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.Work out ∛64.
(a)21.3
(b)4
(c)192
(d)8
3.Work out 6² − 4².
(a)2
(b)52
(c)20
(d)4
4.Work out −(−3)⁴ + (−3)³
(a)−108
(b)54
(c)−54
(d)108
5.4ˣ = 64. Work out the value of x.
(a)16
(b)3
(c)4
(d)6
6.Work out ⁴√81
(a)3
(b)20.25
(c)4.5
(d)9
7.Work out the exact value of √(2² + 3²)
(a)13
(b)√5
(c)5
(d)√13
8.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
9.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
10.Work out √225 ÷ 3.
(a)8.7
(b)5
(c)75
(d)45
11.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
12.Work out the value of 6² − 4³.
(a)100
(b)28
(c)−28
(d)0
13.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
14.Without using a calculator, estimate √20 × √12, giving your answer to the nearest whole number.
(a)240
(b)12
(c)8
(d)15
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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