Indices and the Index Laws: Fluency and Exam Drill - Worksheets, Questions and Revision

20 original exam-style questions - 4 pages of questions with a full mark scheme - free printable PDF.

Download PDF Jump to mark scheme (page 5)Read the revision guide

Next in this strand

Revision Library

revisionlibrary.co.uk

KS3 · Number

KS3.M-N12D Indices and the Index Laws: Fluency and Exam Drill

AQA KS3.M-N12 · Calculators not allowed · about 50 minutes

Name: _______________________________ Date: ____ / ____ / ______

Answer ALL questions. Show all your working.

Write down the value of 3³.

(1)

Write down the value of 6².

(1)

Write down the value of 10⁴.

(1)

Write down the value of 5⁰.

(1)

Write down the value of 2^-3.

(1)

Write down the value of 4^-1.

(1)

Simplify y⁵ x y², giving your answer as a single power.

(2)

Simplify 7⁶ / 7⁴, giving your answer as a single power or a number.

(2)

Simplify (m³)⁴, giving your answer as a single power.

(2)

Work out 2² x 2⁴, giving your answer as an integer.

(2)

Simplify (2y)³, giving your answer in the form kyⁿ.

(2)

Simplify p⁰ x p⁶.

(2)

Simplify k⁹ / k⁹.

(2)

Work out 5³ / 5¹, giving your answer as an integer.

(2)

Simplify (3x²)³, giving your answer in the form kxⁿ.

(3)

Work out the value of (2³ x 2²) / 2⁴, giving your answer as an integer.

(3)

A quantity doubles every hour. At time zero it is 2⁰ = 1 unit. Find the quantity after 5 hours, giving your answer as a power of 2 and as an integer.

(3)

Simplify (a⁴ b³) x (a² b⁵), giving your answer as a single term.

(3)

Work out (4³) / (2⁴), giving your answer as an integer. Use index laws to help.

(3)

Simplify (5x³)² / x⁴, giving your answer in the form kxⁿ.

(3)

Mark scheme · KS3.M-N12D Indices and the Index Laws: Fluency and Exam Drill

Question 1

B1 27 cao
Answer: 27

Question 2

B1 36 cao
Answer: 36

Question 3

B1 10000 cao
Answer: 10000

Question 4

B1 1 cao
Answer: 1

Question 5

B1 1/8 or 0.125 cao
Answer: 1/8

Question 6

B1 1/4 or 0.25 cao
Answer: 1/4

Question 7

M1 adds indices: 5 + 2 = 7
A1 y⁷ cao
Answer: y⁷

Question 8

M1 subtracts indices: 6 - 4 = 2
A1 7² or 49 cao
Answer: 7²

Question 9

M1 multiplies indices: 3 x 4 = 12
A1 m¹² cao
Answer: m¹²

Question 10

M1 adds indices to get 2⁶
A1 64 cao
Answer: 64

Question 11

M1 cubes the 2 to get 8 and multiplies the index on y: 1 x 3 = 3
A1 8y³ cao
Answer: 8y³

Question 12

M1 recognises p⁰ = 1
A1 p⁶ cao
Answer: p⁶

Question 13

M1 subtracts indices to get k⁰
A1 1 cao
Answer: 1

Question 14

M1 subtracts indices to get 5²
A1 25 cao
Answer: 25

Question 15

M1 cubes the 3 to get 27
M1 multiplies the index on x: 2 x 3 = 6
A1 27x⁶ cao
Answer: 27x⁶

Question 16

M1 adds the indices in the numerator: 3 + 2 = 5
M1 subtracts the denominator's index: 5 - 4 = 1
A1 2 cao
Answer: 2

Question 17

M1 recognises the quantity after n hours is 2ⁿ
M1 substitutes n = 5 to get 2⁵
A1 32 units cao
Answer: 32

Question 18

M1 adds the indices of a: 4 + 2 = 6
M1 adds the indices of b: 3 + 5 = 8
A1 a⁶ b⁸ cao
Answer: a⁶ b⁸

Question 19

M1 recognises 4 = 2² so 4³ = 2⁶
M1 subtracts indices: 6 - 4 = 2
A1 4 cao
Answer: 4

Question 20

M1 squares the 5 to get 25 and multiplies the index on x: 3 x 2 = 6, giving 25x⁶
M1 subtracts the index in the denominator: 6 - 4 = 2
A1 25x² cao
Answer: 25x²

Mark my answers

Indices and the Index Laws: Fluency and Exam Drill - Worksheets, Questions and Revision

More on this topic

Next in this strand

KS3.M-N12D Indices and the Index Laws: 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 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