Number worksheet — GCSE Higher

1.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.

2.Given that 4³ = 64 and 5³ = 125, estimate ∛100 to 1 decimal place.

3.Work out 3³ + 2⁴.

4.Write these fractions in order, starting with the smallest: 2/3, 3/5, 5/6, 1/2

5.A charity shop buys a coat for £24 and sells it for a profit that is 3/8 of the buying price. Work out the selling price.

6.Write down the exact decimal value of the fraction 1/6.

7.A shape is made by joining a rectangle measuring 10 cm by 6 cm to a semicircle of diameter 6 cm along one of the rectangle's shorter sides. Work out the exact area of the shape, in terms of π.

8.Work out an estimate for 2.9² + 3.1², by rounding each number to the nearest whole number.

9.Robert is converting 0.999... (with the 9s recurring forever) into a fraction. He lets x = 0.999... . Multiplying by 10 gives 10x = 9.999... . Subtracting x from 10x gives 9x = 9, so x = 1. Which statement correctly explains this result?

10.A cinema has 250 seats. 12% of the seats are reserved. Work out how many of the seats are reserved.

11.A restaurant adds a service charge of 15% to a bill of £120. Work out the service charge.

12.A school orders 187 packed lunches for a trip. Each packed lunch costs £4.85. The school has £900 to spend. By rounding each number to 1 significant figure, work out an estimate for the total cost and decide whether £900 is enough.

13.A metal cube has a mass of 540 g and a volume of 60 cm³. Work out its density in g/cm³.

14.Simplify (x⁻²)³, giving your answer as a fraction.

15.A charity trek covers 830 miles over roughly 19 days. By rounding each number to 1 significant figure, work out an estimate for the number of miles walked per day.