Powers and Roots - Worksheets, Questions and Revision

20 original exam-style questions - 7 pages of questions with a full mark scheme - free printable PDF.

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1.9 Powers and Roots

EDEXCEL 1MA1 · Calculator allowed · about 70 minutes
Total Marks
Name: _______________________________    Date: ____ / ____ / ______
Answer ALL questions. Show all your working.
1
Write down the value of each power.
(a)22(1)
(b)102(1)
(c)52(1)
(d)15(1)
(Total for Question 1 is 4 marks)
2
Work out the value of each square root.
(a)√36(1)
(b)√64(1)
(c)√1(1)
(d)√121(1)
(Total for Question 2 is 4 marks)
3
Work out the value of each cube.
(a)23(1)
(b)33(1)
(c)103(1)
(Total for Question 3 is 3 marks)
4
Circle the correct value of 62.
  • A) 12
  • B) 36
  • C) 18
  • D) 8
(Total for Question 4 is 1 mark)
5
Write down the value of each power of 10.
(a)101(1)
(b)103(1)
(c)100(1)
(Total for Question 5 is 3 marks)
6
Priya has a square vegetable patch. Each side of the patch has length 9 m.
Diagram NOT accurately drawn
9 m 9 m 9 m 9 m
(Total for Question 6 is 2 marks)
7
A square rug has an area of 144 cm2. Work out the length of one side of the rug.
Diagram NOT accurately drawn
144 cm² ?
(Total for Question 7 is 2 marks)
8
Look carefully at the brackets in each calculation.
(a)Work out (-6)2(1)
(b)Work out -62(1)
(Total for Question 8 is 2 marks)
9
Work out each cube root.
(a)cbrt(-27)(1)
(b)cbrt(-1000)(1)
(Total for Question 9 is 2 marks)
10
Remember to use the correct order of operations.
(a)Work out 4 + 32(2)
(b)Work out (4 + 3)2(2)
(Total for Question 10 is 4 marks)
11
Work out the value of each expression, using the correct order of operations.
(a)2 x 52 - 32(2)
(b)20 - 2 x 32(2)
(Total for Question 11 is 4 marks)
12
Use estimation to answer each part.
(a)√30 lies between which two consecutive whole numbers?(1)
(b)√90 lies between which two consecutive whole numbers?(1)
(Total for Question 12 is 2 marks)
13
For each statement, write True or False.
(i)√25 = 5(1)
(ii)32 = 6(1)
(iii)√0 = 0(1)
(iv)1100 = 1(1)
(Total for Question 13 is 4 marks)
14
Simplify each expression, leaving your answer as a single power.
(a)a4 x a3(1)
(b)y5 x y(1)
(Total for Question 14 is 2 marks)
15
Simplify each expression, leaving your answer as a single power.
(a)b7 / b2(1)
(b)c6 / c6(1)
(Total for Question 15 is 2 marks)
16
Look at the pattern of powers to help you answer this question.
(a)Work out 80(1)
(b)Work out 150(1)
(c)Explain why any non-zero number raised to the power 0 is equal to 1.(2)
(Total for Question 16 is 4 marks)
17
Four identical square tiles, each with area 100 cm2, are arranged edge-to-edge (2 tiles by 2 tiles) to form one larger square.
Diagram NOT accurately drawn
Area 100 cm² Area 100 cm² Area 100 cm² Area 100 cm²
(Total for Question 17 is 3 marks)
18
Show that 42 + 32 = 52
(Total for Question 18 is 2 marks)
19
Tom says: "√16 + √9 = √25". Explain why Tom is wrong.
(Total for Question 19 is 2 marks)
20
Simplify d3 x d4 / d2, leaving your answer as a single power.
(Total for Question 20 is 2 marks)
Mark scheme · 1.9 Powers and Roots

Question 1

Question 2

Question 3

Question 4

Question 5

Question 6

Question 7

Question 8

Question 9

Question 10

Question 11

Question 12

Question 13

Question 14

Question 15

Question 16

Question 17

Question 18

Question 19

Question 20