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

VersionsA only A + B A + B + Csame questions, different order

AnswersQuestions only With answer key Key only

CalculatorMixed Non-calculator (Paper 1)Calculator (Papers 2 and 3)

New sheet

Exact calculation: fractions, surds and π worksheet — GCSE Higher

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

MathsUKwww.geekhero.co.uk

1.Work out 1 1/2 ÷ 3/4 exactly, giving your answer in its simplest form.
(a)9/8
(b)2/3
(c)2
(d)1/2
2.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
3.Simplify √45.
(a)9√5
(b)6√5
(c)15
(d)3√5
4.3/5 of a 5/6 litre bottle of juice is poured out. Work out the exact volume poured out, in litres.
(a)1/2
(b)43/30
(c)18/25
(d)25/36
5.Rationalise the denominator of 6/√3, giving your answer in its simplest form.
(a)2√3
(b)6
(c)2
(d)3√3
6.Rationalise the denominator of 10/(4 − √6), giving your answer in its simplest form.
(a)4 + √6
(b)4
(c)4 − √6
(d)4 + 10√6
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.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.
(a)144√2
(b)24√2
(c)6√2
(d)12√2
9.Expand and simplify √3(2 + √12).
(a)6 + √6
(b)√15 + 2√3
(c)2√3
(d)6 + 2√3
10.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.
(a)5/4
(b)3/4
(c)3/2
(d)3/8
11.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
12.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
13.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
14.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
15.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

Build your own mix at the worksheet builder.