The Laws Of Surds.
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Transcript The Laws Of Surds.
Algebraic Operations
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S5 Int2
Adding / Sub Indices
Negative Indices
Fraction Indices
Harder Indices
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Starter Questions
S5 Int2
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1.
Simplify the following fractions :
7 7
(a)
b b
a
a
(b)
2a 2d
2.
Simplify 2c(4 - c) - 5(4 + c)
3.
Multiply out (x +1)(x -5)
4.
Simplify 2 27 -5 3
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Algebraic Operations
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S5 Int2
Learning Intention
Success Criteria
1. To explain how to multiply
and divide indices by
adding / subtracting
powers.
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1. Understand basic rules for
indices.
2. Simplify indices.
Indices
S5 Int2
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an is a short hand way of writing
a x a x a ……. (n factors)
a is called the base number
and n is called the index number
Calculate :
23 x 2 2
Calculate :
25
2 x 2 x 2 x 2 x 2 = 32
= 32
Can you spot the connection !
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Indices
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S5 Int2
Calculate :
43 ÷ 42
Calculate :
41 = 4
4x4x4 ÷4x4 =4
Can you spot the connection !
am x an = a(m + n)
am ÷ an = a(m - n)
simply add powers
simply subtract powers
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What Goes In The Box ?
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S5 Int2
f4 x g5 =
b3 x b 5 =
b8
f g
4 5
y9 ÷ y5 =
a3 x a0 =
y4
a
3
Exercise 11 Page 209
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Starter Questions
S5 Int2
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1.
Simplify the following fractions :
u 5
(a)
3
10 u
a
a
(b)
2a 2d
2.
Factorise 3x 9x
3.
Factorise x2 +3x +2
4.
Simplify 10 27 5 3
2
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Algebraic Operations
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S5 Int2
Learning Intention
Success Criteria
1. To explain how to hand
fractional indices of
powers.
1. Understand basic rules for
fractional indices.
2. Simplify fractional indices.
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Fractions as Indices
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S5 Int2
More Rules
a = aaa = 1
2
5
a aaaaa a
3
By the division rule
a
3-5
-2
=a
=a
5
a
3
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1
-n
=a
n
a
Fractions as Indices
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S5 Int2
More Rules
a =aaaaa
=
1
5
aaaaa
a
5
a
5
a
5
=a
5-5
=a
0
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a =1
0
Fractions as Indices
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S5 Int2
More Rules
a
5 3
= a a a =a
5
a = a
3 5
3
5
5
5+5+5
a
15
a a a a
3
3
=a
3+3+3+3+3
3
3
a
15
(a ) = a
m n
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mn
Fractions as Indices
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S5 Int2
Exercise 12 Page 210
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Starter Questions
S5 Int2
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1.
Rationalise the denominator :
5
(1 - 2)
2.
Find the volume of sphere
with diameter 50cm.
3.
Factorise y + 5y + 6
2
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Algebraic Operations
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S5 Int2
Learning Intention
Success Criteria
1. To explain how to hand
fractional indices of
powers.
1. Understand basic rules for
fractional indices.
2. Simplify fractional indices.
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Fractions as Indices
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S5 Int2
1
2
1
2
= a a = a
1 1
+
2 2
a a = a
a =a
1
2
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=a
Fractions as Indices
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S5 Int2
1
3
1
3
1
3
a a a = a
3
1 1 1
+ +
3 3 3
=a=a
1
a a a = a = a
3
1
3
3
a =a
1
3
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Fractions as Indices
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S5 Int2
In general we have
1
n
a =
n
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a
Fractions as Indices
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S5 Int2
Examples : Simplify the following
8
a
3
a
2
3
3
8
2
2
a
=a ÷a
1
1
13
2 = 4 = a
2a
1
3
=a
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3
4
2
3
a
1
4
3 1
4 4
2
1
2
a
2
Fractions as Indices
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S5 Int2
Exercise 13 Page 211
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Starter Questions
S5 Int2
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1.
Rationalise the denominator :
6
(4 - 7 )
2.
Find the volume of cone
with diameter 20cm and height 10.
3.
Factorise
m - 7m +10
2
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Algebraic Operations
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S5 Int2
Learning Intention
Success Criteria
1. To show how to simplify
harder fractional indices.
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1. Simplify harder fractional
indices.
Fractions as Indices
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S5 Int2
Final Rule
a
m
n
n
m
=a =
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m
a
n
Fractions as Indices
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S5 Int2
m
Examples
3
4
y
16
3
4
8
=
=y
4
n
a
24
4
n
m
=a =
=y
3
m
an
6
16 = (2)
3
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=8
Fractions as Indices
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S5 Int2
m
Examples
27
5
3
=
1
27
2a b
2 3 4
a
5
3
n
=
n
m
=a =
1
3
27
m
5
an
1
1
= 5 =
3
243
= 2 a b = 16a b
4
8 12
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8 12
Fractions as Indices
S5 Int2
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Example :
Change to index form
2
5a
Example :
1
-4 3
-3
=
2
5a
1
-3 2
2
=
1
2
5 a
3
2
=
2a
5
3
2
1
2
Change to surd form
1
3
4
3
3m = 3 m
=
3
3
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3
m
4
3
= 3 4
m
Fractions as Indices
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S5 Int2
Exercise 213 Page 213
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