Indices: Fluency and Exam Drill - Worksheets, Questions and Revision

23 original exam-style questions - 5 pages of questions with a full mark scheme - free printable PDF.

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GCSE · Number - Indices

4.2D Indices: Fluency and Exam Drill

EDEXCEL 1MA1 · Calculators not allowed · about 55 minutes
Total Marks
Name: _______________________________    Date: ____ / ____ / ______
Answer ALL questions. Show all your working.

Index Laws Checklist

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Multiplying powers of the same base: add the indices, a^m * a^n = a^(m+n). Dividing powers of the same base: subtract the indices, a^m / a^n = a^(m-n). Raising a power to a power: multiply the indices, (a^m)^n = a^(m*n). Any non-zero number to the power 0 is 1: a^0 = 1. A negative index gives a reciprocal: a^-n = 1/a^n. A fractional index gives a root: a^(1/n) = nth root of a, and more generally a^(m/n) = (nth root of a)^m. Work through the fluency questions first to build speed with these rules, then use the exam-style questions to practise applying them in longer, marked problems.

1
Work out the value of 34.
(Total for Question 1 is 1 mark)
2
Work out the value of 100.
(Total for Question 2 is 1 mark)
3
Work out the value of 5-1. Give your answer as a fraction.
(Total for Question 3 is 1 mark)
4
Work out the value of 2-4.
(Total for Question 4 is 1 mark)
5
Simplify p5 * p3.
(Total for Question 5 is 1 mark)
6
Simplify q9 / q4.
(Total for Question 6 is 1 mark)
7
Simplify (r3)4.
(Total for Question 7 is 1 mark)
8
Work out the value of 161/2.
(Total for Question 8 is 1 mark)
9
Work out the value of 1251/3.
(Total for Question 9 is 1 mark)
10
Work out the value of 49-1/2.
(Total for Question 10 is 2 marks)
11
Simplify 4x5 * 3x2.
(Total for Question 11 is 2 marks)
12
Simplify 20y9 / 5y3.
(Total for Question 12 is 2 marks)
13
Simplify (3d2)3.
(Total for Question 13 is 2 marks)
14
Work out the value of 642/3.
(Total for Question 14 is 2 marks)
15
Simplify fully (3x4y)2 / (9x5y^2).
(Total for Question 15 is 3 marks)
16
Solve each of the following equations.
(a)6x = 216(1)
(b)72x-1 = 343(3)
(Total for Question 16 is 4 marks)
17
Show that 23 / 25 = 1/4
(Total for Question 17 is 2 marks)
18
The volume of a cube is 64x12 cm3. Find an expression, in terms of x, for the length of one edge of the cube. Give your answer in its simplest form.
(Total for Question 18 is 3 marks)
19
n is a positive integer. Show that (2n * 2n+1) / 22n-1 = 4 for all values of n.
(Total for Question 19 is 3 marks)
20
Answer each of the following.
(a)Write (53)2 * 5-4 as a single power of 5.(2)
(b)Hence work out the value of (53)2 * 5-4.(2)
(Total for Question 20 is 4 marks)
21
The number 212 is written in the form 4k. Find the value of k.
(Total for Question 21 is 3 marks)
22
Solve the equation 125x = 25x+1 / 5, giving your answer as an integer.
(Total for Question 22 is 4 marks)
23
Simplify fully (x3/4 * x1/3) / x1/2, giving your answer in the form xk where k is a fraction in its simplest form.
(Total for Question 23 is 3 marks)
Mark scheme · 4.2D Indices: Fluency and Exam Drill

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

Question 21

Question 22

Question 23