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

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

2.3/5 of a 5/6 litre bottle of juice is poured out. Work out the exact volume poured out, in litres.

3.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?

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

5.Expand and simplify (2 + √3)², giving your answer in the form a + b√3.

6.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.

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

8.Expand and simplify √3(2 + √12).

9.Simplify √45.

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

11.Rationalise the denominator of 6/√3, giving your answer in its simplest form.

12.Work out √3 × √12, giving your answer as an integer.

13.A square tile has an area of 72 cm². Work out the exact perimeter of the tile, giving your answer in the form k√2 cm.

14.Simplify √8 + √18, giving your answer in the form k√2.

15.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.