Number worksheet — GCSE Higher

1.A number, y, is equal to 8.2 when rounded to 1 decimal place. Write down the error interval for y.

2.Work out the value of 6² − 4³.

3.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.

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

5.A semicircle has a diameter of 8 cm. Work out the exact area of the semicircle, in terms of π.

6.During one night on a mountain, four hikers each recorded the temperature they felt: Ben −6 °C, Priya −2 °C, Sam −9 °C, Alex 1 °C. Work out the difference between the coldest and the warmest of these four temperatures.

7.Work out 3/4 − 5/12 exactly, giving your answer in its simplest form.

8.Simplify 5⁻² × 5⁴, giving your answer as a single power of 5.

9.A bag of flour is labelled 1.5 kg, correct to the nearest 0.1 kg. The true mass of the flour is m kg. Which inequality gives all the possible values of m?

10.Write 5,000,000 in standard form.

11.By considering fourth powers, work out which two consecutive integers ⁴√200 lies between.

12.Work out (−2/5) × (−10/3). Give your answer as a fraction in its simplest form.

13.By listing systematically, work out how many two-digit multiples of 5 can be made using the digits 0, 3 and 5, if each digit can be used at most once and the number cannot start with 0.

14.Work out (4 × 10⁻³) × (2 × 10⁵). Give your answer in standard form.

15.In a box of chocolates 5/8 are milk chocolates and the rest are dark chocolates. Work out the number of dark chocolates as a fraction of the number of milk chocolates.