Number worksheet — GCSE Higher

1.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?

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

3.A quarter-circle has a radius of 6 cm. Work out the exact perimeter of the quarter-circle, giving your answer in terms of π.

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

5.Work out ∛64.

6.A school orders 187 packed lunches for a trip. Each packed lunch costs £4.85. The school has £900 to spend. By rounding each number to 1 significant figure, work out an estimate for the total cost and decide whether £900 is enough.

7.In a school, 3/5 of the students study French. Of these students, 2/3 also study Spanish. What fraction of all the students study both French and Spanish?

8.The length of a pencil is 8.4 cm, correct to 1 decimal place. Using L for the length of the pencil in centimetres, write down the error interval for L.

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

10.Simplify (5² × 2³)³ ÷ (5³ × 2²)²

11.A tank contains 120 litres of water. Water is drained out at a rate of 8 litres per minute for 6 minutes, and then a hose adds 15 litres. Work out how much water is left in the tank.

12.Work out the value of √49 + ∛27

13.A cake recipe needs 3/4 of a kilogram of sugar. Aisha wants to make half the recipe. Work out how much sugar she needs, giving your answer as a fraction of a kilogram in its simplest form.

14.A photograph uses 4 × 10⁶ bytes of storage. A memory card holds 3.2 × 10¹⁰ bytes. Work out how many of these photographs the card can hold. Give your answer in standard form.

15.A sponsored walk is 36 km long. Aisha has completed 8/12 of the walk. Work out how far she has walked.