Number worksheet — GCSE Higher

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

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

3.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.

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

5.Work out 6² − 4².

6.Given that 5³ = 125 and 6³ = 216, use a midpoint test to estimate ∛130 to 1 decimal place.

7.A box stands on a table. The box exerts a force of 240 N on the table, and the base of the box has an area of 0.8 m². Work out the pressure the box exerts on the table, in N/m².

8.Work out ⁴√16

9.Simplify x⁷ × x⁴, giving your answer as a single power of x.

10.Write these three numbers in order, starting with the smallest: 7/20, 0.3, 32%

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.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?

13.A shop assistant says that 7.2 × 3.9 = 56.16. Work out an estimate for 7.2 × 3.9, by rounding each number to the nearest whole number, to show that the assistant’s answer cannot be correct.

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.Work out −(−3)⁴ + (−3)³