10a review of index laws 10b 10c 10d - weebly€¦ · 10a review of index laws 10b raising a power...
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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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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
number AnD AlgebrA • pAtterns AnD AlgebrA
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
number AnD AlgebrA • pAtterns AnD AlgebrA
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
number AnD AlgebrA • pAtterns AnD AlgebrA
330 maths Quest 9 for the Australian Curriculum
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
number AnD AlgebrA • pAtterns AnD AlgebrA
331Chapter 10 indices
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
number AnD AlgebrA • pAtterns AnD AlgebrA
332 maths Quest 9 for the Australian Curriculum
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
number AnD AlgebrA • pAtterns AnD AlgebrA
333Chapter 10 indices
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
5 We5 ■Simplify■each■of■the■following.
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
× ×× ×
6 We6 ■Simplify■each■of■the■following.
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
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■ 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
✔
number AnD AlgebrA • pAtterns AnD AlgebrA
334 maths Quest 9 for the Australian Curriculum
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
✔
✔
✔
✔
number AnD AlgebrA • pAtterns AnD AlgebrA
335Chapter 10 indices
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
number AnD AlgebrA • pAtterns AnD AlgebrA
336 maths Quest 9 for the Australian Curriculum
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
3 We9 ■Simplify■each■of■the■following.
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
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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
number AnD AlgebrA • pAtterns AnD AlgebrA
337Chapter 10 indices
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
number AnD AlgebrA • pAtterns AnD AlgebrA
338 maths Quest 9 for the Australian Curriculum
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
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● 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