Free GCSE Algebra Practice Test (10 Questions, Worked Answers)

1. Solve 5x − 7 = 18

x = 2.2 x = 5 x = 11 x = 25

Answer: Add 7: 5x = 25. Divide by 5: x = 5.

2. Expand (x + 3)(x + 4)

x² + 7x + 12 x² + 12x + 7 x² + 7x + 7 2x + 7

Answer: x × x = x², x × 4 + 3 × x = 7x, 3 × 4 = 12: x² + 7x + 12.

3. Factorise 6x + 9

3(2x + 3) 6(x + 9) 3(2x + 9) 9(x + 6)

Answer: The highest common factor of 6x and 9 is 3: 3(2x + 3).

4. Make x the subject of y = 3x + 2

x = (y − 2)/3 x = y/3 − 2 x = 3y + 2 x = (y + 2)/3

Answer: Subtract 2: y − 2 = 3x. Divide by 3: x = (y − 2)/3.

5. Solve x² = 49

x = 7 x = 7 or x = −7 x = 24.5 x = −7

Answer: Both 7² and (−7)² equal 49, so x = 7 or x = −7.

6. What is the nth term of 5, 8, 11, 14, …?

3n + 2 3n + 5 5n + 3 n + 3

Answer: It goes up by 3, so 3n; the first term is 5 = 3 + 2, so 3n + 2.

7. Simplify x⁵ × x³

x¹⁵ x⁸ x² 2x⁸

Answer: When multiplying, add the powers: 5 + 3 = 8, so x⁸.

8. Solve 2x + 1 > 9

x > 4 x > 5 x < 4 x > 8

Answer: Subtract 1: 2x > 8. Divide by 2: x > 4.

9. What is the gradient of the line y = 4x − 1?

−1 1 4 −4

Answer: In y = mx + c, m is the gradient, so 4.

10. Factorise x² − 9

(x − 3)² (x + 3)(x − 3) (x + 9)(x − 1) x(x − 9)

Answer: x² − 9 = x² − 3², a difference of two squares: (x + 3)(x − 3).

About this test

Algebra appears in some form in most GCSE maths questions, so confidence here lifts the whole paper. These ten questions move from Foundation basics to typical Higher techniques.

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