Number worksheet — GCSE Higher

1.In a music collection, the ratio of pop albums to rock albums is 5 : 3. Work out the number of rock albums as a fraction of the number of pop albums.

2.Work out (6 × 10⁷) + (3 × 10⁶). Give your answer in standard form.

3.A space probe is 7.5 × 10⁸ km from Earth. Write this distance as an ordinary number.

4.Work out 3/4 − 5/12 exactly, giving your answer in its simplest form.

5.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.

6.Four locations each record a temperature one winter morning. Which of these temperatures is the coldest?

7.Simplify x⁽³⁄⁴⁾ ÷ x⁽¹⁄⁴⁾

8.Work out (−3) × 4 + 2 × (−5)

9.Write 7/12 as a decimal, showing clearly which digit is recurring.

10.Write these numbers in order, starting with the largest: −0.6, 0.45, −0.15, 0.5, −0.09

11.Write down the symbol that makes this statement true: −2/3 ___ −5/6

12.A grain of fine sand has a mass of 0.001 grams. Write this mass in standard form.

13.Work out the value of √(16 + 9)

14.A driving instructor is working out how many current-style UK number plates are possible. The format is 2 letters, then 2 digits, then a space, then 3 letters (for example AB12 CDE). The letters I, O and Q are never used in any letter position, leaving 23 allowed letters, but every letter and every digit may repeat anywhere on the plate. Work out how many different number plates are possible, giving your answer in standard form to 2 significant figures.

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