Number worksheet — GCSE Higher

1.A car manufacturer offers a car in 6 colours and 4 trim levels. Two colour-and-trim combinations are not available: red with sport trim, and white with sport trim. Work out how many different colour-and-trim combinations are available.

2.Write 200 as a product of its prime factors, using index notation.

3.Simplify 5⁻² × 5⁴, giving your answer as a single power of 5.

4.A florist has 60 red roses and 84 white roses. She wants to make identical bunches using all the flowers, with the greatest possible number of bunches. Work out how many red roses will be in each bunch.

5.Simplify √8 + √18, giving your answer in the form k√2.

6.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.

7.Work out ⁴√81

8.In a science experiment, the temperature of a liquid is recorded as 18.6 °C, correct to the nearest 0.2 °C. Write down the error interval for the actual temperature, T °C.

9.A gym increases its membership price by 1/5. The original price is £60. Work out the new price.

10.Work out the value of √49 + ∛27

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

12.Work out √25 + 4² − 12 ÷ 3

13.A length, L cm, has the error interval 24.5 ≤ L < 25.5. Write down the degree of accuracy to which the length was measured.

14.A tap fills a 20 litre bucket in 2 minutes 30 seconds. Work out the rate of flow, in litres per minute.

15.A fabric is dyed blue and yellow in the ratio 3 : 5. A tailor uses 1.5 m of blue fabric and the matching amount of yellow fabric needed for the ratio. Work out the total length of fabric used.