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 ⁴√16
(a)4
(b)8
(c)64
(d)2
2.Work out 6² − 4².
(a)2
(b)52
(c)20
(d)4
3.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
4.Given that 2⁵ = 32, work out 2⁶.
(a)34
(b)37
(c)192
(d)64
5.Work out the value of 6² − 4³.
(a)100
(b)28
(c)−28
(d)0
6.√700 lies between which two consecutive integers?
(a)35 and 36
(b)7 and 8
(c)25 and 26
(d)26 and 27
7.A cube-shaped storage box has edges of length 7 cm. A shelf can hold a total volume of 2,000 cm³. Work out the greatest number of these boxes that will fit in that volume.
(a)5.8
(b)6
(c)5
(d)343
8.Work out −(−3)⁴ + (−3)³
(a)−108
(b)54
(c)−54
(d)108
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.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
11.Work out ∛64.
(a)21.3
(b)4
(c)192
(d)8
12.Without using a calculator, estimate √20 × √12, giving your answer to the nearest whole number.
(a)240
(b)12
(c)8
(d)15
13.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
14.Work out 5⁰ + 5¹ + 5²
(a)125
(b)30
(c)31
(d)35
15.Work out ∛(−27) + ∛8
(a)5
(b)−5
(c)−1
(d)−6

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