Number worksheet — GCSE Higher

1.In a science experiment, the temperature of a liquid is recorded as 18.6 °C, correct to the nearest 0.2 °C. Write down the error interval for the actual temperature, T °C.

2.The population of a planet is 8 × 10⁹. Write this population as an ordinary number.

3.Simplify (y³)⁴, giving your answer as a single power of y.

4.Work out (−2)³ + (−3)² − (−4)

5.Tickets to a theme park cost £38.50 for an adult and £19.75 for a child. A family estimates the total cost for 4 adults and 3 children, by rounding each ticket price to the nearest £5. Work out their estimate for the total cost.

6.Simplify ⁴√(16a⁸b¹²)

7.An allotment is divided into two plots in the ratio 2:3. The larger plot has an area of 18 m². Work out the fraction of the total area taken up by the smaller plot.

8.A plumber charges a call-out fee of £45 and then £28 for each hour she works. She is at a house from 09:15 until 12:45. Work out the total charge.

9.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?

10.A tank contains 120 litres of water. Water is drained out at a rate of 8 litres per minute for 6 minutes, and then a hose adds 15 litres. Work out how much water is left in the tank.

11.Work out −4.5 + 2.8.

12.A rectangular tile measures 45 cm by 0.6 m. Work out its area, in square centimetres.

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

14.Write these decimals in order, starting with the smallest: 0.6, 0.55, 0.601, 0.5, 0.56

15.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.