Number worksheet — GCSE Higher

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

2.Last year a company made a profit of £5,200,000. Write this amount in standard form.

3.A train journey takes 45 minutes, correct to the nearest 5 minutes. Using t for the actual time of the journey in minutes, write down the error interval for t.

4.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.

5.p = 24 and q = 6, each correct to the nearest integer. Work out the greatest degree of accuracy to which p ÷ q can be guaranteed correct.

6.The number 36 can be written as 2² × 3², and the number 84 can be written as 2² × 3 × 7. Work out the highest common factor of 36 and 84.

7.A jumper is reduced by 15% in a sale to a price of £42.50. Work out the original price.

8.A market trader buys 8 melons at £1.35 each. He sells all of them for a total of £15.60. Work out his profit.

9.Simplify x⁷ × x⁴, giving your answer as a single power of x.

10.By first working out 2.9², then squaring your result, estimate 2.9⁴ to 2 significant figures.

11.The number 24 can be written as 2³ × 3, and the number 60 can be written as 2² × 3 × 5. Work out the lowest common multiple of 24 and 60.

12.n is a whole number and 2 ≤ n < 6. Write down all the possible values of n.

13.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.

14.A water tank holds 80 litres when full. It currently contains 60 litres. Work out what fraction of the tank is empty.

15.A charity bake sale sells 187 cakes at £2.95 each. By rounding each number to 1 significant figure, work out an estimate for the total amount raised.