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HomeGrade 12Mathematics

Grade 12Mathematics

🗓️Past Papers & Memos by Term

🧭 Practise by Topic

📚 Grade 12 Mathematics lessons(17)

Each lesson covers one sub-topic in full, with a printable worksheet and an exam paper with its memo.

Term 1

Annuities & Loan Repayments (Grade 12)Future value for savings and present value for loans, working out a monthly instalment, and finding the outstanding balance part-way through a loan.12min read · lesson, worksheet & exam paperArithmetic & Geometric Sequences: Full GuideBoth sequence types and every exam question — finding a term, finding which term equals a value, the sum of a series, and the sum to infinity — each worked in full, with a worksheet.15min read · lesson, worksheet & exam paperAverage Gradient & Average Rate of Change (Grade 12)The gradient of the straight line joining two points on a curve, why it is an average rather than the gradient at a point, and how it becomes the derivative as the two points close together.9min read · lesson, worksheet & exam paperInverse Functions (Grade 12)Finding the inverse of a line, a parabola and an exponential function, why y = x² needs a restricted domain, and how to state whether an inverse is a function.11min read · lesson, worksheet & exam paperLogarithms: The Complete Grade 12 GuideLogs as the reverse of exponents, plus every exam type — evaluating, converting between log and exponent form, the log laws, change of base, and solving exponential equations with logs — each worked in full, with a worksheet.14min read · lesson, worksheet & exam paperQuadratic Number Patterns (Grade 11 & 12)Recognising a quadratic pattern from its constant second difference, finding Tₙ = an² + bn + c, and answering the standard NSC follow-ups about which term equals a given value.11min read · lesson, worksheet & exam paperSeries, Sigma Notation & Convergence (Grade 12)Sum formulae for arithmetic and geometric series, reading and writing sigma notation, and the sum to infinity — including the values of the ratio for which a series converges.12min read · lesson, worksheet & exam paperThree-Dimensional Trigonometry (Grade 12)Applying the sine, cosine and area rules to problems set in three dimensions — identifying the right triangle to work in, finding the shared side first, and then answering the question.12min read · lesson, worksheet & exam paper

Term 2

Compound & Double Angle Identities (Grade 12)The formulae for sin(A ± B) and cos(A ± B), the three forms of cos2A, using them to find exact values without a calculator, and proving identities.12min read · lesson, worksheet & exam paperOptimisation & Rates of Change (Grade 12)Building a formula from a described situation, differentiating it to find the maximum or minimum, and interpreting a derivative as a rate of change — including velocity and acceleration.12min read · lesson, worksheet & exam paperPolynomials: Remainder & Factor Theorem (Grade 12)Using the remainder theorem to find a remainder without dividing, the factor theorem to find the first factor of a cubic, and then factorising and solving the cubic completely.10min read · lesson, worksheet & exam paperProportionality & Similarity Theorems (Grade 12)The proportion theorem for a line parallel to a side of a triangle, similar triangles and the AAA condition, and how to lay out a proportion so the ratios cannot be flipped.11min read · lesson, worksheet & exam paperSketching Cubic Graphs (Grade 12)Using the derivative to find stationary points, deciding which is a maximum and which a minimum, locating the point of inflection, and putting it all together in a sketch.12min read · lesson, worksheet & exam paperThe Circle & Its Tangent (Grade 12)The equation (x − a)² + (y − b)² = r², completing the square to find the centre and radius from the general form, and finding the tangent at a point on the circle.11min read · lesson, worksheet & exam paper

Term 3

📖How to use these Grade 12 Mathematics resourcesRead more ▾

Mathematics in the CAPS curriculum is a cumulative subject: each year builds directly on the last, and each term's work feeds into the next. The resources below are organised the same way your school year is — by term — so you can revise exactly what will be assessed next. Term cards contain full tests and examinations with their memorandums; topic cards collect papers and worksheets that focus on one area of the curriculum.

The most effective way to use this page is simple. Before a test or exam, open the matching term card, download a paper, and write it under timed conditions without looking at the memo. Then mark yourself honestly, identify the question types you lost marks on, and redo those questions a few days later. Learners who repeat this cycle three or four times before an exam consistently outperform those who only read through notes.

Grade 12 is the NSC (matric) year. The final examinations in October/November are nationally set and externally marked, and the results determine university admission through APS scores. The Grade 12 curriculum adds calculus, sequences and series, and inverse functions on top of everything from Grades 10 and 11 — roughly a third of the final papers examine work from earlier grades, which is why revising Grade 11 trigonometry and geometry is part of every good matric study plan. This page carries past NSC papers, provincial trial (prelim) papers and memorandums. See the full Grade 12 curriculum guide →