Grade 12 Mathematics is the NSC year. The CAPS curriculum consolidates all FET content — algebra, functions, calculus, trigonometry, Euclidean geometry, analytical geometry, statistics and probability — and introduces differential calculus as a major new topic. Paper 1 covers algebra, functions, calculus, finance and probability. Paper 2 covers statistics, analytical geometry, trigonometry and Euclidean geometry. Every concept from Grades 10 and 11 reappears — mastery of prior content is non-negotiable.
- Limits: definition, calculate limits from first principles — f'(x) = lim[f(x+h)−f(x)]/h
- Differentiate from first principles: polynomials, f(x) = xⁿ
- Differentiation rules: power rule, sum/difference rule, constant multiple
- Notation: f'(x), dy/dx, Dₓ[f(x)]
- Differentiate: polynomials, rational functions (rewrite first), surd functions
- Applications: gradient of tangent at a point — find equation of tangent and normal
- Second derivative: f''(x) — concavity, points of inflection
- Cubic functions: sketch using derivatives — intercepts, stationary points, concavity
- Quadratic, exponential, logarithmic functions: full revision — transformations, inverses
- Determine equations of functions from graphs — all types
- Exponential equations and logarithms: solve using log laws
- Arithmetic sequences: Tₙ = a + (n−1)d, Sₙ = n/2(2a + (n−1)d)
- Geometric sequences: Tₙ = arⁿ⁻¹, Sₙ = a(rⁿ−1)/(r−1), S∞ = a/(1−r) for |r| < 1
- Financial mathematics: nominal vs effective interest rates — convert between them
- Annuities: future value F = x[(1+i)ⁿ−1]/i, present value P = x[1−(1+i)^(−n)]/i
- Sinking fund: set up and solve — replace an asset after depreciation
- Trig identities: full revision — prove compound angle, double angle identities
- Trig equations: general solution and specific interval
- 2D and 3D trig problems: sine rule, cosine rule, area formula — multi-step
- Euclidean geometry: full revision — triangle theorems, circle theorems
- Circle theorem proofs: write formal proofs — state theorem, reason at every step
- Analytical geometry: circle equation, tangent to circle, perpendicular bisector
- Trial exam: full Papers 1 and 2 under exam conditions
- Mark trial exam: use marking guidelines — identify specific topics losing marks
- Targeted revision: calculus, trig identities, circle geometry, sequences — based on trial exam gaps
- Past papers: at least three full sets under timed conditions
- Paper 1 technique: calculus questions — show derivative first, then application
- Paper 2 technique: geometry proofs — state theorem at every step, never assume
- Statistics: regression, correlation — interpret r-value, use least-squares line
- Probability: counting principles, permutations, combinations — practise varied question types
- Examination: Paper 1 (3 hours), Paper 2 (3 hours)
- Post-exam: reflect on the journey — you have grown enormously 🌱
Calculus: show the derivative before applying it. Write f'(x) = ... before finding the gradient, maximum or minimum. Examiners award a method mark for the derivative.
Geometry proofs: every statement needs a reason. (angles of a triangle = 180°), (tangent ⊥ radius), (opp. angles of cyclic quad. are supp.). No reason = no mark.
Series: identify arithmetic or geometric first. Check if there is a common difference (arithmetic) or common ratio (geometric) before choosing a formula.
Calculus applications follow a fixed method. Find the derivative → set it to zero → solve → classify using second derivative. Always in that order.
Every past paper marks the same topics. Calculus, trig identities and circle geometry appear in every NSC paper. Master these three first.