Question 1 2 marks
Simplify √48.
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4√3
√48 = √(16 × 3) = 4√3.
GCSE Maths Higher practice paper
Algebra answers are exact. A calculator helps only with the percentage question. This is a short paper, not a full 80-mark exam. 28 marks.
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Question 2 3 marks
Solve x² − 5x + 6 = 0 by factorising.
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x = 2 or x = 3
(x − 2)(x − 3) = 0.
Question 3 2 marks
Expand (2x + 3)(x − 4).
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2x² − 5x − 12
2x² − 8x + 3x − 12.
Question 4 3 marks
Write x² + 6x + 5 in the form (x + p)² + q.
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(x + 3)² − 4
(x + 3)² = x² + 6x + 9, so subtract 9 and put 5 back: −4.
Question 5 2 marks
The gradient of the line through (1, 2) and (4, 11).
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3
(11 − 2) / (4 − 1) = 9 / 3 = 3.
Question 6 3 marks
£200 earns 5% compound interest for 2 years. Work out the amount.
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£220.50
200 × 1.05² = 200 × 1.1025 = 220.50.
Question 7 2 marks
A right-angled triangle has hypotenuse 10 cm and an angle of 30°. Work out the side opposite 30°.
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5 cm
Opposite = 10 × sin 30° = 10 × ½ = 5.
Question 8 3 marks
Solve the simultaneous equations 2x + y = 7 and x − y = 2.
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x = 3, y = 1
Add them: 3x = 9, so x = 3. Then 3 − y = 2, so y = 1.
Question 9 2 marks
A length is 6.4 cm to 1 decimal place. Write the error interval.
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6.35 ≤ x < 6.45
Half of 0.1 is 0.05. The upper bound is not included.
Question 10 2 marks
Work out 8^(2/3).
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4
The cube root of 8 is 2, and 2² = 4.
Question 11 1 marks
Factorise x² − 16.
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(x − 4)(x + 4)
Difference of two squares.
Question 12 3 marks
A price is £80 after a 20% reduction. Work out the original price.
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£100
£80 is 80% of the original. 80 ÷ 0.8 = 100.