Indices and the Index Laws - Worksheets, Questions and Revision

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

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KS3 · Number

KS3.M-N12 Indices and the Index Laws

AQA KS3.M-N12 · Calculators not allowed · about 60 minutes
Name: _______________________________    Date: ____ / ____ / ______
Answer ALL questions. Show all your working.
1
Write down the value of each power.
(a)24(1)
(b)52(1)
(c)101(1)
(d)15(1)
2
Write down the value of each expression with zero or negative indices.
(a)70(1)
(b)2-2(1)
(c)(-3)0(1)
3
Use index laws to simplify each product. Give your answer as a single power.
(a)x3 x4(1)
(b)23 x 25(1)
(c)a1 x a6(1)
4
Use index laws to simplify each quotient. Give your answer as a single power or a number.
(a)x7 / x2(1)
(b)35 / 33(1)
(c)b4 / b4(1)
5
Calculate the value. Show a short method.
(a)32 x 33(2)
6
Use the power-of-a-power rule to simplify. Give your answer as a single power.
(a)(x3)4(2)
7
Simplify fully. Expand brackets where needed and give a final single-term answer.
(a)(2x2)3(3)
8
Simplify each expression. Give answers as single powers or numbers.
(a)(3x2)2(2)
9
Calculate and write each answer as an exact number. Show the index law step.
(a)(23)2(3)
10
Use index laws to simplify each expression. Give answers in simplest form.
(a)(a3 b2) (a2 b4)(2)
(b)54 / 52(2)
11
Rewrite each expression using index laws and then evaluate if possible.
(a)x0 x5(2)
(b)60 x 23(2)
12
A small electronic device uses power in units proportional to 2n, where n is the version number. Version 0 uses 1 unit of power. Version 4 uses 16 units. A technician compares Version 4 to Version -1.
(a)State the power used by Version -1, showing your method using index laws.(3)
(b)How many times greater is the power of Version 4 compared to Version -1? Show your working.(3)
13
Fully simplify each expression. Show index steps where helpful.
(a)p5 / p2 x p0(2)
(b)43 / (23)(2)
14
Challenge problem. Simplify the expression fully and give the answer as a single number or single power.
(a)(23 x 2-2) x (42 / 23)(5)
Mark scheme · KS3.M-N12 Indices and the Index Laws

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