Roughly how the marks are spread
Treat these as a planning guide only. Confirm the current weighting in the DBE examination guidelines for your exam year.
- Algebra, equations, inequalities and surds — a large opening block worth about 25 to 35 marks.
- Number patterns, sequences and series — about 25 to 35 marks.
- Functions, graphs and inverses — about 35 marks.
- Financial mathematics, growth and decay — about 15 marks.
- Differential calculus — about 35 marks.
- Probability and counting — about 15 marks.
Worked example: quadratic inequality
Solve x² − x − 6 > 0. Factorise: (x − 3)(x + 2) > 0. Critical values are x = 3 and x = −2. Test a value in each interval: the product is positive when x < −2 and when x > 3.
Answer: x < −2 or x > 3. Write the answer in interval or inequality form, and never divide an inequality by a variable — you lose the sign information and the marks.
Worked example: first principles
If f(x) = 2x², then f'(x) = lim(h→0) [f(x+h) − f(x)]/h = lim(h→0) [2(x+h)² − 2x²]/h = lim(h→0) [4xh + 2h²]/h = lim(h→0) (4x + 2h) = 4x.
Marks are given for writing the definition, expanding correctly, simplifying and taking the limit. Write every line — the answer alone rarely earns full marks.
Where learners usually lose marks
- Not stating restrictions when solving equations with fractions or logs.
- Mixing arithmetic and geometric formulas in sequences.
- Forgetting to test endpoints in inequalities.
- Leaving out units, rounding too early, or rounding money to the wrong number of decimals.
- Using the calculator for a question that says 'show that', where the method is the mark.
Official sources
Check the latest information with your school and the Department of Basic Education.