Number worksheet — GCSE Higher

1.A student works out the exact area of a circle with radius 4 cm by squaring the radius but forgetting to multiply by π. Work out the correct exact area of the circle, in terms of π.

2.Work out 3/4 − 5/12 exactly, giving your answer in its simplest form.

3.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.

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

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

6.In a class, 1/3 of the pupils are girls. There are 12 girls in the class. Work out how many pupils are in the class.

7.Work out 5/6 × 2/9, giving your answer in its simplest form.

8.Write ∛(x²) as a single power of x.

9.Work out √144 − 2 × 3 + √25

10.3/5 of the students in a year group walk to school. 90 students walk to school. Work out the total number of students in the year group.

11.A photography studio offers 4 backdrops and 3 outfits for a portrait session. The plain grey backdrop, one of the 4 backdrops, cannot be used with the formal suit outfit, one of the 3 outfits. Work out how many different backdrop-and-outfit combinations are possible.

12.A shop assistant says that 7.2 × 3.9 = 56.16. Work out an estimate for 7.2 × 3.9, by rounding each number to the nearest whole number, to show that the assistant’s answer cannot be correct.

13.Simplify 3² ÷ 3⁵, giving your answer as a single power of 3.

14.Round 0.006852 to 2 significant figures.

15.Work out ⁴√81