Number worksheet — GCSE Higher

1.Work out ((−3) + 5) × (−4) − (−6) ÷ 2

2.Work out (−2)² − 3

3.A weather app records the temperature at three points in one day: 6 °C at noon, −2 °C at midnight, and −7 °C just before dawn. Work out the difference between the highest and lowest of these three temperatures.

4.Work out 3/7 × 14/9. Give your answer as a fraction in its simplest form.

5.The population of a planet is 8 × 10⁹. Write this population as an ordinary number.

6.Write 5/6 as a decimal, showing clearly which digit recurs.

7.A café is planning its lunch menu. It will offer one soup from 3 choices and one sandwich from 4 choices, but the mushroom soup, one of the 3 soups, will only be served with the cheese sandwich, one of the 4 sandwiches, on a normal day. Work out how many different soup-and-sandwich combinations are available on a normal day.

8.A padlock code is formed from 3 different digits chosen from 1, 2, 3, 4, 5 and 6 (no digit may be used twice in the same code). Work out how many different codes can be made.

9.Work out (2/3)² + (1/2)². Give your answer as a fraction.

10.A school orders 187 packed lunches for a trip. Each packed lunch costs £4.85. The school has £900 to spend. By rounding each number to 1 significant figure, work out an estimate for the total cost and decide whether £900 is enough.

11.Which of these is written correctly in standard form?

12.Work out the value of √49 + ∛27

13.A semicircle has a diameter of 8 cm. Work out the exact area of the semicircle, in terms of π.

14.Write 5,000,000 in standard form.

15.A carton of orange juice holds 1.35 litres. Ruby pours the juice equally into 4 identical glasses. Work out how much juice is in each glass, giving your answer as a fraction of a litre in its simplest form.