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Grade 12

44 resources across 4 subjects

Mathematics

14 topics

📄 34 files🎬 2 videos

Browse Mathematics

Mathematical Literacy

4 topics

📄 8 files🎬 1 videos

Browse Mathematical Literacy

Technical Mathematics

1 topics

Browse Technical Mathematics

Physical Science

1 topics

Browse Physical Science

📚 Grade 12 lessons(17)

Every lesson is one focused sub-topic, worked 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 paper Arithmetic & 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 paper Average 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 paper Inverse 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 paper Logarithms: 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 paper Quadratic 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 paper Series, 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 paper Three-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 paper Optimisation & 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 paper Polynomials: 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 paper Proportionality & 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 paper Sketching 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 paper The 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

Counting Principles & Probability (Grade 12)The fundamental counting principle, arrangements with n!, handling items that must stay together or that repeat, and using counting to work out a probability.12min read · lesson, worksheet & exam paper Differentiation: The Rules and How Exams Use ThemThe power rule plus every way an exam applies it — differentiating polynomials, rewriting surds and fractions first, first principles, gradients and tangents, and turning points — each worked in full, with a worksheet.15min read · lesson, worksheet & exam paper Regression & Correlation (Grade 12)Drawing a scatter plot, finding the least squares regression line y = A + Bx on the calculator, using it to predict, and interpreting the correlation coefficient r.11min read · lesson, worksheet & exam paper

📖Grade 12 Mathematics: curriculum guide & study tipsRead more ▾

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.

Topics by term (CAPS)

Term 1

Number patterns, sequences and series (arithmetic and geometric, sigma notation, sum to infinity), functions (inverses, logarithms), and finance (annuities, present and future value).

Term 2

Trigonometry (compound and double angles, general solutions), differential calculus (first principles, rules of differentiation, cubic graphs, optimisation), and the June examination.

Term 3

Analytical geometry (circles and tangents), Euclidean geometry (proportionality and similarity theorems), statistics (regression and correlation), counting and probability, and the Trial (Preliminary) examination — the full-length dress rehearsal for the NSC.

Term 4

Intensive revision of all topics from Grades 10–12, followed by the NSC final examinations in October/November.

How you'll be assessed

The NSC Mathematics examination consists of two 3-hour papers of 150 marks each. Paper 1: algebra and equations, patterns and sequences, functions, finance, calculus, and probability. Paper 2: statistics, analytical geometry, trigonometry, and Euclidean geometry. The Trial examinations in Term 3 follow exactly the same structure, which makes trial papers from every province valuable practice material.

Study tips from the classroom

Past papers are the core of matric revision: write at least the last five years of NSC papers under timed conditions before the finals.
Calculus optimisation and cubic graph questions follow recurring patterns — learn the standard question types rather than treating each as new.
Keep a personal error log: every mistake from a practice paper gets written down and re-tested a week later.
In Paper 2, attempt Euclidean geometry riders even when unsure — partial marks for correct statements and reasons add up.