Number worksheet — GCSE Higher

1.Put these numbers in order, starting with the smallest: 3.2 × 10⁴, 2.9 × 10⁵, 4.1 × 10³

2.A lift has a safe working load of 500 kg. Four people get in the lift and the lift's display records their total mass as 493 kg, correct to the nearest kg. Decide whether the four people are definitely within the safe working load.

3.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.

4.Write 12 as a product of its prime factors.

5.Work out 6² − 4².

6.A number is divided by 5, then 6 is subtracted, giving the result −1. Work out the number.

7.Write these numbers in order, starting with the largest: −0.6, 0.45, −0.15, 0.5, −0.09

8.The number 72 can be written as 2³ × 3², and the number 108 can be written as 2² × 3³. Work out the highest common factor of 72 and 108.

9.A restaurant offers a lunch deal of one starter from 5 options, one main from 6 options and one dessert from 3 options. Work out how many different lunch deals are possible.

10.A paint mix is made from white paint and blue paint in the ratio 5 : 3. Priya uses 1.2 litres of blue paint and the matching amount of white paint. Work out the total volume of the mix.

11.A photograph uses 4 × 10⁶ bytes of storage. A memory card holds 3.2 × 10¹⁰ bytes. Work out how many of these photographs the card can hold. Give your answer in standard form.

12.The number 36 can be written as 2² × 3², and the number 84 can be written as 2² × 3 × 7. Work out the highest common factor of 36 and 84.

13.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?

14.A cyclist travels 40 km, correct to the nearest 10 km, in a time of 3 hours, correct to the nearest hour. Work out the maximum possible average speed, in km/h.

15.Round 0.006852 to 2 significant figures.