Number worksheet — GCSE Higher

1.A circle has a circumference of 8π cm. Work out the exact area of the circle in terms of π.

2.Ten athletes run in a final. Gold, silver and bronze medals are awarded to the first three athletes to finish, and there are no ties. Work out how many different ways the three medals can be awarded.

3.Oliver drives 95 km at an average speed of 50 km/h. Work out an estimate for the time the journey takes, by rounding the distance to the nearest 100 km.

4.Work out (−3) × 4 + 2 × (−5)

5.Work out (3 × 10²) × (2 × 10⁵). Give your answer in standard form.

6.Work out √144 − 2 × 3 + √25

7.A paint mix is made from white paint and blue paint in the ratio 5 : 3. Priya uses 1.2 litres of blue paint and the matching amount of white paint. Work out the total volume of the mix.

8.A number, x, is truncated (not rounded) to 1 decimal place and the result is 6.2. Write down the error interval for x.

9.A café is planning its lunch menu. It will offer one soup from 3 choices and one sandwich from 4 choices, but the mushroom soup, one of the 3 soups, will only be served with the cheese sandwich, one of the 4 sandwiches, on a normal day. Work out how many different soup-and-sandwich combinations are available on a normal day.

10.A garden path is measured by Jon as 12 m, correct to the nearest metre, and by Mia as 12.6 m, correct to the nearest 0.1 m. Which statement about the two measurements is correct?

11.A rectangular tile measures 45 cm by 0.6 m. Work out its area, in square centimetres.

12.A flight departs at 21:35 and lands at 06:10 the following morning. Work out the total flight time.

13.Work out 3³ + 2⁴.

14.Work out 35% of 180.

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