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.
part Higher
Exact calculation: fractions, surds and π worksheet — GCSE Higher
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- 1.The two shorter sides of a right-angled triangle are √12 cm and √24 cm. Work out the exact length of the hypotenuse.
- 2.A circle has a radius of 3 cm. Which of these is the exact area of the circle?
- 3.A circle has a circumference of 8π cm. Work out the exact area of the circle in terms of π.
- 4.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.
- 5.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.
- 6.Simplify √45.
- 7.Simplify √8 + √18, giving your answer in the form k√2.
- 8.Work out √3 × √12, giving your answer as an integer.
- 9.Work out 3/4 − 5/12 exactly, giving your answer in its simplest form.
- 10.Work out 1 1/2 ÷ 3/4 exactly, giving your answer in its simplest form.
- 11.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.
- 12.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.
- 13.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?
- 14.Rationalise the denominator of 6/√3, giving your answer in its simplest form.
- 15.Expand and simplify √3(2 + √12).
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