Grade 12 Mathematics (CAPS)

About Course

Grade 12 Mathematics CAPS Syllabus Course Description

This course provides a comprehensive and structured overview of the Grade 12 Mathematics CAPS syllabus. It is designed to help learners understand the full scope of the Grade 12 Mathematics curriculum, including the key topics, subtopics, assessment expectations and examination focus areas required for success in the National Senior Certificate examinations.

The course introduces learners to the major content areas in Grade 12 Mathematics, including functions, algebra, calculus, financial mathematics, trigonometry, analytical geometry, Euclidean geometry, statistics and probability. Each topic is explained in a clear and systematic manner, with emphasis on conceptual understanding, problem-solving techniques and exam-style application.

Learners will also have access to over 500 practice and exam-related questions designed to help them master key concepts, strengthen problem-solving skills and prepare effectively for tests and final examinations. These questions support progressive learning by allowing learners to practise core skills, apply formulas, identify common question patterns and build confidence in answering CAPS-aligned mathematical problems.

The course guides learners through the structure of the CAPS curriculum so that they understand what is expected in Paper 1 and Paper 2. It also highlights common areas of difficulty, important formulas, key definitions and the types of questions learners are likely to encounter in school-based assessments and final examinations.

By the end of this course, learners should be able to:

understand the structure and requirements of the Grade 12 Mathematics CAPS syllabus;
identify the main topics and subtopics assessed in the final examination;
recognise the difference between Paper 1 and Paper 2 content;
connect mathematical concepts across different sections of the syllabus;
practise with over 500 CAPS-aligned practice and exam-style questions;
prepare more effectively for school-based assessments and final examinations;
approach Grade 12 Mathematics with greater confidence and clarity.

This course is suitable for Grade 12 learners, revision students, tutors, parents and anyone who wants a clear roadmap of the Grade 12 Mathematics CAPS curriculum.

This course serves as a roadmap to exam success by helping learners know what to study, how topics are connected and how to master the concepts through focused practice and exam-style preparation.

Understand the full Grade 12 Mathematics CAPS syllabus and how each topic fits into Paper 1 and Paper 2.
Master key concepts in exponents and surds, algebra, sequences and series, functions, finance, calculus, probability, analytical geometry, trigonometry, Euclidean geometry and statistics.
Learn how to solve CAPS-aligned mathematics problems using clear step-by-step methods.
Improve graph interpretation, algebraic manipulation, geometric reasoning and exam-style problem-solving skills.
Practise with over 500 practice and exam-related questions designed to strengthen understanding and build confidence.
Prepare effectively for school tests, assessments and the Grade 12 final Mathematics examination.

Course Content

Unit 1 – Exponents and Surds
This unit develops learners’ ability to simplify, manipulate and solve expressions involving exponents and surds. Learners revise the laws of exponents, work with rational exponents, simplify surd expressions and apply algebraic rules to solve CAPS-aligned problems.

Unit 2 – Algebra
This unit strengthens core algebraic skills required throughout Grade 12 Mathematics. It covers algebraic manipulation, factorisation, equations, inequalities and problem-solving techniques. The unit prepares learners to handle more advanced topics such as functions, calculus and analytical geometry.

Unit 3 – Patterns, Sequences and Series
This unit covers arithmetic and geometric patterns, sequences and series. Learners study general terms, recursive patterns, sigma notation, finite series and infinite geometric series. The focus is on identifying patterns, applying formulas and solving exam-style sequence and series problems.

Unit 4 – Functions
This unit introduces the major Grade 12 functions, including linear, quadratic, hyperbolic, exponential and logarithmic functions. Learners study domain, range, intercepts, asymptotes, turning points and transformations. Emphasis is placed on interpreting and sketching graphs accurately.

Unit 5 – Trigonometric Functions
This unit focuses on the graphs and behaviour of trigonometric functions. Learners examine sine, cosine and tangent functions, including amplitude, period, transformations and key graph features. The unit builds the foundation for solving trigonometric equations and interpreting trigonometric graphs.

Unit 6 – Finance, Growth and Decay
This unit applies mathematics to real-life financial situations. Learners study simple interest, compound interest, depreciation, inflation, loans, investments and growth or decay models. The unit helps learners interpret financial scenarios and solve related CAPS examination questions.

Unit 7 – Calculus
This unit introduces differential calculus, including limits, average gradient, instantaneous gradient and the derivative. Learners apply differentiation to cubic functions, stationary points, tangents, increasing and decreasing intervals, points of inflection and optimisation problems.

Unit 8 – Probability
This unit develops learners’ understanding of probability concepts and rules. It covers independent and dependent events, mutually exclusive events, complementary events, Venn diagrams, tree diagrams and contingency tables. Learners practise applying probability principles to structured exam-style questions.

Unit 9 – Analytical Geometry
This unit focuses on coordinate geometry in the Cartesian plane. Learners study distance, midpoint, gradient, inclination, equations of straight lines, parallel and perpendicular lines, circles and tangents. The unit supports Paper 2 problem-solving through algebraic and geometric reasoning.

Unit 10 – Trigonometry
This unit develops broader trigonometric problem-solving skills. It covers trigonometric identities, equations, reduction formulae, compound angles and general solutions. Learners apply trigonometric methods to solve both algebraic and diagram-based problems.

Unit 11 – Sine, Cosine and Area Rules
This unit focuses on applying the sine rule, cosine rule and area rule in two-dimensional and three-dimensional problems. Learners solve problems involving non-right-angled triangles, bearings, angles of elevation and depression, and contextual geometric applications.

Unit 12 – Euclidean Geometry
This unit develops formal geometric reasoning and proof-writing skills. Learners study circle geometry, proportionality, tangents, chords, cyclic quadrilaterals and related theorems. The focus is on constructing logical, well-structured proofs for Paper 2.

Unit 13 – Statistics
This unit covers data handling, analysis and interpretation. Learners study measures of central tendency, measures of dispersion, quartiles, percentiles, five-number summaries, box-and-whisker diagrams, scatter plots, correlation and regression. The unit prepares learners to interpret data critically in examination contexts.

About Course