Number worksheet — GCSE Higher

1.The number 72 can be written as 2³ × 3², and the number 108 can be written as 2² × 3³. Work out the highest common factor of 72 and 108.

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

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

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

5.Work out how many factors 100 has.

6.Work out 35% of 180.

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.A spreadsheet shows that 812 − 397 = 315. Work out an estimate for 812 − 397, by rounding each number to the nearest 100, to check whether the spreadsheet's answer is reasonable.

9.c = 50, correct to the nearest 10. d = 18, correct to the nearest whole number. Work out the upper bound of c − d.

10.A country's population is 8,340,000, and it is estimated that 1,950,000 of them live in the capital city. By rounding each number to 1 significant figure, work out an estimate for the number of people who do not live in the capital city.

11.A minibus can carry 16 passengers. A school is taking 179 pupils on a trip. By rounding 179 to the nearest 10, work out an estimate for the number of minibuses needed, given that the school cannot hire part of a minibus.

12.Expand and simplify √3(2 + √12).

13.In a class, 1/3 of the pupils are girls. There are 12 girls in the class. Work out how many pupils are in the class.

14.Work out ⁴√16

15.At a bus station one bus leaves every 6 minutes and another leaves every 9 minutes. The two buses leave together at the start of the day. Work out how long it is until they next leave together.