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 −(−3)⁴ + (−3)³
(a)−108
(b)54
(c)−54
(d)108
2.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
3.Without using a calculator, estimate √20 × √12, giving your answer to the nearest whole number.
(a)240
(b)12
(c)8
(d)15
4.4ˣ = 64. Work out the value of x.
(a)16
(b)3
(c)4
(d)6
5.Work out ∛64.
(a)21.3
(b)4
(c)192
(d)8
6.Simplify ⁴√(16a⁸b¹²)
(a)2a²b³
(b)2a⁴b⁶
(c)4a²b³
(d)2a²b⁴
7.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
8.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
9.Work out ∛(−27) + ∛8
(a)5
(b)−5
(c)−1
(d)−6
10.Work out ⁴√16
(a)4
(b)8
(c)64
(d)2
11.Work out √225 ÷ 3.
(a)8.7
(b)5
(c)75
(d)45
12.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
13.Work out 6² − 4².
(a)2
(b)52
(c)20
(d)4
14.Work out the exact value of √(2² + 3²)
(a)13
(b)√5
(c)5
(d)√13
15.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

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