Fractional and Negative Indices - Worksheets, Questions and Revision

18 original exam-style questions - 6 pages of questions with a full mark scheme - free printable PDF.

Download PDFJump to mark scheme (page 7)Read the revision guide
« Previous: Recurring Decimals to Fractions: Fluency and Exam DrillNext: Fractional and Negative Indices: Fluency and Exam Drill »
Revision Library
revisionlibrary.co.uk
HIGHER

6.2 Fractional and Negative Indices

EDEXCEL 1MA1 · Calculator allowed · about 75 minutes
Total Marks
Name: _______________________________    Date: ____ / ____ / ______
Answer ALL questions. Show all your working.
1
Write down the value of:
(a)60(1)
(b)2-3(1)
(c)5-1(1)
(Total for Question 1 is 3 marks)
2
Which of the following is equal to 5-2?
  • A) 25
  • B) -25
  • C) 1/25
  • D) -1/25
(Total for Question 2 is 1 mark)
3
Work out the value of:
(a)641/2(1)
(b)81/3(1)
(c)811/4(1)
(Total for Question 3 is 3 marks)
4
Work out the value of:
(a)4-1/2(2)
(b)9-3/2(2)
(Total for Question 4 is 4 marks)
5
Simplify, leaving your answer in index form:
(a)x5 x x-2(1)
(b)y3 / y-4(1)
(c)(m-2)3(1)
(Total for Question 5 is 3 marks)
6
Which of the following is equal to 1/(x3)?
  • A) x-3
  • B) x3
  • C) -x3
  • D) x1/3
(Total for Question 6 is 1 mark)
7
Work out the value of:
(a)82/3(2)
(b)253/2(2)
(c)16-1/4(2)
(Total for Question 7 is 6 marks)
8
Simplify fully:
(a)(x4 y-2) / (x-1 y3)(2)
(b)Write (2a3)-2 in the form k an, stating the values of k and n.(2)
(Total for Question 8 is 4 marks)
9
Solve the equation 2x = 1/32
(Total for Question 9 is 2 marks)
10
Solve the equations:
(a)x1/2 = 7(1)
(b)x2/3 = 25(2)
(Total for Question 10 is 3 marks)
11
Show that 9-1/2 x 34 = 27
(Total for Question 11 is 3 marks)
12
Work out the value of 27-2/3. Give your answer as a fraction.
(Total for Question 12 is 3 marks)
13
The number of bacteria, P, in a culture is modelled by P = 200 x 3t, where t is the time in hours after the culture begins.
(a)Work out the number of bacteria when t = 0.(1)
(b)Work out the number of bacteria after 4 hours.(2)
(Total for Question 13 is 3 marks)
14
The mass, M grams, of a radioactive sample after t years is given by M = 80 x 2-t/12.
(a)Find the mass after 12 years.(2)
(b)Find the mass after 24 years.(1)
(c)State what the number 80 represents in this context.(1)
(Total for Question 14 is 4 marks)
15
Given that y = x-3/2, find the value of y when x = 4.
(Total for Question 15 is 2 marks)
16
Simplify fully (a1/2 x a5/2) / a2. Give your answer in the form an.
(Total for Question 16 is 3 marks)
17
Show that 4-3/2 x 82/3 = 1/2
(Total for Question 17 is 3 marks)
18
A cube-shaped storage box has volume V = 512 cm3. The side length of the cube is given by l = V1/3.
(a)Work out the side length, l, of the cube.(1)
(b)The total surface area of a cube is given by A = 6l2. Work out the total surface area of the box, stating the correct units.(2)
(Total for Question 18 is 3 marks)
Mark scheme · 6.2 Fractional and Negative 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