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

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

2.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.

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

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

5.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?

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

7.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.

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

9.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.

10.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?

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

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

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

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 circle has a radius of 5 cm. Work out the exact circumference of the circle, in terms of π.