The South African Curriculum and Assessment Policy Statement (CAPS) for Mathematics in the Further Education and Training (FET) phase (Grades 10–12) is designed to prepare students for technical, tertiary, and professional careers.
Unlike the US system, which often splits subjects by year, the CAPS curriculum is integrated, meaning students study Algebra, Geometry, and Trigonometry concurrently every year, with increasing complexity.
1. Core Content Areas
The curriculum is divided into 10 main topics, which are assessed across two final 3-hour exam papers (Paper 1 and Paper 2).
| Topic | Primary Focus | Weighting (Matric) |
| Functions & Graphs | Parabolas, Hyperbolas, Exponentials, and Inverses. | 35 ± 3 Marks |
| Algebra & Equations | Surds, Quadratics, and Simultaneous Equations. | 25 ± 3 Marks |
| Euclidean Geometry | Circle Theorems and Proportionality. | 40 ± 3 Marks |
| Trigonometry | Identities, Reduction Formulae, and Sine/Cosine Rules. | 50 ± 3 Marks |
| Differential Calculus | Limits and Optimization. | 35 ± 3 Marks |
2. Key Equations & Concepts
Paper 1: Algebraic & Calculus Focus
Paper 1 focuses on abstract reasoning and numerical patterns.
- Quadratic Formula: Used extensively from Grade 10-12.$$x = \frac{-b \pm \sqrt{b^2 – 4ac}}{2a}$$
- Financial Maths (Compound Interest): Grade 12 introduces “Annuities” for loans and investments.$$A = P(1 + i)^n \quad \text{and} \quad F = \frac{x[(1 + i)^n – 1]}{i}$$
- Calculus (First Principles): Students must be able to derive a derivative from scratch.$$f'(x) = \lim_{h \to 0} \frac{f(x+h) – f(x)}{h}$$
Paper 2: Spatial & Statistical Focus
Paper 2 is heavily visual and requires a deep understanding of geometric proofs.
- Analytical Geometry (Distance): Finding the length between two points on a Cartesian plane.$$d = \sqrt{(x_2 – x_1)^2 + (y_2 – y_1)^2}$$
- Trigonometry (Cosine Rule): Used for non-right-angled triangles.$$a^2 = b^2 + c^2 – 2bc \cos A$$
- Circle Geometry: In Grade 12, students master the equation of a circle.$$(x – a)^2 + (y – b)^2 = r^2$$
3. The “Standard” Expectations
The CAPS curriculum is known for its rigorous assessment. Marks are awarded based on four cognitive levels:
- Knowledge (20%): Recalling facts and simple formulas.
- Routine Procedures (35%): Solving problems similar to those in textbooks.
- Complex Procedures (30%): Multi-step problems that integrate different topics.
- Problem Solving (15%): Unseen, non-routine challenges.
Note on Euclidean Geometry: South Africa is one of the few countries that still requires students to memorize and reproduce formal “Statement and Reason” proofs for circle theorems.
4. Grade 12 Weighting Breakdown
At the end of Grade 12, the “Matric” exam is the ultimate decider for university entrance.
- Paper 1 (150 Marks): Algebra, Sequences, Finance, Functions, Calculus, Probability.
- Paper 2 (150 Marks): Statistics, Analytical Geometry, Trigonometry, Euclidean Geometry.
Would you like a step-by-step walkthrough of one of the examinable Euclidean Geometry proofs, such as why the angle at the center is twice the angle at the circumference?
South African Grade 12 Mathematics revision
This video provides a practical look at how CAPS-specific topics like Exponents and Surds are assessed in South African past papers, which is helpful for understanding the specific difficulty level of the curriculum.