Number worksheet — GCSE Higher

1.A cake recipe needs 3/4 of a kilogram of sugar. Aisha wants to make half the recipe. Work out how much sugar she needs, giving your answer as a fraction of a kilogram in its simplest form.

2.At a book fair the ratio of fiction books to non-fiction books is 4 : 5. Of the non-fiction books, 3/5 are about history. Work out the fraction of all the books at the fair that are history books.

3.Work out 35% of 180.

4.To estimate the cost of buying 38.7 m of rope at £21.40 per metre, both numbers are first rounded to 1 significant figure. Work out the estimate.

5.A speed camera measures a car's speed as 34 mph, correct to the nearest mph. Work out the smallest possible actual speed of the car, in mph.

6.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.

7.Work out √3 × √12, giving your answer as an integer.

8.A market trader buys 8 melons at £1.35 each. He sells all of them for a total of £15.60. Work out his profit.

9.Work out 100 − 4 × 5²

10.The number of visitors to a museum on Saturday is given as 1,800, correct to the nearest 100. Which of these could not be the actual number of visitors?

11.Ava measures a metal rod and records its length as 15 cm, correct to the nearest centimetre. Ben measures the same rod and records its length as 14.8 cm, correct to the nearest 0.1 cm. Decide whether both records can be correct, and give a reason for your answer.

12.Write 0.875 as a fraction in its simplest form.

13.By listing systematically, work out how many two-digit multiples of 5 can be made using the digits 0, 3 and 5, if each digit can be used at most once and the number cannot start with 0.

14.Work out 3/7 × 14/9. Give your answer as a fraction in its simplest form.

15.Simplify x⁶ ÷ x²