Number worksheet — GCSE Higher

1.Work out ((−3) + 5) × (−4) − (−6) ÷ 2

2.Write these three numbers in order of size, starting with the smallest: 0.7, 3/4, 0.72

3.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.

4.Given that 5³ = 125 and 6³ = 216, use a midpoint test to estimate ∛130 to 1 decimal place.

5.Given that 2⁵ = 32, work out 2⁶.

6.Work out ⁴√16

7.A country's population is 8,340,000, and it is estimated that 1,950,000 of them live in the capital city. By rounding each number to 1 significant figure, work out an estimate for the number of people who do not live in the capital city.

8.Three-digit numbers are made using the digits 2, 3, 4, 6, 8 and 9. No digit may be used twice in the same number. Work out how many of these three-digit numbers are odd.

9.A number is multiplied by 4, then 8 is added, giving the result 40. Work out the number.

10.A café offers sandwiches with one filling from 5 choices and one type of bread from 4 choices. Cheese and mustard, which is one of the 5 fillings, is not available on gluten-free bread, which is one of the 4 breads. Work out how many different sandwiches are possible.

11.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.

12.The highest common factor of two numbers is 4 and their lowest common multiple is 60. One of the numbers is 20. Work out the other number.

13.A circle has a radius of 3 cm. Which of these is the exact area of the circle?

14.A pizza is cut into 12 equal slices. Ben eats 5 slices and Mia eats 3 slices. What fraction of the pizza is left, giving your answer in its simplest form?

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