Number worksheet — GCSE Higher

1.Work out (−36) ÷ (−6) × 2

2.A student writes 0.08 as the fraction 8/10, reading the 8 as if it stood in the tenths column and ignoring the zero. Work out the correct fraction that 0.08 is equal to, giving your answer in its simplest form.

3.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.

4.Postage on a parcel is calculated as £4.60, correct to the nearest 20p. Which of these could not be the actual cost of the postage?

5.A crowd of 8,400 people is recorded correct to the nearest 100. Work out the smallest possible number of people in the crowd.

6.4ˣ = 64. Work out the value of x.

7.Given that 4³ = 64 and 5³ = 125, estimate ∛100 to 1 decimal place.

8.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.

9.The distance from the Earth to the Moon is 384,000 km. Write this distance in standard form, in kilometres.

10.Work out (8 × 10⁻⁵) × (5 × 10³). Give your answer in standard form.

11.Work out 36 ÷ (2 × 3)

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

13.A shop buys boxes of pens for £4 each. It sells each box on to a school for £3 more than it paid, and charges an extra £2 delivery fee for the whole order. A school orders 5 boxes. Work out the total cost of the order.

14.Work out 3 1/5 + 1 2/3. Give your answer as a mixed number in its simplest form.

15.Tickets for a fairground ride are sold in packs of 6. Tokens for the dodgems are sold in packs of 10. Yusuf wants to buy the smallest number of packs of each so that he ends up with the same number of ride tickets as dodgem tokens. Work out how many ride tickets that is.