Free Year 11 Maths Practice Test (10 Questions)

1. Which is the quadratic formula for ax² + bx + c = 0?

x = (−b ± √(b² − 4ac)) ÷ 2a x = (b ± √(b² − 4ac)) ÷ 2a x = (−b ± √(b² + 4ac)) ÷ 2a x = −b ± √(b² − 4ac) ÷ a

Answer: The formula is x = (−b ± √(b² − 4ac)) ÷ 2a; it works even when a quadratic won't factorise.

2. Solve x² + 4x − 5 = 0

x = 1 or x = −5 x = −1 or x = 5 x = 5 or x = 4 x = −4 or x = 5

Answer: (x + 5)(x − 1) = 0, so x = 1 or x = −5.

3. The angle at the centre of a circle is … the angle at the circumference standing on the same arc.

equal to half twice 90° more than

Answer: The angle at the centre is twice the angle at the circumference.

4. Which is the sine rule?

a ÷ sin A = b ÷ sin B a² = b² + c² − 2bc cos A Area = ½ab sin C sin A = opposite ÷ hypotenuse

Answer: a ÷ sin A = b ÷ sin B (= c ÷ sin C). The second option is the cosine rule.

5. f(x) = 2x + 3. What is f(4)?

7 9 11 14

Answer: Substitute x = 4: 2 × 4 + 3 = 11.

6. y is inversely proportional to x, and y = 6 when x = 2. Find y when x = 3.

2 4 9 12

Answer: y = k ÷ x with k = 6 × 2 = 12, so y = 12 ÷ 3 = 4.

7. Rationalise the denominator of 1 ÷ √2

√2 √2 ÷ 2 2 ÷ √2 1 ÷ 2

Answer: Multiply top and bottom by √2: √2 ÷ 2.

8. What is the turning point of y = (x − 3)² + 2?

(3, 2) (−3, 2) (3, −2) (2, 3)

Answer: y = (x − p)² + q has its turning point at (p, q): (3, 2).

9. Two sides of a triangle are 6 cm and 8 cm with an included angle of 30°. What is its area?

12 cm² 24 cm² 48 cm² 14 cm²

Answer: ½ab sin C = ½ × 6 × 8 × ½ = 12 cm².

10. 8^(2/3) =

4 16/3 16 2

Answer: Cube root first: ∛8 = 2, then square: 2² = 4.

About this test

Year 11 Higher-tier maths adds the topics that separate grades 7, 8 and 9: the quadratic formula, circle theorems, functions, inverse proportion and surds. Exam technique matters as much as content now.

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