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

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Powers and roots worksheet — GCSE Higher

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

MathsUKwww.geekhero.co.uk

1.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
2.Given that 2⁵ = 32, work out 2⁶.
(a)34
(b)37
(c)192
(d)64
3.Work out −(−3)⁴ + (−3)³
(a)−108
(b)54
(c)−54
(d)108
4.Work out the exact value of √(2² + 3²)
(a)13
(b)√5
(c)5
(d)√13
5.Work out 3³ + 2⁴.
(a)35
(b)25
(c)43
(d)432
6.Work out the value of 6² − 4³.
(a)100
(b)28
(c)−28
(d)0
7.Work out ⁴√81
(a)3
(b)20.25
(c)4.5
(d)9
8.Given that 5³ = 125 and 6³ = 216, use a midpoint test to estimate ∛130 to 1 decimal place.
(a)5.2
(b)5.1
(c)6.0
(d)5.0
9.4ˣ = 64. Work out the value of x.
(a)16
(b)3
(c)4
(d)6
10.Simplify ⁴√(16a⁸b¹²)
(a)2a²b³
(b)2a⁴b⁶
(c)4a²b³
(d)2a²b⁴
11.Work out 6² − 4².
(a)2
(b)52
(c)20
(d)4
12.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
13.Work out ∛(−27) + ∛8
(a)5
(b)−5
(c)−1
(d)−6
14.Work out √(4 × 9)
(a)5
(b)18
(c)36
(d)6
15.√700 lies between which two consecutive integers?
(a)35 and 36
(b)7 and 8
(c)25 and 26
(d)26 and 27

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