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 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.
- 2.Simplify √45.
- 3.A circle has a radius of 3 cm. Which of these is the exact area of the circle?
- 4.A semicircle has a diameter of 8 cm. Work out the exact area of the semicircle, in terms of π.
- 5.Rationalise the denominator of 6/√3, giving your answer in its simplest form.
- 6.Rationalise the denominator of 10/(4 − √6), giving your answer in its simplest form.
- 7.The two shorter sides of a right-angled triangle are √12 cm and √24 cm. Work out the exact length of the hypotenuse.
- 8.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.
- 9.Work out 3/4 − 5/12 exactly, giving your answer in its simplest form.
- 10.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.
- 11.3/5 of a 5/6 litre bottle of juice is poured out. Work out the exact volume poured out, in litres.
- 12.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?
- 13.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.
- 14.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?
- 15.Work out 1 1/2 ÷ 3/4 exactly, giving your answer in its simplest form.
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