Algebraic Summary
GCSE Mathematics – Algebra
GCSE Mathematics – Algebra
SLIDE NUMBER 1
February 2019
© VIDLEARN® 2019
Joe Hammond
1
Session Objectives
The purpose of the session is to:
Define key vocabulary and notation used in algebra
Describe simplification by collecting like terms
Demonstrate expanding linear and quadratic expressions
Practice factorising linear and quadratic expressions
Illustrate the process of rearranging formulae
Interpret functions and find inverse functions
Identify composite functions through worked examples
SLIDE NUMBER 2
February 2019
© VIDLEARN® 2019
2
CONSIDER…
At this point you should consider the list of session objectives and ask yourself:
How many of the session objectives am I confident with
Could I explain these objectives in relation to teaching and learning
SLIDE NUMBER 3
February 2019
© VIDLEARN® 2019
3
Session Objectives
SLIDE NUMBER 4
February 2019
© VIDLEARN® 2019
The purpose of the session is to:
Define key vocabulary and notation used in algebra
Describe simplification by collecting like terms
Demonstrate expanding linear and quadratic expressions
Practice factorising linear and quadratic expressions
Illustrate the process of rearranging formulae
Interpret functions and find inverse functions
Identify composite functions through worked examples
4
A new language…
“the part of mathematics in which letters and symbols are used to represent numbers and quantities in formulae, equations and expressions”
A formal efficient way of solving problems
SLIDE NUMBER 5
February 2019
© VIDLEARN® 2019
Algebra
5
For example
2 + = 10
2 + x = 10
SLIDE NUMBER 6
February 2019
© VIDLEARN® 2019
Algebra
?
6
Variable: The letters x, y, z, a, b, c…
Term: x, 2x, 5y, y, -y, -3x2, x ...
3
Expression: x + 3, t - 4 , x2 + 4x - 3…
2
Equation/formulae: y = 2x, C = 3.4t ...
SLIDE NUMBER 7
February 2019
© VIDLEARN® 2019
Algebra
Vocabulary
7
2 x x = 2x
-3 x x = -3x
1 x x = x
-3 x -x = 3x
-x x -4 = 4x
-2x x 4y = -8xy
SLIDE NUMBER 8
February 2019
© VIDLEARN® 2019
Algebra
Multiplying and dividing with algebra
x ÷ 3 = x
3
10x ÷ 2 = 10y = 5y
2
x ÷ y = x
y
8
Pause here
What are “like terms”?
3x 4y -3y -y2 3y 4y3 4y2
Like terms share the same variable with the same power/index
SLIDE NUMBER 9
February 2019
© VIDLEARN® 2019
CONSIDER…
9
Pause here
What are “like terms”?
3x
SLIDE NUMBER 10
February 2019
© VIDLEARN® 2019
CONSIDER…
4y -3y 3y
-y2 4y2
4y3
10
Session Objectives
SLIDE NUMBER 11
February 2019
© VIDLEARN® 2019
The purpose of the session is to:
Define key vocabulary and notation used in algebra
Describe simplification by collecting like terms
Demonstrate expanding linear and quadratic expressions
Practice factorising linear and quadratic expressions
Illustrate the process of rearranging formulae
Interpret functions and find inverse functions
Identify composite functions through worked examples
11
x + 3x + 4x =
y + y + y =
-y + y + y =
2t + 4t - 10t =
4a - 6a + 2b - 4b =
x - 4x2 - 2x + 2x2 =
SLIDE NUMBER 12
February 2019
© VIDLEARN® 2019
Algebra
Collecting like terms
8x
3y
y
-4t
-2a -2b
-x - 2x2
12
4a - 2b - 3a + 4b =
4a - 3a = a
- 2b + 4b = 2b
SLIDE NUMBER 13
February 2019
© VIDLEARN® 2019
Algebra
Modelling in the classroom
x2y + 2x2y - 3xy2 =
x2y + 2x2y = 3x2y
- 3xy2 = - 3xy2
a + 2b
3x2y - 3xy2
13
Pause here
-y + 4y =
3a - 5a + 7b - 3b =
-y2 + 4y2 =
d + 3d - t - 2d + 3t =
4y3 - 10y3 + 2y2 - 2y =
33q100 + 27q99 - 27q100 =
3p-1 - 7p - 3p2 =
SLIDE NUMBER 14
February 2019
© VIDLEARN® 2019
CONSIDER…
14
Pause here
-y + 4y =
3a - 5a + 7b - 3b =
-y2 + 4y2 =
d + 3d - t - 2d + 3t =
4y3 - 10y3 + 2y2 - 2y =
33q100 + 27q99 - 27q100 =
3p-1 - 7p - 3p2 =
SLIDE NUMBER 15
February 2019
© VIDLEARN® 2019
CONSIDER…
3y
- 2a + 4b
3y2
2d + 2t
- 6y3 + 2y2 - 2y
6q100 + 27q99
3p-1 - 7p - 3p2
15
Session Objectives
SLIDE NUMBER 16
February 2019
© VIDLEARN® 2019
The purpose of the session is to:
Define key vocabulary and notation used in algebra
Describe simplification by collecting like terms
Demonstrate expanding linear and quadratic expressions
Practice factorising linear and quadratic expressions
Illustrate the process of rearranging formulae
Interpret functions and find inverse functions
Identify composite functions through worked examples
16
3 x 54
3 x 50 = 150
3 x 4 = 12
162
SLIDE NUMBER 17
February 2019
© VIDLEARN® 2019
Algebra
Expanding brackets
3 x 54
3(50 + 4) = 150 + 12
= 162
17
SLIDE NUMBER 18
February 2019
© VIDLEARN® 2019
Algebra
Expanding brackets
3(x + 8)
-4(x - 8)
6(1 - 2y)
6(1 - 2y) =
-5(-2 - x)
-5(-2 - x) =
3(x + 8) =
3x + 24
-4(x - 8) =
-4x + 32
6 - 12y
10 + 5x
18
SLIDE NUMBER 19
February 2019
© VIDLEARN® 2019
Algebra
Expanding and simplifying
4(2 + x) - 3(x - 2)
4(2 + x) - 3(x - 2)
8 + 4x - 3x + 6
14 + x or x + 14
19
SLIDE NUMBER 20
February 2019
© VIDLEARN® 2019
Algebra
Expanding and simplifying
3(x2 - 2) - 7(2 - x2)
3(x2 - 2) - 7(2 - x2)
3x2 - 6 - 14 + 7x2
10x2 - 20 or - 20 + 10x2
20
SLIDE NUMBER 21
February 2019
© VIDLEARN® 2019
Algebra
Expanding double brackets
3 x 54
3(50 + 4) = 150 + 12
= 162
23 x 54
(20 + 3)(50 + 4) = 1242
20 x 50 = 1000
20 x 4 = 80
3 x 50 = 150
3 x 4 = 12
21
SLIDE NUMBER 22
February 2019
© VIDLEARN® 2019
Algebra
Expanding double brackets
(x + 2)(x + 3)
(x + 2)(x + 3)
= x2 + 3x + 2x + 6
= x2 + 5x + 6
x x x = x2
x x 3 = 3x
2 x x = 2x
2 x 3 = 6
22
SLIDE NUMBER 23
February 2019
© VIDLEARN® 2019
Algebra
Expanding double brackets
(x + 7)(x - 2)
(x + 7)(x - 2)
= x2 + -2x + 7x - 14
= x2 + 5x - 14
x x x = x2
x x -2 = -2x
7 x x = 7x
7 x -2 = -14
23
SLIDE NUMBER 24
February 2019
© VIDLEARN® 2019
Algebra
Expanding double brackets
(3x + 1)(2x + 2)
(3x + 1)(2x + 2)
= 6x2 + 6x + 2x + 2
= 6x2 + 8x + 2
3x x 2x = 6x2
3x x 2 = 6x
1 x 2x = 2x
1 x 2 = 2
24
Pause here
Expand and simplify the following
-3(x + 4)
2(10 + x) + 4(x - 3)
-(x2 + 7)
(x - 4)(x + 6)
(2y + 4)(8 - y)
(3x - 5)(10 + 2x)
SLIDE NUMBER 25
February 2019
© VIDLEARN® 2019
CONSIDER…
25
Pause here
Expand and simplify the following
-3(x + 4)
2(10 + x) + 4(x - 3)
-(x2 + 7)
(x - 4)(x + 6)
(2y + 4)(8 - y)
(3x - 5)(10 + 2x)
SLIDE NUMBER 26
February 2019
© VIDLEARN® 2019
CONSIDER…
-3x - 12
8 + 6x
-x2 - 7
x2 + 2x - 24
-2y2 + 12y + 32
6x2 + 5x - 50
26
Session Objectives
SLIDE NUMBER 27
February 2019
© VIDLEARN® 2019
The purpose of the session is to:
Define key vocabulary and notation used in algebra
Describe simplification by collecting like terms
Demonstrate expanding linear and quadratic expressions
Practice factorising linear and quadratic expressions
Illustrate the process of rearranging formulae
Interpret functions and find inverse functions
Identify composite functions through worked examples
27
The process of writing an expression as a product or combination of factors
Expanding: 3(x + 9) = 3x + 27
Factorising: 3x + 27 = 3(x + 9)
SLIDE NUMBER 28
February 2019
© VIDLEARN® 2019
Algebra
Factorising
28
2x + 10 = 2(x + 5)
5x + 20 = 5(x + 4)
7y - 28 = 7(y - 4)
SLIDE NUMBER 29
February 2019
© VIDLEARN® 2019
Algebra
Some quick factorising examples
7(y - 4) = 7y - 28
29
4x + 18 = 4( __ + __ )
4 isn’t a factor of 18
4x + 18 = 2( __ + __ )
Because 2 is the highest common factor
SLIDE NUMBER 30
February 2019
© VIDLEARN® 2019
Algebra
Trickier factorising examples
= 2(2x + 9)
30
8y - 60 = 8( __ + __ )
8 isn’t a factor of -60
8y - 60 = 4( __ + __ )
Because 4 is the highest common factor
SLIDE NUMBER 31
February 2019
© VIDLEARN® 2019
Algebra
Trickier factorising examples
= 4(2y - 15)
31
8y + 20 = 8( __ + __ )
8 isn’t a factor of 20
8y + 20 = 4( __ + __ )
Because 4 is the highest common factor
SLIDE NUMBER 32
February 2019
© VIDLEARN® 2019
Algebra
Two more examples
= 4(2y + 5)
32
12y2 + 54y = 12( __ + __ )
6 is the HCF of 12 and 54
y is the HCF of y2 and y
12y2 + 54y = 6y( __ + __ )
SLIDE NUMBER 33
February 2019
© VIDLEARN® 2019
Algebra
Two more examples
= 6y(2y + 9)
33
Pause here
Fully factorise
30x2 + 42x
6(5x2 + 7x) b. 2x(15x + 21)
c. 6x(5x + 7) d. 6x(5x + 7x)
SLIDE NUMBER 34
February 2019
© VIDLEARN® 2019
CONSIDER…
34
Pause here
Fully factorise
6x+ 30
14y + 42
10x2 + 42x
12xy + 28x
4xy2 - 8x2y
x2yz2 - xy + xy2
SLIDE NUMBER 35
February 2019
© VIDLEARN® 2019
CONSIDER…
35
Pause here
Fully factorise
6x+ 30
14y + 42
10x2 + 42x
12xy + 28x
4xy2 - 8x2y
x2yz2 - xy + xy2
SLIDE NUMBER 36
February 2019
© VIDLEARN® 2019
CONSIDER…
6(x+ 5)
14(y + 3)
2x(5x + 21)
4x(3y + 7)
4xy(y - 2x)
xy(xz2 - 1 + y)
36
SLIDE NUMBER 37
February 2019
© VIDLEARN® 2019
Algebra
Factorising quadratic expressions
(x + 2)(x + 3)
(x + 2)(x + 3)
= x2 + 3x + 2x + 6
= x2 + 5x + 6
x2 + 5x + 6 = (x + 2)(x + 3)
37
SLIDE NUMBER 38
February 2019
© VIDLEARN® 2019
Algebra
Factorising quadratic expressions
(x + 2)(x + 4) = x2 + 6x + 8
(x + 2)(x + __ ) = x2 + 7x + 10
(x + __ )(x - __ ) = x2 + 2x - 3
(x - __ )(x - __ ) = x2 - 8x + 15
5
3
1
5
3
38
SLIDE NUMBER 39
February 2019
© VIDLEARN® 2019
Algebra
Examples
x2 + 4x + 3 = (x __ )(x __ )
x2 + 2x - 3 = (x __ )(x __ )
x2 - 4x + 3 = (x __ )(x __ )
x2 - 2x - 3 = (x __ )(x __ )
+ 1 + 3
+ 3 - 1
3 - 1
3 + 1
39
SLIDE NUMBER 40
February 2019
© VIDLEARN® 2019
Algebra
Trickier examples
Sometimes we might have something like
2x2 + 9x + 4
= (2x __ )(x __ )
Numbers will multiply to make 4
*
2, 2: (2x + 2)(x + 2) = 2x2 + 6x + 4
4, 1: (2x + 4)(x + 1) = 2x2 + 6x + 4
1, 4: (2x + 1)(x + 4) = 2x2 + 9x + 4
40
SLIDE NUMBER 41
February 2019
© VIDLEARN® 2019
Algebra
A second example
3x2 + x - 14
= (3x __ )(x __ )
Numbers will multiply to make -14
*
-1, 14
14, -1
1, -14
-14, 1
-2, 7
7, -2
2, -7
-7, 2
-1, 42
14, -3
1, -42
-14, 3
-2, 21
7, -6
2, -21
-7, 6
*
(3x + 7)(x - 2)
41
Pause here
Fully factorise
x2 + 10x + 24
x2 - 10x + 24
x2 + 2x - 24
x2 - 2x - 24
2x2 + 11x + 5
3x2 + x - 10
SLIDE NUMBER 42
February 2019
© VIDLEARN® 2019
CONSIDER…
42
Pause here
Fully factorise
x2 + 10x + 24
x2 - 10x + 24
x2 + 2x - 24
x2 - 2x - 24
2x2 + 11x + 5
3x2 + x - 10
SLIDE NUMBER 43
February 2019
© VIDLEARN® 2019
CONSIDER…
(x + 4)(x + 6)
(x - 4)(x - 6)
(x - 4)(x + 6)
(x + 4)(x - 6)
(2x + 1)(x + 5)
(3x - 5)(x + 2)
43
Session Objectives
SLIDE NUMBER 44
February 2019
© VIDLEARN® 2019
The purpose of the session is to:
Define key vocabulary and notation used in algebra.
Describe simplification by collecting like terms.
Demonstrate expanding linear and quadratic expressions.
Practice factorising linear and quadratic expressions.
Illustrate the process of rearranging formulae.
Interpret functions and find inverse functions.
Identify composite functions through worked examples.
44
SLIDE NUMBER 45
February 2019
© VIDLEARN® 2019
Algebra
The basic idea...
“ = ” is equal to
5 + 7 = 12
5 + 7 - 7 = 12 - 7 - 7
5 = 12 - 7
45
SLIDE NUMBER 46
February 2019
© VIDLEARN® 2019
Algebra
The basic idea...
“ = ” is equal to
x + y = z
x + y - y = z - y - y
x = z - y
This is called making x the subject
46
SLIDE NUMBER 47
February 2019
© VIDLEARN® 2019
Algebra
Make x the subject
x + 4 = y
x + 4 - 4 = y - 4 - 4
x = y - 4
x - a = b
x - a + a = b + a + a
x = b + a
3 - x = y
3 = y + x + x
3 - y = x - y
2x = y
x = y ÷ 2
2
47
SLIDE NUMBER 48
February 2019
© VIDLEARN® 2019
Algebra
Make x the subject
4x + b = 2
4x = 2 - b - b
x = 2 - b ÷ 4
4
48
SLIDE NUMBER 49
February 2019
© VIDLEARN® 2019
Algebra
Make x the subject
4(x + b) = 2
4x = 2 - 4b - 4b
x = 2 - 4b ÷ 4
4
49
SLIDE NUMBER 50
February 2019
© VIDLEARN® 2019
Algebra
Make x the subject
3x2 + a = b
3x2 = b - a - a
x2 = b - a ÷ 3
3
x = b - a square root
3
50
Pause here
Make x the subject
m + 3x = ax + d
3x = ax + d - m
3x - ax = d - m
x(3 - a) = d - m
x = d - m
3 - a
SLIDE NUMBER 51
February 2019
© VIDLEARN® 2019
CONSIDER…
51
SLIDE NUMBER 52
February 2019
© VIDLEARN® 2019
Algebra
Make x the subject
y + x = y(x + 2)
y + x = yx + 2y expand
x = yx + 2y - y - y
x - yx = 2y - y - yx
x(1 - y) = 2y - y factorise
x = 2y - 2 ÷ (1 - y)
1 - y
52
Pause here
SLIDE NUMBER 53
February 2019
© VIDLEARN® 2019
CONSIDER…
Make x the subject
3x + 5 = t
4(x - a) = b
y = 1 x + p
2
4. r = 4x2
5. a(x + b) = 2x + a
53
Pause here
SLIDE NUMBER 54
February 2019
© VIDLEARN® 2019
CONSIDER…
t - 5 = x
3
b + 4a = x
4
2(y - p) = x
r = x
4
a - ab = x
a - 2
Make x the subject
3x + 5 = t
4(x - a) = b
y = 1 x + p
2
4. r = 4x2
5. a(x + b) = 2x + a
54
Session Objectives
.
SLIDE NUMBER 55
February 2019
© VIDLEARN® 2019
The purpose of the session is to:
Define key vocabulary and notation used in algebra.
Describe simplification by collecting like terms.
Demonstrate expanding linear and quadratic expressions.
Practice factorising linear and quadratic expressions.
Illustrate the process of rearranging formulae.
Interpret functions and find inverse functions.
Identify composite functions through worked examples.
55
SLIDE NUMBER 56
February 2019
© VIDLEARN® 2019
Algebra
Functions
x 4
x y
56
SLIDE NUMBER 57
February 2019
© VIDLEARN® 2019
Algebra
Functions
x4
x 4
y = 4x
f(x) = 4x
f(2) = 4 x 2 = 8
f(-3) = 4 x -3 = -12
57
SLIDE NUMBER 58
February 2019
© VIDLEARN® 2019
Algebra
Functions
f(x) = x - 7
Find; f(13) =
f(100) =
f(-2) =
f(a) =
13 - 7 = 6
100 - 7 = 93
-2 - 7 = -9
a - 7
58
Pause here
y = 2x + 3
y = x - 3
2
SLIDE NUMBER 59
February 2019
© VIDLEARN® 2019
CONSIDER…
y = 2x + 3
y - 3 = 2x
y - 3 = x
2
59
SLIDE NUMBER 60
February 2019
© VIDLEARN® 2019
Algebra
Inverse functions
y = 2x + 3
y = x - 3
2
y = 2x + 3
y - 3 = 2x
y - 3 = x
2
x - 3 = y
2
y = x - 3 or f-1(x) = x - 3
2 2
60
SLIDE NUMBER 61
February 2019
© VIDLEARN® 2019
Algebra
Inverse functions
x 4
x y
61
SLIDE NUMBER 62
February 2019
© VIDLEARN® 2019
Algebra
Finding the inverse function
f(x) = x2 - 5
y = x2 - 5
y + 5 = x2
y + 5 = x
x + 5 = y
f-1(x) = x + 5
62
Pause here
Find the inverse functions for the following:
SLIDE NUMBER 63
February 2019
© VIDLEARN® 2019
CONSIDER…
63
Pause here
Find the inverse functions for the following:
SLIDE NUMBER 64
February 2019
© VIDLEARN® 2019
CONSIDER…
f -1(x) = x - 2
f-1(x) = x + 2
4
f -1(x) = x
f -1(x) = 3
x
f -1(x) = 1 - 2x
x
64
SLIDE NUMBER 65
February 2019
© VIDLEARN® 2019
Algebra
Finding the inverse function
f (x) = 1
x + 2
f -1(x) = 1 - 2x
x
y = 1
x + 2
y(x + 2)= 1
yx + 2y = 1
yx = 1 - 2y
x = 1 - 2y
y
65
Pause here
SLIDE NUMBER 66
February 2019
© VIDLEARN® 2019
CONSIDER…
www.mathspad.co.uk
66
Session Objectives
SLIDE NUMBER 67
February 2019
© VIDLEARN® 2019
The purpose of the session is to:
Define key vocabulary and notation for algebra
Describe simplification by collecting like terms
Demonstrate expanding linear and quadratic expressions
Practice factorising linear and quadratic expressions
Illustrate the process of rearranging formulae
Interpret functions and find inverse functions
Identify composite functions through worked examples
67
SLIDE NUMBER 68
February 2019
© VIDLEARN® 2019
Algebra
Composite functions
f(x) = x - 7
Find; f(13) =
f(100) =
f(-2) =
f(a) =
13 - 7 = 6
100 - 7 = 93
-2 - 7 = -9
a - 7
68
SLIDE NUMBER 69
February 2019
© VIDLEARN® 2019
Algebra
Composite functions
f(x) = x - 7
Find; f(2x) =
f(x - 4) =
f(x + 4) =
f(3x + 1) =
2x - 7
x - 4 - 7 = x - 11
x + 4 - 7 = x - 3
3x + 1 - 7 = 3x - 6
69
SLIDE NUMBER 70
February 2019
© VIDLEARN® 2019
Algebra
Composite functions
f(x) = 3x + 2
Find; f(2x) =
f(x - 4) =
f(x + 4) =
f(3x + 1) =
3(2x) + 2 = 6x + 2
3(x - 4) + 2 = 3x - 10
3(x + 4) + 2 = 3x + 14
3(3x + 1) + 2 = 9x + 5
70
SLIDE NUMBER 71
February 2019
© VIDLEARN® 2019
Algebra
An example
Given f(x) = 2x + 3 and g(x) = 4x
Find:
fg(x) gf(x)
= f(g(x))
= 2(4x) + 3
= 8x + 3
= g(f(x))
= 4(2x + 3)
= 8x + 12
71
SLIDE NUMBER 72
February 2019
© VIDLEARN® 2019
Algebra
An example
Given f(x) = x2 + x and g(x) = -2x
Find:
fg(x) gf(x)
= f(g(x))
= (-2x)2 + (-2x)
= 4x2 - 2x
= g(f(x))
= -2(x2 + x)
= -2x2 - 2x
72
SLIDE NUMBER 73
February 2019
© VIDLEARN® 2019
Algebra
An example
Given g(x) = 3 + x and h(x) = x2 + 2
Find:
gh(x) hg(x)
= g(h(x))
= 3 + (x2 + 2)
= 5 + x2
= h(g(x))
= (3 + x)2 + 2
= 9 + 6x + x2 + 2
= x2 + 6x + 11
73
Pause here
Given that g(x) = (x + 2)(x + 4), h(x) = x2 - 1, j(x) = x + 3, show that hj(x) = g(x)
SLIDE NUMBER 74
February 2019
© VIDLEARN® 2019
CONSIDER…
www.mathspad.co.uk
74
Pause here
Given that g(x) = (x + 2)(x + 4), h(x) = x2 - 1, j(x) = x + 3, show that hj(x) = g(x)
SLIDE NUMBER 75
February 2019
© VIDLEARN® 2019
CONSIDER…
hj(x) = h(j(x))
= (x + 3)2 - 1
= x2 + 6x + 9 - 1
= x2 + 6x + 8
= (x + 2)(x + 4)
= g(x)
www.mathspad.co.uk
75
SLIDE NUMBER 76
February 2019
© VIDLEARN® 2019
CONSIDER…
Pause here
f(x) = x2 - 4x + 2, g(x) = 3x - 7, find fg(x)
g(x) = -6x + 5 and h(x) = -9x - 11, find gh(x)
f(x) = 2x - 5 and g(x) = 5x2 - 3, find gf(x)
f(x) = -2x + 9 and g(x) = -4x2 + 5x - 3, find fg(x)
f(x) = x - 3 and g(x) = 4x2 - 3x - 9, find gf(x)
www.mathspad.co.uk
76
SLIDE NUMBER 77
February 2019
© VIDLEARN® 2019
CONSIDER…
Answers
f(x) = x2 - 4x + 2, g(x) = 3x - 7, find fg(x)
fg(x) = 9x2 - 54x + 79
www.mathspad.co.uk
77
SLIDE NUMBER 78
February 2019
© VIDLEARN® 2019
CONSIDER…
Answers
g(x) = -6x + 5 and h(x) = -9x - 11, find gh(x)
gh(x) = 54x + 71
www.mathspad.co.uk
78
SLIDE NUMBER 79
February 2019
© VIDLEARN® 2019
CONSIDER…
Answers
f(x) = 2x - 5 and g(x) = 5x2 - 3, find gf(x)
gf(x) = 10x - 28
www.mathspad.co.uk
79
SLIDE NUMBER 80
February 2019
© VIDLEARN® 2019
CONSIDER…
Answers
f(x) = -2x + 9 and g(x) = -4x2 + 5x - 3, find fg(x)
fg(x) = 8x2 - 10x + 15
www.mathspad.co.uk
80
SLIDE NUMBER 81
February 2019
© VIDLEARN® 2019
CONSIDER…
Answers
f(x) = x - 3 and g(x) = 4x2 - 3x - 9, find gf(x)
gf(x) = 4x2 - 27x + 36
www.mathspad.co.uk
81
Session Objectives
SLIDE NUMBER 82
February 2019
© VIDLEARN® 2019
The purpose of the session is to:
Define key vocabulary and notation for algebra
Describe simplification by collecting like terms
Demonstrate expanding linear and quadratic expressions
Practice factorising linear and quadratic expressions
Illustrate the process of rearranging formulae
Interpret functions and find inverse functions
Identify composite functions through worked examples
82
SLIDE NUMBER 83
February 2019
© VIDLEARN® 2019
CONSIDER…
End of Presentation
At this point it would be advisable to go back over the presentation. Ensure that you are fully able to deal accurately and effectively with each session objective.
You should supplement the content of this session with suitable reading, research and discussion with others.
GCSE Mathematics – Algebra
SLIDE NUMBER 84
February 2019
© VIDLEARN® 2019
Joe Hammond
End of presentation
84