GCSE Maths Higher Paper 1: non-calculator
80 marks · 90 minutes · Higher tier · method marks for your working · estimated grade · step-by-step answers
How it works
- Like the real AQA 8300 style paper: 80 marks, 90 minutes, no calculator. Answer all the questions. Solve it right here: no sign-up.
- Each part shows its marks, like [2 marks]. Type your answer and show your working, one line at a time: if the answer is wrong, right working still earns method marks, as in the exam. In all calculations, show clearly how you work out your answer.
- 1 part needs a drawing or words (a construction, a graph, a proof): do it on paper. At the end you mark it yourself with the mark scheme.
- Use Back and Next, or the question list at the bottom. Mark for review the ones to look at again. The timer counts down (you can hide it).
- At the end: your marks out of 80, an estimated grade, your marks in each area, and every part marked, with your working line by line, the right answer and its step-by-step solution.
The grade is only an estimate: real grade boundaries change every year and use all the papers together. Foundation papers lead to grades 1 to 5, Higher papers to 3 to 9. Your answers are kept in this browser, so you can close the page and come back.
1 Question 1
Write 252 as a product of its prime factors. Give your answer in index form.[2 marks]
2 Question 2
Work out 3 14 − 1 5/6. Give your answer as a mixed number.[3 marks]
3 Question 3
Work out the value of 642/3.[2 marks]
5 Question 5
Write the recurring decimal 0.2727... as a fraction in its simplest form. Show your working.[3 marks]
6(a) Question 6(a)
Simplify √75 − √12.[2 marks]
6(b) Question 6(b)
Rationalise the denominator and simplify 6/(√3 + 1).[3 marks]
7 Question 7
Work out (8 × 10⁴) × (6 × 10⁻⁷). Give your answer in standard form.[2 marks]
8 Question 8
Factorise fully 3x² − 12.[2 marks]
9 Question 9
Solve 3x² − 10x − 8 = 0.[3 marks]
10 Question 10
Write x² + 8x + 3 in the form (x + a)² + b.[3 marks]
11 Question 11
Solve x² − x − 12 < 0.[3 marks]
12 Question 12
Solve the simultaneous equations 4x + 3y = 17 and 3x − 2y = 0.[4 marks]
13 Question 13
Simplify fully x² − 16x² − 2x − 8.[3 marks]
14 Question 14
Write 3/(x − 1) − 2/(x + 2) as a single fraction.[3 marks]
f(x) = 3x − 2 and g(x) = x² + 1.
15(a) Question 15(a)
Work out fg(2).[2 marks]
15(b) Question 15(b)
Work out f⁻¹(x).[2 marks]
16 Question 16
Work out an expression for the nth term of 6, 9, 14, 21, 30, ...[3 marks]
17 Question 17
Work out the equation of the line through (4, 1) that is perpendicular to y = 2x − 5.[3 marks]
18 Question 18
A circle has centre (0, 0) and radius 7. Write down its equation.[2 marks]
19 Question 19
Describe the transformation that maps y = x² onto y = (x − 3)² + 1.[2 marks]
20 Question 20
A, B and C lie on a circle with centre O. Angle AOB = 124°. Work out angle ACB. Give a reason.[2 marks]
22 Question 22
A tangent from P touches a circle, centre O, at T. The radius is 6 cm and OP = 10 cm. Work out PT.[2 marks]
24 Question 24
A bag has 4 red and 5 blue sweets. Two sweets are taken at random without replacement. Work out the probability that both are red.[3 marks]
25 Question 25
A survey: men, 18 said yes and 6 said no; women, 14 said yes and 12 said no. A man is chosen at random. Work out the probability he said yes.[2 marks]
26 Question 26
y is inversely proportional to x. When x = 3, y = 8. Work out y when x = 6.[3 marks]
27 Question 27
Two similar shapes have lengths in the ratio 2 : 5. The small shape has area 12 cm². Work out the area of the large shape.[2 marks]
28 Question 28
Make x the subject of 5x + a = bx − 1.[3 marks]
29 Question 29
Expand and simplify (x + 2)(x − 1)(x + 4).[3 marks]
30 Question 30
Solve 10x − 3 = 2.[3 marks]
32 Question 32
Work out the equation of the perpendicular bisector of the line from (2, 0) to (6, 4).[3 marks]
33 Question 33
Prove that the sum of any two odd numbers is even.[2 marks]
Steply practice papers are our own questions in the style of GCSE Mathematics papers in England (layout and timing as AQA 8300); they are not official and not endorsed by AQA or any exam board. Official past papers: your exam board's website.