Number worksheet — GCSE Higher

1.The number 36 can be written as 2² × 3², and the number 84 can be written as 2² × 3 × 7. Work out the highest common factor of 36 and 84.

2.Four friends share a restaurant bill of £53.90 equally. A calculator gives each share as 13.475. Work out how much each friend should pay.

3.Meera says that 0.7 ÷ 0.1 = 0.07. Work out the correct value of 0.7 ÷ 0.1.

4.Rationalise the denominator of 6/√3, giving your answer in its simplest form.

5.In a box of chocolates 5/8 are milk chocolates and the rest are dark chocolates. Work out the number of dark chocolates as a fraction of the number of milk chocolates.

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

7.Work out (5 + 2) × 3²

8.Insert one pair of brackets into 2 + 3 × 5 − 1 so that the calculation is equal to 24. Which calculation is correct?

9.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.

10.In a school long jump competition Priya's jump is recorded as 3.8 m and Nadia's jump is recorded as 3.9 m, each correct to the nearest 0.1 m. Priya says she may have jumped further than Nadia. Decide whether Priya is right, and give a reason for your answer.

11.Work out an estimate for 6.4 × 3.9, by rounding each number to the nearest whole number.

12.A number, x, is truncated (not rounded) to 1 decimal place and the result is 6.2. Write down the error interval for x.

13.Rationalise the denominator of 10/(4 − √6), giving your answer in its simplest form.

14.Simplify x⁽³⁄⁴⁾ ÷ x⁽¹⁄⁴⁾

15.A photography studio offers 4 backdrops and 3 outfits for a portrait session. The plain grey backdrop, one of the 4 backdrops, cannot be used with the formal suit outfit, one of the 3 outfits. Work out how many different backdrop-and-outfit combinations are possible.