Free Year 9 Maths Practice Test (10 Questions)

1. Expand (x + 2)(x − 5)

x² − 3x − 10 x² + 3x − 10 x² − 7x − 10 x² − 10

Answer: x² − 5x + 2x − 10 = x² − 3x − 10.

2. Factorise x² + 7x + 10

(x + 1)(x + 10) (x + 2)(x + 5) (x − 2)(x − 5) x(x + 17)

Answer: Two numbers that multiply to 10 and add to 7: 2 and 5, so (x + 2)(x + 5).

3. Solve 4x − 3 = 2x + 9

x = 2 x = 3 x = 6 x = 12

Answer: Subtract 2x: 2x − 3 = 9. Add 3: 2x = 12, so x = 6.

4. A right-angled triangle has shorter sides of 9 cm and 12 cm. How long is the hypotenuse?

15 cm 18 cm 21 cm 225 cm

Answer: 9² + 12² = 81 + 144 = 225, and √225 = 15 cm.

5. Write 0.00032 in standard form

3.2 × 10⁻⁴ 3.2 × 10⁴ 32 × 10⁻⁵ 3.2 × 10⁻³

Answer: Move the decimal point 4 places right to get 3.2, so 3.2 × 10⁻⁴.

6. Solve 3x − 1 ≤ 11

x ≤ 3 x ≤ 4 x ≥ 4 x ≤ 10/3

Answer: Add 1: 3x ≤ 12. Divide by 3: x ≤ 4.

7. What is the gradient of the line through (0, 1) and (2, 7)?

2 3 4 6

Answer: Gradient = change in y ÷ change in x = 6 ÷ 2 = 3.

8. Two shapes are similar with scale factor 3. A side of the smaller shape is 4 cm. How long is the matching side of the larger shape?

7 cm 12 cm 16 cm 36 cm

Answer: Multiply by the scale factor: 4 × 3 = 12 cm.

9. In a right-angled triangle the opposite and adjacent sides are both 5 cm. What is the angle?

30° 45° 60° 90°

Answer: tan θ = 5 ÷ 5 = 1, and tan 45° = 1, so 45°.

10. Simplify (x³)²

x⁵ x⁶ x⁹ 2x³

Answer: A power of a power: multiply the indices, 3 × 2 = 6, so x⁶.

About this test

Year 9 is effectively the start of GCSE preparation: expanding and factorising quadratics, Pythagoras, inequalities and straight-line graphs all reappear on the GCSE papers.

Want a tutor to work on these topics with your child every week? See our KS3 tutoring or plans from £60 a month.

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