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 these numbers in order of size. Start with the smallest.
0.6 2/3 65% 0.606
(2 marks)
(b) Round 6.4857 to 2 decimal places.
(1 mark)
(c) Round 6.4857 to 1 significant figure.
(1 mark)
2. A film starts at 19 40. It lasts 2 hours 25 minutes.
(a) At what time does the film end? Give your answer using the 24-hour clock.
(1 mark)
(b) Write your answer to part (a) using the 12-hour clock.
(1 mark)
3. Concrete is made by mixing cement, sand and gravel in the ratio
cement : sand : gravel = 1 : 2 : 4
A builder makes 350 kg of concrete. Work out the mass of sand she uses.
(2 marks)
4. A floor is in the shape of a letter L. It is made from a rectangle 10 m long and 6 m wide, with a rectangle 4 m long and 3 m wide cut out of one corner.
(a) Work out the area of the floor.
(2 marks)
(b) Work out the perimeter of the floor.
(2 marks)
5. (a) Work out 3/8 of 96.
(1 mark)
(b) Ella has £240. She spends 2/5 of it on a coat. She then spends 1/3 of the money she has left on shoes.
How much money does Ella have left at the end?
(3 marks)
6. Ravi is choosing between two phone deals. Each deal lasts for 24 months.
Deal A: £18 per month. The phone is free. Deal B: £12 per month, plus £150 to pay for the phone at the start.
Which deal is cheaper over the 24 months, and by how much? You must show your working.
(4 marks)
7. A is the point (2, 7). B is the point (8, −1).
(a) Work out the coordinates of the midpoint of AB.
(2 marks)
(b) Work out the gradient of the line AB.
(2 marks)
8. 60 students were asked how they travel to school. The two-way table shows some of the information.
| Walk | Bus | Car | Total | |
|---|---|---|---|---|
| Boys | 14 | 7 | ||
| Girls | 9 | 28 | ||
| Total | 25 | 15 | 60 |
(a) Complete the two-way table.
(3 marks)
(b) One of the girls is chosen at random. Work out the probability that she travels to school by car.
(2 marks)
9. A pizza shop sells two sizes of round pizza.
A large pizza has a diameter of 30 cm. A medium pizza has a diameter of 20 cm.
Sam says, "Two medium pizzas give you more pizza than one large pizza."
Is Sam correct? You must show your working.
(3 marks)
10. (a) The price of a TV is £84 before VAT is added. VAT is charged at 20%.
Work out the price of the TV including VAT.
(2 marks)
(b) In a sale, a jacket that normally costs £64 is reduced by 35%.
Work out the sale price of the jacket.
(2 marks)
11. (a) Expand and simplify 3(2x + 5) − 2(x − 4)
(2 marks)
(b) Factorise fully 6x² − 9x
(2 marks)
12. ABC is a right-angled triangle. Angle ABC = 90°. BC = 7 cm and AB = 11 cm.
Work out the size of angle BAC. Give your answer correct to 1 decimal place.
(2 marks)
13. A television screen is a rectangle 120 cm wide and 68 cm high. TV screens are described by the length of their diagonal in inches.
1 inch = 2.54 cm
The shop describes this television as a "55-inch TV". Work out the length of the diagonal in inches, and say whether the shop's description is accurate to the nearest inch.
(3 marks)
14. A car travels at an average speed of 48 miles per hour for 2 hours 15 minutes.
Work out the distance the car travels.
(2 marks)
15. It takes 6 workers 15 days to build a wall. All the workers work at the same rate.
How many days would it take 9 workers to build the same wall?
(2 marks)
16. A cuboid measures 8 cm by 5 cm by 3 cm.
Work out the total surface area of the cuboid.
(2 marks)
17. Spinner P has four equal sections numbered 1, 2, 3 and 4. Spinner Q has three equal sections numbered 1, 2 and 3. Both spinners are spun and the two numbers are added to give a score.
(a) List all the possible outcomes, or draw a sample space diagram.
(1 mark)
(b) Work out the probability that the score is 5.
(2 marks)
18. Megan has £5000 to invest for 4 years. She can choose one of two accounts.
Account 1: 3% simple interest per year. Account 2: 2.9% compound interest per year.
Which account gives Megan more interest after 4 years, and by how much? You must show your working.
(4 marks)
19. Solve (x + 4)/3 = 2x − 7
(3 marks)
20. The perimeter, P, of a rectangle with length l and width w is given by
P = 2l + 2w
Make w the subject of the formula.
(2 marks)
21. (a) Complete the table of values for y = x² − 2x − 3
| x | −2 | −1 | 0 | 1 | 2 | 3 | 4 |
|---|---|---|---|---|---|---|---|
| y | 5 | −3 | 0 |
(2 marks)
(b) Use your table to write down the solutions of x² − 2x − 3 = 0
(1 mark)
22. Triangles P and Q are mathematically similar. Triangle P has sides 4 cm and 6 cm. The corresponding sides of triangle Q are 10 cm and x cm.
Work out the value of x.
(2 marks)
23. Light travels at 3 × 10⁸ metres per second. The distance from the Sun to the Earth is 1.5 × 10¹¹ metres.
Work out how long it takes light to travel from the Sun to the Earth. Give your answer in minutes and seconds.
(3 marks)
24. A number, x, is truncated to 1 decimal place. The result is 4.7.
Write down the error interval for x.
(2 marks)
25. Two classes took the same test.
Class A: mean 62 marks, range 30 marks. Class B: mean 58 marks, range 12 marks.
Compare the marks of the two classes.
(2 marks)
26. The bearing of B from A is 065°.
Work out the bearing of A from B.
(2 marks)
27. The price of a bike went up by 12%. The new price is £61.60.
Work out the price of the bike before the increase.
(3 marks)
TOTAL FOR PAPER: 80 MARKS