Number worksheet — GCSE Higher

1.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?

2.A lorry travels 105 miles in 1 hour 45 minutes. Work out its average speed in miles per hour.

3.Rationalise the denominator of 6/√3, giving your answer in its simplest form.

4.A grain of fine sand has a mass of 0.001 grams. Write this mass in standard form.

5.Work out 2 3/4 − 1 5/6. Give your answer as a fraction in its simplest form.

6.A shop assistant says that 7.2 × 3.9 = 56.16. Work out an estimate for 7.2 × 3.9, by rounding each number to the nearest whole number, to show that the assistant’s answer cannot be correct.

7.A shape is made by joining a rectangle measuring 10 cm by 6 cm to a semicircle of diameter 6 cm along one of the rectangle's shorter sides. Work out the exact area of the shape, in terms of π.

8.Work out (−6) + (−4) × 3

9.A three-digit code is made using the digits 1, 2 and 3, and each digit may be used more than once. Work out how many different three-digit codes can be made.

10.A student works out the exact area of a circle with radius 4 cm by squaring the radius but forgetting to multiply by π. Work out the correct exact area of the circle, in terms of π.

11.Light travels at 2.998 × 10⁸ metres per second. A distant object in space is 3.1 × 10¹⁵ metres from Earth. Work out an estimate for the number of seconds light takes to travel from the object to Earth, by rounding each number to 1 significant figure.

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

13.A school council must choose a committee of 3 pupils from 8 volunteers. The three places on the committee are all the same, so only which pupils are chosen matters. Work out how many different committees could be formed.

14.Work out an estimate for 2.9² + 3.1², by rounding each number to the nearest whole number.

15.Work out the value of (1/3)⁻²