GCSE Maths Higher Paper 2: 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, a calculator is allowed (one is on the screen). 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 0.03846 correct to 3 significant figures.[1 mark]
2 Question 2
£4500 is invested at 3.2% compound interest per year. Work out its value after 5 years.[3 marks]
3 Question 3
A van is bought for £24 000. Its value falls by 18% each year. Work out its value after 3 years.[3 marks]
4 Question 4
Tom gets a 15% pay rise. He now earns £575 a week. Work out how much he earned each week before the rise.[3 marks]
5 Question 5
x = 36 and y = 8, both correct to the nearest whole number. Work out the upper bound of x ÷ y. Give your answer to 3 significant figures.[3 marks]
In triangle PQR, PQ = 9 cm, PR = 12 cm and angle QPR = 38°.
6(a) Question 6(a)
Work out QR.[3 marks]
6(b) Question 6(b)
Work out the area of triangle PQR.[2 marks]
7 Question 7
In triangle ABC, angle A = 48°, angle B = 63° and BC = 14 cm. Work out AC.[3 marks]
8 Question 8
A cuboid measures 4 cm by 7 cm by 9 cm. Work out the length of the longest straight rod that fits inside it.[3 marks]
9 Question 9
A cone has base radius 5 cm and slant height 13 cm. Work out its volume.[3 marks]
10 Question 10
A hemisphere has radius 4 cm. Work out its total surface area (curved surface and flat face).[2 marks]
11 Question 11
A sector has radius 12 cm and angle 150°. Work out its area.[2 marks]
12 Question 12
Solve 3x² + 4x − 2 = 0. Give your answers to 2 decimal places.[4 marks]
13 Question 13
Solve the simultaneous equations x² + y² = 10 and y = 3x.[5 marks]
14 Question 14
Ages of people at a club: 0 < age ≤ 10: 8, 10 < age ≤ 20: 6, 20 < age ≤ 40: 10. Work out the frequency densities for a histogram.[3 marks]
15 Question 15
Times, t minutes: 0 < t ≤ 10: 4, 10 < t ≤ 20: 9, 20 < t ≤ 30: 15, 30 < t ≤ 40: 8, 40 < t ≤ 50: 4. Use cumulative frequency to estimate the median time.[3 marks]
16 Question 16
Two similar solids have lengths 3 cm and 7.5 cm. The small one has volume 16 cm³. Work out the volume of the large one.[2 marks]
17 Question 17
A cuboid has a base 6 cm by 8 cm and height 10 cm. Work out the angle between a long diagonal and the base.[3 marks]
18 Question 18
Solve 2 cos x − 1 = 0 for 0° ≤ x ≤ 360°.[3 marks]
19 Question 19
Solve 2x − 1 = 64.[2 marks]
20 Question 20
y is directly proportional to the square of x. When x = 2, y = 20. Work out y when x = 5.[3 marks]
21 Question 21
A cyclist speeds up from rest to 10 ms in 2 s, keeps that speed for 6 s, then slows to rest in 2 s. Work out the total distance travelled.[3 marks]
22 Question 22
A fair coin is thrown 4 times. Work out the probability of exactly 2 heads.[3 marks]
23 Question 23
Work out (5.4 × 10⁸) ÷ (1.8 × 10⁻³). Give your answer in standard form.[2 marks]
24 Question 24
A boat sails 10 km on a bearing of 030°. How far north and how far east of its start is it?[3 marks]
25 Question 25
A kite string is 50 m long and makes an angle of 20° with the ground. Work out the height of the kite.[3 marks]
26 Question 26
Work out the average rate of change of f(x) = x² from x = 1 to x = 4.[2 marks]
27 Question 27
x = 15.2 and y = 9.7, both correct to 1 decimal place. Work out the upper bound of x − y.[2 marks]
28 Question 28
A cone has base radius 8 m and perpendicular height 6 m. Work out its total surface area.[3 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.