Number worksheet — GCSE Higher

1.Simplify √45.

2.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.

3.A circle has a circumference of 8π cm. Work out the exact area of the circle in terms of π.

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

5.A paint mix is made from white paint and blue paint in the ratio 5 : 3. Priya uses 1.2 litres of blue paint and the matching amount of white paint. Work out the total volume of the mix.

6.Work out (−36) ÷ (−6) × 2

7.Round 0.006482 to 2 significant figures.

8.Work out ⁴√16

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

10.Chloe wants to work out 3 1/4 − 1 2/3. She converts both mixed numbers to twelfths, then subtracts the whole numbers and the fraction parts separately, without checking whether she needs to exchange first. Work out the correct value of 3 1/4 − 1 2/3, giving your answer as a mixed number in its simplest form.

11.The number 72 can be written as 2³ × 3², and the number 108 can be written as 2² × 3³. Work out the highest common factor of 72 and 108.

12.By first working out 2.9², then squaring your result, estimate 2.9⁴ to 2 significant figures.

13.A rectangular tile measures 45 cm by 0.6 m. Work out its area, in square centimetres.

14.Two fair six-sided dice are rolled together. One die is red and the other is blue. Work out how many different outcomes are possible.

15.Two bags of mixed nuts are combined. Bag A has peanuts and cashews in the ratio 2 : 3. Bag B has peanuts and cashews in the ratio 1 : 4. Both bags contain the same total number of nuts. Work out the fraction of the combined mixture that is peanuts.