Number worksheet — GCSE Higher

1.Work out (5 × 10⁴) ÷ (2 × 10⁻²). Give your answer in standard form.

2.Two fair six-sided dice are rolled together. One die is red and the other is blue. Work out how many different outcomes are possible.

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

4.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.

5.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.

6.Three-digit numbers are made using the digits 2, 3, 4, 6, 8 and 9. No digit may be used twice in the same number. Work out how many of these three-digit numbers are odd.

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

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

9.Round 0.006482 to 2 significant figures.

10.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.

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

12.A charity raises 8 × 10⁶ pounds. This total is shared equally among 2 × 10² local projects. Work out how much each project receives, in standard form.

13.A number, y, is equal to 8.2 when rounded to 1 decimal place. Write down the error interval for y.

14.Hannah works out 3.1 × 19.6 on her calculator and writes down 6.076. Work out an estimate for 3.1 × 19.6, by rounding each number to 1 significant figure.

15.A metal cube has a mass of 540 g and a volume of 60 cm³. Work out its density in g/cm³.