Number worksheet — GCSE Higher

1.n is a whole number and 2 ≤ n < 6. Write down all the possible values of n.

2.A plank of wood is 5 1/4 m long. Pieces of length 3/4 m are cut from it. Work out how many complete pieces of 3/4 m can be cut from the plank.

3.Work out an estimate for 588 ÷ 31, by rounding each number to 1 significant figure.

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

5.Work out the value of (√5)⁴

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

7.Without using a calculator, estimate the value of √70 × ∛65, giving your answer to 1 significant figure.

8.A florist has 60 red roses and 84 white roses. She wants to make identical bunches using all the flowers, with the greatest possible number of bunches. Work out how many red roses will be in each bunch.

9.The decimal 0.2333... has one non-recurring digit (the 2) followed by a single recurring digit (the 3), so it can be written as 0.2 recurring 3. Let x = 0.2333... . Work out x as a fraction in its simplest form.

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

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

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

13.A washing machine costs £320 before VAT. VAT is charged at 20%. Work out the total price including VAT.

14.A café sells ice cream in three flavours: vanilla, mango and pistachio. Isla buys a cone with two scoops, using two different flavours, one for the bottom scoop and one for the top scoop. Work out how many different cones she could buy.

15.A lorry travels 105 miles in 1 hour 45 minutes. Work out its average speed in miles per hour.