Number worksheet — GCSE Higher

1.A student works out the exact area of a circle with radius 4 cm by squaring the radius but forgetting to multiply by π. Work out the correct exact area of the circle, in terms of π.

2.A netball team has 8 players. Two of them are chosen to be captains, and the two captains have equal standing. Work out how many different pairs of captains could be chosen.

3.Simplify x⁽³⁄⁴⁾ ÷ x⁽¹⁄⁴⁾

4.Write these decimals in order, starting with the smallest: 0.6, 0.55, 0.601, 0.5, 0.56

5.A recipe uses 160 g of flour. Sam wants to increase the amount by 1/4. Work out the new amount of flour.

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

7.The decimal 0.111... has the digit 1 repeating for ever. Write 0.1 recurring as a fraction in its simplest form.

8.The rainfall in a town during April is recorded as 62.4 mm, correct to 1 decimal place. Write down the error interval for the actual rainfall, r mm.

9.A box stands on a table. The box exerts a force of 240 N on the table, and the base of the box has an area of 0.8 m². Work out the pressure the box exerts on the table, in N/m².

10.A sponsored walk is 36 km long. Aisha has completed 8/12 of the walk. Work out how far she has walked.

11.Simplify (y³)⁴, giving your answer as a single power of y.

12.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.

13.Work out 5⁰ + 5¹ + 5²

14.A board game has 5 different character pieces and 4 different colour tokens. The dragon piece can only be used with the gold token. Work out how many different combinations of one character piece and one colour token are possible.

15.Work out √144 − 2 × 3 + √25