Number worksheet — GCSE Higher

1.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.

2.Jack buys 3 books, each costing £4.25, and pays with a £20 note. Work out how much change he receives.

3.Which one of these statements is true?

4.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.

5.The density of a metal is calculated using density = mass ÷ volume. A sample has a mass of 156 g, correct to the nearest gram, and a volume of 12 cm³, correct to the nearest cm³. Work out the minimum possible density, in g/cm³.

6.Work out 2 3/4 − 1 5/6. Give your answer as a fraction in its simplest form.

7.The distance from the Earth to the Moon is 384,000 km. Write this distance in standard form, in kilometres.

8.In a school, 3/5 of the students study French. Of these students, 2/3 also study Spanish. What fraction of all the students study both French and Spanish?

9.By listing systematically, work out how many two-digit multiples of 5 can be made using the digits 0, 3 and 5, if each digit can be used at most once and the number cannot start with 0.

10.Work out √(4 × 9)

11.Round 0.006482 to 2 significant figures.

12.Write these three numbers in order of size, starting with the smallest: 0.7, 3/4, 0.72

13.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.

14.A number is divided by 5, then 6 is subtracted, giving the result −1. Work out the number.

15.The two shorter sides of a right-angled triangle are √12 cm and √24 cm. Work out the exact length of the hypotenuse.