Number worksheet — GCSE Foundation

1.For any two whole numbers, the product of the numbers is equal to the product of their highest common factor and their lowest common multiple. The highest common factor of 6 and 8 is 2, and 6 × 8 = 48. Work out the lowest common multiple of 6 and 8.

2.In a car park the ratio of vans to cars is 2 : 7. Work out the number of vans as a fraction of the number of cars.

3.The diameter of an artificial silk fibre is 4 × 10⁻⁶ metres. One nanometre is 10⁻⁹ metres. Work out the diameter of the fibre in nanometres.

4.Write these numbers in order, starting with the largest: 7/8, 0.8, 78%, 17/20

5.Nadia has £84. She spends 3/7 of it on a jacket and the rest on a bag. Work out the ratio of the amount spent on the jacket to the amount spent on the bag, in its simplest form.

6.Work out (4 × 10³) × (3 × 10¹). Give your answer in standard form.

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

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

9.A cyclist rides at a steady speed of 8 metres per second. Work out this speed in kilometres per hour.

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

11.Work out ∛64.

12.A carpenter has a plank of wood 4.8 m long. She cuts off 3 pieces, each 0.9 m long, to make shelves. Work out the length of wood remaining.

13.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.

14.A number line runs from 0 to 1 and is divided into 4 equal parts. Which mark on the line represents 1/4?

15.The mass of a radioactive sample, in grams, n years after it was first weighed is modelled by M = 200 × (1/2)ⁿ. Work out the mass the model gives after 3 years.