Number worksheet — GCSE Higher

1.Work out the exact value of √(2² + 3²)

2.Work out an estimate for 6.4 × 3.9, by rounding each number to the nearest whole number.

3.A restaurant adds a service charge of 15% to a bill of £120. Work out the service charge.

4.A rectangular field measures 19.6 m by 48.3 m. Work out an estimate for the area of the field, by rounding each length to 1 significant figure.

5.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.

6.A gardener has 42 tulip bulbs and 56 daffodil bulbs. She plants them in rows, with every row containing the same number of tulip bulbs and the same number of daffodil bulbs, and no bulbs left over. Work out the greatest number of rows she can plant.

7.Round 592.5 to the nearest 10.

8.Work out 1 − 1/2 − 1/4 − 1/8 − 1/16. Give your answer as a fraction.

9.Sam compares 0.6 and 5/8 by comparing the digit 6 with the digit 5, and says that 0.6 is the larger number. Convert 5/8 to a decimal to find the correct larger value.

10.Work out (−6) + (−4) × 3

11.Simplify (5² × 2³)³ ÷ (5³ × 2²)²

12.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.

13.A choir has sopranos, altos and tenors in the ratio 6 : 4 : 5. What fraction of the choir is not tenors?

14.Simplify 3² ÷ 3⁵, giving your answer as a single power of 3.

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.