Number worksheet — GCSE Higher

1.Simplify 2³ × 2⁴, giving your answer as a single power of 2.

2.Simplify (x⁻²)³, giving your answer as a fraction.

3.Expand and simplify √3(2 + √12).

4.A recipe needs 0.485 kg of flour per cake. A bakery estimates its flour order by rounding this amount to 1 significant figure, then multiplying by the 60 cakes it plans to bake. Work out the bakery's estimate for the total flour needed, in kg.

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.A space probe is 7.5 × 10⁸ km from Earth. Write this distance as an ordinary number.

7.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.

8.Work out 4368 ÷ 12.

9.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.

10.Write 7/12 as a decimal, showing clearly which digit is recurring.

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

12.A window display has red baubles, gold baubles and green baubles in the ratio 4 : 5 : 6. What fraction of the baubles are not green?

13.A quarter-circle has a radius of 6 cm. Work out the exact perimeter of the quarter-circle, giving your answer in terms of π.

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

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