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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 and Triple 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
 
 
 
21
 
Expanding triple brackets
 
 
 

Factorising into Single Brackets

22
 
Factorising expressions into single brackets part 1
 
 
 
23
 
Factorising expressions into single brackets part 2
 
 
 
24
 
Factorising expressions with mixed letters in the terms
 
 
 

Substituting Numbers into Formula

25
 
Substituting numbers into formula, part 1
 
 
 
26
 
Substituting numbers into formula, part 2
 
 
 
27
 
Substituting numbers into formula, part 3
 
 
 

Rearranging Formula

28
 
Rearranging formula part 1
 
 
 
29
 
Rearranging formula part 2
 
 
 
30
 
Rearranging formula Higher only
 
 
 
31
 
Rearranging formula when the subject is on the bottom of a divide line (Higher Only)
 
 
 

Rearranging Formula when the Subject Appears Twice (Higher Only)

32
 
Rearranging Formula when the Subject Appears Twice Part 1
 
 
 
33
 
Rearranging Formula when the Subject Appears Twice Part 2
 
 
 
34
 
Rearranging Formula when the Subject Appears Twice Part 3
 
 
 
35
 
Rearranging Formula when the Subject Appears Twice Part 4
 
 
 
36
 
Rearranging Formula when the Subject Appears Twice Exam Question
 
 

Sequences

37
 
Introduction to sequences
 
 
 
38
 
Finding the Terms of a Sequence when you`re given the term rule - Part 1
 
 
 
39
 
Finding the Terms of a Sequence when you`re given the term rule - Part 2
 
 
 
40
 
Finding the term
 
 
 
41
 
Finding a number in the sequence using the term rule
 
 
 
42
 
Finding the Next Term in a Sequence that has a Changing Difference
 
 
 
43
 
Triangle numbers
 
 
44
 
Finding triangle numbers using the term rule
 
 

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

45
 
Finding the Term Rule of simple Quadratic sequences - Part 1
 
 
 
46
 
Finding the Term Rule of simple Quadratic sequences - Part 2
 
 
 
47
 
Finding the Term Rule of simple Quadratic sequences - Exam Tip
 
 
48
 
Finding the n term of a quadratic sequence Part 1
 
 
49
 
Finding the term of a quadratic sequence Part 2
 
 
 

Solving Equations

50
 
Solving equations, part 1
 
 
 
51
 
Solving equations, part 2
 
 
 
52
 
Solving equations, part 3
 
 
 
53
 
Solving equations with brackets
 
 
 
54
 
Solving equations with a divide or fraction
 
 
 
55
 
Solving equations with 's on both sides
 
 
 

Solving Equations Using Number Machines

56
 
Solving equations, using number machines
 
 
 
57
 
Solving equations with brackets, using number machines
 
 
 
58
 
Solving equations with a divide in, using a number machine
 
 
 
59
 
Solving equations with 's on both sides using number machines
 
 
 

Forming and Solving Linear Equations

60
 
Forming and Solving Linear Equations Part 1
 
 
 
61
 
Forming and Solving Linear Equations Part 2
 
 
 
62
 
Forming and Solving Linear Equations Exam Question
 
 

Inequalities

63
 
Introduction to inequalities
 
 
64
 
Writing a list of integers from inequalities
 
 
 
65
 
Showing inequalities on number lines part 1
 
 
 
66
 
Showing inequalities on number lines, part 2
 
 
 
67
 
Showing inequalities on number lines, part 3
 
 
 
68
 
Writing inequalities from number lines
 
 
 

Solving Inequalities

69
 
Solving inequalities, part 1
 
 
 
70
 
Solving inequalities, part 2
 
 
 
71
 
Solving inequalities with brackets
 
 
 
72
 
Solving inequalities with a divide or fraction
 
 
 
73
 
Solving inequalities with 's on both sides
 
 
 
74
 
Solving 2 inequalities at the same time
 
 
 

Direct Proportion

75
 
Direct Proportion m is proportional to p
 
 
 
76
 
Direct Proportion y is proportional to
 
 
 
77
 
Using Formula Triangles in Direct Proportion Questions
 
 

Inverse Proportion

78
 
Inverse Proportion y is Inversely Proportional to x
 
 
 
79
 
Inverse Proportion y is Inversely Proportional to
 
 
 
80
 
Using Formula Triangles in Inverse Proportion Questions
 
 

Straight Line Graphs

81
 
Introduction to straight line graphs
 
 
 
82
 
Exam tip -- completing a table of values
 
 
 
83
 
Rearranging equations in the form of
 
 
 
84
 
Plotting straight line graphs from a table of values
 
 
 
85
 
Plotting straight line graphs of number and number
 
 
 
86
 
Finding the gradient of a line
 
 
 
87
 
Finding the intercept
 
 
 
88
 
Finding the equation of a straight line graph
 
 
 
89
 
Finding the equation of a line passing through a coordinate (Higher Only)
 
 
 
90
 
Finding equations of parallel lines (Higher Only)
 
 
 
91
 
Finding equations of parallel lines that pass through a point (Higher Only)
 
 
 
92
 
Equations of parallel lines passing through a coordinate (Higher Only)
 
 
 
93
 
Finding equations of perpendicular lines (Higher Only)
 
 
 
94
 
Finding equations of perpendicular lines passing through a point (Higher Only)
 
 
 
95
 
Equations of perpendicular lines passing through a coordinate (Higher Only)
 
 
 

Finding Gradients and Equations of Lines between 2 Points

96
 
Introduction to Finding the Gradient of a Line Joining 2 Points
 
 
97
 
Finding the Gradient of a Line Joining 2 Points
 
 
 
98
 
Finding the Gradient of a Line Joining 2 Points Exam Tip
 
 
99
 
Finding the Equation of a Line Joining 2 Points
 
 
 

Formula 1 Distance/time, Velocity/time Graphs

100
 
Calculating average speed from a D/t graph part 1
 
 
101
 
Calculating average speed from a D/t graph part 2
 
 
 
102
 
Speed/distance/time questions - Common mistakes
 
 
 
103
 
Calculating acceleration from a V/t graph part 1
 
 
104
 
Calculating acceleration from a V/t graph part 2
 
 
 
105
 
Calculating the deceleration from a V/t graph
 
 
 
106
 
Calculating total distance travelled from a V/t graph
 
 
 
107
 
Estimating distance travelled under a curved V/t graph
 
 
 

Graphs of Inequalities (Higher Only)

108
 
Graphs of inequalities and shading regions, part 1
 
 
 
109
 
Graphs of inequalities and shading regions, part 2
 
 
 
110
 
Graphs of inequalities and shading regions, part 3
 
 
 
111
 
Graphs of inequalities and shading regions, part 4
 
 
 

Factorising Quadratics

112
 
Factorising quadratics with positive terms only
 
 
 
113
 
Factorising quadratics with a negative number term and/or negative term
 
 
 
114
 
Factorising quadratics with a negative term and positive number term
 
 
 
115
 
Factorising quadratics the difference of 2 squares, 16
 
 
 
116
 
Factorising quadratics with a number in front of the term part 1
 
 
117
 
Factorising quadratics with a number in front of the term part 2
 
 
118
 
Factorising quadratics with a number in front of the term part 3
 
 

Completing the Square (Higher Only)

119
 
Completing the Square Part 1a
 
 
 
120
 
Completing the Square Part 1b
 
 
 
121
 
Completing the Square Exam Question 1
 
 
122
 
Completing the Square Exam Question 2
 
 
123
 
When the term has a number in front Part 1
 
 
 
124
 
When the term has a number in front Part 2
 
 
 
125
 
Finding the Vertex when Completing the Square
 
 
 

Solving Quadratic Equations (Higher Only)

126
 
Solving quadratic equations by factorising part 1
 
 
 
127
 
Solving quadratic equations by factorising part 2
 
 
 
128
 
Solving quadratics using the quadratic formula, part 1
 
 
 
129
 
Solving quadratics using the quadratic formula, part 2
 
 
 
130
 
Solving Quadratics by Completing the Square Part 1
 
 
 
131
 
Solving Quadratics by Completing the Square Part 2
 
 
 

Forming and Solving Quadratic Equations (Higher only)

132
 
Forming and Solving Quadratic Equations Part 1
 
 
 
133
 
Forming and Solving Quadratic Equations Part 2
 
 
 
134
 
Forming and Solving Quadratic Equations Exam Question
 
 

Quadratic Graphs (Higher Only)

135
 
Quadratic graphs, making a table of values
 
 
 
136
 
Plotting quadratic graphs and finding the minimum value
 
 
 

Further Graphs

137
 
The 4 Types of Further Graphs
 
 
138
 
Introduction to Cubic Graphs
 
 
139
 
Plotting Cubic Graphs
 
 
 
140
 
Introduction to the Graph of the Reciprocal Function
 
 
141
 
Plotting the Reciprocal Function
 
 
 
142
 
Plotting Circle Graphs
 
 
 
143
 
Plotting Circle Graphs Exam Question
 
 
144
 
Plotting Exponential Graphs
 
 
 

Solving Equations Using Graphs (Higher Only)

145
 
Solving Equations using Graphs Part 1
 
 
 
146
 
Solving Equations using Graphs Part 2
 
 
 
147
 
Solving Equations using Graphs Part 3
 
 
 
148
 
Solving Equations using Graphs Part 4
 
 
 

Simultaneous Equations

149
 
Solving simultaneous equations graphically
 
 
 
150
 
Solving simultaneous equations, part 1
 
 
 
151
 
Solving simultaneous equations, part 2
 
 
 
152
 
Solving simultaneous equations, part 3
 
 
 
153
 
Solving simultaneous equations, part 4
 
 
 
154
 
Solving simultaneous equations, part 5
 
 
 
155
 
Solving quadratic simultaneous equations, part 1
 
 
 
156
 
Solving quadratic simultaneous equations, part 2
 
 
 
157
 
Solving simultaneous equations, with a circle equation
 
 
 
158
 
Simultaneous equations, exam tip
 
 

Simplifying Algebraic Fractions (Higher Only)

159
 
Introduction to Simplifying Algebraic Fractions
 
 
160
 
Simplifying Algebraic Fractions Part 1
 
 
 
161
 
Simplifying Algebraic Fractions Part 2
 
 
 
162
 
Simplifying Algebraic Fractions Part 3
 
 
 
163
 
Multiplying Algebraic Fractions and Simplifying Part 1
 
 
 
164
 
Multiplying Algebraic Fractions and Simplifying Part 2
 
 
 
165
 
Dividing Algebraic Fractions and Simplifying
 
 
 
166
 
Adding Algebraic Fractions and Simplifying Part 1
 
 
 
167
 
Adding Algebraic Fractions and Simplifying Part 2
 
 
 
168
 
Adding Algebraic Fractions and Simplifying Exam Question
 
 
169
 
Subtracting Algebraic Fractions and Simplifying
 
 
 

Solving Equations Containing Algebraic Fractions (Higher Only)

170
 
Solving Linear Equations Containing Algebraic Fractions Part 1
 
 
 
171
 
Solving Linear Equations Containing Algebraic Fractions Part 2
 
 
 
172
 
Forming and Solving Quadratic Equations from Algebraic Fractions
 
 
 
173
 
Forming and Solving Quadratic Equations from Algebraic Fractions Exam Question
 
 

Transformations of Graphs (Higher Only)

174
 
Transforming Graphs Up or Down
 
 
 
175
 
Transforming Graphs Up and Down using f(x)notation
 
 
 
176
 
Transforming Graphs Up or Down - Exam Question
 
 
177
 
Transforming Graphs Up and Down using f(x)notation - Exam Question
 
 
178
 
Transforming Graphs Left or Right
 
 
 
179
 
Transforming Graphs Left or Right using f(x)notation
 
 
 
180
 
Transforming Graphs Left - Exam Question
 
 
181
 
Transforming Graphs Sideways using f(x)notation - Exam Question
 
 
182
 
Stretching Graphs in the x direction
 
 
 
183
 
Stretching Graphs in x direction using f(x)notation
 
 
 
184
 
Stretching Graphs in x direction - Exam Question
 
 
185
 
Stretching Graphs in the y direction
 
 
186
 
Stretching Graphs in y direction using f(x)notation
 
 
 
187
 
Stretching Graphs in y direction - Exam Question
 
 
188
 
Reflecting Graphs in the x axis
 
 
 
189
 
Reflecting graphs in the x axis using f(x)notation
 
 
 
190
 
Reflecting graphs in the y axis
 
 
 
191
 
Reflecting graphs in the y axis using f(x)notation
 
 
 
192
 
Transforming Graphs using f(x)notation - Exam Question
 
 

Transformations of Trigonometric Graphs (Higher Only)

193
 
Transforming Trigonometric Graphs Up and Down
 
 
 
194
 
Transforming Trigonometric Graphs Up and Down using f(x)notation
 
 
 
195
 
Transforming Trigonometric Graphs Sideways
 
 
 
196
 
Transforming Trigonometric Graphs Sideways using f(x)notation
 
 
 
197
 
Stretching Trigonometric Graphs in the x direction
 
 
 
198
 
Stretching Trigonometric Graphs in the x direction using f(x)notation
 
 
 
199
 
Stretching Trigonometric Graphs in the y direction
 
 
 
200
 
Stretching Trigonometric Graphs in the y direction using f(x)notation
 
 
 
201
 
Reflecting Trigonometric Graphs in the x axis
 
 
 
202
 
Reflecting Trigonometric Graphs in the x axis using f(x)notation
 
 
 
203
 
Transforming Trigonometric Graphs - Exam Tip
 
 
204
 
Transforming Trigonometric Graphs - Exam Question 1
 
 
205
 
Transforming Trigonometric Graphs - Exam Question 2
 
 

Trigonometric Graphs and Exact Values

206
 
The Graph of Cos x
 
 
207
 
The Graph of Sin x
 
 
208
 
Graph of Tan x
 
 
209
 
Exact values of sin and cos - Part 1
 
 
210
 
Exact values of sin and cos - Part 2
 
 
211
 
Exact values of sin and cos - Part 3
 
 
 
212
 
Exact values of sin, cos and tan - Exam Trick
 
 
213
 
Finding the exact values of tan
 
 
 
 
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