Number worksheet — GCSE Higher

1.Work out (5 + 2) × 3²

2.Two bags of mixed nuts are combined. Bag A has peanuts and cashews in the ratio 2 : 3. Bag B has peanuts and cashews in the ratio 1 : 4. Both bags contain the same total number of nuts. Work out the fraction of the combined mixture that is peanuts.

3.4ˣ = 64. Work out the value of x.

4.In a youth club the number of girls is 2/3 of the number of boys. What fraction of the members of the club are girls?

5.Write 0.35 as a fraction in its lowest terms.

6.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.

7.Insert one pair of brackets into 2 + 3 × 5 − 1 so that the calculation is equal to 24. Which calculation is correct?

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

9.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.

10.Work out the value of (√5)⁴

11.A washing machine costs £320 before VAT. VAT is charged at 20%. Work out the total price including VAT.

12.Simplify √45.

13.At a swimming pool the ratio of adults to children is 3 : 5. Of the children, 2/5 are boys. What fraction of the people at the pool are boys?

14.A car travels 100 km, correct to the nearest km, in a time of 2 hours, correct to the nearest 0.1 hour. Work out the average speed, in km/h, to the greatest degree of accuracy the bounds can guarantee.

15.A cube-shaped storage box has edges of length 7 cm. A shelf can hold a total volume of 2,000 cm³. Work out the greatest number of these boxes that will fit in that volume.