Total marks: 80 · Duration: 90 minutes · Tier: Foundation
Instructions to candidates
- Use black ink or black ball-point pen. Draw diagrams in pencil.
- Answer all questions.
- You must answer the questions in the spaces provided.
- In all calculations, show clearly how you work out your answer.
- You may use a calculator.
- Diagrams are not accurately drawn, unless otherwise indicated. Where a question describes a shape in words, you may find it helpful to sketch it.
Information
- The marks for questions are shown in brackets.
- The maximum mark for this paper is 80.
- Where a question asks you to circle your answer, choose one of the four options.
Paper
1 Circle the prime number.
21 27 29 33
[1 mark]
2 Circle 3/8 written as a decimal.
0.38 0.375 3.8 0.0375
[1 mark]
3 Circle the name of a polygon with 8 sides.
heptagon nonagon decagon octagon
[1 mark]
4 Circle 1% of 4500
45 4.5 450 0.45
[1 mark]
5 (a) Write these numbers in order of size. Start with the smallest.
0.6 5/8 0.58 62%
[2 marks]
5 (b) Work out 2.6³ − 1.4 × 5.2
Write down all the figures on your calculator display.
[1 mark]
6 Here is a function machine.
Input → × 3 → − 5 → Output
The output is 16. Work out the input.
[2 marks]
7 A recipe for 4 people uses
300 g flour 2 eggs 150 ml milk
Lena makes the recipe for 10 people. Work out how much of each ingredient she needs.
[3 marks]
8 A trapezium has parallel sides of length 7 cm and 11 cm. The perpendicular distance between the parallel sides is 5 cm.
Work out the area of the trapezium.
[2 marks]
9 The table shows the number of pets owned by 20 students.
| Number of pets | Frequency |
|---|---|
| 0 | 6 |
| 1 | 9 |
| 2 | 4 |
| 3 | 1 |
9 (a) Write down the mode.
[1 mark]
9 (b) Work out the mean number of pets.
[3 marks]
10 PQ and RS are parallel straight lines. P is directly above R, so P and R are on the left. A straight line crosses PQ at A and RS at B.
Angle PAB = 68°
Work out the size of angle ABR. Give a reason for your answer.
[2 marks]
11 The exchange rate is £1 = €1.16
11 (a) Tom changes £350 into euros. How many euros does he get?
[1 mark]
11 (b) Tom changes €100 back into pounds at the same rate. How many pounds does he get? Give your answer to the nearest penny.
[2 marks]
12 Asha invests £2000 for 4 years at 3% per year simple interest.
Work out the total value of her investment after 4 years.
[2 marks]
13 T = 3a² − 2b
Work out the value of T when a = 4 and b = −5
[2 marks]
14 Write the ratio 450 g : 1.2 kg in its simplest form.
[2 marks]
15 P is the point (3, 1).
15 (a) P is reflected in the y-axis. Write down the coordinates of the new point.
[1 mark]
15 (b) P is translated 2 units right and 5 units down. Write down the coordinates of the new point.
[1 mark]
16 Kai walks 9.6 km at an average speed of 4 km/h. He sets off at 10:45
At what time does he finish his walk?
[3 marks]
17 A rectangle has length (2x − 1) cm and width (x + 5) cm. The perimeter of the rectangle is 50 cm.
Work out the value of x.
[3 marks]
18 80 students were asked how they travel to school. The table shows some of the results.
| Walk | Bus | Car | Total | |
|---|---|---|---|---|
| Boys | 14 | 9 | 38 | |
| Girls | 12 | 42 | ||
| Total | 30 | 80 |
18 (a) Work out the missing values in the table.
[3 marks]
18 (b) One of the girls is chosen at random. Work out the probability that she travels by bus.
[1 mark]
19 A shape is a semicircle with diameter 12 cm.
Work out the perimeter of the shape. Give your answer to 1 decimal place.
[3 marks]
20 Amy, Ben and Cal share £720. Amy gets 1/4 of the money. Ben and Cal share the rest in the ratio 2 : 7.
How much does Cal get?
[3 marks]
21 Solve 5x − 3 > 2x + 9
[2 marks]
22 A trader buys 40 vases for £12 each. She sells 30 of the vases for £20 each. She sells the other 10 vases at half of this price.
Work out her percentage profit. Give your answer to 1 decimal place.
[4 marks]
23 A prism is 15 cm long. Its cross-section is a triangle with a base of 6 cm and a perpendicular height of 4 cm.
Work out the volume of the prism.
[2 marks]
24 The table shows the number of hours of sunshine and the number of ice creams sold at a beach café on 8 days.
| Hours of sunshine | 2 | 3 | 4 | 5 | 6 | 7 | 9 | 10 |
|---|---|---|---|---|---|---|---|---|
| Ice creams sold | 14 | 20 | 23 | 31 | 34 | 40 | 52 | 55 |
24 (a) Describe the type of correlation shown by the data.
[1 mark]
24 (b) Explain why it would not be reliable to use these data to estimate the number of ice creams sold on a day with 14 hours of sunshine.
[1 mark]
25 Factorise fully 12x² + 8x
[2 marks]
26 A fish tank is a cuboid. It is 80 cm long, 50 cm wide and 60 cm high. Water flows into the empty tank at 12 litres per minute.
1 litre = 1000 cm³
How many minutes does it take to fill the tank?
[3 marks]
27 Triangles ABC and PQR are mathematically similar. AB = 6 cm, BC = 8 cm and PQ = 15 cm. AB corresponds to PQ, and BC corresponds to QR.
Work out the length of QR.
[2 marks]
28 Light travels at 3 × 10⁸ metres per second. The distance from the Sun to the Earth is 1.5 × 10¹¹ metres.
How many seconds does it take light to travel from the Sun to the Earth?
[2 marks]
29 A is the point (2, 7) and B is the point (8, −1).
29 (a) Work out the coordinates of the midpoint of AB.
[1 mark]
29 (b) Work out the gradient of the line AB.
[2 marks]
30 ξ = {whole numbers from 1 to 12} A = {multiples of 3} B = {factors of 12}
30 (a) List the members of A ∩ B.
[2 marks]
30 (b) A number is chosen at random from ξ. Work out the probability that it is in A ∪ B.
[1 mark]
31 A triangle has sides of length 9 cm, 12 cm and 15 cm.
Show that the triangle is right-angled.
[2 marks]
32 (a) Complete the table of values for y = 2x² − 3
| x | −2 | −1 | 0 | 1 | 2 |
|---|---|---|---|---|---|
| y | 5 | 5 |
[2 marks]
32 (b) Write down the coordinates of the lowest point on the graph of y = 2x² − 3
[1 mark]
33 Solve x² + 2x − 15 = 0
[3 marks]