Printable · GCSE Higher · ages 14-16
Exact calculation: fractions, surds and π worksheet — GCSE Higher
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 Higher
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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.Work out √3 × √12, giving your answer as an integer.
- 3.Expand and simplify (2 + √3)², giving your answer in the form a + b√3.
- 4.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?
- 5.Rationalise the denominator of 10/(4 − √6), giving your answer in its simplest form.
- 6.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.
- 7.Work out 3/4 − 5/12 exactly, giving your answer in its simplest form.
- 8.A semicircle has a diameter of 8 cm. Work out the exact area of the semicircle, in terms of π.
- 9.3/5 of a 5/6 litre bottle of juice is poured out. Work out the exact volume poured out, in litres.
- 10.The two shorter sides of a right-angled triangle are √12 cm and √24 cm. Work out the exact length of the hypotenuse.
- 11.Simplify √8 + √18, giving your answer in the form k√2.
- 12.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.
- 13.Work out 1 1/2 ÷ 3/4 exactly, giving your answer in its simplest form.
- 14.Simplify √45.
- 15.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?
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