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.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
2.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
3.Work out −(−3)⁴ + (−3)³
(a)−108
(b)54
(c)−54
(d)108
4.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
5.Work out ∛(−27) + ∛8
(a)5
(b)−5
(c)−1
(d)−6
6.Given that 2⁵ = 32, work out 2⁶.
(a)34
(b)37
(c)192
(d)64
7.4ˣ = 64. Work out the value of x.
(a)16
(b)3
(c)4
(d)6
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.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 5⁰ + 5¹ + 5²
(a)125
(b)30
(c)31
(d)35
12.Work out the value of 6² − 4³.
(a)100
(b)28
(c)−28
(d)0
13.Work out ⁴√16
(a)4
(b)8
(c)64
(d)2
14.Work out 3³ + 2⁴.
(a)35
(b)25
(c)43
(d)432
15.Simplify ⁴√(16a⁸b¹²)
(a)2a²b³
(b)2a⁴b⁶
(c)4a²b³
(d)2a²b⁴

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