Printable · GCSE Foundation · ages 14-16
Exact calculation: fractions, surds and π worksheet — GCSE Foundation
Fifteen questions on "exact calculation: fractions, surds and π" — DfE statement N8. Print it, or print three versions so neighbours cannot copy by letter; the key gives the letter for each version.
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Exact calculation: fractions, surds and π worksheet — GCSE Foundation
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- 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.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?
- 3.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.
- 4.Work out 4π + 2π, giving your answer as a multiple of π.
- 5.Work out 1 1/2 ÷ 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 5 cm. Work out the exact circumference of the circle, in terms of π.
- 8.3/5 of a 5/6 litre bottle of juice is poured out. Work out the exact volume poured out, in litres.
- 9.Work out 3π − π, giving your answer as a multiple of π.
- 10.Work out 5/6 × 2/9, giving your answer in its simplest form.
- 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.Work out 2/5 + 1/4, giving your answer in its simplest form.
- 13.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.
- 14.Work out 3/4 − 5/12 exactly, giving your answer in its simplest form.
- 15.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.
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