10A Review of index laws 10B 10C 10D - Weebly€¦ · 10A Review of index laws 10B Raising a power to another power 10C Negative indices 10D Square roots and cube roots WhAt Do you

10A Review of index laws10B Raising a power to another power10C Negative indices10D Square roots and cube roots

WhAt Do you knoW?

1 List what you know about indices. Create a concept map to show your list.

2 Share what you know with a partner and then with a small group.

3 As a class, create a large concept map that shows your class’s knowledge of indices.

opening Question

If you could count all the stars in the sky, how might you write the number?

10

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number AnD AlgebrA • pAtterns AnD AlgebrA

indicesContentsIndicesAre■you■ready?Review■of■index■lawsReview■of■index■lawsRaising■a■power■to■another■powerRaising■a■power■to■another■powerNegative■indicesNegative■indicesSquare■roots■and■cube■rootsSquare■roots■and■cube■rootsSummaryChapter■reviewActivities


328 maths Quest 9 for the Australian Curriculum

Are you ready?Try■the■questions■below.■If■you■have■diffi■culty■with■any■of■them,■extra■help■can■be■obtained■by■completing■the■matching■SkillSHEET■located■on■your■eBookPLUS.

Index form 1 State■the■base■and■power■for■each■of■the■following.

a 34 b 25 c 157

Using a calculator to evaluate numbers in index form 2 Calculate■each■of■the■following.

a 24 b 53 c 46

Linking squares with square roots 3 Complete■the■following■statements.

a If■32■=■9,■then■ 9 ■=■.■■.■■. b If■112■=■121,■then■ 121■=■.■■.■■.

c If■172■=■289,■then■ 289 ■=■.■■.■■.

Calculating square roots 4 Calculate■each■of■the■following.

a 64 b 100 c 25

Linking cubes with cube roots 5 Complete■the■following■statements.

a If■23■=■8,■then■ 83 ■=■.■■.■■. b If■53■=■125,■then■ 1253 ■=■.■■.■■.

c If■93■=■729,■then■ 7293 =■.■■.■■.

Calculating cube roots 6 Calculate■each■of■the■following.

a 643 b 2163 c 13

Estimating square roots and cube roots 7 Estimate,■to■the■nearest■whole■number,■the■value■of■each■of■the■following.■(Do■not■use■a■

■calculator.)

a 23 b 102 c 40

d 603 e 113 f 1203

Using a calculator to evaluate square roots and cube roots 8 Use■a■calculator■to■fi■nd■the■value,■correct■to■4■decimal■places,■of■each■square■root■or■cube■root■

in■question■7.

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■ Base■is■3,■power■is■4. Base■is■2,■power■is■5. Base■is■15,■power■is■7.

16 125 4096

■ 3 11

17

■ 8 10 5

■ 2 5

9

■ 4 6 1

■ 5 10 6

4 2 5

a■ 4.7958 b 10.0995 c 6.3246

d 3.9149 e 2.2240 f 4.9324


329Chapter 10 indices

review of index lawsindex notation

■■ The■product■of■factors■can■be■written■in■a■shorter■form■by■using■index■notation.■■ There■are■two■parts:■a■base■and■a■power■(also■called■index,■exponent■or■logarithm).■■ The■base■indicates■what■will■be■multiplied.■■ The■power■(index■or■exponent)■indicates■how■many■times■the■base■will■be■written■and■multiplied■by■itself.

■■ When■written■in■factor■form,■all■the■multiplications■are■shown.■■ When■the■answer■corresponds■to■a■number,■it■is■called■a■basic■numeral.

6 4 = 6 ì 6 ì 6 ì 6= 1296

Power, index, exponentPower, index, exponent

Base

Basic numeral

Factorform

■■ Any■composite■number■can■be■written■as■a■product■of■powers■of■prime■factors■using■a■factor■tree.

100

2 50

2 25

5 5

100 = 2 ì 2 ì 5 ì 5 = 22 ì 52

Express 360 as a product of powers of prime factors using index notation.

think Write

1 Express■360■as■a■product■of■a■factor■pair. 360■=■6■ì■60

2 Determine■whether■each■number■of■the■factor■pair■is■prime.■If■the■factors■are■prime,■no■further■calculations■are■required.■If■the■factors■are■not■prime,■then■each■must■be■expressed■as■a■product■of■another■factor■pair.

■ =■2■ì■3■ì■4■ì15

3 Repeat■step■2■until■each■of■the■factors■is■prime. ■ =■2■ì■3■ì■2■ì■2■ì■3■ì■5

4 Group■the■prime■factors■of■the■same■type■together. ■ =■2■ì■2■ì■2■ì■3■ì■3■ì■5

5 Write■the■answer■using■index■notation.Note:■The■factors■are■generally■expressed■with■bases■in■ascending■order.

360■=■23■ì■32■ì■5

10A

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InteractivityIndex laws

int-2769

WorkeD exAmple 1



multiplication using indices■■ The■First■Index■Law■states:■am■ì■an■=■am +■n

■■ In■algebraic■expressions,■multiply■the■coefficients■of■the■base■number■and■apply■the■First■Index■Law■to■the■pronumeral■indices■separately.

Simplify 5e10 ì 2e3.

think Write

1 Write■the■problem. 5e10■ì■2e3

2 The■order■is■not■important■when■multiplying,■so■place■the■coefficients■first.

=■5■ì■2■ì■e10■ì■e3

3 Multiply■the■coefficients. =■10■ì■e10■ì■e3

4 Check■to■see■if■the■bases■are■the■same.■They■are■both■e.

=■10e10■+■3

5 Simplify■by■using■the■First■Index■Law■(add■the■indices).

=■10e13

■■ When■more■than■one■type■of■base■is■involved,■apply■the■First■Index■Law■to■each■pronumeral■base■separately.

Simplify 7m3 ì 3n5 ì 2m8 ì n4.

think Write

1 Write■the■problem. 7m3■ì■3n5■ì■2m8■ì■n4

2 The■order■is■not■important■when■multiplying,■so■place■coefficients■first■and■group■the■same■pronumerals■together.

=■7■ì■3■ì■2■ì■m3■ì■m8■ì■n5■ì■n4

3 Simplify■by■multiplying■the■coefficients■and■using■the■First■Index■Law■for■bases■that■are■the■same■(add■the■indices).

=■42■ì■m3■+■8■ì■n5■+■4

=■42m11n9

Division using indices■■ The■Second■Index■Law■states:■am■÷■an■=■am − n

■■ In■algebraic■expressions,■divide■the■coefficients■normally■and■apply■the■Second■Index■Law■to■each■base■separately.

WorkeD exAmple 2

WorkeD exAmple 3



Simplify 25 8

10 4

6 9

4 5

v w

v w

××

.

think Write

1 Write■the■problem. 25 8

10 4

6 9

4 5

v w

v w

××

2 First■multiply■the■coefficients■in■the■numerator■and■then■the■coefficients■in■the■denominator.■Write■the■pronumerals■as■a■single■term.

= 200

40

6 9

4 5

v w

v w

3 Simplify■by■dividing■the■coefficients■and■applying■the■Second■Index■Law■for■each■pronumeral■separately■(subtract■the■indices).

=5 6 9

14 5

200

40

v w

v w=■5v6■-■4w9■-■5

=■5v2w4

■■ Where■the■coefficients■do■not■divide■evenly,■simplify■by■cancelling.

Simplify 7 4

12

3 8

4

t t

t

×.

think Write

1 Write■the■problem. 7 4

12

3 8

4

t t

t

×

2 Multiply■the■coefficients■in■the■numerator■and■apply■the■First■Index■Law■in■the■numerator.■

= 28

12

11

4

t

t

3 Simplify■the■fraction■formed■and■apply■the■Second■Index■Law■for■the■pronumeral■base.

=7 11

34

28

12

t

t

=−7

3

11 4t

= 73

7t

Zero index■■ Any■base■that■has■an■index■(power)■of■zero■is■equal■to■1.■■ This■is■the■Third■Index■Law:■a0■=■1,■where■a■ò■0.

WorkeD exAmple 4

WorkeD exAmple 5



Simplify 9 4

6 2

7 4

3 8

g g

g g

××

.

think Write

1 Write■the■problem.9 4

6 2

7 4

3 8

g g

g g

××

2 First■multiply■the■coefficients■in■the■numerator■and■then■the■coefficients■in■the■denominator.■Then■apply■the■First■Index■Law■in■both■the■numerator■and■denominator.

= 36

12

11

11

g

g

3 Divide■the■coefficients■and■simplify■using■the■Second■Index■Law.

=3 11

111

36

12

g

g

=■3g11■- 11

=■3g0

4 Simplify■using■the■Third■Index■Law. =■3■ì■1=■3

remember

1.■ A■number■written■in■index■form■has■two■parts:■(a)■ a■base,■and(b)■a■power■(index,■exponent■or■logarithm).For■example

6 4 = 6 ì 6 ì 6 ì 6= 1296

Power, index, exponentPower, index, exponent

Base

Basic numeral

Factorform

2.■ The■base■tells■us■what■will■be■multiplied.3.■ The■power■tells■us■how■many■times■the■base■will■be■written■and■multiplied■by■itself.4.■ Factor■form■is■when■all■the■multiplications■are■shown.5.■ When■the■answer■to■a■problem■is■a■number■we■call■it■the■basic■numeral.6.■ Numbers■can■be■written■as■a■product■of■powers■of■prime■numbers.7.■ We■can■add■the■indices■when■multiplying■bases■that■are■the■same.■This■is■known■as■

the■First■Index■Law.■First■Index■Law:■am■ì■an■=■am■+■n

8.■ Whole■number■coefficients■of■the■bases■can■be■multiplied■as■usual.9.■ We■can■subtract■the■indices■when■dividing■bases■that■are■the■same.■This■is■known■as■

the■Second■Index■Law.■Second■Index■Law:■am■ó■an■=■am■-■n

10.■ Any■base■that■has■an■index■(power)■of■zero■is■equal■to■1.■This■is■known■as■the■Third■Index■Law.■Third■Index■Law:■a0■=■1■where■a■ò■0

WorkeD exAmple 6



review of index lawsfluenCy

1 We 1 ■Express■each■of■the■following■as■a■product■of■powers■of■prime■factors■using■index■■notation.a 12 b 72 c 75d 240 e 640 f 9800

2 We2 ■Simplify■each■of■the■following.a 4p7■ì■5p4 b 2x 2■ì■3x 6 c 8y6■ì■7y4

d 3p■ì■7p7 e 12t■3■ì■t 2■ì■7t f 6q2■ì■q5■ì■5q8

3 We3 ■Simplify■each■of■the■following.a 2a2■ì■3a4■ì■e3■ì■e4 b 4p3■ì■2h7■ì■h5■ì■p3

c 2m3■ì■5m2■ì■8m4 d 2gh■ì■3g2h5

e 5p4q2■ì■6p2q7 f 8u3w■ì■3uw2■ì■2u5w4

g 9y8d■ì■y5d3■ì■3y4d7 h 7b3c2■ì■2b6c4■ì■3b5c3

i 4r 2s2■ì■3r6s12■ì■2r8s4 j 10h10v2■ì■2h8v6■ì■3h20v12

4 We4 ■Simplify■each■of■the■following.

a15

5

12

8

p

pb

18

3

6

2

r

rc

45

5

5

2

a

a

d6020

7bb

e100

5

10

6

r

rf

9 2qq


a8 3

16

6 4

5

p p

p

×b

12 4

18

5 2

2

b b

b

×c

25 4

15 8

12 7

2

m n

m n

××

d27

12

9 3

2

x y

xye

16

12

7 4

6

h k

h kf

12 6

8 3

8 5

3 2

j f

j f

××

g8 7 2

6 14

3 2p r sp r× ×

×h

27 18 4

18 12 2

9 5 2

4 2

a b c

a b c

× ×× ×

i81 25 16

27 15 12

15 12 34

9 10 30

f g h

f g h

× ×× ×


a2 6

12

3 2

5

a a

a

×b

3 6

9

6 3

9

c c

c

×

c5 10

25

7 5

12

b b

b

×d

8 3

4 3

3 7

5 5

f f

f f

××

e9 4

18

12 10

4 18

k k

k k

××

f2 5

20

4 2

2 2

h k

h k

××

gp q

p

3 4

35

×h

m n

m m

7 3

3 45

××

i8

2 4

9 2

5 4

u v

u u

××

j9 2

3 3

6 12

10 2

x y

y y

××

unDerstAnDing

7 mC ■a■ ■12a8b2c4(de)0f■when■simplifi■ed■is■equal■to:A 12a8b2c4 B 12a8b2c4f C 12a8b2fD 12a8b2 E 12f

exerCise

10A

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Activity 10-A-1Reviewing the fi rst

four index lawsdoc-4101

Activity 10-A-2Using the fi rst four

index lawsdoc-4102

Activity 10-A-3Applying the fi rst

four index lawsdoc-4103

inDiviDuAl pAthWAys

■ 22■ì■3 23■ì■32 3■ì■52

24■ì■3■ì■5 27■ì■5 23■ì■52■ì■72

■ 20p11 6x8 56y10

21p8 84t6 30q15

■ 6a6e7 8p6h12

80m9 6g3h6

30p6q9 48u9w7

27d11y17 42b14c9

24r16s18 60h38v20

■ 3p4 6r4 9a3

3b6 20r4 9q

32

5p 83

5b 56

10 6m n

9

4

8x y 43

3hk 3j 5f 3

4

3

2p rs 9

2

5 3a b c

203

6 2 4f g h

■ 1 2

2 2

2 h2

2

q4

5

n3

5

v2 2■x6

✔



b 611

2 70

a b

■ì -(3a2b11)0■+■7a0b■when■simplified■is■equal■to:

A 7b B 1■+■7b C -1■+■7ab D -1■+■7b E 6c You■are■told■that■there■is■an■error■in■the■statement■3p7q3r 5s6■=■3p7s6.■To■make■the■

statement■correct,■what■should■the■left-hand■side■be?A (3p7q3r5s6)0 B (3p7)0q3r5s6 C 3p7(q3r5s6)0

D 3p7(q3r5)0s6 E 3(p7q3r5s6)0

d You■are■told■that■there■is■an■error■in■the■statement■8

6

86 7 3

4 2

2

2

f g h

f g h

f

g= .■To■make■the■statement■

correct,■what■should■the■left-hand■side■be?

A8

6

6 7 3 0

0 4 2 0

f g h

f g h

( )

( ) ( )B

8

6

6 7 3 0

4 2 0

( )

( )

f g h

f g hC

8

6

6 7 0 3

4 0 2

( )

( )

f g h

f g h

D8

6

6 7 3

4 2 0

f g h

f g h( )E

8

6

6 7 3 0

4 2 0

f g h

f g h

( )

( )

e What■does■6

4

7 2 8

7 6 0

k m n

k m n( )■equal?■

A 64

B32 C

32

8n

D3

2

2mE

32

2 8m n

raising a power to another power■■ (32)3■can■be■written■as■32■ì■32■ì■32.■■ It■can■then■be■simplified■using■the■First■Index■Law■as■32■+■2■+■2■=■36.From■this,■and■other■similar■examples,■it■can■be■seen■that■(32)3■=■32■ì■3.

■■ The■indices■are■multiplied■when■raising■a■power■to■another■power.This■is■the■Fourth■Index■Law:■(am)n■=■am ì n.

■■ The■Fifth■and■Sixth■Index■Laws■are■variations■of■the■Fourth■Index■Law.Fifth■Index■Law:■(a■ì■b)m■=■am■ì■bm.

Sixth■Index■Law:■ ab

a

b

m m

m

= .

■■ Remember■that■a■base■which■does■not■have■an■index■really■has■an■index■of■1.

Simplify the following.a (74)8 b (3a2b5)3

think Write

a 1 Write■the■problem. a (74)8

2 Simplify■using■the■Fourth■Index■Law■(multiply■the■indices).

=■74 ì 8

=■732

refleCtion

How do the index laws aid calculations?

10b

WorkeD exAmple 7

✔

✔

✔

✔



b 1 Write■the■problem. b (3a2b5)3

2 Simplify■using■the■Fifth■Index■Law■for■each■term■inside■the■brackets■(multiply■the■indices).

=■31 ì 3a2 ì 3b5 ì 3

=■33a6b15

3 Simplify■the■coefficient. =■27a6b15

Simplify (2b5)2 ì (5b8)3.

think Write

1 Write■the■problem.■ (2b5)2■ì■(5b8)3

2 Simplify■using■the■Fifth■Index■Law.■ =■21 ì 2b5 ì 2■ì■51 ì 3b8 ì 3

=■22b10■ì■53b24

3 Calculate■the■coefficient. =■4b10■ì■125b24

=■500b10■ì■b24

=■500b10■+ 24

4 Simplify■using■the■First■Index■Law. =■500b34

Simplify 2 5

2

3a

d

.

think Write

1 Write■the■problem.2 5

2

3a

d

2 Simplify■using■the■Sixth■Index■Law■for■each■term■inside■the■brackets.

=× ×

×21 3 5 3

2 3

a

d

= 23 15

6

a

d

3 Calculate■the■coefficient.■ = 8 15

6

a

d

remember

1.■ When■raising■a■power■to■another■power,■we■multiply■the■indices.■This■is■known■as■the■Fourth■Index■Law.■■Fourth■Index■Law:■(am)n■=■am ì n

2.■ The■Fifth■and■Sixth■Index■Laws■are■really■variations■of■the■Fourth■Index■Law.■Fifth■Index■Law:■(a■ì■b)m■=■am■ì■bm

Sixth■Index■Law:■ab

a

b

m m

m

=

WorkeD exAmple 8

WorkeD exAmple 9



raising a power to another powerfluenCy

1 We 7 ■Simplify■each■of■the■following.a (e2)3 b (f 8)10 c (■p25)4

d (r12)12 e (a2b3)4 f (■pq3)5

g (g3h2)10 h (3w9q2)4 i (7e5r2q4)2

2 We8 ■Simplify■each■of■the■following.a (■p4)2■ì■(q3)2 b (r5)3■ì■(w3)3 c (b5)2■ì■(n3)6

d (■j 6)3■ì■(g4)3 e (q2)2■ì■(r4)5 f (h3)8■ì■(■j2)8

g (■f 4)4■ì■(a7)3 h (t 5)2■ì■(u4)2 i (i3)5■ì■(j2)6


a 3 4

3

2b

d

b 5

2

10

2

2h

j

c 2

3

5

8

3k

t

d 7 9p

8 22

2

q

e 5

3

7

13

3y

z

f

4

7

3

5

4a

c

g −

4

7

2

6

3k

mh

−

2

3

7

11

4g

h

unDerstAnDing

4 Simplify■each■of■the■following.a (23)4■ì■(24)2 b (t7)3■ì■(t3)4 c (a4)0■ì■(a3)7

d (b6)2■ì■(b4)3 e (e7)8■ì■(e5)2 f (g7)3■ì■(g9)2

g (3a2)4■ì■(2a6)2 h (2d7)3■ì■(3d2)3 i (10r12)4■ì■(2r3)2

5 mC ■What■does■(■p7)2 ó p2■equal?A p7 B p12 C p16

D p4.5 E p

6 mC ■What■does■( ) ( )

( ) ( )

w p

w p

5 2 7 3

2 2 3 5

××

■equal?

A w2p6 B (wp)6 C w14p36

D w2p2 E (wp)3

7 mC ■What■does■(r6)3■ó■(r4)2■equal?A r 3 B r4 C r8 D r 26 E r10

8 Simplify■each■of■the■following.a (a3)4■ó■(a2)3 b (m8)2■ó (m3)4 c (n5)3■ó (n6)2 d (b4)5■ó (b6)2

e (■■f 7)3■ó (■■f■■2)2 f (g8)2■ó (g5)2 g (■p9)3■ó (■p6)3 h (■y4)4■ó (■y7)2

i( )

( )

c

c

6 5

5 2j

( )

( )

f

f

5 3

2 4k

( )

( )

k

k

3 10

2 8l

( )

( )

p

p

12 3

10 2

reAsoning

9 a■ Simplify■each■of■the■following. i (-1)10 ii (-1)7

iii (-1)15 iv (-1)6

b Write■a■general■rule■for■the■result■obtained■when■-1■is■raised■to■a■positive■power.

exerCise

10b

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Activity 10-B-1Reviewing powers of

powersdoc-4104

Activity 10-B-2Using powers of

powersdoc-4105

Activity 10-B-3Applying powers of

powersdoc-4106

inDiviDuAl pAthWAys

eBookpluseBookplus

Digital docWorkSHEET 10.1

doc-6233

refleCtion

What difference, if any, is there between the operation of the index laws on numeric terms compared with similar operations on algebraic terms?

■ e6 f 80 p100

r144 a8b12 p5q15

g30h20 81w36q8 49e10r4q8

■ p8q6 r15w9 b10n18

j18g12 q4r 20 h24j16

f 16a21 t10u8 i15j12

■9 8b

d6 25

4

20

4

h

j

8

27

15

24

k

t

49

64

18

44

p

q

125

27

21

39

y

z

256

2401

12

20

a

c

−64

343

6

18

k

m

16

81

28

44

g

h

■ 220 t33 a21

b24 e66 g39

324a20 216d27 40■■000r54

✔

✔

✔

a6 m4 n3 b8

f 17 g6 p9 y2

c20 f 7 k14 p16

(-1)even■=■1■ ■ (-1)odd■=■-1

1 -1 -1 1



negative indices■■ Using■the■Second■Index■Law,

2

2

3

4 ■=■23■−■4■ Also■ ■2

2

3

4■=■

816

■ =■2−1

■ =■12

It■then■follows■that■2−1■=■12.

This■can■be■generalised■as■a−1■=■1a

.

a Write 3-1 in fractional form b Write 1y

in index form.

think Write

a Use■the■rule■a-1■=■1a

. a 3-1■=■13

b Reverse■the■rule■a-1 = 1a

. b 1y

■=■y-1

■■ This■rule■can■be■extended■for■negative■indices■other■than■−1.For■example,■using■the■Second■Index■Law,

x

x

2

4■=■x2■−■4

■ =■x−2

Also

x

x

2

4■=■

x xx x x x

×× × ×

■ =■12x

It■then■follows■that■x−2■=■12x.

In■general,■a−n■=■1

an.

a Write 4-2 in fractional form. b Write 14a

using a negative index.

think Write

a Use■the■rule■a-n■=■1

an. a 4-2■=■

1

42

■ =■1

16

b Reverse■the■rule■a-n =■1

an. b

14a

■=■a-4

10C

WorkeD exAmple 10

WorkeD exAmple 11



remember

1.■ A■negative■index■is■used■to■represent■a■fractional■expression.

2.■ a-1■=■1a

3.■ a-n■=■1

an

negative indicesfluenCy

1 We 10a ■Write■each■of■the■following■in■fractional■form.a 4-1 b 6-1 c m-1 d p-1

2 We 10b ■Write■each■of■the■following■using■a■negative■index.

a 15

b 18

c 1a

d1q

3 We 11a ■Write■each■of■the■following■in■fractional■form.a 5-2 b 2-3 c g-4 d k-6

4 We 11b ■Write■each■of■the■following■using■a■negative■index.

a 1

72b

15y

c14z

d13v

unDerstAnDing

5 Simplify■each■of■the■following■using■only■positive■indices.■(That■is,■if■a■negative■index■appears■in■the■answer,■write■the■answer■in■frac■tional■form.)a x3■ó■x4 b a8■ó■a9

c b

b

4

5d w

w

10

11

6 Simplify■each■of■the■following■giving■your■answer■in■fractional■form.a x5■ó■x8 b y6■ó■y10

c z■ó■z7 d q2■ó■q9

e m0■ó■m4 f 12m3■ó■4m5

g 20

4 2

pq

ph 5

30

2

3

m

m 7 Use■the■index■laws■to■simplify■each■of■the■following.■Express■each■of■your■answers■with■

positive■indices.a a3■ì■a-4 b 12p-2■ì■3p-3

c 7g5h-2■ì■3gh-1 d 4p■ì■5p-2

e s-2■ó■s-3 f 42p2q-3■ó■6p-2qg 6r2■ó■2r-4 h 45a2b-3c■ó■3abc

reAsoning

8 What■is■the■ten’s■digit■of■333?

9 What■is■the■one’s■digit■of■6305?10 What■is■the■one’s■digit■of■81007?

exerCise

10C

eBookpluseBookplus

Activity 10-C-1Reviewing negative

indicesdoc-4107

Activity 10-C-2Using negative

indicesdoc-4108

Activity 10-C-3Applying negative

indicesdoc-4109

inDiviDuAl pAthWAys

refleCtion

What strategy will you use to remember the index laws?

■14

16 1

m

1p

■ 5-1 8-1 a-1 q-1

■ 125

18

14g

16k

■ 7-2 y-5 z-4 v-3

■1x

1a

1b

1w

■13x

14y

16z

17q

1

4m

32m

5qp

1

6m

21 6

3

g

h

20p

s

3r6 15

4

a

b

8

6

2

1a

7 4

4

p

q

36

5p

2018 Year 10/10A Mathematics v1 & v2 exam structure

Mathematics 10 Mathematics 10A extra questions

Section A

Multiple choice questions

20 questions

(20 marks)

12 questions

(12 marks)

Section B

Short answer questions

10 questions

(50 marks)

7 questions

(28 marks)

Section C

Extended response

3 questions

(30 marks)

3 questions

(30 marks)

Total 100 marks 70 marks

Teachers please note: ● our 10 & 10A exams cover the entire Year 10/10A content ● all exams are emailed in pdf format ● some schools asked about the two versions of our exams, so we would like to clarify: version 1 and version 2 exams consist of completely different questions. ● if you purchased a single version for $100 (say version 1), you will receive two of the following exams:

● 10 exam version 1 ● 10A exam version 1

● if you purchased both versions of exams for $200, you receive all of the following exams:

● 10 exam version 1 ● 10A exam version 1 ● 10 exam version 2 ● 10A exam version 2

● please feel free to modify the time allocated to 10/10A exams if necessary

Documents

10A Review of index laws 10B 10C 10D - Weebly€¦ · 10A Review of index laws 10B Raising a power to another power 10C Negative indices 10D Square roots and cube roots WhAt Do you