GCSE Maths Foundation Paper 3 (calculator)
Name: ______________________ Date: __________ Marks: ____ / 80
Time: 90 minutes. You may use a calculator. Answer all questions. Show your working. The marks for each part are shown in brackets. steplyclass.com/gcse-maths/foundation-paper-3/
1 Question 1
Write down all the factors of 28.[1 mark]
Answer: ____________________
2 Question 2
Work out −8 − (−5).[1 mark]
Answer: ____________________
3 Question 3
Work out 2.5² + √12.25.[1 mark]
Answer: ____________________
4(a) Question 4(a)
Expand and simplify (x + 4)(x + 3).[2 marks]
Answer: ____________________
4(b) Question 4(b)
Solve x² + 5x + 6 = 0.[3 marks]
Answer: ____________________
5 Question 5
Solve 5x − 3 > 2x + 9.[2 marks]
Answer: ____________________
6 Question 6
The sequence 2, 9, 16, 23, ... continues in the same way. Work out the 40th term.[2 marks]
Answer: ____________________
7 Question 7
Work out the gradient of the straight line through (−1, 4) and (3, 12).[2 marks]
Answer: ____________________
8 Question 8
Write 3x + y = 7 in the form y = mx + c.[2 marks]
Answer: ____________________
9 Question 9
Work out the midpoint of the line from (1, 5) to (7, −3).[2 marks]
Answer: ____________________
10 Question 10
Five angles of a hexagon are 110°, 125°, 130°, 115° and 120°. Work out the sixth angle.[2 marks]
Answer: ____________________
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]
Answer: ____________________
12 Question 12
A cuboid measures 6 cm by 4.5 cm by 2 cm. Work out its volume.[2 marks]
Answer: ____________________
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]
Answer: ____________________
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]
Answer: ____________________
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]
Answer: ____________________
15(b) Question 15(b)
Work out the mean.[2 marks]
Answer: ____________________
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]
Answer: ____________________
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]
Answer: ____________________
18 Question 18
y is directly proportional to x. When x = 5, y = 35. Work out y when x = 8.[3 marks]
Answer: ____________________
19 Question 19
A boat sails 54 km in 3 hours. Work out its average speed in km/h.[2 marks]
Answer: ____________________
20 Question 20
Change 4 m² into cm².[2 marks]
Answer: ____________________
21 Question 21
Write 3.07 × 10⁵ as an ordinary number.[1 mark]
Answer: ____________________
22 Question 22
Work out the highest common factor (HCF) of 45 and 60.[2 marks]
Answer: ____________________
23 Question 23
Write 45 minutes : 2 hours as a ratio in its simplest form.[2 marks]
Answer: ____________________
24 Question 24
B is due south of A. Write down the bearing of B from A.[1 mark]
Answer: ____________________
25 Question 25
The point (5, 2) is rotated 90° clockwise about the origin. Write down the coordinates of its image.[1 mark]
Answer: ____________________
26 Question 26
Work out the value of 2a² − 3b when a = 4 and b = 5.[2 marks]
Answer: ____________________
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]
Answer: ____________________
28 Question 28
A sphere has radius 6 cm. Work out its volume.[2 marks]
Answer: ____________________
29 Question 29
A cone has radius 4 cm and perpendicular height 9 cm. Work out its volume.[2 marks]
Answer: ____________________
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]
Answer: ____________________
32 Question 32
A sector of a circle has radius 10 cm and angle 72°. Work out the arc length.[3 marks]
Answer: ____________________
33 Question 33
Two fair coins are thrown. Work out the probability of getting exactly one head.[2 marks]
Answer: ____________________
34 Question 34
An isosceles triangle has a top angle of 52°. Work out each of the two equal angles.[2 marks]
Answer: ____________________
35 Question 35
Change 3.5 km into metres.[1 mark]
Answer: ____________________
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]
Answer: ____________________
Answers
- 1 1, 2, 4, 7, 14, 28
- 2 −3
- 3 9.75
- 4(a) x2 + 7x + 12
- 4(b) x = −2 or x = −3
- 5 x > 4
- 6 a40 = 275
- 7 m = 2
- 8 y = −3x + 7
- 9 M = (4, 1)
- 10 x = 120
- 11 A = 84
- 12 V = 54 cm3
- 13 θ ≈ 33.7°
- 14 b = 15
- 15(a) median = 2
- 15(b) mean = 2.5
- 16 P(heads and 6) = 112
- 17 x = 55
- 18 y = 56
- 19 x = 18
- 20 40,000 cm²
- 21 307000
- 22 15
- 23 3 : 8
- 24 bearing 180°
- 25 P' = (2, −5)
- 26 17
- 27 40°, 80°, 60°
- 28 V ≈ 904.32
- 29 V ≈ 150.72 cm3
- 30 strong negative correlation
- 31 £48
- 32 arc = 4π ≈ 12.57 cm
- 33 P(exactly 1 head) = 12
- 34 x = 64
- 35 3.5 km = 3500 m
- 36 (x, y) = (80, 70)
Full mark scheme: steplyclass.com/gcse-maths/foundation-paper-3/mark-scheme/
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