Number worksheet — GCSE Higher

1.Chloe wants to work out 3 1/4 − 1 2/3. She converts both mixed numbers to twelfths, then subtracts the whole numbers and the fraction parts separately, without checking whether she needs to exchange first. Work out the correct value of 3 1/4 − 1 2/3, giving your answer as a mixed number in its simplest form.

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

3.Decide which of 2³⁰ and 3²⁰ is the larger number, and write down the correct statement.

4.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.

5.Round 0.006482 to 2 significant figures.

6.A jug holds 3 1/3 litres of juice. Each glass holds 2/3 of a litre. Work out how many glasses can be filled from the jug.

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

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

9.Work out ∛64.

10.Four friends share a restaurant bill of £53.90 equally. A calculator gives each share as 13.475. Work out how much each friend should pay.

11.Work out the value of 6² − 4³.

12.Simplify ⁴√(16a⁸b¹²)

13.Work out 3.7 × 24.

14.Work out ((−3) + 5) × (−4) − (−6) ÷ 2

15.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.