Number worksheet — GCSE Higher

1.Write 90 as a product of its prime factors.

2.A choir has sopranos, altos and tenors in the ratio 6 : 4 : 5. What fraction of the choir is not tenors?

3.Work out the value of 2⁻²

4.A country has an area of 25,000,000 hectares. Write this area in standard form.

5.A car manufacturer offers a car in 6 colours and 4 trim levels. Two colour-and-trim combinations are not available: red with sport trim, and white with sport trim. Work out how many different colour-and-trim combinations are available.

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

7.Write 0.005 in standard form.

8.Oliver drives 95 km at an average speed of 50 km/h. Work out an estimate for the time the journey takes, by rounding the distance to the nearest 100 km.

9.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.

10.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.

11.Priya adds 3.6 and 0.45 on paper and writes down 3.65 as her answer. Work out the correct value of 3.6 + 0.45.

12.A recipe uses 160 g of flour. Sam wants to increase the amount by 1/4. Work out the new amount of flour.

13.Rationalise the denominator of 10/(4 − √6), giving your answer in its simplest form.

14.Write down the symbol that makes this statement true: −2/3 ___ −5/6

15.A three-digit code is made using the digits 1, 2 and 3, and each digit may be used more than once. Work out how many different three-digit codes can be made.