Mathematics — Grade 12

Patterns, Sequences and Series

Patterns, sequences, and series appear throughout mathematics and everyday life. They describe how savings accounts grow, how populations change, and how payments add up over time. In this unit, you will build on your Grade 11 knowledge to derive formulas, use sigma notation, and work with infinite series.

Functions and Inverse Functions

In this unit, you will explore functions and their inverses. Think of a function as a machine that transforms inputs into outputs. An inverse function reverses this process—it takes the output and gives back the original input.

Exponential and Logarithmic Functions

This unit builds on your work with inverse functions. You learned that the exponential function y = b^x has an inverse. That inverse is called the logarithmic function.

Finance, Growth and Decay

This unit connects mathematics to real money decisions. You will learn how savings grow, how loans work, and how to use logarithms to solve financial problems. These skills will help you throughout your life—whether you're saving for studies, buying a car, or planning for the future.

Trigonometry — Compound Angle Identities

In this unit, you will learn how to work with compound angles — angles that are written as sums or differences of other angles, such as \alpha + \beta or \alpha - \beta.

Term 1 Revision: Grade 12 Mathematics

This revision unit covers the main topics from Term 1:

Trigonometry in Two and Three Dimensions

This unit builds on the compound and double angle identities you learned in Term 1. Now you will apply trigonometry to solve problems involving triangles that are not right-angled, and extend these skills to three-dimensional situations.

Polynomial Functions: Factorisation and Cubic Equations

In this unit, you will learn how to work with third-degree polynomials, also called cubic functions. You already know how to factorise quadratics like x^2 - 5x + 6 into (x-2)(x-3). Now you will learn how to factorise expressions like x^3 - 6x^2 + 11x - 6.

Differential Calculus: The Mathematics of Change

Differential calculus is the mathematics of change. It gives us tools to understand how things vary, how fast they change, and how to find the best possible outcomes.

Analytical Geometry: Circles and Tangents

In this unit, you will combine algebra and geometry to study circles in the Cartesian plane. You already know how to work with straight lines, gradients, and the distance formula. Now you will use those skills to write equations for circles, find tangent lines, and solve problems involving both.

Grade 12 Mathematics Term 2 Revision

This revision unit brings together all the major topics from Term 2. You will consolidate your understanding, identify gaps, and build the problem-solving skills needed for your examinations.

Mid-Year Examination: Complete Revision Guide

This guide prepares you for your Grade 12 Mid-Year Mathematics Examination. The mid-year exam follows the same structure as your final NSC examination in October/November, so this preparation builds skills you will use twice.

Euclidean Geometry — Similarity and Proportion

This unit builds on your earlier work with congruent triangles and circle geometry. You will now learn how to work with similar figures — shapes that have the same form but different sizes.

Statistics — Regression and Correlation

This unit teaches you how to find patterns in data involving two variables. You will learn to answer questions like: "Does studying more hours improve your marks?" or "Is there a link between advertising spending and sales?"

Counting and Probability

This unit covers Counting and Probability — skills you use more often than you might realise. When you decide whether to carry an umbrella or estimate your chances of passing a test, you are thinking about probability.

Grade 12 Mathematics Term 3 Revision

This revision unit covers the three main topics from Term 3: Euclidean Geometry (similarity and proportion), Statistics (regression and correlation), and Counting and Probability. These topics appear in Paper 2 of your NSC examination.

Trial and Preliminary Examinations: Your Final Preparation for NSC Success

The Trial Examinations are your main practice opportunity before the final NSC Mathematics examinations. Think of this as a full dress rehearsal—a chance to test your skills, find your strengths, and fix weak areas while you still have time.

Revision: Conquering NSC Mathematics

This revision unit brings together everything you have learned in Grade 12 Mathematics. You will consolidate skills across algebra, calculus, trigonometry, geometry, statistics, and probability—the topics tested in your NSC examinations.

Mathematics Term 4 Revision: Complete NSC Preparation

This revision guide brings together everything you have learned in Grade 12 Mathematics. Use it to consolidate your understanding, practise examination techniques, and build confidence before the NSC examinations.

Final NSC Examinations: Your Complete Guide to Success

This is the final stretch of your Grade 12 Mathematics journey—the National Senior Certificate Examinations. You have already covered every concept, formula, and technique you need. Now the focus is on bringing it all together with confidence, strategy, and smart examination technique.