Number worksheet — GCSE Higher

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

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

3.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?

4.A rectangular tile measures 45 cm by 0.6 m. Work out its area, in square centimetres.

5.Two-digit numbers are formed using the digits 2, 5, 7 and 8, and each digit may be used only once in a number. Work out how many of these two-digit numbers are even.

6.A rectangular plywood panel measures 2.4 m by 0.75 m. Work out the area of the panel in square metres, giving your answer as a fraction in its simplest form.

7.p = 24 and q = 6, each correct to the nearest integer. Work out the greatest degree of accuracy to which p ÷ q can be guaranteed correct.

8.Two-digit numbers are made using the digits 1, 2, 3 and 4, and no digit may be used twice in the same number. Work out how many different two-digit numbers can be made.

9.Work out the value of 6² − 4³.

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

11.Chloe wants to work out 3 1/4 − 1 2/3. She converts both mixed numbers to twelfths, then subtracts the whole numbers and the fraction parts separately, without checking whether she needs to exchange first. Work out the correct value of 3 1/4 − 1 2/3, giving your answer as a mixed number in its simplest form.

12.A rope is measured as 15 m, correct to the nearest metre. Write down the error interval for the true length, l, of the rope.

13.Write 0.005 in standard form.

14.A recipe for one cake needs 2/3 of a cup of sugar. Priya has 3 1/2 cups of sugar. Work out how many complete cakes she can make.

15.Last year a company made a profit of £5,200,000. Write this amount in standard form.