Number worksheet — GCSE Higher

1.Write down the exact decimal value of the fraction 1/6.

2.Five different books are placed in a row on a shelf. Work out how many different orders the five books can be placed in.

3.Work out (2 × 10³) × (3 × 10⁴). Give your answer in standard form.

4.A café sells ice cream in three flavours: vanilla, mango and pistachio. Isla buys a cone with two scoops, using two different flavours, one for the bottom scoop and one for the top scoop. Work out how many different cones she could buy.

5.A garden path is measured by Jon as 12 m, correct to the nearest metre, and by Mia as 12.6 m, correct to the nearest 0.1 m. Which statement about the two measurements is correct?

6.Round 0.006482 to 2 significant figures.

7.By first working out 2.9², then squaring your result, estimate 2.9⁴ to 2 significant figures.

8.A plank of wood is 5 1/4 m long. Pieces of length 3/4 m are cut from it. Work out how many complete pieces of 3/4 m can be cut from the plank.

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

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

11.Nadia has £84. She spends 3/7 of it on a jacket and the rest on a bag. Work out the ratio of the amount spent on the jacket to the amount spent on the bag, in its simplest form.

12.Without using a calculator, estimate √20 × √12, giving your answer to the nearest whole number.

13.A padlock code is formed from 3 different digits chosen from 1, 2, 3, 4, 5 and 6 (no digit may be used twice in the same code). Work out how many different codes can be made.

14.Rice is sold in a 400 g bag for £1.12 and in a 1.5 kg bag for £3.90. Work out how much less the rice in the larger bag costs per kilogram.

15.Work out how many factors 36 has.