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

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.Zoe worked out 3/8 + 1/8 by adding the numerators and the denominators, and got 4/16. Work out the correct value of 3/8 + 1/8, giving your answer in its simplest form.

3.3/5 of a 5/6 litre bottle of juice is poured out. Work out the exact volume poured out, in litres.

4.Work out 3π − π, giving your answer as a multiple of π.

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

6.In a school, 3/5 of the students study French. Of these students, 2/3 also study Spanish. What fraction of all the students study both French and Spanish?

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

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

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

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

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

12.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.

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

14.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.

15.A cake recipe needs 3/4 of a kilogram of sugar. Aisha wants to make half the recipe. Work out how much sugar she needs, giving your answer as a fraction of a kilogram in its simplest form.