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.

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Powers and roots worksheet — GCSE Higher

Maths · GCSE Higher · N6 · Powers and roots · 15 questions

MathsUKwww.geekhero.co.uk

1.Work out 5⁰ + 5¹ + 5²
(a)125
(b)30
(c)31
(d)35
2.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
3.Simplify ⁴√(16a⁸b¹²)
(a)2a²b³
(b)2a⁴b⁶
(c)4a²b³
(d)2a²b⁴
4.Work out √(4 × 9)
(a)5
(b)18
(c)36
(d)6
5.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
6.Work out −(−3)⁴ + (−3)³
(a)−108
(b)54
(c)−54
(d)108
7.4ˣ = 64. Work out the value of x.
(a)16
(b)3
(c)4
(d)6
8.Work out the exact value of √(2² + 3²)
(a)13
(b)√5
(c)5
(d)√13
9.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
10.Given that 2⁵ = 32, work out 2⁶.
(a)34
(b)37
(c)192
(d)64
11.Work out ⁴√81
(a)3
(b)20.25
(c)4.5
(d)9
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.Without using a calculator, estimate √20 × √12, giving your answer to the nearest whole number.
(a)240
(b)12
(c)8
(d)15
14.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
15.Work out the value of 6² − 4³.
(a)100
(b)28
(c)−28
(d)0

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