Indices and Surds - moreeinfo.com RESOURCES...16 EXCEL ESSENTIAL SKILLS: YEAR 9 MATHEMATICS REVISION AND EXAM WORKBOOK 2 – EXTENSION Indices and surds UNIT 6: Addition and subtraction

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Mathletics Instant

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Mathletics Instant

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Student Book - Series J-2

Indices and Surds

23, x3, y°, 3-1

Indices and surdsStudent Book - Series J 2

Contents

Topics

Topic 1 - Index laws __/__/__ Date completed

Topic 2 - Negative indices __/__/__ Topic 3 - Fractional indices __/__/__ Topic 4 - Scientific notation __/__/__ Topic 5 - Simplifying surds __/__/__ Topic 6 - Addition and subtraction of surds __/__/__

Topic 8 - Binomial products and conjugate surds __/__/__ Topic 9 - Rationalising the denominator __/__/__

Topic 7 - Multiplication and division of surds __/__/__

Indices and surdsMathletics Instant Workbooks – Series J 2 Copyright © 3P Learning

Author of The Topics and Topic Tests: AS Kalra

Practice Tests

Topic 1 - Topic test A __/__/__ Topic 2 - Topic test B __/__/__

1

Indices and surds


Topic 1: Index laws

11Chapter 2: Indices and surds

Indices and surdsCHAPTER 2

UNIT 1: Index laws

EXCEL YEARS 9 & 10 ADVANCED MATHS

Page 22

QUESTION 1 Simplify the following leaving answers in index form.

a m m4 5× = _____________ b n n2 5× = ______________ c y y6 2× = ______________

d p p6 6× = ______________ e a a2 × = ______________ f a a a2 3× × = __________

g 4 2 3x x× = _____________ h 5 23 2x x× = ____________ i 6 3 2m m× = ____________

QUESTION 2 Simplify, giving answers in index form.

a x x9 6÷ = ______________ b y y8 5÷ = ______________ c a a7 5÷ = _____________

d 15 55 3m m÷ = __________ e 16 87 4n n÷ = ___________ f 36 98 6a a÷ = __________

g 24 86y y÷ = ____________ h x y x y6 3 4÷ = ___________ i a b a b7 6 4 3÷ = _________

QUESTION 3 Give the answers in simplest index form.

a 32 3( ) = ________________ b 23 2( ) = ________________ c x3 2( ) = _______________

d m3 4( ) = _______________ e a a3 2 4( ) × = ____________ f y y7 2 6( ) ÷ = ___________

g a a4 3 5 2( ) × ( ) = __________ h x5 6( ) = ________________ i 2 3 4y( ) = ______________

QUESTION 4 Simplify the following.

a 4 0m = ________________ b 6 0m( ) = _______________ c 8 0n = ________________

d 5 80 0m m× ( ) = __________ e a b6 0 = ________________ f x2 0( ) = _______________

g 5 3 0y( ) = _______________ h a a7 7÷ = ______________ i 9 95 5x x÷ = ___________

QUESTION 5 Simplify the following, giving the answers in index form.

a a a7 2÷ =_______________ b a a9 2× = ______________ c a5 4( ) = _______________

d 9 3 2x( ) = _______________ e 27 93x x÷ = ____________ f 7 42 2a b a b× = _________

g m n m n2 3 4 3× = __________ h 24 123 6 2 4x y x y÷ = _______ i 9 32x y xy× = ___________

j 9 94 2x y xy÷ = __________ k 36 187 9 5 7x y x y÷ =________ l 8 2 2x( ) = ______________

2

Indices and surds


12 EXCEL ESSENTIAL SKILLS: YEAR 9 MATHEMATICS REVISION AND EXAM WORKBOOK 2 – EXTENSION

Indices and surdsUNIT 2: Negative indices

QUESTION 1 Evaluate the following.

a 3 2− = _________________ b 2 3− = _________________ c 5 2− = ________________

d 4 3− = _________________ e 10 3− = ________________ f 8 2− = ________________

g 64 2 3× − = _____________ h 2 23 5− × = _____________ i 3 23 2− −× = ____________

j 7 2 0×( ) = _____________ k 3 2 1×( )− = _____________ l 5

3 2− = ________________

m 3

4

2

− = _______________ n 1

2

5

− = ______________ o 3 37 5− × = _____________


Page 23

QUESTION 2 Write the following with positive indices.

a a−3 = _________________ b m−5 = ________________ c p q2 3− = ______________

d x y−7 6 = _______________ e 4 3 6p q− = ______________ f1

3y− = ________________

ga

b−2 = ________________ h1

2 5x y− = ______________ i x x3 5× − = ____________

j x x3 10÷ = _____________ k 10 3 9a a÷ = ____________ l xy( )−2 = ______________

m 5 2 3 2a b− −( ) = ____________ n a a− ×7 4 = _____________ o 4 2 2

a− −( ) = ____________

QUESTION 3 Simplify, giving your answer without negative indices.

a x x5 3× − = _____________________________ b x x3 5× − = ____________________________

c 5 25 2x x− −× = __________________________ d 6 22 1a a− −× = _________________________

e 8 46 4m m× − = __________________________ f 3 53 5a a− −× = _________________________

g 20 106 4m m− ÷ = ________________________ h 20 106 4x x− −÷ = _______________________

i 15 152 1a a− −÷ = _________________________ j 5 1 2x−( ) = _____________________________

k 8 3 2x−( ) = ______________________________ l 2 6 2

a− −( ) = ____________________________

Topic 2: Negative indices

3

Indices and surds



Indices and surdsUNIT 3: Fractional indices

QUESTION 1 Evaluate the following.

a 91

2 = __________________ b 161

4( ) = _____________ c 271

3( ) = _______________

d 1001

2( ) = ______________ e 6251

2( ) = ______________ f 1251

3( ) = ______________

g 82

3 = __________________ h 322

5( ) = _______________ i 811

4( ) = _______________

j 251

2−

= ________________ k 361

2−

= ________________ l 641

3−

= _______________

m 11

3 = __________________ n 11

3−

= _________________ o 491

2−

= _______________


Page 23


a m61

2( ) = _______________ b 16 41

2p( ) = _____________ c x y3 31

3( ) = _____________

d 9 2 21

2m n( ) = ____________ e 8 31

3

2

3m m× = ___________ f 61

2

2

y

= _____________

g x y3 61

2( ) = ______________ h a a a1

3

1

3

1

3× × = __________ i m n2

3

2

3

3

×

= __________

j 81

3ab( ) = ______________ k 9 61

2

1

2x x× = ___________ l m21

4( ) = ______________

m 8 52

3

1

3a a× = ____________ n 27 6 61

3a b( ) = ___________ o m m m1

2

1

4

1

4× × = ________

QUESTION 3 Evaluate the following without using a calculator.

a 41

2 = _________________ b 81

3 = _________________ c 161

4 = ________________

d 271

3 = ________________ e 811

4 = _________________ f 1211

2 = _______________

g 10002

3 = _______________ h 642

3 = _________________ i 1254

3( ) = ______________

j 251

2

3

= ______________ k 64

1

2−

= ________________ l 811

4−

= _______________

Topic 3: Fractional indices

4

Indices and surds



Indices and surdsUNIT 4: Scientific notation

QUESTION 1 Express the following in scientific notation.

a 350 = _________________________________ b 2500 = _______________________________

c 15 000 = _______________________________ d 386 000 = _____________________________

e 500 000 = ______________________________ f 856 = ________________________________

g 9500 = ________________________________ h 3687 = _______________________________

i 864 300 = ______________________________ j 53 630 = ______________________________

k 9643 = ________________________________ l 83 000 = ______________________________

EXCEL YEARS 9 & 10 INTERMEDIATE MATHS

Page 75

QUESTION 2 Express the following in scientific notation.

a 0.007 = _______________________________ b 0.00098 = _____________________________

c 0.05 = ________________________________ d 0.00009 = _____________________________

e 0.528 = _______________________________ f 0.000681 = ____________________________

g 0.009 = _______________________________ h 0.6 = _________________________________

i 0.632 = _______________________________ j 0.001 = _______________________________

k 0.000007 = _____________________________ l 0.000835 = ____________________________

QUESTION 3 Write the basic numeral for the following.

a 3 7 102. × = _____________________________ b 8 5 104. × = ____________________________

c 4 95 103. × = ____________________________ d 7 89 105. × = ___________________________

e 2 57 105. × = ____________________________ f 1 7 104. × = ____________________________

g 3 08 10 2. × − = ___________________________ h 4 6 10 3. × − = ___________________________

i 9 7 10 4. × − = ____________________________ j 2 39 10 2. × − = __________________________

QUESTION 4 Use your calculator to answer the following correct to 3 significant figures.

a 1 2 10 2 3 103 4. .×( ) × ×( ) = _________________ b 2 10 2 5 104 3×( ) × ×( ). = __________________

c 4 9 1 8 103. .× ×( ) = _______________________ d 5 9 10 2 3 105 3. .×( ) ÷ ×( ) = ________________

e 8 5 10 6 3 102 1. .×( ) × ×( )− = ________________ f 8 1 10 6 3 102 4. .× × ×− = __________________

g 4 5 10 3 2 105 3. .×( ) × ×( ) = _________________ h 5 6 10 2 8 104 2. .×( ) ÷ ×( ) = ________________

Topic 4: Scientific notation

5

Indices and surds



Indices and surdsUNIT 5: Simplifying surds


Page 18

QUESTION 2 Write the following surds in simplest form.

a 54 = ________________ b 150 = _______________ c 96 = _______________

d 160 = _______________ e 450 = _______________ f 125 = _______________

g 63 = ________________ h 108 = _______________ i 192 = _______________

j 288 = _______________ k 162 = _______________ l 243 = _______________

QUESTION 1 Simplify the following surds.

a 8 = _________________ b 12 = ________________ c 18 = _______________

d 24 = ________________ e 28 = ________________ f 50 = _______________

g 40 = ________________ h 44 = ________________ i 75 = _______________

j 48 = ________________ k 27 = ________________ l 32 = _______________

m 72 = ________________ n 98 = ________________ o 242 = _______________

QUESTION 3 Simplify the following surds.

a 32( ) = _______________ b 5

2( ) = _______________ c 82( ) = ______________

d 92( ) = _______________ e 200 = _______________ f − 12 = ______________

g x2 = ________________ h 9 2x = _______________ i 18 2x = _____________

j 3 12 = _______________ k 4 18 = _______________ l 5 27 = _______________

m 3 18 = ________________ n 4 48 = _______________ o 2 54 = ______________

p 6 72 = _______________ q 16 4 6x y = ___________ r 7 56 = ______________

s 5 32 = ______________ t 3 162 = _____________ u 7 6x = ______________

v 3 8y = _______________ w 16 10m = ____________ x 28 4x = ______________

Topic 5: Simplifying surds

6

Indices and surds



Indices and surdsUNIT 6: Addition and subtraction of surds


Page 19

QUESTION 1 Simplify the following by collecting like surds.

a 5 2 6 2+ = ___________________________ b 8 5 7 5+ = __________________________

c 6 3 9 3+ = ___________________________ d 8 5 4 5− = __________________________

e 9 3 4 3 2 3+ − = _____________________ f 12 2 6 2 5 2+ − = ____________________

g 2 3x x+ = __________________________ h 5 6 3y y y+ − = _____________________

i 8 15 7m m m+ − = ___________________ j 16 3 7 3 2 3− + = ____________________

k 11 3 15 3 16 3+ − = ___________________ l 3 2a x a x+ = ________________________


a 2 3 5 2 8 3+ + = _____________________ b 3 7 5 7 2 11+ − = ____________________

c 3 3 6 2 7 3 4 2+ − − = ________________ d 8 5 2 3 5 5 8 3− − + = ________________

e 9 2 6 2 5 2− + =______________________ f 6 3 2 3 3− + = ______________________

g 2 5 2 5− = ___________________________ h 8 3 7 3+ = __________________________

i 5 10 3 10 3− + = _____________________ j 4 5 8 5 7 5− + = _____________________

k 9 2 8 2 6 3+ − = _____________________ l 4 7 6 7 3 7+ − = _____________________

m 2 12 2 2+ − = ______________________ n 8 3 11 3 3 5+ − = ____________________

QUESTION 3 Simplify.

a 8 18+ = ____________________________ b 90 160+ = _________________________

c 27 75+ = ___________________________ d 54 24− = __________________________

e 48 27− = ___________________________ f 81 96− = __________________________

g 18 50+ = ___________________________ h 3 24 2 96− = ________________________

i 12 3 72+ = __________________________ j 5 125 20+ − = _____________________

k 12 4 48+ = __________________________ l 8 32 18+ − = ______________________

m 20 45 75+ − =______________________ n 242 162 18− + = ___________________

Topic 6: Addition and subtraction of surds

7

Indices and surds



Indices and surdsUNIT 7: Multiplication and division of surds

QUESTION 3 Expand and simplify.

a 2 7 3+( ) = _________________________ b 3 5 3+( ) = ________________________

c 5 5 3+( ) = _________________________ d 7 3 7 2−( ) = _________________________

e 5 5 3−( ) = ___________________________ f 2 3 2 2−( ) = _______________________

g 3 5 2 3−( ) = ________________________ h 3 2 5 7−( ) = _______________________

i 2 11 2 7+( ) =________________________ j 5 2 3+( ) = ________________________

k 11 2 3 6 11−( ) = _____________________ l 5 5 3+( ) = _________________________

m 2 3 2 8+( ) = _________________________ n 5 3 6 5+( ) = ___________________________


Page 19

QUESTION 2 Simplify these divisions.

a 12 3÷ = ____________________________ b 15 5÷ = ___________________________

c 8 2÷ = _____________________________ d 48 3÷ = ___________________________

e 32 8÷ = ____________________________ f 72 2÷ = ___________________________

g 8 5 5÷ = ____________________________ h 25 3 5 3÷ = _________________________

i 50 7 10 7÷ = _________________________ j 18 8 2 8÷ = _________________________

k 50 5÷ = _____________________________ l 27 9÷ = ___________________________

m 10 18 5 2÷ = _________________________ n 28 5 7 5÷ = _________________________

QUESTION 1 Simplify these products.

a 2 3× = _____________________________ b 5 6× = ____________________________

c 2 7× = _____________________________ d 5 9× = ____________________________

e 3 11× = ____________________________ f 5 20× = ___________________________

g 3 27× = ____________________________ h 8 2× = ____________________________

i 2 3 4 3× = ___________________________ j 5 2 6 3× = __________________________

k 3 2 7 2× = ___________________________ l 5 6 2 8× = ___________________________

Topic 7: Multiplication and division of surds

8

Indices and surds



Indices and surdsUNIT 8: Binomial products and conjugate surds


Page 20


a 3 2 3 4+( ) +( ) = _____________________ b 5 2 3 7+( ) +( ) = ____________________

c 2 3 1 2 3 4+( ) −( ) = _____________________ d 5 3 2 3 4+( ) −( ) = _____________________

e 3 2 3 2 1+( ) +( ) = _____________________ f 7 3 5 2−( ) +( ) = ______________________

g 5 2 2 5 2+( ) −( ) = _____________________ h 2 11 2 11 1+( ) −( ) = ____________________

i 3 2 2 1+( ) +( ) = _____________________ j 7 2 3 5 2 2+( ) +( ) = __________________

k 2 3 3 2 3 1+( ) +( ) = ___________________ l 2 2 5 2 3+( ) −( ) = _____________________


a 2 12

+( ) = ____________________________ b 2 3 32

+( ) = __________________________

c 5 72

+( ) = __________________________ d 3 52

−( ) = __________________________

e 3 12

−( ) = ____________________________ f 7 22

−( ) = __________________________

g 6 32

−( ) = ____________________________ h 2 3 52

+( ) = ___________________________

i 3 5 12

−( ) = ___________________________ j 2 32

+( ) = __________________________

k 3 22

−( ) = __________________________ l 2 5 3 22

+( ) = ________________________

m 2 5 12

+( ) = ___________________________ n 2 7 12

−( ) = ___________________________

QUESTION 3 Find the product of each pair of conjugate surds.

a 3 2 3 2+( ) −( ) = ___________________ b 7 2 7 2+( ) −( ) = ___________________c 9 2 7 9 2 7+( ) −( ) = ____________________ d 5 3 5 3+( ) −( ) = ___________________

e 11 7 11 7−( ) +( ) = __________________ f 3 2 3 3 2 3+( ) −( ) = ____________________

g 7 2 7 2−( ) +( ) = ______________________ h 5 5 5 5+( ) −( ) = ______________________

i 8 2 2 8 2 2−( ) +( ) = ____________________ j 2 11 5 2 11 5+( ) −( ) = __________________

k 3 7 3 3 7 3+( ) −( ) = _____________________ l 5 2 1 5 2 1−( ) +( ) = ____________________

m 3 6 7 3 6 7+( ) −( ) = ____________________ n 8 3 5 8 3 5+( ) −( ) = ____________________

Topic 8: Binomial products and conjugate surds

9

Indices and surds



Indices and surdsUNIT 9: Rationalising the denominator


Pages 20–21

QUESTION 2 Simplify the following by rationalising the denominator.

a3

5 =_________________

b27

=_________________

c5

11 =_______________

d3

5 3 =________________

e2 1

2−

=______________

f3 53 7

=_______________

g5

2 2 =

_______________h

7

3 3 =________________

i9

5 5 =_______________

j182

=________________

k4 23 7

=________________

l2 1

5

+ =______________

m3 2

3+

=______________

n5 3

7−

=____________

o3 2 7

5

+ =

___________

QUESTION 1 Rationalise the denominator of the following.

a3

7 =_________________

b5

11 =________________

c5

2 =________________

d6

15 =________________

e7

5 =_________________

f2 3

7 =_______________

g3 2

5 =

________________h

2 73

=________________

i7 2

5 =

_______________

QUESTION 3 Rationalise the denominator of the following.

a1

2 1+ =______________________________

b1

3 1− =_____________________________

c1

5 1− =______________________________

d3

2 1− =_____________________________

e5

5 2+ =______________________________

f2

7 5− =____________________________

g3

5 2− =____________________________

h8

7 3− =____________________________

i1

2 3 8+ =_____________________________

j2

5 3− =_____________________________

k3

5 7+ =______________________________

l2

3 5+ =____________________________

Topic 9: Rationalising the denominator


Indices and surdsTOPIC TEST SECTION 1

Instructions for SECTION 1 • You have 15 minutes to answer Section 1• Each question is worth 1 mark• Attempt ALL questions• Calculators are NOT to be used• Fill in only ONE CIRCLE for each question

1 2 23 4× =

A 212 B 27 C 412 D 47

2 3 2a− equals

A1

3 2a B32a C

−1

3 2a D−3

2a

3 2 2 3b( ) equals

A 6 5b B 6 6b C 8 6b D 8 8b

4 12 46 3m m÷ equals

A 3 3m B 3 2m C 8 3m D 8 2m

5a b

a b

6

2 2 equals

Aa

b

4

B a b4 Ca

b

3

D a b3

6 a a3 3+ equals

A a6 B a9 C 2 3a D 2 6a

7 If 2 find the value of 4 2 0 b b= ( ) .

A 4 2b B 8 C 0 D 1

8 Which of the following numbers is not a surd?

A 5 B 3 C 101 D − 49

942

=

A 2 2 B 4 2 C 2 D 2

10 Which of the following statements is true? I: a b ab× = , II : a b a + b+ =

A I only B II only C Both I and II D Neither

Marks

Total marks achieved for SECTION 110

1

1

1

1

1

1

1

1

1

1

Indices and surds



Instructions for SECTION 1 • You have 15 minutes to answer Section 1• Each question is worth 1 mark• Attempt ALL questions• Calculators are NOT to be used• Fill in only ONE CIRCLE for each question

1 2 23 4× =

A 212 B 27 C 412 D 47

2 3 2a− equals

A1

3 2a B32a C

−1

3 2a D−3

2a

3 2 2 3b( ) equals

A 6 5b B 6 6b C 8 6b D 8 8b

4 12 46 3m m÷ equals

A 3 3m B 3 2m C 8 3m D 8 2m

5a b

a b

6

2 2 equals

Aa

b

4

B a b4 Ca

b

3

D a b3

6 a a3 3+ equals

A a6 B a9 C 2 3a D 2 6a

7 If 2 find the value of 4 2 0 b b= ( ) .

A 4 2b B 8 C 0 D 1

8 Which of the following numbers is not a surd?

A 5 B 3 C 101 D − 49

942

=

A 2 2 B 4 2 C 2 D 2

10 Which of the following statements is true? I: a b ab× = , II : a b a + b+ =

A I only B II only C Both I and II D Neither

Marks


1

1

1

1

1

1

1

1

1

1

Indices and surds

10Indices and surdsMathletics Instant Workbooks – Series J 2 Copyright © 3P Learning

Indices and surdsTopic Test PART A

Marks

Total marks achieved for PART A 10

Instructions This part consists of 10 multiple-choice questions Each question is worth 1 mark Attempt ALL questions Calculators are NOT to be used Fill in only ONE CIRCLE for each question

Time allowed: 15 minutes Total marks = 10

Instructions This part consists of 15 questions Each question is worth 1 marks Attempt ALL questions Calculators may be usedTime allowed: 20 minutes Total marks = 15

Questions Answers only

Total marks achieved for PART B 15

Marks

Indices and surdsTopic Test PART B

11Indices and surdsMathletics Instant Workbooks – Series J 2 Copyright © 3P Learning



Instructions for SECTION 2 • You have 20 minutes to answer ALL of Section 2• Each question is worth 2 marks• Attempt ALL questions• Calculators may be used

Marks


Simplify the following:

1 2 3 3a( ) ___________________

2 16 83 2a a b÷ ___________________

3 25 612x( ) ___________________

4 5 3 80 0 2 0p p p+ ( ) + ( ) ___________________

5 n n8 2 3÷ ( ) ___________________

6 3 35 2× ___________________

7 12 46 4m m÷ ___________________

8x y zx y

3 2

2 ___________________

9ab

ab

2

( )2 ___________________

10 4 162 2 3xy y( ) ÷ ___________________

11 2 3 8 3 5 7 7+ − + ___________________

12 3 2 3× ___________________

13 20 45+ ___________________

14 Express 7 3 7+( ) in its simplest surd form. ___________________

15 Expand and simplify 5 2 3 5 2 3−( ) +( ) . ___________________

Questions Answers

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Indices and surds




Marks



1 2 3 3a( ) ___________________

2 16 83 2a a b÷ ___________________

3 25 612x( ) ___________________

4 5 3 80 0 2 0p p p+ ( ) + ( ) ___________________

5 n n8 2 3÷ ( ) ___________________

6 3 35 2× ___________________

7 12 46 4m m÷ ___________________

8x y zx y

3 2

2 ___________________

9ab

ab

2

( )2 ___________________

10 4 162 2 3xy y( ) ÷ ___________________

11 2 3 8 3 5 7 7+ − + ___________________

12 3 2 3× ___________________

13 20 45+ ___________________



Questions Answers

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Indices and surds




Marks



1 2 3 3a( ) ___________________

2 16 83 2a a b÷ ___________________

3 25 612x( ) ___________________

4 5 3 80 0 2 0p p p+ ( ) + ( ) ___________________

5 n n8 2 3÷ ( ) ___________________

6 3 35 2× ___________________

7 12 46 4m m÷ ___________________

8x y zx y

3 2

2 ___________________

9ab

ab

2

( )2 ___________________

10 4 162 2 3xy y( ) ÷ ___________________

11 2 3 8 3 5 7 7+ − + ___________________

12 3 2 3× ___________________

13 20 45+ ___________________



Questions Answers

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Indices and surds

Documents

Indices and Surds - moreeinfo.com RESOURCES...16 EXCEL ESSENTIAL SKILLS: YEAR 9 MATHEMATICS REVISION AND EXAM WORKBOOK 2 – EXTENSION Indices and surds UNIT 6: Addition and subtraction