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.

part Higher

VersionsA only A + B A + B + Csame questions, different order

AnswersQuestions only With answer key Key only

CalculatorMixed Non-calculator (Paper 1)Calculator (Papers 2 and 3)

New sheet

Powers and roots worksheet — GCSE Higher

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

MathsUKwww.geekhero.co.uk

1.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
2.Work out ⁴√81
(a)3
(b)20.25
(c)4.5
(d)9
3.Work out 6² − 4².
(a)2
(b)52
(c)20
(d)4
4.√700 lies between which two consecutive integers?
(a)35 and 36
(b)7 and 8
(c)25 and 26
(d)26 and 27
5.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
6.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
7.Work out ∛(−27) + ∛8
(a)5
(b)−5
(c)−1
(d)−6
8.Work out the exact value of √(2² + 3²)
(a)13
(b)√5
(c)5
(d)√13
9.Given that 2⁵ = 32, work out 2⁶.
(a)34
(b)37
(c)192
(d)64
10.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
11.Work out ⁴√16
(a)4
(b)8
(c)64
(d)2
12.Work out −(−3)⁴ + (−3)³
(a)−108
(b)54
(c)−54
(d)108
13.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
14.4ˣ = 64. Work out the value of x.
(a)16
(b)3
(c)4
(d)6
15.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

Build your own mix at the worksheet builder.