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Introduction to Algebra

1
 
Introduction to Basic Algebra Part 1
 
 
 
2
 
Introduction to Basic Algebra Part 2
 
 
 

Simplifying Expressions

3
 
Simplifying Expressions Part 1
 
 
 
4
 
Simplifying Expressions Part 2
 
 
 
5
 
Simplifying Expressions Part 3
 
 
 

Simplifying Powers

6
 
Multiplying Powers
 
 
 
7
 
Multiplying Powers with numbers in front of the letters
 
 
 
8
 
Multiplying negative powers
 
 
 
9
 
Dividing powers
 
 
 
10
 
Dividing powers with negative numbers
 
 
 
11
 
Dividing powers with numbers in front of the letters
 
 
 
12
 
Simplifying Powers inside brackets, raised to another power
 
 
 

Multiplying Out Brackets

13
 
Multiplying out brackets
 
 
 
14
 
Multiplying out brackets with negative numbers or letters
 
 
 
15
 
Expand and Simplify Common Mistakes (Higher Only)
 
 
 
16
 
Expand and Simplify Common Mistakes (Higher Only) - Exam Question
 
 

Multiplying Out Double Brackets

17
 
Multiplying out double brackets (Higher Only)
 
 
 
18
 
Multiplying out double brackets with negative numbers or letters (Higher Only)
 
 
 
19
 
Expand and Simplify brackets that are squared
 
 
 
20
 
Expand and Simplify brackets that are squared Exam Question
 
 
 

Factorising into Single Brackets

21
 
Factorising expressions into single brackets part 1
 
 
 
22
 
Factorising expressions into single brackets part 2
 
 
 
23
 
Factorising expressions with mixed letters in the terms
 
 
 

Substituting Numbers into Formula

24
 
Substituting numbers into formula, part 1
 
 
 
25
 
Substituting numbers into formula, part 2
 
 
 
26
 
Substituting numbers into formula, part 3
 
 
 

Rearranging Formula

27
 
Rearranging formula part 1
 
 
 
28
 
Rearranging formula part 2
 
 
 
29
 
Rearranging formula Higher only
 
 
 
30
 
Rearranging formula when the subject is on the bottom of a divide line (Higher Only)
 
 
 

Rearranging Formula when the Subject Appears Twice (Higher Only)

31
 
Rearranging Formula when the Subject Appears Twice Part 1
 
 
 
32
 
Rearranging Formula when the Subject Appears Twice Part 2
 
 
 
33
 
Rearranging Formula when the Subject Appears Twice Part 3
 
 
 
34
 
Rearranging Formula when the Subject Appears Twice Part 4
 
 
 
35
 
Rearranging Formula when the Subject Appears Twice Exam Question
 
 

Sequences

36
 
Introduction to sequences
 
 
 
37
 
Finding the Terms of a Sequence when you`re given the term rule - Part 1
 
 
 
38
 
Finding the Terms of a Sequence when you`re given the term rule - Part 2
 
 
 
39
 
Finding the term
 
 
 
40
 
Finding a number in the sequence using the term rule
 
 
 
41
 
Finding the Next Term in a Sequence that has a Changing Difference
 
 
 
42
 
Triangle numbers
 
 
43
 
Finding triangle numbers using the term rule
 
 

Finding the nth Term of a Quadratic Sequence (Higher Only)

44
 
Finding the Term Rule of simple Quadratic sequences - Part 1
 
 
 
45
 
Finding the Term Rule of simple Quadratic sequences - Part 2
 
 
 
46
 
Finding the Term Rule of simple Quadratic sequences - Exam Tip
 
 
47
 
Finding the n term of a quadratic sequence Part 1
 
 
48
 
Finding the term of a quadratic sequence Part 2
 
 
 

Solving Equations

49
 
Solving equations, part 1
 
 
 
50
 
Solving equations, part 2
 
 
 
51
 
Solving equations, part 3
 
 
 
52
 
Solving equations with brackets
 
 
 
53
 
Solving equations with a divide or fraction
 
 
 
54
 
Solving equations with 's on both sides
 
 
 

Solving Equations Using Number Machines

55
 
Solving equations, using number machines
 
 
 
56
 
Solving equations with brackets, using number machines
 
 
 
57
 
Solving equations with a divide in, using a number machine
 
 
 
58
 
Solving equations with 's on both sides using number machines
 
 
 

Forming and Solving Linear Equations

59
 
Forming and Solving Linear Equations Part 1
 
 
 
60
 
Forming and Solving Linear Equations Part 2
 
 
 
61
 
Forming and Solving Linear Equations Exam Question
 
 

Inequalities

62
 
Introduction to inequalities
 
 
63
 
Writing a list of integers from inequalities
 
 
 
64
 
Showing inequalities on number lines part 1
 
 
 
65
 
Writing inequalities from number lines
 
 
 
66
 
Showing inequalities on number lines, part 2
 
 
 
67
 
Showing inequalities on number lines, part 3
 
 
 

Solving Inequalities

68
 
Solving inequalities, part 1
 
 
 
69
 
Solving inequalities, part 2
 
 
 
70
 
Solving inequalities with brackets
 
 
 
71
 
Solving inequalities with a divide or fraction
 
 
 
72
 
Solving inequalities with 's on both sides
 
 
 
73
 
Solving 2 inequalities at the same time
 
 
 

Direct Proportion

74
 
Direct Proportion m is proportional to p
 
 
 
75
 
Direct Proportion y is proportional to
 
 
 
76
 
Using Formula Triangles in Direct Proportion Questions
 
 

Inverse Proportion

77
 
Inverse Proportion y is Inversely Proportional to x
 
 
 
78
 
Inverse Proportion y is Inversely Proportional to
 
 
 
79
 
Using Formula Triangles in Inverse Proportion Questions
 
 

Straight Line Graphs

80
 
Introduction to straight line graphs
 
 
 
81
 
Exam tip -- completing a table of values
 
 
 
82
 
Rearranging equations in the form of
 
 
 
83
 
Plotting straight line graphs from a table of values
 
 
 
84
 
Plotting straight line graphs of number and number
 
 
 
85
 
Finding the gradient of a line
 
 
 
86
 
Finding the intercept
 
 
 
87
 
Finding the equation of a straight line graph
 
 
 
88
 
Finding the equation of a line passing through a coordinate (Higher Only)
 
 
 
89
 
Finding equations of parallel lines (Higher Only)
 
 
 
90
 
Finding equations of parallel lines that pass through a point (Higher Only)
 
 
 
91
 
Equations of parallel lines passing through a coordinate (Higher Only)
 
 
 
92
 
Finding equations of perpendicular lines (Higher Only)
 
 
 
93
 
Finding equations of perpendicular lines passing through a point (Higher Only)
 
 
 
94
 
Equations of perpendicular lines passing through a coordinate (Higher Only)
 
 
 

Finding Gradients and Equations of Lines between 2 Points

95
 
Introduction to Finding the Gradient of a Line Joining 2 Points
 
 
96
 
Finding the Gradient of a Line Joining 2 Points
 
 
 
97
 
Finding the Gradient of a Line Joining 2 Points Exam Tip
 
 
98
 
Finding the Equation of a Line Joining 2 Points
 
 
 

Graphs of Inequalities (Higher Only)

99
 
Graphs of inequalities and shading regions, part 1
 
 
 
100
 
Graphs of inequalities and shading regions, part 2
 
 
 
101
 
Graphs of inequalities and shading regions, part 3
 
 
 
102
 
Graphs of inequalities and shading regions, part 4
 
 
 

Factorising Quadratics

103
 
Factorising quadratics with positive terms only
 
 
 
104
 
Factorising quadratics with a negative number term and/or negative term
 
 
 
105
 
Factorising quadratics with a negative term and positive number term
 
 
 
106
 
Factorising quadratics the difference of 2 squares, 16
 
 
 
107
 
Factorising quadratics with a number in front of the term part 1
 
 
108
 
Factorising quadratics with a number in front of the term part 2
 
 
109
 
Factorising quadratics with a number in front of the term part 3
 
 

Completing the Square (Higher Only)

110
 
Completing the Square Part 1a
 
 
 
111
 
Completing the Square Part 1b
 
 
 
112
 
Completing the Square Exam Question 1
 
 
113
 
Completing the Square Exam Question 2
 
 
114
 
When the term has a number in front Part 1
 
 
 
115
 
When the term has a number in front Part 2
 
 
 
116
 
Finding the Vertex when Completing the Square
 
 
 

Solving Quadratic Equations (Higher Only)

117
 
Solving quadratic equations by factorising part 1
 
 
 
118
 
Solving quadratic equations by factorising part 2
 
 
 
119
 
Solving quadratics using the quadratic formula, part 1
 
 
 
120
 
Solving quadratics using the quadratic formula, part 2
 
 
 
121
 
Solving Quadratics by Completing the Square Part 1
 
 
 
122
 
Solving Quadratics by Completing the Square Part 2
 
 
 

Forming and Solving Quadratic Equations (Higher only)

123
 
Forming and Solving Quadratic Equations Part 1
 
 
 
124
 
Forming and Solving Quadratic Equations Part 2
 
 
 
125
 
Forming and Solving Quadratic Equations Exam Question
 
 

Quadratic Graphs (Higher Only)

126
 
Quadratic graphs, making a table of values
 
 
 
127
 
Plotting quadratic graphs and finding the minimum value
 
 
 

Further Graphs

128
 
The 4 Types of Further Graphs
 
 
129
 
Introduction to Cubic Graphs
 
 
130
 
Plotting Cubic Graphs
 
 
 
131
 
Introduction to the Graph of the Reciprocal Function
 
 
132
 
Plotting the Reciprocal Function
 
 
 
133
 
Plotting Circle Graphs
 
 
 
134
 
Plotting Circle Graphs Exam Question
 
 
135
 
Plotting Exponential Graphs
 
 
 

Solving Equations Using Graphs (Higher Only)

136
 
Solving Equations using Graphs Part 1
 
 
 
137
 
Solving Equations using Graphs Part 2
 
 
 
138
 
Solving Equations using Graphs Part 3
 
 
 
139
 
Solving Equations using Graphs Part 4
 
 
 

Simultaneous Equations

140
 
Solving simultaneous equations graphically
 
 
 
141
 
Solving simultaneous equations, part 1
 
 
 
142
 
Solving simultaneous equations, part 2
 
 
 
143
 
Solving simultaneous equations, part 3
 
 
 
144
 
Solving simultaneous equations, part 4
 
 
 
145
 
Solving simultaneous equations, part 5
 
 
 
146
 
Solving quadratic simultaneous equations, part 1
 
 
 
147
 
Solving quadratic simultaneous equations, part 2
 
 
 
148
 
Solving simultaneous equations, with a circle equation
 
 
 
149
 
Simultaneous equations, exam tip
 
 

Simplifying Algebraic Fractions (Higher Only)

150
 
Introduction to Simplifying Algebraic Fractions
 
 
151
 
Simplifying Algebraic Fractions Part 1
 
 
 
152
 
Simplifying Algebraic Fractions Part 2
 
 
 
153
 
Simplifying Algebraic Fractions Part 3
 
 
 
154
 
Multiplying Algebraic Fractions and Simplifying Part 1
 
 
 
155
 
Multiplying Algebraic Fractions and Simplifying Part 2
 
 
 
156
 
Dividing Algebraic Fractions and Simplifying
 
 
 
157
 
Adding Algebraic Fractions and Simplifying Part 1
 
 
 
158
 
Adding Algebraic Fractions and Simplifying Part 2
 
 
 
159
 
Adding Algebraic Fractions and Simplifying Exam Question
 
 
160
 
Subtracting Algebraic Fractions and Simplifying
 
 
 

Solving Equations Containing Algebraic Fractions (Higher Only)

161
 
Solving Linear Equations Containing Algebraic Fractions Part 1
 
 
 
162
 
Solving Linear Equations Containing Algebraic Fractions Part 2
 
 
 
163
 
Forming and Solving Quadratic Equations from Algebraic Fractions
 
 
 
164
 
Forming and Solving Quadratic Equations from Algebraic Fractions Exam Question
 
 

Transformations of Graphs (Higher Only)

165
 
Transforming Graphs Up or Down
 
 
 
166
 
Transforming Graphs Up and Down using f(x)notation
 
 
 
167
 
Transforming Graphs Up or Down - Exam Question
 
 
168
 
Transforming Graphs Up and Down using f(x)notation - Exam Question
 
 
169
 
Transforming Graphs Left or Right
 
 
 
170
 
Transforming Graphs Left or Right using f(x)notation
 
 
 
171
 
Transforming Graphs Left - Exam Question
 
 
172
 
Transforming Graphs Sideways using f(x)notation - Exam Question
 
 
173
 
Stretching Graphs in the x direction
 
 
 
174
 
Stretching Graphs in x direction using f(x)notation
 
 
 
175
 
Stretching Graphs in x direction - Exam Question
 
 
176
 
Stretching Graphs in the y direction
 
 
177
 
Stretching Graphs in y direction using f(x)notation
 
 
 
178
 
Stretching Graphs in y direction - Exam Question
 
 
179
 
Reflecting Graphs in the x axis
 
 
 
180
 
Reflecting graphs in the x axis using f(x)notation
 
 
 
181
 
Reflecting graphs in the y axis
 
 
 
182
 
Reflecting graphs in the y axis using f(x)notation
 
 
 
183
 
Transforming Graphs using f(x)notation - Exam Question
 
 

Transformations of Trigonometric Graphs (Higher Only)

184
 
Transforming Trigonometric Graphs Up and Down
 
 
 
185
 
Transforming Trigonometric Graphs Up and Down using f(x)notation
 
 
 
186
 
Transforming Trigonometric Graphs Sideways
 
 
 
187
 
Transforming Trigonometric Graphs Sideways using f(x)notation
 
 
 
188
 
Stretching Trigonometric Graphs in the x direction
 
 
 
189
 
Stretching Trigonometric Graphs in the x direction using f(x)notation
 
 
 
190
 
Stretching Trigonometric Graphs in the y direction
 
 
 
191
 
Stretching Trigonometric Graphs in the y direction using f(x)notation
 
 
 
192
 
Reflecting Trigonometric Graphs in the x axis
 
 
 
193
 
Reflecting Trigonometric Graphs in the x axis using f(x)notation
 
 
 
194
 
Transforming Trigonometric Graphs - Exam Tip
 
 
195
 
Transforming Trigonometric Graphs - Exam Question 1
 
 
196
 
Transforming Trigonometric Graphs - Exam Question 2
 
 

Trigonometric Graphs and Exact Values

197
 
The Graph of Cos x
 
 
198
 
The Graph of Sin x
 
 
199
 
Graph of Tan x
 
 
200
 
Exact values of sin and cos - Part 1
 
 
201
 
Exact values of sin and cos - Part 2
 
 
202
 
Exact values of sin and cos - Part 3
 
 
 
203
 
Exact values of sin, cos and tan - Exam Trick
 
 
204
 
Finding the exact values of tan
 
 
 
 
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