Number worksheet — GCSE Higher

1.Find the missing number: ▢ ÷ 15 = 24

2.Work out an estimate for 588 ÷ 31, by rounding each number to 1 significant figure.

3.A lorry travels 105 miles in 1 hour 45 minutes. Work out its average speed in miles per hour.

4.Two allotments are combined. Allotment A grows vegetables and flowers in the ratio 3 : 2, and has 20 plots in total. Allotment B grows vegetables and flowers in the ratio 1 : 4, and has 20 plots in total. Work out the fraction of all the plots, in both allotments combined, that grow vegetables.

5.Grace works out 7 × 99 by writing 99 as 100 − 1. Use her method to work out 7 × 99.

6.A length, L cm, has the error interval 24.5 ≤ L < 25.5. Write down the degree of accuracy to which the length was measured.

7.Work out (−2)² − 3

8.Work out the reciprocal of (2 + 3)

9.A shape is made by joining a rectangle measuring 10 cm by 6 cm to a semicircle of diameter 6 cm along one of the rectangle's shorter sides. Work out the exact area of the shape, in terms of π.

10.A grain of fine sand has a mass of 0.001 grams. Write this mass in standard form.

11.Round 592.5 to the nearest 10.

12.Simplify x⁵ × x³ ÷ x², giving your answer as a single power of x.

13.A café sells ice cream in three flavours: vanilla, mango and pistachio. Isla buys a cone with two scoops, using two different flavours, one for the bottom scoop and one for the top scoop. Work out how many different cones she could buy.

14.Work out 3³ + 2⁴.

15.Write 60 as a product of its prime factors, using index notation.