Printable · GCSE Foundation · ages 14-16

Powers and roots worksheet — GCSE Foundation

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 Foundation

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

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1.Work out the value of 6² − 4³.
(a)100
(b)28
(c)−28
(d)0
2.Work out 3³ + 2⁴.
(a)35
(b)25
(c)43
(d)432
3.Work out 6² − 4².
(a)2
(b)52
(c)20
(d)4
4.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
5.Given that 2⁵ = 32, work out 2⁶.
(a)34
(b)37
(c)192
(d)64
6.Work out (3 × 5)²
(a)225
(b)30
(c)75
(d)34
7.4ˣ = 64. Work out the value of x.
(a)16
(b)3
(c)4
(d)6
8.Work out ∛(−27) + ∛8
(a)5
(b)−5
(c)−1
(d)−6
9.Work out ⁴√81
(a)3
(b)20.25
(c)4.5
(d)9
10.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
11.Work out √225 ÷ 3.
(a)8.7
(b)5
(c)75
(d)45
12.Work out ⁴√16
(a)4
(b)8
(c)64
(d)2
13.Work out 5⁰ + 5¹ + 5²
(a)125
(b)30
(c)31
(d)35
14.Work out −(−3)⁴ + (−3)³
(a)−108
(b)54
(c)−54
(d)108
15.Work out √49
(a)9
(b)24.5
(c)7
(d)2401

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