Number worksheet — GCSE Higher

1.For any two whole numbers, the product of the numbers is equal to the product of their highest common factor and their lowest common multiple. The highest common factor of 6 and 8 is 2, and 6 × 8 = 48. Work out the lowest common multiple of 6 and 8.

2.A roll of ribbon is 8.4 m long. Ribbon is cut into pieces that are each 0.6 m long. Work out how many complete pieces can be cut from the roll.

3.Without using a calculator, estimate the value of √70 × ∛65, giving your answer to 1 significant figure.

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

5.Work out √3 × √12, giving your answer as an integer.

6.In a school long jump competition Priya's jump is recorded as 3.8 m and Nadia's jump is recorded as 3.9 m, each correct to the nearest 0.1 m. Priya says she may have jumped further than Nadia. Decide whether Priya is right, and give a reason for your answer.

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

8.By considering fourth powers, work out which two consecutive integers ⁴√200 lies between.

9.Leah measures the length of her classroom with a tape measure marked in centimetres. She writes the length down as 7.3157 m. Give a reason why this is not an appropriate degree of accuracy.

10.Simplify (x⁻²)³, giving your answer as a fraction.

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

12.c = 50, correct to the nearest 10. d = 18, correct to the nearest whole number. Work out the upper bound of c − d.

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

14.Light travels at 3 × 10⁸ metres per second. Work out how far light travels in 2 × 10⁻⁶ seconds. Give your answer in standard form.

15.At a swimming pool the ratio of adults to children is 3 : 5. Of the children, 2/5 are boys. What fraction of the people at the pool are boys?