Total marks: 80 · Duration: 90 minutes · Tier: Foundation
Instructions to candidates
- Use black ink or ball-point pen.
- Answer all questions.
- You must show all your working. Answers given without working may not gain full marks.
- You may use a calculator.
- If your calculator does not have a π button, take the value of π to be 3.142 unless the question says otherwise.
- Diagrams are NOT accurately drawn. Where a question describes a shape in words, you may find it helpful to sketch it before you start.
- The total mark for this paper is 80. The marks for each question are shown in brackets.
Information
- Questions get harder as the paper goes on. If you get stuck, move on and come back later.
- Write down the full calculator display before you round, so that you can earn method marks.
Paper
1. (a) Write 7/8 as a decimal.
(1 mark)
(b) Work out √17.64
(1 mark)
(c) Work out 3.7² + 2.1³. Write down all the figures on your calculator display.
(2 marks)
2. Here is a list of numbers.
23 27 36 49 56 12
From the list, write down
(a) a multiple of 7 that is between 50 and 60
(1 mark)
(b) a factor of 36 that is greater than 10
(1 mark)
(c) a prime number
(1 mark)
3. The Patel family's electricity bill is worked out using these charges.
Standing charge: 45p per day Electricity used: 28.4p per kWh (kilowatt-hour)
In one quarter there were 92 days and the family used 760 kWh.
Work out the total cost of the electricity bill for the quarter. Give your answer in pounds.
(4 marks)
4. Here are the ages, in years, of 7 children at a party.
12 15 9 15 20 11 18
(a) Work out the median age.
(1 mark)
(b) Work out the range of the ages.
(1 mark)
(c) Work out the mean age. Give your answer correct to 1 decimal place.
(2 marks)
5. Carla wants to buy a pair of headphones.
In the UK, the headphones cost £340. In France, the same headphones cost €395.
The exchange rate is £1 = €1.16.
In which country are the headphones cheaper, and by how much? Give your answer in pounds. You must show your working.
(3 marks)
6. AB and CD are two parallel straight lines. A third straight line crosses AB at the point P and crosses CD at the point Q. Points A and C are on the left, points B and D are on the right, and P is above Q.
Angle BPQ = 64°.
Work out the size of angle PQC. Give a reason for your answer.
(2 marks)
7. A garden lawn is in the shape of a trapezium. The parallel sides are 8 m and 12 m long. The perpendicular distance between them is 5 m.
Turf costs £4.85 per square metre.
Work out the cost of buying enough turf to cover the whole lawn.
(3 marks)
8. (a) Dan's salary is £24 500 per year. He gets a pay rise of 3.5%.
Work out his new salary.
(2 marks)
(b) The price of a house increased from £180 000 to £207 000.
Work out the percentage increase in the price.
(2 marks)
9. The time, T minutes, needed to cook a chicken that weighs w kg is given by the formula
T = 40w + 20
(a) Work out the cooking time for a chicken that weighs 2.5 kg.
(2 marks)
(b) Another chicken needs 180 minutes to cook. Work out its weight.
(2 marks)
10. Joe rolls a six-sided dice 200 times. He gets a six 52 times.
(a) Work out the relative frequency of getting a six.
(1 mark)
(b) Joe says, "The dice is biased towards six." Is there evidence to support Joe? You must show your working.
(2 marks)
11. A bicycle wheel has a diameter of 64 cm. The wheel turns 500 times.
Work out the distance the bicycle travels. Give your answer in metres, correct to the nearest metre.
(3 marks)
12. 5 pens cost £3.40. Work out the cost of 8 of the same pens.
(2 marks)
13. Amira runs 10 km in 52 minutes 30 seconds.
Work out her average speed in kilometres per hour. Give your answer correct to 1 decimal place.
(3 marks)
14. A wheelchair ramp rises 0.45 m vertically over a horizontal distance of 3.2 m.
Building rules say that the angle between a ramp and the horizontal must be no more than 10°.
Does this ramp follow the building rules? You must show your working.
(3 marks)
15. A cylinder has radius 3.5 cm and height 12 cm.
Work out the volume of the cylinder. Give your answer correct to 1 decimal place.
(2 marks)
16. Work out (6.4 × 10⁶) ÷ (1.6 × 10²). Give your answer in standard form.
(2 marks)
17. At a theme park:
2 adult tickets and 3 child tickets cost £47. 1 adult ticket and 2 child tickets cost £27.50.
Work out the cost of one adult ticket and the cost of one child ticket.
(4 marks)
18. Hannah invests £2000 in an account paying 2.5% compound interest per year.
Work out the amount in the account after 3 years. Give your answer to the nearest penny.
(3 marks)
19. ABC is a right-angled triangle. Angle ABC = 90°, AC = 9 cm and angle BAC = 38°.
Work out the length of BC. Give your answer correct to 3 significant figures.
(2 marks)
20. Solve x² − 5x − 14 = 0 by factorising.
(3 marks)
21. The length, L cm, of a pencil is 7.4 cm, correct to 1 decimal place.
Write down the error interval for L.
(2 marks)
22. The table shows the hours of revision and the test marks of 8 students.
| Hours of revision | 2 | 5 | 1 | 8 | 4 | 6 | 3 | 7 |
|---|---|---|---|---|---|---|---|---|
| Test mark | 34 | 55 | 30 | 72 | 48 | 61 | 41 | 18 |
(a) One student's result does not fit the pattern of the others. Write down the hours of revision and the test mark for this student.
(1 mark)
(b) Ignoring that student, describe the relationship between hours of revision and test mark.
(1 mark)
23. (a) Here are the first four terms of a Fibonacci-type sequence, where each term is the sum of the two terms before it.
3 4 7 11
Write down the next two terms.
(1 mark)
(b) Here are the first three terms of a geometric sequence.
2 6 18
Work out the 6th term of the sequence.
(2 marks)
24. A map has a scale of 1 : 25 000. On the map, the distance between two villages is 6.4 cm.
Work out the real distance between the villages. Give your answer in kilometres.
(2 marks)
25. 72 people were asked how they travel to work. The results are to be shown in a pie chart.
(a) 18 people walk. Work out the angle of the sector for walking.
(2 marks)
(b) The angle of the sector for bus is 140°. Work out how many people travel by bus.
(2 marks)
26. Solve 4x − 3 > 2x + 9
(2 marks)
27. (a) A block of metal has a mass of 540 g and a volume of 200 cm³. Work out the density of the metal.
(2 marks)
(b) Another block is made of the same metal. Its volume is 350 cm³. Work out its mass.
(2 marks)
TOTAL FOR PAPER: 80 MARKS