Exact calculation: fractions, surds and π worksheet — GCSE Foundation

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

2.A circle has a diameter of 10 cm. Work out the exact circumference of the circle, in terms of π.

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

4.Work out 2/5 + 1/4, giving your answer in its simplest form.

5.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.

6.A pizza is cut into 12 equal slices. Ben eats 5 slices and Mia eats 3 slices. What fraction of the pizza is left, giving your answer in its simplest form?

7.Work out 4π + 2π, giving your answer as a multiple of π.

8.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.

9.Work out 1 1/2 ÷ 3/4 exactly, giving your answer in its simplest form.

10.A quarter-circle has a radius of 6 cm. Work out the exact perimeter of the quarter-circle, giving your answer in terms of π.

11.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.

12.A semicircle has a diameter of 8 cm. Work out the exact area of the semicircle, in terms of π.

13.A circle has a radius of 3 cm. Which of these is the exact area of the circle?

14.Work out 2/3 × 3/4 exactly, giving your answer in its simplest form.

15.3/5 of a 5/6 litre bottle of juice is poured out. Work out the exact volume poured out, in litres.