Number worksheet — GCSE Higher

1.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.

2.Work out (3 × 10²) × (2 × 10⁵). Give your answer in standard form.

3.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.

4.Work out the value of 2⁻²

5.By considering fourth powers, work out which two consecutive integers ⁴√200 lies between.

6.A number, x, is truncated (not rounded) to 1 decimal place and the result is 6.2. Write down the error interval for x.

7.Work out −(−3)⁴ + (−3)³

8.Write these fractions in order, starting with the smallest: 2/3, 3/5, 5/6, 1/2

9.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.

10.A car travels 180 km using 6 litres of fuel. Work out the car's fuel consumption in kilometres per litre, then work out how many kilometres it can travel on a full tank of 12 litres at this rate.

11.A triangle has a base of 8 cm and a perpendicular height of 5 cm, each correct to the nearest centimetre. Work out the upper bound of the area.

12.After a price increase of 10%, a laptop costs £330. Work out the original price.

13.Work out 35% of 180.

14.Sam compares 0.6 and 5/8 by comparing the digit 6 with the digit 5, and says that 0.6 is the larger number. Convert 5/8 to a decimal to find the correct larger value.

15.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.