GCSE Maths Foundation Paper 3: calculator
80 marks · 90 minutes · Foundation 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 down all the factors of 28.[1 mark]
2 Question 2
Work out −8 − (−5).[1 mark]
3 Question 3
Work out 2.5² + √12.25.[1 mark]
4(a) Question 4(a)
Expand and simplify (x + 4)(x + 3).[2 marks]
4(b) Question 4(b)
Solve x² + 5x + 6 = 0.[3 marks]
5 Question 5
Solve 5x − 3 > 2x + 9.[2 marks]
6 Question 6
The sequence 2, 9, 16, 23, ... continues in the same way. Work out the 40th term.[2 marks]
7 Question 7
Work out the gradient of the straight line through (−1, 4) and (3, 12).[2 marks]
8 Question 8
Write 3x + y = 7 in the form y = mx + c.[2 marks]
9 Question 9
Work out the midpoint of the line from (1, 5) to (7, −3).[2 marks]
10 Question 10
Five angles of a hexagon are 110°, 125°, 130°, 115° and 120°. Work out the sixth angle.[2 marks]
11 Question 11
A shape is a rectangle 12 cm by 8 cm with a 4 cm by 3 cm rectangle cut out of it. Work out the area of the shape.[3 marks]
12 Question 12
A cuboid measures 6 cm by 4.5 cm by 2 cm. Work out its volume.[2 marks]
13 Question 13
In a right-angled triangle, the side opposite angle x is 5 cm and the hypotenuse is 9 cm. Work out x.[3 marks]
14 Question 14
A right-angled triangle has hypotenuse 17 cm and one of the shorter sides 8 cm. Work out the length of the third side.[3 marks]
The number of goals scored in 8 matches: 2, 0, 3, 1, 4, 2, 2, 6.
15(a) Question 15(a)
Work out the median.[1 mark]
15(b) Question 15(b)
Work out the mean.[2 marks]
16 Question 16
A fair coin is thrown and a fair six-sided dice is rolled. Work out the probability of a head and a 6.[2 marks]
17 Question 17
In a sale, prices are reduced by 20%. A jacket costs £44 in the sale. Work out the price before the sale.[3 marks]
18 Question 18
y is directly proportional to x. When x = 5, y = 35. Work out y when x = 8.[3 marks]
19 Question 19
A boat sails 54 km in 3 hours. Work out its average speed in km/h.[2 marks]
20 Question 20
Change 4 m² into cm².[2 marks]
21 Question 21
Write 3.07 × 10⁵ as an ordinary number.[1 mark]
22 Question 22
Work out the highest common factor (HCF) of 45 and 60.[2 marks]
23 Question 23
Write 45 minutes : 2 hours as a ratio in its simplest form.[2 marks]
24 Question 24
B is due south of A. Write down the bearing of B from A.[1 mark]
25 Question 25
The point (5, 2) is rotated 90° clockwise about the origin. Write down the coordinates of its image.[1 mark]
26 Question 26
Work out the value of 2a² − 3b when a = 4 and b = 5.[2 marks]
27 Question 27
The angles of a triangle are x°, 2x° and (x + 20)°. Form an equation and solve it to find x.[3 marks]
28 Question 28
A sphere has radius 6 cm. Work out its volume.[2 marks]
29 Question 29
A cone has radius 4 cm and perpendicular height 9 cm. Work out its volume.[2 marks]
30 Question 30
Plot the points (1, 9), (2, 8), (3, 8), (4, 5), (5, 6), (6, 3) on a scatter graph and write down the type of correlation.[2 marks]
31 Question 31
A £50 shirt goes up in price by 20%. Then the new price goes down by 20%. Work out the final price.[3 marks]
32 Question 32
A sector of a circle has radius 10 cm and angle 72°. Work out the arc length.[3 marks]
33 Question 33
Two fair coins are thrown. Work out the probability of getting exactly one head.[2 marks]
34 Question 34
An isosceles triangle has a top angle of 52°. Work out each of the two equal angles.[2 marks]
35 Question 35
Change 3.5 km into metres.[1 mark]
36 Question 36
A pen costs x pence and a ruler costs y pence. 3 pens and 2 rulers cost 380p, so 3x + 2y = 380. 1 pen and 2 rulers cost 220p, so x + 2y = 220. Solve the simultaneous equations to find x and y.[5 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.