reference M3 (offline reconstruction); Δ > 0 distinct real, Δ = 0 equal real, Δ < 0 non-real

Returns

discriminant
Δ = b² − 4ac
nature
two distinct real roots | equal real roots | non-real (complex) roots

The example

{
  "a": 1,
  "b": 2,
  "c": 5
}

Agents: POST /faculty/matric-nqf4/maths_nature_of_roots with JSON {pan, …inputs} and the x-402-payment header. Manifest.

Simultaneous linear/quadratic system · maths_simultaneous

Try with the example

Where the line y = mx + k meets the parabola y = x² + px + q — equate, solve, substitute back.

Reference: CAPS Grade 12 Mathematics, worked reference M4 (offline reconstruction); equate the two expressions for y and solve the quadratic

Returns

x1
smaller x of intersection
y1
its y
x2
larger x of intersection
y2
its y

The example

{
  "p": -3,
  "q": 2,
  "m": 2,
  "k": -4
}

Agents: POST /faculty/matric-nqf4/maths_simultaneous with JSON {pan, …inputs} and the x-402-payment header. Manifest.

Arithmetic sequence and series · maths_arithmetic_sequence

Try with the example

Tₙ = a + (n − 1)d and Sₙ = n/2 [2a + (n − 1)d], with the Sₙ = n/2 (a + l) cross-check.

Reference: CAPS Grade 12 Mathematics, worked reference M5 (offline reconstruction); Tₙ = a + (n − 1)d; Sₙ = n/2 [2a + (n − 1)d]

Returns

tn
the nth term
sn
the sum of the first n terms

The example

{
  "a": 4,
  "d": 3,
  "n": 20
}

Agents: POST /faculty/matric-nqf4/maths_arithmetic_sequence with JSON {pan, …inputs} and the x-402-payment header. Manifest.

Geometric sequence and series · maths_geometric_sequence

Try with the example

Tₙ = arⁿ⁻¹ and Sₙ = a(rⁿ − 1)/(r − 1), refusing r = 1 where the formula is undefined.

Reference: CAPS Grade 12 Mathematics, worked reference M6 (offline reconstruction); Tₙ = arⁿ⁻¹; Sₙ = a(rⁿ − 1)/(r − 1), r ≠ 1

Returns

tn
the nth term
sn
the sum of the first n terms

The example

{
  "a": 2,
  "r": 3,
  "n": 5
}

Agents: POST /faculty/matric-nqf4/maths_geometric_sequence with JSON {pan, …inputs} and the x-402-payment header. Manifest.

Infinite geometric series · maths_geometric_infinite

Try with the example

S∞ = a/(1 − r) for |r| < 1; a ratio at or beyond 1 in magnitude is refused because the sum does not converge.

Reference: CAPS Grade 12 Mathematics, worked reference M6 (offline reconstruction); S∞ = a/(1 − r), only for |r| < 1

Returns

sInfinity
the infinite sum

The example

{
  "a": 8,
  "r": 0.5
}

Agents: POST /faculty/matric-nqf4/maths_geometric_infinite with JSON {pan, …inputs} and the x-402-payment header. Manifest.

Sigma notation · maths_sigma_sum

Try with the example

Σₖ₌₁ⁿ (pk + q) evaluated with Σk = n(n + 1)/2 and Σ1 = n.

Reference: CAPS Grade 12 Mathematics, worked reference M7 (offline reconstruction); Σₖ₌₁ⁿ k = n(n+1)/2

Returns

sum
the value of the sum

The example

{
  "p": 2,
  "q": 1,
  "n": 10
}

Agents: POST /faculty/matric-nqf4/maths_sigma_sum with JSON {pan, …inputs} and the x-402-payment header. Manifest.

The parabola · maths_parabola

Try with the example

Turning point, axis of symmetry, intercepts and range of f(x) = ax² + bx + c.

Reference: CAPS Grade 12 Mathematics, worked reference M8 (offline reconstruction); turning point at x = −b/(2a)

Returns

tpX
x of the turning point
tpY
y of the turning point
xIntercept1
smaller x-intercept
xIntercept2
larger x-intercept
yIntercept
f(0)
range
the range, e.g. y ≥ −1

The example

{
  "a": 1,
  "b": -4,
  "c": 3
}

Agents: POST /faculty/matric-nqf4/maths_parabola with JSON {pan, …inputs} and the x-402-payment header. Manifest.

Inverse of a linear function · maths_inverse_linear

Try with the example

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.

Reference: CAPS Grade 12 Mathematics, worked reference M8 (offline reconstruction); y = ax + b ⇒ g⁻¹(x) = (x − b)/a, a ≠ 0

Returns

gOfX
g(x)
inverseOfGOfX
g⁻¹(g(x)) — must be x
fOfGOfX
f(g(x)) with the given parabola

The example

{
  "a": 2,
  "b": 1,
  "x": 2,
  "pa": 1,
  "pb": -4,
  "pc": 3
}

Agents: POST /faculty/matric-nqf4/maths_inverse_linear with JSON {pan, …inputs} and the x-402-payment header. Manifest.

Exponential and logarithmic equations · maths_exponential_log

Try with the example

Solve baseˣ = value: x = log_base(value), refusing non-positive arguments and degenerate bases.

Reference: CAPS Grade 12 Mathematics, worked reference M9 (offline reconstruction); logarithm defined only for argument > 0 and base > 0, base ≠ 1

Returns

exponent
x with baseˣ = value

The example

{
  "base": 2,
  "value": 16
}

Agents: POST /faculty/matric-nqf4/maths_exponential_log with JSON {pan, …inputs} and the x-402-payment header. Manifest.

Differentiation from first principles · maths_first_principles

Try with the example

f′(x) of f(x) = ax² + bx from the limit definition, the derivative at a point, and the tangent's equation there.

Reference: CAPS Grade 12 Mathematics, worked reference M10 (offline reconstruction); f′(x) = limₕ→₀ [f(x+h) − f(x)]/h

Returns

derivativeAt
f′(x0)
fAt
f(x0)
tangentSlope
gradient of the tangent
tangentIntercept
c of the tangent y = mx + c

The example

{
  "a": 1,
  "b": 3,
  "x0": 2
}

Agents: POST /faculty/matric-nqf4/maths_first_principles with JSON {pan, …inputs} and the x-402-payment header. Manifest.

Stationary points of a cubic · maths_cubic_stationary

Try with the example

The stationary points of f(x) = x³ + bx² + cx + d, classified by the second derivative, with the point of inflection.

Reference: CAPS Grade 12 Mathematics, worked reference M11 (offline reconstruction); f′(x) = 0 at stationary points; f″ classifies them

Returns

x1
first stationary x (smaller)
y1
f(x1)
type1
local maximum | local minimum
x2
second stationary x (larger)
y2
f(x2)
type2
local maximum | local minimum
inflectionX
x of the point of inflection

The example

{
  "b": -6,
  "c": 9,
  "d": 1
}

Agents: POST /faculty/matric-nqf4/maths_cubic_stationary with JSON {pan, …inputs} and the x-402-payment header. Manifest.

Optimisation — the largest rectangle · maths_optimisation

Try with the example

The rectangle of greatest area for a fixed perimeter, by differentiating A(x) = x(P/2 − x).

Reference: CAPS Grade 12 Mathematics, worked reference M12 (offline reconstruction); A′(x) = 0 at the maximum, A″ < 0 confirms it

Returns

sideX
the optimal width (m)
sideY
the optimal height (m)
maxArea
the maximal area (m²)

The example

{
  "perimeter": 40
}

Agents: POST /faculty/matric-nqf4/maths_optimisation with JSON {pan, …inputs} and the x-402-payment header. Manifest.

Compound-angle identity · maths_compound_angle

Try with the example

sin(A + B) = sinA cosB + cosA sinB, every substitution shown — sin 75° exactly and numerically.

Reference: CAPS Grade 12 Mathematics, worked reference M13 (offline reconstruction); sin(A ± B) = sinA cosB ± cosA sinB

Returns

sinAB
sin(A + B)

The example

{
  "angleA": 45,
  "angleB": 30
}

Agents: POST /faculty/matric-nqf4/maths_compound_angle with JSON {pan, …inputs} and the x-402-payment header. Manifest.

General solution of a trig equation · maths_trig_general_solution

Try with the example

Solve p·sinθ = q on [0° ; 360°] with the general solution, refusing |q/p| > 1 because sine never leaves [−1 ; 1].

Reference: CAPS Grade 12 Mathematics, worked reference M14 (offline reconstruction); sinθ = k ⇒ θ = α + 360°k or 180° − α + 360°k

Returns

alpha
the reference angle (°)
solution1
first solution in [0 ; 360] (°)
solution2
second solution in [0 ; 360] (°)

The example

{
  "p": 2,
  "q": 1
}

Agents: POST /faculty/matric-nqf4/maths_trig_general_solution with JSON {pan, …inputs} and the x-402-payment header. Manifest.

Tangent to a circle · maths_circle_tangent

Try with the example

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.

Reference: CAPS Grade 12 Mathematics, worked reference M15 (offline reconstruction); gradient of tangent = −1/(gradient of radius)

Returns

tangentGradient
gradient of the tangent
lineA
A of Ax + By + C = 0
lineB
B of Ax + By + C = 0
lineC
C of Ax + By + C = 0

The example

{
  "a": 2,
  "b": -1,
  "r": 5,
  "px": 5,
  "py": 3
}

Agents: POST /faculty/matric-nqf4/maths_circle_tangent with JSON {pan, …inputs} and the x-402-payment header. Manifest.

Probability from a contingency table · maths_probability_table

Try with the example

P(A | B) and P(neither) for two subject choices over one class, refusing any probability outside [0 ; 1].

Reference: CAPS Grade 12 Mathematics, worked reference M16 (offline reconstruction); P(A∪B) = P(A) + P(B) − P(A∩B)

Returns

pAGivenB
P(A | B)
pNeither
P(neither)

The example

{
  "total": 100,
  "nA": 60,
  "nB": 40,
  "nBoth": 30
}

Agents: POST /faculty/matric-nqf4/maths_probability_table with JSON {pan, …inputs} and the x-402-payment header. Manifest.

Probability without replacement · maths_probability_draws

Try with the example

P(both red) for two draws without replacement from a mixed set of counters.

Reference: CAPS Grade 12 Mathematics, worked reference M16 (offline reconstruction); dependent events multiply along the branch

Returns

pBothRed
P(first red and second red)

The example

{
  "red": 5,
  "blue": 3,
  "green": 2
}

Agents: POST /faculty/matric-nqf4/maths_probability_draws with JSON {pan, …inputs} and the x-402-payment header. Manifest.

Compound interest · maths_compound_interest

Try with the example

A = P(1 + i)ⁿ and the interest earned, each substitution shown.

Reference: CAPS Grade 12 Mathematics, worked reference M17 (offline reconstruction); A = P(1 + i)ⁿ, i > −1

Returns

amount
A after n years
interestEarned
A − P

The example

{
  "principal": 10000,
  "ratePercent": 8,
  "years": 3
}

Agents: POST /faculty/matric-nqf4/maths_compound_interest with JSON {pan, …inputs} and the x-402-payment header. Manifest.

Descriptive statistics · maths_statistics

Try with the example

Mean, population variance and standard deviation, the five-number summary (inclusive quartiles), IQR and the outlier fences.

Reference: CAPS Grade 12 Mathematics, worked reference M18 (offline reconstruction); σ = √(Σ(x − x̄)²/n); quartiles include the median in each half

Returns

mean
x̄
variance
σ² (population)
standardDeviation
σ, 4 d.p.
min
minimum
q1
lower quartile
median
median
q3
upper quartile
max
maximum
iqr
Q3 − Q1
outliers
how many values lie outside the 1.5·IQR fences

The example

{
  "data": [
    2,
    4,
    6,
    8,
    10
  ]
}

Agents: POST /faculty/matric-nqf4/maths_statistics with JSON {pan, …inputs} and the x-402-payment header. Manifest.

Least-squares regression line · maths_regression_line

Try with the example

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.

Reference: CAPS Grade 12 Mathematics, worked reference M19 (offline reconstruction); r is interpreted, never used as proof of causation

Returns

slope
b
intercept
a

The example

{
  "r": 0.8,
  "sigmaX": 2,
  "sigmaY": 3,
  "meanX": 10,
  "meanY": 20
}

Agents: POST /faculty/matric-nqf4/maths_regression_line with JSON {pan, …inputs} and the x-402-payment header. Manifest.

Newton's second law — horizontal motion · sci_newton_second_law

Try with the example

The acceleration of a block under an applied force and kinetic friction: a = F_net/m.

Reference: CAPS Grade 12 Physical Sciences, worked reference P1 (offline reconstruction); F_net = ma

Returns

netForce
F_net (N)
acceleration
a (m·s⁻²)

The example

{
  "mass": 5,
  "appliedForce": 20,
  "friction": 5
}

Agents: POST /faculty/matric-nqf4/sci_newton_second_law with JSON {pan, …inputs} and the x-402-payment header. Manifest.

Inclined plane with friction · sci_inclined_plane

Try with the example

The acceleration of a block sliding down a rough incline: components, the normal, μN, F_net, a — every substitution shown.

Reference: CAPS Grade 12 Physical Sciences, worked reference P2 (offline reconstruction); f = μN; up the slope is positive for the friction on a sliding block

Returns

downSlopeComponent
mg sinθ (N)
normalForce
N = mg cosθ (N)
frictionForce
f = μN (N)
netForce
F_net (N)
acceleration
a (m·s⁻², 2 d.p.)

The example

{
  "mass": 10,
  "angleDeg": 30,
  "mu": 0.2
}

Agents: POST /faculty/matric-nqf4/sci_inclined_plane with JSON {pan, …inputs} and the x-402-payment header. Manifest.

Impulse and rebound · sci_impulse

Try with the example

Δp = m(v − u) for a rebound, the impulse magnitude, the average force, and the direction stated — never just the magnitude.

Reference: CAPS Grade 12 Physical Sciences, worked reference P3 (offline reconstruction); F_net Δt = Δp; toward the wall is positive

Returns

momentumChange
Δp (kg·m·s⁻¹, signed)
impulseMagnitude
|J| (N·s)
averageForceMagnitude
|F| (N)
direction
away from the wall | toward the wall

The example

{
  "mass": 0.2,
  "uToward": 4,
  "vRebound": -3,
  "contactTime": 0.01
}

Agents: POST /faculty/matric-nqf4/sci_impulse with JSON {pan, …inputs} and the x-402-payment header. Manifest.

Work–energy theorem · sci_work_energy

Try with the example

The net work on a vehicle from its change in kinetic energy: W_net = ΔKE = ½m(v² − u²).

Reference: CAPS Grade 12 Physical Sciences, worked reference P4 (offline reconstruction); W_net = ΔKE

Returns

workJoule
W_net (J)
workKilojoule
W_net (kJ)

The example

{
  "mass": 1200,
  "uSpeed": 10,
  "vSpeed": 25
}

Agents: POST /faculty/matric-nqf4/sci_work_energy with JSON {pan, …inputs} and the x-402-payment header. Manifest.

Vertical projectile motion · sci_projectile

Try with the example

Time to the top, maximum height and total flight time for a projectile launched straight up at u, constant g, no air resistance.

Reference: CAPS Grade 12 Physical Sciences, worked reference P5 (offline reconstruction); t_up = u/g; h_max = u²/(2g)

Returns

timeUp
t to the highest point (s, 3 d.p.)
maxHeight
h_max (m, 3 d.p.)
flightTime
total time back to launch height (s, 3 d.p.)

The example

{
  "uUp": 20
}

Agents: POST /faculty/matric-nqf4/sci_projectile with JSON {pan, …inputs} and the x-402-payment header. Manifest.

Doppler effect · sci_doppler

Try with the example

The observed frequency for a source approaching or receding from a stationary listener; a source at or beyond the speed of sound is refused.

Reference: CAPS Grade 12 Physical Sciences, worked reference P6 (offline reconstruction); f_L = v/(v ∓ v_s) · f_s; v = 340 m·s⁻¹ working value

Returns

observedFrequency
f_L (Hz)

The example

{
  "sourceFrequency": 500,
  "sourceSpeed": 20,
  "motion": "approaching"
}

Agents: POST /faculty/matric-nqf4/sci_doppler with JSON {pan, …inputs} and the x-402-payment header. Manifest.

Snell's law and the critical angle · sci_snell

Try with the example

The refraction angle for n₁ sinθ₁ = n₂ sinθ₂ and the critical angle for the reverse passage; total internal reflection is refused by name.

Reference: CAPS Grade 12 Physical Sciences, worked reference P7 (offline reconstruction); sinθ_c = n₁/n₂ for the denser-to-rarer passage

Returns

theta2
angle of refraction (°, 2 d.p.)
criticalAngle
critical angle for the denser-to-rarer passage (°, 2 d.p.)

The example

{
  "n1": 1,
  "n2": 1.5,
  "theta1": 30
}

Agents: POST /faculty/matric-nqf4/sci_snell with JSON {pan, …inputs} and the x-402-payment header. Manifest.

Coulomb's law · sci_coulomb

Try with the example

The electrostatic force between two point charges, its magnitude and its nature (attractive or repulsive).

Reference: CAPS Grade 12 Physical Sciences, worked reference P8 (offline reconstruction); F = k|Q₁Q₂|/r², k = 9,0 × 10⁹ N·m²·C⁻²

Returns

forceNewton
|F| (N)
nature
attractive | repulsive

The example

{
  "q1MicroC": 2,
  "q2MicroC": -3,
  "distance": 0.3
}

Agents: POST /faculty/matric-nqf4/sci_coulomb with JSON {pan, …inputs} and the x-402-payment header. Manifest.

EMF and internal resistance · sci_internal_resistance

Try with the example

Current, terminal potential difference and the power split for ε = I(R + r), with the energy check εI = P_R + P_r.

Reference: CAPS Grade 12 Physical Sciences, worked reference P9 (offline reconstruction); ε = I(R + r); P = I²R

Returns

current
I (A)
terminalPd
V = IR (V)
powerLoad
P_R = I²R (W)
powerInternal
P_r = I²r (W)

The example

{
  "emf": 12,
  "internalResistance": 1,
  "loadResistance": 5
}

Agents: POST /faculty/matric-nqf4/sci_internal_resistance with JSON {pan, …inputs} and the x-402-payment header. Manifest.

Faraday's law · sci_faraday

Try with the example

The magnitude of the induced emf for a changing flux through N turns; the sign follows Lenz and is stated, not dropped.

Reference: CAPS Grade 12 Physical Sciences, worked reference P10 (offline reconstruction); ε = −NΔΦ/Δt

Returns

emfMagnitude
|ε| (V)

The example

{
  "turns": 200,
  "fluxFrom": 0.02,
  "fluxTo": 0,
  "timeSeconds": 0.1
}

Agents: POST /faculty/matric-nqf4/sci_faraday with JSON {pan, …inputs} and the x-402-payment header. Manifest.

The ideal gas law · sci_ideal_gas

Try with the example

The pressure from pV = nRT, kelvin only — a Celsius temperature is refused with the conversion shown.

Reference: CAPS Grade 12 Physical Sciences, worked reference P11 (offline reconstruction); pV = nRT, R = 8,314 J·K⁻¹·mol⁻¹

Returns

pressurePa
p (Pa)
pressureKPa
p (kPa, 1 d.p.)

The example

{
  "moles": 2,
  "temperature": 300,
  "volume": 0.05,
  "temperatureUnit": "K"
}

Agents: POST /faculty/matric-nqf4/sci_ideal_gas with JSON {pan, …inputs} and the x-402-payment header. Manifest.

Stoichiometry — 2H₂ + O₂ → 2H₂O · sci_stoichiometry

Try with the example

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).

Reference: CAPS Grade 12 Physical Sciences, worked reference P12 (offline reconstruction); the limiting reagent fixes the product

Returns

molH2
n(H₂) (mol)
molO2
n(O₂) (mol)
limiting
H2 | O2 | stoichiometric
massWater
mass of H₂O formed (g)

The example

{
  "massH2": 4,
  "massO2": 32
}

Agents: POST /faculty/matric-nqf4/sci_stoichiometry with JSON {pan, …inputs} and the x-402-payment header. Manifest.

Concentration · sci_concentration

Try with the example

c = n/V with the volume converted from cm³ to dm³ first.

Reference: CAPS Grade 12 Physical Sciences, worked reference P13 (offline reconstruction); c = n/V, V in dm³

Returns

concentration
c (mol·dm⁻³)

The example

{
  "moles": 0.5,
  "volumeCm3": 250
}

Agents: POST /faculty/matric-nqf4/sci_concentration with JSON {pan, …inputs} and the x-402-payment header. Manifest.

pH of a strong acid · sci_ph

Try with the example

pH = −log[H⁺] for a fully dissociated monoprotic acid; a weak acid without Ka is refused with that reason.

Reference: CAPS Grade 12 Physical Sciences, worked reference P14 (offline reconstruction); pH = −log[H⁺]

Returns

pH
pH (2 d.p.)

The example

{
  "concentration": 0.01,
  "acidStrength": "strong"
}

Agents: POST /faculty/matric-nqf4/sci_ph with JSON {pan, …inputs} and the x-402-payment header. Manifest.

Equilibrium constant — N₂ + 3H₂ ⇌ 2NH₃ · sci_equilibrium_kc

Try with the example

Kc = [NH₃]²/([N₂][H₂]³) from the equilibrium concentrations; a zero denominator is refused.

Reference: CAPS Grade 12 Physical Sciences, worked reference P15 (offline reconstruction); Kc carries no unit in the house's convention

Returns

kc
Kc (4 d.p.)

The example

{
  "concN2": 0.5,
  "concH2": 1.5,
  "concNH3": 1
}

Agents: POST /faculty/matric-nqf4/sci_equilibrium_kc with JSON {pan, …inputs} and the x-402-payment header. Manifest.

Standard cell potential · sci_cell_potential

Try with the example

E°cell = E°cathode − E°anode; a negative answer is reported as non-spontaneous as written, never called an error.

Reference: CAPS Grade 12 Physical Sciences, worked reference P16 (offline reconstruction); working electrode potentials Zn²⁺/Zn −0,76 V, Cu²⁺/Cu +0,34 V

Returns

cellPotential
E°cell (V)
spontaneity
spontaneous as written | non-spontaneous as written

The example

{
  "eCathode": 0.34,
  "eAnode": -0.76
}

Agents: POST /faculty/matric-nqf4/sci_cell_potential with JSON {pan, …inputs} and the x-402-payment header. Manifest.

Photon energy · sci_photon_energy

Try with the example

E = hc/λ in joule and electron-volt for a given wavelength; λ ≤ 0 is refused.

Reference: CAPS Grade 12 Physical Sciences, worked reference P17 (offline reconstruction); h = 6,63 × 10⁻³⁴ J·s, c = 3,0 × 10⁸ m·s⁻¹, e = 1,6 × 10⁻¹⁹ C

Returns

energyJoule
E (J)
energyEv
E (eV, 2 d.p.)

The example

{
  "wavelengthNm": 500
}

Agents: POST /faculty/matric-nqf4/sci_photon_energy with JSON {pan, …inputs} and the x-402-payment header. Manifest.

Practical data exercise (offline) · sci_practical_data

Try with the example

The gradient of extension against load, the mean of repeated readings and their spread — over SUPPLIED readings; no experiment was performed.

Reference: CAPS Grade 12 Physical Sciences, worked reference P18 (offline reconstruction); the practical is a data exercise, not a performed experiment

Returns

gradient
Δ(extension)/Δ(load) (cm·N⁻¹)
meanRepeat
mean of the repeated readings (cm)
spread
range of the repeated readings (cm)

The example

{
  "loads": [
    0,
    2,
    4,
    6,
    8
  ],
  "extensions": [
    0,
    0.8,
    1.6,
    2.4,
    3.2
  ],
  "repeats": [
    3.1,
    3.2,
    3.3
  ]
}

Agents: POST /faculty/matric-nqf4/sci_practical_data with JSON {pan, …inputs} and the x-402-payment header. Manifest.

Weighted final mark · lang_final_mark

Try with the example

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.

Reference: Umalusi/NSC subject catalogue, worked reference (offline reconstruction); working split 25% SBA / 75% exam for exam subjects; the Senior Certificate (Amended) route has no SBA (verify item §12)

Returns

finalMark
the final mark (percent)

The example

{
  "sbaMark": 60,
  "examMark": 68,
  "route": "nsc"
}

Agents: POST /faculty/matric-nqf4/lang_final_mark with JSON {pan, …inputs} and the x-402-payment header. Manifest.

Reading statistic on a fixed text · lang_reading_statistic

Example filled in — consult below

Word count, sentence count and average word length of a supplied passage — a deterministic text measure, never a model-marked essay.

Reference: Umalusi/NSC subject catalogue, worked reference (offline reconstruction); a fixed-text statistic (languages row of §4)

Returns

words
word count
sentences
sentence count
averageWordLength
letters per word (2 d.p.)

The example

{
  "text": "The sun rose over the valley. Every learner opened a book. Reading builds the mind."
}

Agents: POST /faculty/matric-nqf4/lang_reading_statistic with JSON {pan, …inputs} and the x-402-payment header. Manifest.

Stepped tariff · mathlit_tariff

Try with the example

The cost of consumption under a two-block stepped tariff, block by block.

Reference: Umalusi/NSC subject catalogue, worked reference (offline reconstruction); Mathematical Literacy row of §4 — a tariff computation

Returns

totalCost
the total cost (2 d.p.)

The example

{
  "unitsUsed": 150,
  "blockOneLimit": 100,
  "blockOneRate": 1.5,
  "blockTwoRate": 2.1
}

Agents: POST /faculty/matric-nqf4/mathlit_tariff with JSON {pan, …inputs} and the x-402-payment header. Manifest.

School-based assessment total · lo_sba_total

Try with the example

The Life Orientation SBA percentage from task marks and task totals — 100% school-based, no external paper (working reconstruction).

Reference: Umalusi/NSC subject catalogue, worked reference (offline reconstruction); Life Orientation is 100% SBA with no external examination (verify item §12)

Returns

sbaPercent
the SBA percentage (2 d.p.)

The example

{
  "taskMarks": [
    38,
    42,
    71,
    85
  ],
  "taskTotals": [
    50,
    50,
    80,
    100
  ]
}

Agents: POST /faculty/matric-nqf4/lo_sba_total with JSON {pan, …inputs} and the x-402-payment header. Manifest.

Punnett square — monohybrid cross · lifesci_punnett

Try with the example

The genotype and phenotype ratios of a monohybrid cross, by enumerating the four gamete combinations.

Reference: Umalusi/NSC subject catalogue, worked reference (offline reconstruction); Life Sciences row of §4 — a Punnett-square ratio

Returns

genotypeRatio
AA : Aa : aa
dominantFraction
fraction showing the dominant phenotype

The example

{
  "parentOne": "Aa",
  "parentTwo": "Aa"
}

Agents: POST /faculty/matric-nqf4/lifesci_punnett with JSON {pan, …inputs} and the x-402-payment header. Manifest.

Fertiliser nutrient mass · agrisci_npk

Try with the example

The mass of N, P and K in a bag from its stated percentages.

Reference: Umalusi/NSC subject catalogue, worked reference (offline reconstruction); Agricultural Sciences row of §4 — nutrient mass from a fertiliser label

Returns

massN
kg of N
massP
kg of P
massK
kg of K

The example

{
  "bagMassKg": 50,
  "nPercent": 10,
  "pPercent": 6,
  "kPercent": 4
}

Agents: POST /faculty/matric-nqf4/agrisci_npk with JSON {pan, …inputs} and the x-402-payment header. Manifest.

Depreciation · acc_depreciation

Try with the example

Depreciation for a chosen year and the carrying value, on the straight-line or the diminishing-balance method.

Reference: Umalusi/NSC subject catalogue, worked reference (offline reconstruction); Accounting row of §4 — depreciation and carrying value

Returns

depreciationForYear
depreciation in that year (2 d.p.)
carryingValue
carrying value at the end of that year (2 d.p.)

The example

{
  "cost": 100000,
  "ratePercent": 20,
  "year": 3,
  "method": "diminishing-balance"
}

Agents: POST /faculty/matric-nqf4/acc_depreciation with JSON {pan, …inputs} and the x-402-payment header. Manifest.

Break-even quantity · bus_breakeven

Try with the example

Fixed cost over the contribution per unit; a selling price at or below the variable cost is refused because no volume can break even.

Reference: Umalusi/NSC subject catalogue, worked reference (offline reconstruction); Business Studies row of §4 — break-even from fixed cost, price and variable cost

Returns

breakEvenUnits
units to break even (rounded up)

The example

{
  "fixedCost": 60000,
  "sellingPrice": 50,
  "variableCost": 30
}

Agents: POST /faculty/matric-nqf4/bus_breakeven with JSON {pan, …inputs} and the x-402-payment header. Manifest.

Inflation rate from two index values · econ_inflation

Try with the example

The percentage change of a price index between two readings.

Reference: Umalusi/NSC subject catalogue, worked reference (offline reconstruction); Economics row of §4 — an inflation rate from two index values

Returns

inflationPercent
the rate (%, 2 d.p.)

The example

{
  "indexOld": 120,
  "indexNew": 129
}

Agents: POST /faculty/matric-nqf4/econ_inflation with JSON {pan, …inputs} and the x-402-payment header. Manifest.

Map scale and gradient · geo_map_scale

Try with the example

The ground distance from a map measurement and a 1 : n scale, and the gradient as 1 : (run/rise).

Reference: Umalusi/NSC subject catalogue, worked reference (offline reconstruction); Geography row of §4 — a map scale distance and a gradient

Returns

groundDistanceKm
ground distance (km, 3 d.p.)
gradientRun
the n of gradient 1 : n (1 d.p.)

The example

{
  "mapDistanceCm": 4.5,
  "scaleDenominator": 50000,
  "riseM": 120
}

Agents: POST /faculty/matric-nqf4/geo_map_scale with JSON {pan, …inputs} and the x-402-payment header. Manifest.

Timeline span · hist_timeline

Try with the example

The span in years between two dated events; an end year before the start year is refused.

Reference: Umalusi/NSC subject catalogue, worked reference (offline reconstruction); History row of §4 — a timeline span and a source-weighting total

Returns

spanYears
years between the two

The example

{
  "startYear": 1948,
  "endYear": 1994
}

Agents: POST /faculty/matric-nqf4/hist_timeline with JSON {pan, …inputs} and the x-402-payment header. Manifest.

Fixed-text comparison statistic · rel_text_compare

Try with the example

The shared and unique word counts of two supplied passages — a deterministic comparison, never a model-marked essay.

Reference: Umalusi/NSC subject catalogue, worked reference (offline reconstruction); Religion Studies row of §4 — a fixed-text comparison statistic

Returns

sharedWords
distinct words in both
uniqueToA
distinct words only in A
uniqueToB
distinct words only in B

The example

{
  "textA": "Compassion and justice guide the community.",
  "textB": "Justice and mercy guide the household."
}

Agents: POST /faculty/matric-nqf4/rel_text_compare with JSON {pan, …inputs} and the x-402-payment header. Manifest.

Currency conversion and occupancy · tour_currency

Try with the example

A currency conversion at a stated rate, and the occupancy percentage of a lodge.

Reference: Umalusi/NSC subject catalogue, worked reference (offline reconstruction); Tourism row of §4 — a currency conversion and an occupancy percentage

Returns

converted
converted amount (2 d.p.)
occupancyPercent
occupancy (%, 1 d.p.)

The example

{
  "amount": 1000,
  "rate": 18.5,
  "roomsSold": 45,
  "roomsAvailable": 60
}

Agents: POST /faculty/matric-nqf4/tour_currency with JSON {pan, …inputs} and the x-402-payment header. Manifest.

Unit price and recipe scaling · cons_unit_price

Try with the example

The price per unit of a pack and the factor to scale a recipe between serving counts.

Reference: Umalusi/NSC subject catalogue, worked reference (offline reconstruction); Consumer Studies row of §4 — a unit price and a recipe scale factor

Returns

unitPrice
price per unit (2 d.p.)
scaleFactor
multiply every ingredient by this (2 d.p.)

The example

{
  "packPrice": 36,
  "packSize": 6,
  "servingsHave": 4,
  "servingsNeed": 10
}

Agents: POST /faculty/matric-nqf4/cons_unit_price with JSON {pan, …inputs} and the x-402-payment header. Manifest.

Portion cost · hosp_portion_cost

Try with the example

The cost per portion from a batch cost and a portion count.

Reference: Umalusi/NSC subject catalogue, worked reference (offline reconstruction); Hospitality Studies row of §4 — a portion cost and a cover count

Returns

costPerPortion
cost per portion (2 d.p.)

The example

{
  "batchCost": 480,
  "portions": 32
}

Agents: POST /faculty/matric-nqf4/hosp_portion_cost with JSON {pan, …inputs} and the x-402-payment header. Manifest.

File-size total · cat_filesize

Try with the example

The total of a list of file sizes in KB, converted to MB at 1024 KB per MB.

Reference: Umalusi/NSC subject catalogue, worked reference (offline reconstruction); CAT row of §4 — a file-size total

Returns

totalKb
total (KB)
totalMb
total (MB, 3 d.p.)

The example

{
  "fileSizesKb": [
    512,
    256,
    1280
  ]
}

Agents: POST /faculty/matric-nqf4/cat_filesize with JSON {pan, …inputs} and the x-402-payment header. Manifest.

Binary and decimal conversion · it_binary

Try with the example

The binary representation of a whole number (0–65535) and the round-trip back to decimal.

Reference: Umalusi/NSC subject catalogue, worked reference (offline reconstruction); IT row of §4 — a binary/decimal conversion

Returns

binary
binary digits
bits
how many bits
roundTrip
parsed back to decimal — must equal the input

The example

{
  "value": 156
}

Agents: POST /faculty/matric-nqf4/it_binary with JSON {pan, …inputs} and the x-402-payment header. Manifest.

Scale drawing length · egd_scale

Try with the example

The actual length from a drawing measurement and a 1 : n scale.

Reference: Umalusi/NSC subject catalogue, worked reference (offline reconstruction); EGD row of §4 — a scale drawing length

Returns

actualMm
actual length (mm)
actualM
actual length (m, 3 d.p.)

The example

{
  "drawingMm": 45,
  "scaleDenominator": 20
}

Agents: POST /faculty/matric-nqf4/egd_scale with JSON {pan, …inputs} and the x-402-payment header. Manifest.

Load per area · civtech_load

Try with the example

The distributed load on a slab: force over area.

Reference: Umalusi/NSC subject catalogue, worked reference (offline reconstruction); Civil Technology row of §4 — a load per area

Returns

loadPerArea
kN/m² (3 d.p.)

The example

{
  "loadKn": 12,
  "areaM2": 2.5
}

Agents: POST /faculty/matric-nqf4/civtech_load with JSON {pan, …inputs} and the x-402-payment header. Manifest.

Gear ratio and torque · mechtech_gear

Try with the example

The velocity ratio of a gear pair and the ideal output torque.

Reference: Umalusi/NSC subject catalogue, worked reference (offline reconstruction); Mechanical Technology row of §4 — a gear ratio and a torque

Returns

gearRatio
driven/driver (3 d.p.)
outputTorque
ideal output torque (N·m, 3 d.p.)

The example

{
  "teethDriver": 20,
  "teethDriven": 60,
  "inputTorque": 50
}

Agents: POST /faculty/matric-nqf4/mechtech_gear with JSON {pan, …inputs} and the x-402-payment header. Manifest.

Series and parallel resistance · electech_resistance

Try with the example

The total resistance of a set of resistors in series or in parallel; a zero resistor in parallel is refused.

Reference: Umalusi/NSC subject catalogue, worked reference (offline reconstruction); Electrical Technology row of §4 — a series/parallel resistance

Returns

totalResistance
total (Ω, 3 d.p.)

The example

{
  "resistors": [
    10,
    20,
    30
  ],
  "arrangement": "series"
}

Agents: POST /faculty/matric-nqf4/electech_resistance with JSON {pan, …inputs} and the x-402-payment header. Manifest.

Colour-mix ratio and frame area · art_colour_mix

Try with the example

The fraction of each pigment in a stated mix, and the area of a picture frame border.

Reference: Umalusi/NSC subject catalogue, worked reference (offline reconstruction); Visual Arts row of §4 — a colour-mix ratio and a frame area

Returns

fractionA
fraction of pigment A (4 d.p.)
frameAreaCm2
area of the border (cm²)

The example

{
  "partsA": 2,
  "partsB": 3,
  "innerWidthCm": 40,
  "innerHeightCm": 30,
  "borderCm": 5
}

Agents: POST /faculty/matric-nqf4/art_colour_mix with JSON {pan, …inputs} and the x-402-payment header. Manifest.

Interval frequency ratio · music_interval

Try with the example

The just-intonation frequency ratio of a named interval and the upper note from a base frequency.

Reference: Umalusi/NSC subject catalogue, worked reference (offline reconstruction); Music row of §4 — a frequency ratio for an interval

Returns

ratio
the frequency ratio (4 d.p.)
upperFrequencyHz
the upper note (Hz, 2 d.p.)

The example

{
  "interval": "perfect fifth",
  "baseFrequencyHz": 440
}

Agents: POST /faculty/matric-nqf4/music_interval with JSON {pan, …inputs} and the x-402-payment header. Manifest.

Lighting-cue duration total · drama_cue

Try with the example

The total running time of a cue list in seconds and minutes:seconds.

Reference: Umalusi/NSC subject catalogue, worked reference (offline reconstruction); Drama row of §4 — a lighting-cue duration total

Returns

totalSeconds
total (s)
clock
m:ss

The example

{
  "cueSeconds": [
    12,
    45,
    8,
    95
  ]
}

Agents: POST /faculty/matric-nqf4/drama_cue with JSON {pan, …inputs} and the x-402-payment header. Manifest.

Tempo and bar count · dance_tempo

Try with the example

How many beats and full bars fit a piece at a stated tempo and time signature.

Reference: Umalusi/NSC subject catalogue, worked reference (offline reconstruction); Dance Studies row of §4 — a tempo/bar count

Returns

beats
total beats
fullBars
complete bars

The example

{
  "tempoBpm": 120,
  "beatsPerBar": 4,
  "durationSeconds": 90
}

Agents: POST /faculty/matric-nqf4/dance_tempo with JSON {pan, …inputs} and the x-402-payment header. Manifest.

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