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

Maths · GCSE Higher · N8 · Exact calculation: fractions, surds and π · 15 questions

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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.
(a)64π cm²
(b)4π cm²
(c)8π cm²
(d)16π cm²
2.Expand and simplify √3(2 + √12).
(a)6 + √6
(b)√15 + 2√3
(c)2√3
(d)6 + 2√3
3.Rationalise the denominator of 6/√3, giving your answer in its simplest form.
(a)2√3
(b)6
(c)2
(d)3√3
4.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.
(a)(12 + 12π) cm
(b)3π cm
(c)(12 + 3π) cm
(d)(6 + 3π) cm
5.Simplify √45.
(a)9√5
(b)6√5
(c)15
(d)3√5
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.
(a)(60 + 3π) cm²
(b)(60 + 4.5π) cm²
(c)(60 + 9π) cm²
(d)(60 + 18π) cm²
7.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?
(a)3/5
(b)9/10
(c)2/5
(d)3/4
8.Work out 5/6 × 2/9, giving your answer in its simplest form.
(a)7/15
(b)5/27
(c)15/4
(d)5/3
9.A circle has a radius of 3 cm. Which of these is the exact area of the circle?
(a)28.3 cm²
(b)28.26 cm²
(c)9π cm²
(d)27 cm²
10.A circle has a circumference of 8π cm. Work out the exact area of the circle in terms of π.
(a)64π
(b)16π
(c)4π
(d)8π
11.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.
(a)1 3/4
(b)2 5/12
(c)8
(d)1 7/12
12.Work out √3 × √12, giving your answer as an integer.
(a)6
(b)√15
(c)2√3
(d)36
13.A semicircle has a diameter of 8 cm. Work out the exact area of the semicircle, in terms of π.
(a)4π cm²
(b)8π cm²
(c)16π cm²
(d)32π cm²
14.Expand and simplify (2 + √3)², giving your answer in the form a + b√3.
(a)7
(b)4 + 5√3
(c)7 + 4√3
(d)5 + 4√3
15.Simplify √8 + √18, giving your answer in the form k√2.
(a)5√2
(b)√26
(c)7√2
(d)11√2

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