Number worksheet — GCSE Higher

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

2.Work out 3 + 4 × (−2).

3.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.

4.The decimal 0.272727... repeats the block 27 for ever. Write 0.27 recurring as a fraction in its simplest form.

5.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.

6.The thickness of a sheet of card is 0.02384 cm. Write this thickness correct to 2 significant figures.

7.Hannah works out 3.1 × 19.6 on her calculator and writes down 6.076. Work out an estimate for 3.1 × 19.6, by rounding each number to 1 significant figure.

8.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.

9.Grace works out 7 × 99 by writing 99 as 100 − 1. Use her method to work out 7 × 99.

10.Which of these statements about −0.7 and −0.25 is true?

11.Work out an estimate for 8,900 ÷ 29, by rounding each number to 1 significant figure.

12.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.

13.Expand and simplify (2 + √3)², giving your answer in the form a + b√3.

14.A machine fills bags of sugar and shows the mass of each bag to the nearest 10 g. A checker rejects any bag whose actual mass is less than 996 g. One bag shows a mass of 1,000 g on the machine. Decide whether this bag could be rejected, and give a reason for your answer.

15.Work out 3/7 × 14/9. Give your answer as a fraction in its simplest form.