Indices - 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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GCSE · Number

4.2 Indices

EDEXCEL 1MA1 · Calculator allowed · about 90 minutes
Total Marks
Name: _______________________________    Date: ____ / ____ / ______
Answer ALL questions. Show all your working.
1
Work out the value of each of the following.
(a)62(1)
(b)25(1)
(c)90(1)
(Total for Question 1 is 3 marks)
2
Write each of the following as a single power.
(a)4 x 4 x 4 x 4 x 4(1)
(b)7 x 7 x 7(1)
(c)2 x 2 x 2 x 2 x 2 x 2 x 2(1)
(Total for Question 2 is 3 marks)
3
Simplify each of the following, giving your answer as a single power.
(a)53 x 54(1)
(b)89 / 86(1)
(c)(32)4(1)
(Total for Question 3 is 3 marks)
4
Simplify each of the following.
(a)a5 x a2(1)
(b)b9 / b4(1)
(c)(c3)3(1)
(Total for Question 4 is 3 marks)
5
Work out the value of each of the following. Give each answer as a fraction or a decimal.
(a)4-2(1)
(b)10-3(1)
(c)3-2(1)
(Total for Question 5 is 3 marks)
6
Work out the value of each of the following.
(a)80(1)
(b)3 x 40(1)
(c)(70)5(1)
(Total for Question 6 is 3 marks)
7
Simplify each of the following.
(a)p-3 x p5(2)
(b)q2 / q5(2)
(Total for Question 7 is 4 marks)
8
Simplify each of the following.
(a)(a3 x a5) / a4(2)
(b)(2c2)3 x c(2)
(Total for Question 8 is 4 marks)
9
A rectangle has a width of 32 cm and a length of 35 cm.
Diagram NOT accurately drawn
35 cm 32 cm Rectangle 1 ? cm 33 cm Rectangle 2
(a)Work out the area of the rectangle, giving your answer as a single power of 3.(2)
(b)A second rectangle has the same area as the rectangle in part (a). Its width is 33 cm. Work out its length, giving your answer as a single power of 3.(3)
(Total for Question 9 is 5 marks)
10
Work out the value of each of the following.
(a)251/2(1)
(b)81/3(1)
(c)811/4(1)
(Total for Question 10 is 3 marks)
11
Simplify each of the following.
(a)(2x3)2(2)
(b)(5y2)3(2)
(Total for Question 11 is 4 marks)
12
Solve each of the following equations.
(a)2x = 32(2)
(b)3x+1 = 81(2)
(Total for Question 12 is 4 marks)
13
Answer each of the following.
(a)Given that 2a x 25 = 212, work out the value of a.(2)
(b)Given that (3b)2 = 310, work out the value of b.(2)
(Total for Question 13 is 4 marks)
14
Simplify fully (6x5 y3) / (2x2 y5)
(Total for Question 14 is 4 marks)
15
Which of these is equal to 5-2 ?
  • A) 1/25
  • B) -25
  • C) 25
  • D) -1/25
(Total for Question 15 is 1 mark)
16
Show that (34 x 3-2) / 3 = 3
(Total for Question 16 is 3 marks)
17
Work out the value of each of the following.
(a)82/3(2)
(b)43/2(2)
(Total for Question 17 is 4 marks)
18
Work out the value of each of the following.
(a)16-1/2(2)
(b)27-2/3(2)
(Total for Question 18 is 4 marks)
19
Simplify fully (4n3/2 x 2n1/2) / (8n-1)
(Total for Question 19 is 3 marks)
20
Answer each of the following.
(a)Solve x2/3 = 25(3)
(b)Simplify fully (27x6)-2/3(4)
(Total for Question 20 is 7 marks)
Mark scheme · 4.2 Indices

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