10A Review of index laws 10B Raising a power to another power 10C Negative indices 10D 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 Digital doc Hungry brain activity Chapter 10 doc-6224 eBook plus eBook plus NUMBER AND ALGEBRA • PATTERNS AND ALGEBRA Indices
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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
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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?
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■=■.■■.■■.
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■
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
eBookpluseBookplus
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
✔
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.
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
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
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