Number worksheet — GCSE Higher

1.Work out 5/6 × 2/9, giving your answer in its simplest form.

2.Write these three numbers in order of size, starting with the smallest: 0.7, 3/4, 0.72

3.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.

4.Work out the reciprocal of (2 + 3)

5.p = 24 and q = 6, each correct to the nearest integer. Work out the greatest degree of accuracy to which p ÷ q can be guaranteed correct.

6.Simplify x⁷ × x⁴, giving your answer as a single power of x.

7.A car travels 100 km, correct to the nearest km, in a time of 2 hours, correct to the nearest 0.1 hour. Work out the average speed, in km/h, to the greatest degree of accuracy the bounds can guarantee.

8.Work out (−2)³ + (−3)² − (−4)

9.A number is divided by 5, then 6 is subtracted, giving the result −1. Work out the number.

10.Simplify x⁶ ÷ x²

11.A set of kitchen scales displays the mass of a bag of sugar as 0.63 recurring kilograms, meaning 0.636363... kg with the block '63' repeating forever. Convert this mass to a fraction of a kilogram, then work out the mass in grams, giving your answer to the nearest gram.

12.Write 12 as a product of its prime factors.

13.Amelia estimates 48 × 21 by working out 50 × 20 = 1,000. Work out whether her estimate is an under-estimate or an over-estimate, and by how much.

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

15.A company sells 4 × 10³ items per day, each priced at £2.50. It operates for 3 × 10² days a year. Work out the company's total revenue for the year. Give your answer in standard form.