Number worksheet — GCSE Higher

1.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.

2.A cinema has 250 seats. 12% of the seats are reserved. Work out how many of the seats are reserved.

3.Write 0.325 as a fraction in its simplest form.

4.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.

5.A digital timer truncates every time to 1 decimal place. It shows a swimmer's time for one length as 12.3 seconds. Using t for the swimmer's actual time in seconds, write down the error interval for t.

6.A café buys 18 boxes of teabags at £3.45 each, and sells all the teabags for £108 in total. Work out the café's profit.

7.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.

8.Rationalise the denominator of 10/(4 − √6), giving your answer in its simplest form.

9.A plank has length a = 12 cm and a second plank has length b = 7 cm, each correct to the nearest centimetre. Work out the upper bound of a + b.

10.Put these numbers in order, starting with the smallest: 3.2 × 10⁴, 2.9 × 10⁵, 4.1 × 10³

11.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.

12.A number is multiplied by 4, then 8 is added, giving the result 40. Work out the number.

13.In standard form, 2,000 is written as 2 × 10ⁿ. Write down the value of n.

14.A semicircle has a diameter of 8 cm. Work out the exact area of the semicircle, in terms of π.

15.Work out how many factors 36 has.