Number worksheet — GCSE Higher

1.Work out ⁴√81

2.A shape is made by joining a rectangle measuring 10 cm by 6 cm to a semicircle of diameter 6 cm along one of the rectangle's shorter sides. Work out the exact area of the shape, in terms of π.

3.The number 72 can be written as 2³ × 3², and the number 108 can be written as 2² × 3³. Work out the highest common factor of 72 and 108.

4.Work out (2 × 10³) × (3 × 10⁴). Give your answer in standard form.

5.Work out the value of 2⁻²

6.By listing systematically, work out how many two-digit multiples of 5 can be made using the digits 0, 3 and 5, if each digit can be used at most once and the number cannot start with 0.

7.Work out an estimate for 8,900 ÷ 29, by rounding each number to 1 significant figure.

8.Work out 100 − 4 × 5²

9.Postage on a parcel is calculated as £4.60, correct to the nearest 20p. Which of these could not be the actual cost of the postage?

10.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.

11.Two bags of mixed nuts are combined. Bag A has peanuts and cashews in the ratio 2 : 3. Bag B has peanuts and cashews in the ratio 1 : 4. Both bags contain the same total number of nuts. Work out the fraction of the combined mixture that is peanuts.

12.A window display has red baubles, gold baubles and green baubles in the ratio 4 : 5 : 6. What fraction of the baubles are not green?

13.Work out −(−3)⁴ + (−3)³

14.Work out (4 × 10³) × (3 × 10¹). Give your answer in standard form.

15.Work out an estimate for 79.3 − 24.6, by rounding each number to the nearest whole number.