Number worksheet — GCSE Higher

1.Simplify √8 + √18, giving your answer in the form k√2.

2.A cinema has 250 seats. 12% of the seats are reserved. Work out how many of the seats are reserved.

3.Work out 3/7 × 14/9. Give your answer as a fraction in its simplest form.

4.Which of these numbers rounds to 0.048 when rounded to 2 significant figures?

5.Simplify ⁴√(16a⁸b¹²)

6.Work out (−6) + (−4) × 3

7.The two shorter sides of a right-angled triangle are √12 cm and √24 cm. Work out the exact length of the hypotenuse.

8.A gardener has 42 tulip bulbs and 56 daffodil bulbs. She plants them in rows, with every row containing the same number of tulip bulbs and the same number of daffodil bulbs, and no bulbs left over. Work out the greatest number of rows she can plant.

9.A charity bake sale sells 187 cakes at £2.95 each. By rounding each number to 1 significant figure, work out an estimate for the total amount raised.

10.Work out (−36) ÷ (−6) × 2

11.Decide which of 2³⁰ and 3²⁰ is the larger number, and write down the correct statement.

12.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.

13.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.

14.A shortbread recipe uses flour and butter in the ratio 5 : 2. Yuki changes the recipe by doubling the amount of butter but keeping the amount of flour the same. Work out the fraction of the new mixture that is butter.

15.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.