Last modified 23 rd August 2013 Starter In pairs or otherwise try and match the blue and orange cards A reminder of the Laws of Indices ID: 675552
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Slide1
GCSE: Indices
Dr J Frost (jfrost@tiffin.kingston.sch.uk)
Last modified: 23
rd
August 2013Slide2
Starter
In pairs or otherwise, try and match the blue and orange cards.
Slide3
A reminder of the Laws of Indices
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Examples
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Mastermind
Occupation:
Student
Favourite Teacher:
Dr Frost
Specialist Subject:
Laws of IndicesSlide6
Instructions:
Everyone starts by standing up. You’ll get a question with a time limit to answer. If you run out of time or get the question wrong, you sit down. The winner is the last man standing.
Warmup
:
2
3
×
24
= 27?
Start Question >
(23)4 = 212
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Start Question >2
623
= 23
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Start Question >Slide7
_1_
2
4
7
×
4
3 = 410
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Start Question >
(35)2
= 310?
Start Question >
91192
= 99
?Start Question >
7
4 × 76 = 710
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Start Question >5
753
= 54?
Start Question >
(46)3 = 418
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Start Question >
(22
)2 = 24
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Start Question >2-1 =
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Start Question >
a
b
c
d
e
f
g
hSlide8
_1_
8
_1_
16
7
7
×
7-2
= 75?
Start Question >
(53)-2 = 5-6
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Start Question >10
5102
= 103?
Start Question >
8-2 × 8
4 = 82
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Start Question >
878-2= 89
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Start Question >2
-3 =
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Start Question >5
0 = 1?
Start Question >
4-2 =
?
Start Question >
a
b
c
d
e
f
g
hSlide9
_1_
5
6
_1_27
4
-2
×
4
-2 = 4-4?
Start Question >
(3-2)-2 = 3
4
?Start Question >
9-29-2
= 90 = 1
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Start Question >14
× 16
= 110 = 1
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Start Question >10110-3
= 104
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Start Question >(5
-3)2 =5-6 =
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Start Question >
3-3 =
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Start Question >
a
b
c
d
e
g
h
Start Question >
fSlide10
_1_
81
5
0
= 1
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Start Question >
(3
0
)2 = 1
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Start Question >
50
5-2= 52
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Start Question >(24
× 26)
2 = 220?
Start Question >
51 x 52
x 53 = 5
6?Start Question >
((4
1)2)3 = 46
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Start Question >
(23 ×
23)3 = 218
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Start Question >
3-4 =
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Start Question >
a
b
c
d
e
f
ghSlide11
4
7
×
4
3
42
(3
5)43
3a= 4
8
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Start Question >= 3
17?
Start Question >
b(73)
3(72)
3= 73
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Start Question >
c
58 × 5851 ×
5-1
((32)2)23
2
= 516
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Start Question >= 36
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Start Question >
e
(71)3(72
)1
×74 = 7
5
?
Start Question >
fdSlide12
Exercises
Simplify the following.
1
2
or
3
4
6
7
8
9
10
14
12
15
16
17
11
13
5
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Fractional Indices
And how could we prove this?Slide14
Fractional Indices
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Examples
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Harder Examples
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Exercises
1
Write the following expression without using indices:
2
3
4
5
6
7
8
9
10
11
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Applying indices to products and fractions
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Applying indices to products and fractions
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‘Flip Root Power’ method
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Exercises
1
2
3
5
Simplify:
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6
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7
9
10
11
Evaluate:
12
8
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Skill 3: Changing bases
What do you notice about all of the numbers:
They’re all powers of 2! We could replace the numbers with
,
and
so that we have a consistent base.
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Skill 3: Changing bases
Solve
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Solve
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a) Express in terms of
and/or
. i)
ii)
iii)
b) Given that:
find the value of
and
Difficult GCSE question
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Exercises
1
2
3
5
Solve for
:
6
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