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.Without using a calculator, estimate √20 × √12, giving your answer to the nearest whole number.
(a)240
(b)12
(c)8
(d)15
2.Work out ⁴√81
(a)3
(b)20.25
(c)4.5
(d)9
3.Simplify ⁴√(16a⁸b¹²)
(a)2a²b³
(b)2a⁴b⁶
(c)4a²b³
(d)2a²b⁴
4.Work out ∛64.
(a)21.3
(b)4
(c)192
(d)8
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.Work out √(4 × 9)
(a)5
(b)18
(c)36
(d)6
7.Work out 3³ + 2⁴.
(a)35
(b)25
(c)43
(d)432
8.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
9.Work out 5⁰ + 5¹ + 5²
(a)125
(b)30
(c)31
(d)35
10.Work out the exact value of √(2² + 3²)
(a)13
(b)√5
(c)5
(d)√13
11.√700 lies between which two consecutive integers?
(a)35 and 36
(b)7 and 8
(c)25 and 26
(d)26 and 27
12.Work out the value of 6² − 4³.
(a)100
(b)28
(c)−28
(d)0
13.Work out ∛(−27) + ∛8
(a)5
(b)−5
(c)−1
(d)−6
14.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
15.4ˣ = 64. Work out the value of x.
(a)16
(b)3
(c)4
(d)6

Build your own mix at the worksheet builder.