Number worksheet — GCSE Higher

1.Write 5,000,000 in standard form.

2.Simplify 5⁻² × 5⁴, giving your answer as a single power of 5.

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

4.Tickets for a fairground ride are sold in packs of 6. Tokens for the dodgems are sold in packs of 10. Yusuf wants to buy the smallest number of packs of each so that he ends up with the same number of ride tickets as dodgem tokens. Work out how many ride tickets that is.

5.In a youth club the number of girls is 2/3 of the number of boys. What fraction of the members of the club are girls?

6.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.

7.A concrete mix is made from cement and sand in the ratio 3 : 5 by mass. A builder mixes 96 kg of concrete. Work out the mass of cement in the mix.

8.A number is multiplied by 4, then 8 is added, giving the result 40. Work out the number.

9.In standard form, 2,000 is written as 2 × 10ⁿ. Write down the value of n.

10.A car is hired from 10:00 on Monday until 16:00 on Thursday. Work out the total length of the hire, in hours.

11.In a box of chocolates 5/8 are milk chocolates and the rest are dark chocolates. Work out the number of dark chocolates as a fraction of the number of milk chocolates.

12.Work out an estimate for 79.3 − 24.6, by rounding each number to the nearest whole number.

13.The error interval for the mass of a suitcase, m kg, is given as 22.5 ≤ m < 23.5. Write down the mass of the suitcase, correct to the nearest whole number.

14.A shape is made by joining a rectangle measuring 10 cm by 6 cm to a semicircle of diameter 6 cm along one of the rectangle's shorter sides. Work out the exact area of the shape, in terms of π.

15.The mass of a radioactive sample, in grams, n years after it was first weighed is modelled by M = 200 × (1/2)ⁿ. Work out the mass the model gives after 3 years.