Number worksheet — GCSE Higher

1.Work out 5/6 × 2/9, giving your answer in its simplest form.

2.Work out (2/3)² + (1/2)². Give your answer as a fraction.

3.The radius of a circular pond is given as 3.2 m, correct to 1 decimal place. Calculate the upper bound for the area of the pond, giving your answer correct to 3 significant figures.

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

5.By considering fourth powers, work out which two consecutive integers ⁴√200 lies between.

6.A charity raises 8 × 10⁶ pounds. This total is shared equally among 2 × 10² local projects. Work out how much each project receives, in standard form.

7.Amelia estimates 48 × 21 by working out 50 × 20 = 1,000. Work out whether her estimate is an under-estimate or an over-estimate, and by how much.

8.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.

9.On a number line, point A is at −1. Point B is 4 units from point A. Write down the two possible positions of point B.

10.A square tile has an area of 72 cm². Work out the exact perimeter of the tile, giving your answer in the form k√2 cm.

11.A school orders 187 packed lunches for a trip. Each packed lunch costs £4.85. The school has £900 to spend. By rounding each number to 1 significant figure, work out an estimate for the total cost and decide whether £900 is enough.

12.Work out (−36) ÷ (−6) × 2

13.Given that 2⁵ = 32, work out 2⁶.

14.Work out (5 × 10⁴) ÷ (2 × 10⁻²). Give your answer in standard form.

15.A cube-shaped storage tank has a volume of 15,625 cubic centimetres. Work out the length of one edge of the tank.