GCSE Maths Higher Paper 3: 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 58 as a percentage.[1 mark]
2 Question 2
A £200 bag goes down in price by 10%. Later the new price goes up by 10%. Work out the final price.[3 marks]
3 Question 3
A metal has density 8.9 g/cm³. A block of it has volume 25 cm³. Work out its mass.[2 marks]
4 Question 4
Solve 4(2x − 3) = 5(x + 6).[3 marks]
5 Question 5
Simplify (3a²b)³.[2 marks]
6 Question 6
Factorise x³ + 4x² + 3x + 12 by grouping.[2 marks]
7 Question 7
The sequence 50, 46, 42, 38, ... continues in the same way. Work out the 20th term.[2 marks]
8 Question 8
Work out the equation of the line through (1, 4) and (4, 13).[3 marks]
9 Question 9
Work out the distance between (−2, 1) and (4, 9).[2 marks]
10 Question 10
Each exterior angle of a regular polygon is 24°. How many sides does it have?[2 marks]
11 Question 11
In a right-angled triangle, the sides next to the right angle are 7 cm and 11 cm. Work out the smaller angle of the triangle.[3 marks]
12 Question 12
A frustum is cut from a cone of radius 6 cm and height 12 cm by removing a cone of radius 2 cm and height 4 cm from the top. Work out the volume of the frustum.[4 marks]
13 Question 13
A sector has radius 8 cm and arc length 4π cm. Work out the angle of the sector.[3 marks]
14 Question 14
Here are 9 marks: 3, 7, 8, 5, 12, 14, 21, 13, 18. Work out the median and the quartiles, and draw a box plot.[3 marks]
15 Question 15
Masses, m kg, of 30 parcels: 0 < m ≤ 4: 5, 4 < m ≤ 8: 12, 8 < m ≤ 12: 9, 12 < m ≤ 16: 4. Work out an estimate of the mean mass.[4 marks]
16 Question 16
In a class of 32 students, 20 study French, 15 study Spanish and 6 study both. A student is chosen at random. Work out the probability that they study French only.[3 marks]
17 Question 17
A box has 6 red and 4 blue counters. Two are taken at random without replacement. Work out the probability that both are blue.[3 marks]
18 Question 18
Solve x² − 4x = 12 by completing the square.[3 marks]
19 Question 19
Work out the equation of the tangent to y = x² at the point (2, 4).[3 marks]
20 Question 20
A colony of 500 bacteria grows by 8% every hour. How many bacteria are there after 6 hours?[3 marks]
21 Question 21
Triangle XYZ has XY = 7 cm, XZ = 10 cm and angle YXZ = 125°. Work out its area.[3 marks]
22 Question 22
A triangle has sides 7 cm, 8 cm and 9 cm. Work out the largest angle.[3 marks]
23 Question 23
£1 = €1.16. Change €290 into pounds.[2 marks]
24 Question 24
Work out the centre and radius of the circle x² + y² − 6x = 7.[3 marks]
25 Question 25
Ana can paint a fence in 6 hours. Ben can paint the same fence in 12 hours. How long does it take them working together?[3 marks]
26 Question 26
The point (5, 2) is rotated 180° about the point (2, 1). Write down the coordinates of its image.[2 marks]
27 Question 27
A length is 6.4 cm, correct to 1 decimal place. Write down the error interval.[2 marks]
28 Question 28
Here are some data: 2, 15, 17, 18, 20, 21, 23, 45. Use the rule "more than 1.5 × IQR beyond a quartile" to find any outliers.[2 marks]
29 Question 29
Solve 15x − 2 = 3.[3 marks]
30 Question 30
A square has sides of 6 cm. A quarter circle of radius 6 cm, centred on one corner, is cut out. Work out the area that is left.[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.