Number worksheet — GCSE Higher

1.Write these fractions in order, starting with the smallest: 2/3, 3/5, 5/6, 1/2

2.Three-digit numbers are made using the digits 2, 3, 4, 6, 8 and 9. No digit may be used twice in the same number. Work out how many of these three-digit numbers are odd.

3.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.

4.2/3 of an amount of money is £30. Work out the amount.

5.A space probe is 7.5 × 10⁸ km from Earth. Write this distance as an ordinary number.

6.Work out √25 + 4² − 12 ÷ 3

7.Two lighthouses flash at the start of the same minute. The first lighthouse flashes every 8 minutes and the second flashes every 12 minutes. Work out how many minutes it will be until they next flash together.

8.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.

9.Simplify (y³)⁴, giving your answer as a single power of y.

10.A recipe uses 0.625 kg of flour. Write this mass as a fraction of a kilogram, in its simplest form.

11.Four students each estimate √70 without a calculator. Ben says: '8² = 64 and 9² = 81, and 70 is about a third of the way from 64 to 81, so √70 ≈ 8.3.' Chloe says: '8.5² = 72.25, which is close to 70 but a little too big, so I'll bring it down slightly to √70 ≈ 8.4.' Dan says: '9² = 81 is closer to 70 than 8² = 64 is, so √70 ≈ 8.9.' Ella says: '8² = 64 and 9² = 81, so I'll just take the midpoint of 8 and 9: √70 ≈ 8.5.' Given that √70 = 8.3666... to 4 decimal places, whose estimate is closest?

12.Round 592.5 to the nearest 10.

13.Decide which of 2³⁰ and 3²⁰ is the larger number, and write down the correct statement.

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

15.Work out the value of 2⁻²