Number worksheet — GCSE Higher

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

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

3.Work out the value of (1/3)⁻²

4.The recurring decimal 0.181818... can be written as 0.18 recurring, where both digits repeat forever. Let x = 0.18 recurring. Work out x as a fraction in its simplest form.

5.For any two whole numbers, the product of the numbers is equal to the product of their highest common factor and their lowest common multiple. The highest common factor of 6 and 8 is 2, and 6 × 8 = 48. Work out the lowest common multiple of 6 and 8.

6.A minibus can carry 16 passengers. A school is taking 179 pupils on a trip. By rounding 179 to the nearest 10, work out an estimate for the number of minibuses needed, given that the school cannot hire part of a minibus.

7.Simplify √45.

8.Work out ⁴√81

9.A charity raises money from a raffle and a cake sale in the ratio 5 : 3. Altogether the charity raises £320. Work out how much money the cake sale raised.

10.The number of visitors to a museum on Saturday is given as 1,800, correct to the nearest 100. Which of these could not be the actual number of visitors?

11.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?

12.Tickets to a theme park cost £38.50 for an adult and £19.75 for a child. A family estimates the total cost for 4 adults and 3 children, by rounding each ticket price to the nearest £5. Work out their estimate for the total cost.

13.Work out the value of 6² − 4³.

14.A number, n, is a multiple of both 6 and 9. Work out the smallest possible value of n that is greater than 20.

15.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.