Printable · GCSE Higher · ages 14-16

Powers and roots worksheet — GCSE Higher

Fifteen questions on "powers and roots" — DfE statement N6. Print it, or print three versions so neighbours cannot copy by letter; the key gives the letter for each version.

part HigherNon-calculator

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

Powers and roots worksheet — GCSE Higher

Maths · GCSE Higher · N6 · Powers and roots · Non-calculator · 15 questions

MathsUKwww.geekhero.co.uk

1.Simplify ⁴√(16a⁸b¹²)
(a)2a²b³
(b)2a⁴b⁶
(c)4a²b³
(d)2a²b⁴
2.Work out ∛(−27) + ∛8
(a)5
(b)−5
(c)−1
(d)−6
3.Work out √(4 × 9)
(a)5
(b)18
(c)36
(d)6
4.Without using a calculator, estimate √20 × √12, giving your answer to the nearest whole number.
(a)240
(b)12
(c)8
(d)15
5.Work out ⁴√16
(a)4
(b)8
(c)64
(d)2
6.Given that 4³ = 64 and 5³ = 125, estimate ∛100 to 1 decimal place.
(a)4.7
(b)5.0
(c)4.6
(d)4.5
7.Without using a calculator, estimate the value of √70 × ∛65, giving your answer to 1 significant figure.
(a)10
(b)30
(c)40
(d)50
8.By considering fourth powers, work out which two consecutive integers ⁴√200 lies between.
(a)14 and 15
(b)4 and 5
(c)3 and 4
(d)5 and 6
9.The mass of a radioactive sample, in grams, n years after it was first weighed is modelled by M = 200 × (1/2)ⁿ. Work out the mass the model gives after 3 years.
(a)12.5 g
(b)25 g
(c)0.125 g
(d)300 g
10.Work out ⁴√81
(a)3
(b)20.25
(c)4.5
(d)9
11.Work out √225 ÷ 3.
(a)8.7
(b)5
(c)75
(d)45
12.By first working out 2.9², then squaring your result, estimate 2.9⁴ to 2 significant figures.
(a)71
(b)81
(c)70
(d)64
13.Work out the value of 6² − 4³.
(a)100
(b)28
(c)−28
(d)0
14.4ˣ = 64. Work out the value of x.
(a)16
(b)3
(c)4
(d)6
15.Work out 3³ + 2⁴.
(a)35
(b)25
(c)43
(d)432

Build your own mix at the worksheet builder.