Grade 9 Maths Questions and Answers (CAPS)

Grade 9 maths questions and answers for CAPS tests and exams: expanding, factorising, equations, gradients, Pythagoras and exponents, fully worked.

· 5 min read · Snap&Learn

Grade 9 maths prepares you for your Grade 10 subject choice. Use these questions to practise for a test or your end-of-year exam: try each one on paper first, then compare your working.

Question 1: Expanding

Expand (x + 3)(x − 2). Multiply each term: x² − 2x + 3x − 6. Answer: x² + x − 6.

Question 2: Factorising

Factorise x² − 16. This is a difference of two squares, with x² and 4². Answer: (x − 4)(x + 4).

Question 3: Equations

Solve 2(x − 1) = x + 5. Expand: 2x − 2 = x + 5. Subtract x and add 2. Answer: x = 7. Check: 2(6) = 12 and 7 + 5 = 12.

Question 4: Gradient

Find the gradient of the line through (1; 2) and (3; 8). m = (8 − 2) / (3 − 1) = 6 / 2. Answer: 3.

Question 5: Theorem of Pythagoras

A right-angled triangle has shorter sides of 5 cm and 12 cm. Find the hypotenuse. c² = 25 + 144 = 169. Answer: c = 13 cm.

Question 6: Exponents

Simplify (3x²)³. Cube the number and multiply the exponents: 3³ = 27 and (x²)³ = x⁶. Answer: 27x⁶.

Question 7: Common factors

Factorise 6x² + 9x. The highest common factor of both terms is 3x. Answer: 3x(2x + 3). Check by expanding your answer: you should get the original expression back.

Question 8: Trinomials

Factorise x² + 5x + 6. Find two numbers that multiply to 6 and add to 5. These are 2 and 3. Answer: (x + 2)(x + 3).

Question 9: Intercepts of a straight line

Find the intercepts of y = 2x − 6. Set x = 0 to get y = −6. Set y = 0 to get 2x = 6, so x = 3. Answer: the y-intercept is (0; −6) and the x-intercept is (3; 0).

Question 10: Volume

Find the volume of a rectangular prism that is 5 cm long, 3 cm wide and 2 cm high. Volume = length × width × height = 5 × 3 × 2. Answer: 30 cm³.

When you get stuck

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Frequently asked questions

What should I focus on for Grade 9 maths?

Algebra: expanding, factorising and solving equations. These skills come up in every later year of maths.

How do I spot a difference of two squares?

There are two perfect squares with a minus between them, such as x² − 16. It factorises as (x − 4)(x + 4).

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