Number worksheet — GCSE Higher

1.Five different books are placed in a row on a shelf. Work out how many different orders the five books can be placed in.

2.A plumber charges a call-out fee of £45 and then £28 for each hour she works. She is at a house from 09:15 until 12:45. Work out the total charge.

3.Jack buys 3 books, each costing £4.25, and pays with a £20 note. Work out how much change he receives.

4.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.

5.A rope is measured as 15 m, correct to the nearest metre. Write down the error interval for the true length, l, of the rope.

6.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.

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

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

9.The number 24 can be written as 2³ × 3, and the number 60 can be written as 2² × 3 × 5. Work out the lowest common multiple of 24 and 60.

10.A recipe uses 160 g of flour. Sam wants to increase the amount by 1/4. Work out the new amount of flour.

11.Hannah works out 3.1 × 19.6 on her calculator and writes down 6.076. Work out an estimate for 3.1 × 19.6, by rounding each number to 1 significant figure.

12.Simplify ⁴√(16a⁸b¹²)

13.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.

14.Which statement about the number 91 is correct?

15.A fabric is dyed blue and yellow in the ratio 3 : 5. A tailor uses 1.5 m of blue fabric and the matching amount of yellow fabric needed for the ratio. Work out the total length of fabric used.