Grade 12 Maths Exam Questions and Answers

Practise real Grade 12 Maths exam questions aligned to the South African CAPS curriculum, with step-by-step AI-generated answers.

Looking for Grade 12 Maths exam questions and answers? This collection covers algebra, functions, trigonometry, calculus and more — all aligned to the South African CAPS Matric Mathematics curriculum. Each question comes with a clear step-by-step solution so you understand the method, not just the answer. The questions below follow the order of a real paper: algebra and equations first, then sequences, functions, calculus, trigonometry and statistics. Work through each one on paper before you read the steps, then compare your method line by line. If a step surprises you, that is the skill to practise next. When you get stuck on a question from your textbook or a past paper, snap it to see the full method with the marks each step is likely to earn.

Practice questions with solutions

Solve for x: x² − 5x + 6 = 0

  1. Factorise: (x − 2)(x − 3) = 0
  2. Set each factor to zero
  3. x = 2 or x = 3

Answer: x = 2 or x = 3

If f(x) = 2x + 3 and g(x) = x², find g(f(1)).

  1. f(1) = 2(1) + 3 = 5
  2. g(5) = 5² = 25

Answer: 25

Find the derivative of f(x) = 3x³ − 4x + 7.

  1. Differentiate term-by-term
  2. f'(x) = 9x² − 4

Answer: f'(x) = 9x² − 4

Find the sum of the first 15 terms of 3; 7; 11; …

  1. Arithmetic series: a = 3 and d = 4
  2. S₁₅ = 15/2 [2(3) + 14(4)] = 15/2 × 62

Answer: S₁₅ = 465

Solve for x: 3ˣ = 81

  1. Write 81 as a power of 3: 81 = 3⁴
  2. Equate the exponents

Answer: x = 4

Find the equation of the line through (1; 2) parallel to y = 3x − 5.

  1. Parallel lines have equal gradients, so m = 3
  2. y − 2 = 3(x − 1)

Answer: y = 3x − 1

Find the general solution of tan x = 1.

  1. The reference angle is 45°
  2. The tangent function repeats every 180°

Answer: x = 45° + k·180°, k ∈ ℤ

The mean of 4, 7, x and 9 is 7. Find x.

  1. (4 + 7 + x + 9) / 4 = 7
  2. 20 + x = 28

Answer: x = 8

Tips

  • Practise past papers under timed conditions.
  • Always show your method — markers award method marks.
  • Check units and rounding instructions before submitting.
  • Read the mark allocation: a 4-mark question usually needs about four distinct steps.
  • Know where each formula is on the information sheet so you don't waste time searching.

Snap&Learn gives South African Matric learners instant, CAPS-aligned, step-by-step Mathematics solutions. Snap or upload a question and the AI shows every method mark the way the NSC memo awards them. Your first three AI solutions are free.