REVISION HACKATHON– A LEVEL MATH (H2) (2024)
- Description
- Curriculum
- Reviews
Most students find mathematics difficult to understand because the lessons are more complicated and require computation work not normally required or focused on in their previous mathematics classes.
However, mastering Math and solving its problems doesn’t have to be a complicated affair. With the right strategy, it can be easy and straightforward.
Day 1 - Functions
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1
OPCM Creation Layout - Functions -
2
Definition of Functions & The Vertical Line Test
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3
Type 1: Inverse Functions
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4
Relationship of f(x) and f^-1(x)
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5
Show that Inverse Function exists or not using the Horizontal Line Test
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6
Type 2: Composite Functions
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7
Type 3: Composite Inverse Functions (aka Self-Inverse Functions)
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8
Type 4: Recurring Piecewise Functions
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9
H2 Functions – Create Your OPCM -
10
H2 Functions – Download Your Questions
Day 1 - Sequences & Series I
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11
OPCM Creation Layout - Sequences & Series I
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12
Sequences & Series I - Arithmetic Progression AP
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13
Sequences & Series I - Geometric Progression GP
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14
Sequences & Series I - Simple Interest & Compound Interest
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15
Sequences & Series I - Type 1 - Word Problems
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16
Sequences & Series I - Type 2 - "Bank" Questions
Day 1 - Sequences & Series II
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17
OPCM Creation Layout - Sequences & Series II
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18
Sequences & Series II - Type 1 - Expand and Express Term-by-term using standard results
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19
Sequences & Series II - Type 2 - Comparing Terms (Involves Inequalities)
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20
Sequences & Series II - Type 3 - Method of Difference
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21
Sequences & Series II - Type 4 - Substitution
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22
H2 SnS – Create Your OPCM
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23
H2 SnS - Download Your Questions
Day 2 - Vectors I
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24
OPCM Creation Layout - Vectors I
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25
Vectors I - Definition of a Point
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26
Vectors I - Ratio Theorem
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27
Vectors I - Collinearity
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28
Vectors I - Magnitude of Vector
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29
Vectors I - Unit Vector
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30
Vectors I - Director Cosines
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31
Vectors I - Definition of a Line
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32
Vectors I - Scalar Product and uses
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33
Vectors I - Vector Product and uses
Day 2 - Vectors II
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34
OPCM Creation Layout - Vectors II
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35
Vectors II - Definition of a Line - Vector & Cartesian Equations
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36
Vectors II - Type 1 - Relationship between 2 lines (Parallel, Intersecting or Skewed)
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37
Vectors II - Type 2 - Angles between 2 lines
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38
Vectors II - Type 3 - Vector Projection of AP on line l
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39
Vectors II - Type 4 - Shortest Distance from P to F
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40
Vectors II - Type 5 - Foot of Perpendicular from point P to line l
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41
Vectors II - Type 6 - Shortest distance between 2 parallel lines lie on parallel planes
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42
Vectors II - Type 7 - Reflection of line about a line
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43
H2 Vectors I
Day 2 - Vectors IIIa
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44
OPCM Creation Layout - Vectors IIIa
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45
Vectors IIIa - Definition of a Plane -Vector and Cartesian Equations
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46
Vectors IIIa - Type 1a - Distance between plane and point B
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47
Vectors IIIa - Type 1b - Foot of perpendicular F from point B
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48
Vectors IIIa - Type 1c - Find Reflected point B' about plane
Day 2 - Vectors IIIb
Day 2 - Vectors IIIc
Day 3 - Differentiation
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58
OPCM Creation Layout - Differentiation
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59
Differentiation - Implicit Differentiation
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60
Differentiation - Parametric Differentiation
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61
Differentiation - Type 1 - Rate of Change
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62
Differentiation - Type 2 - Equation of Tangent & Normal
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63
Differentiation - Type 3 - Minima & Maxima
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64
H2 Differentiation – Download Your Questions
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65
H2 Differentiation – Create Your OPCM
Day 3 - Maclaurin Series
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66
OPCM Creation Layout - Maclaurin's Series
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67
Maclaurin's Series - General Formula
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68
Maclaurin's Series - Standard Series Expansions
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69
Maclaurin's Series - Strategy for Maclaurin's Series:Standard Series Questions
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70
Maclaurin's Series - Type 1 - Maclaurin's Expansion (and using Integration to solve)
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71
Maclaurin's Series - Type 2 - Small Angle Approximation
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72
Maclaurin's Series - Type 3 - Binomial Expansion (with Small Angle Approximation)
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73
H2 Maclaurin’s – Create Your OPCM
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74
H2 Maclaurin's - Download Your Questions
Day 4 - Integration Techniques I
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75
OPCM Creation Layout – Integration Techniques I
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76
Integration Techniques I - The Approach Strategy to Integrate Accurately & Quickly
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77
Integration Techniques I - Type 1a
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78
Integration Techniques I - Type 1b
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79
Integration Techniques I - Type 2 n≠-1
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80
Integration Techniques I - Type 2 n=-1
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81
Integration Techniques I - Type 3: Trigo Integration
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82
Integration Techniques I - When Power of Trigo is > 1
Day 4 - Integration Techniques II
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83
Integration Techniques II - The Approach Strategy to Integrate Accurately & Quickly
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84
OPCM Creation Layout - Integration Techniques II
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85
Integration Techniques II - Type 1a
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86
Integration Techniques II - Type 1b
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87
Integration Techniques II - Type 2a
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88
Integration Techniques II - Type 2b
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89
Integration Techniques II - Type 3
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90
Integration Techniques II - Type 4
Day 4 - Integration Techniques III
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91
Integration Techniques III - The Approach Strategy to Integrate Accurately & Quickly
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92
OPCM Creation Layout - Integration Techniques III
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93
Integration Techniques III - Type A1 - Integration by parts (IBP) - Basic
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94
Integration Techniques III - Type A2 - Integration by parts (IBP) Twice & Manipulate
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95
Integration Techniques III - Type A3 - Integration by parts (IBP) - Need to introduce "1"
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96
Integration Techniques III - Type B1 - Integration by substitution - Basic
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97
Integration Techniques III - Type B2 - Integration by substitution involving trigo
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98
Integration Techniques III - Type C - Integration of Modulus
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99
H2 Integration Techniques – Create Your OPCM
Day 4 - Applications of Integration
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100
OPCM Creation Layout - Application of Integration
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101
Application of Integration - Area bounded by x or y axis
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102
Application of Integration - Area between 2 graphs
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103
Application of Integration - Area bounded by parametric curve
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104
Application of Integration - Volume generated when rotated about x or y axis
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105
Application of Integration - Volume generated when rotated about x or y axis (Big - Small)
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106
Application of Integration - Volume generated when rotated about vertical:horizontal line which is NOT x or y axis
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107
Application of Integration - Useful Tips for Application of Integration
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108
H2 Applications of Integration – Create Your OPCM
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109
H2 Applications of Integration & Integration Techniques - Download Your Questions
Day 5 - Complex Numbers I
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110
OPCM Creation Layout - Complex Numbers I
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111
Complex Numbers I - Approach Strategy
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112
Complex Numbers I - Type 1a - Real coefficients - Method 1
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113
Complex Numbers I - Type 1a - Real coefficients - Method 2
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114
Complex Numbers I - Type 1b - Complex coefficients
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115
Complex Numbers I - Type 2 - Simultaneous Equations
Day 5 - Complex Numbers II
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116
OPCM Creation Layout - Complex Numbers II
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117
Complex Numbers II - Type 1 - Modulus-Argument Form
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118
Complex Numbers II - Type 2 - Finding range of values of n
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119
Complex Numbers II - Type 3 - Argand Diagrams
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120
H2 Complex Numbers – Create Your OPCM
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121
H2 Complex Numbers - Download Your Questions
Day 5 - Differential Equations
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122
OPCM Creation Layout - Differential Equations
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123
Differential Equations - Type 1 - Solving DEs using Direct integration
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124
Differential Equations - Type 2 - Solving DEs using Separable Variables
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125
Differential Equations - Type 3 - Solving DEs by Substitution Example 1- Find General Solution
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126
Differential Equations - Type 3 - Solving DEs by Substitution Example 2- Find Particular Solution
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127
Differential Equations - Type 4 - Word Problems
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128
H2 Differential Equations – Create Your OPCM
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129
H2 Differential Equations - Download Your Questions
Day 6 - Permutations & Combinations
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130
OPCM Creation Layout - Permutations & Combinations
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131
Permutations & Combinations I - Addition & Multiplication Principle
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132
Permutations & Combinations I - Definitions of Permutation & Combination
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133
Permutations & Combinations I - Key Strategies Overview
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134
Permutations & Combinations I - Strategy- Using Cases (for Choose Only Questions)
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135
Permutations & Combinations II - Common Misconceptions in P&C
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136
Permutations & Combinations II - Strategy- Using Cases (for Choose then Arrange Questions)
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137
Permutations & Combinations III - Strategy- FGI (Arrangements with Restrictions) - Line Arrangement
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138
H2 PnC – Create Your OPCM
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139
H2 PnC - Download Your Questions
Day 6 - Probability
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140
Probability I - Introduction to Probability
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141
Probability I - 3 Important Results
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142
Probability I - 3 Key Terms & Formulae
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143
Probability I - Solving Questions involving Independent and Mutually Exclusive Events
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144
Probability II - Type 1 - Definition of Probability
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145
Probability III - Type 2 - Tree Diagram (Questions involving a sequence of events)
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146
Probability IV - Type 3 - Venn Diagram (When given multiple events with different probabilities)
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147
Probability V - Type 4 - Table of Outcomes
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148
Probability VI - Type 5 - Using PnC
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149
Probability VII - Type 6 - Probability x Sequences & Series (GP- Sum to Infinity)
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150
H2 Probability – Create Your OPCM
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151
H2 Probability – Download Your Questions
Day 6 - Discrete Random Variables
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152
OPCM Creation Layout - Discrete Random Variables I
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153
Discrete Random Variables I - Type 1 - Probability Distribution
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154
Discrete Random Variables I - Type 2 - Expectation and Variance
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155
Discrete Random Variables I - Approach Strategies Application - Example 1
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156
Discrete Random Variables II - Approach Strategies Application - Example 2
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157
Discrete Random Variables III - Approach Strategies Application - Example 3
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158
Discrete Random Variables IV - Approach Strategies Application - Example 4
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159
H2 DRV – Create Your OPCM
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160
H2 DRV – Download Your Questions
Day 7 - Binomial Distribution
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161
Binomial Distribution I - Introduction to Binomial Distribution
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162
Binomial Distribution I - 4 Important Fundamentals of Binomial Distribution
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163
OPCM Creation Layout - Binomial Distribution II
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164
Binomial Distribution II - Type 1- Standard Question + Binomial within a Binomial
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165
Binomial Distribution III - Type 2- Mode of Binomial Distribution
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166
Binomial Distribution V - Type 3c - n is unknown
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167
Binomial Distribution V - Type 3 - Calculating unknowns (n, p or x)
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168
Binomial Distribution V - Type 3a - p is unknown
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169
Binomial Distribution V - Type 3b - x is unknown
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170
Binomial Distribution V - Type 4 - Using Binomial formula to solve "range of values" + mode questions
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171
H2 Binomial Distribution – Create Your OPCM
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172
H2 Binomial Distribution - Download Your Questions
Day 7 - Normal Distribution
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173
Normal Distribution I - Introduction to Normal Distribution
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174
Normal Distribution I - Fundamentals of Normal Distribution
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175
Normal Distribution I - Properties of E(X) and Var(X)
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176
Normal Distribution I - Using GC for Normal Distribution
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177
Normal Distribution II - Type 1 - Combination of Independent Normal Variables
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178
Normal Distribution II - Approach Strategies Application - Example 1
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179
Normal Distribution III - Type 2 - Standardization
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180
Normal Distribution III - Approach Strategies Application - Example 2
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181
H2 Normal Distribution – Create Your OPCM
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182
H2 Normal Distribution - Download Your Questions
Day 8 - Estimations
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183
Estimations I - Introduction to Estimation
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184
OPCM Creation Layout - Estimations
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185
Estimations I - Part A - Find unbiased estimates using formulae (mainly used in hypothesis testing)
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186
Estimations I - Part B - Find unbiased estimates given raw data
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187
Estimations II - Part C - Find unbiased estimates given 5 different conditions
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188
Estimations – Create Your OPCM
Day 8 - Sampling Distribution
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189
Sampling Distribution - Introduction to Sampling Distribution
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190
Sampling Distribution - Type 1 - Given a Normal Distribution (Standard Sampling Solving)
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191
Sampling Distribution - Type 1 - Example
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192
Sampling Distribution - Type 2 - Non-Normal Distribution (Central Limit Theorem)
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193
Sampling Distribution - Type 2 - Example 1
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194
Sampling Distribution - Type 2 - Example 2
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195
Sampling Distribution - Create Your OPCM
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196
H2 Sampling & Estimation - Download Your Questions
Day 8 - Hypothesis Testing
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197
Hypothesis Testing I - Introduction to Hypothesis Testing
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198
Hypothesis Testing I - Overview of Hypothesis Question Types
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199
Hypothesis Testing I - Approach Strategy for Hypothesis Testing
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200
Hypothesis Testing II - Type 1 - Given Normal Distribution (CLT not required)
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201
Hypothesis Testing II - Type 2 - Non-Normal Distribution (CLT required)
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202
Hypothesis Testing - Create Your OPCM
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203
H2 Hypothesis Testing – Download Your Questions
BONUS - Graphing Techniques Transformation
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204
Graphing Techniques Transformations I - Introduction to Graphing Techniques
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205
Graphing Techniques Transformation I - Approach Strategy for Transformations (Non-Absolute Value Functions)
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206
Graphing Techniques Transformation I - Approach Strategy for Transformations (Absolute Value Functions)
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207
Graphing Techniques Transformation II - 3 Types of Non-Sketching Questions
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208
Graphing Techniques Transformation II - Type 1 - Given Original and Resulting Function
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209
Graphing Techniques Transformation II - Type 2 - Given Original and Successive Transformations
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210
Graphing Techniques Transformation II - Type 3 - Given Resulting Function and Successive Transformations
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211
Graphing Techniques Transformation III - Sketching Questions
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212
Graphing Techniques Transformation III - Sketching Non-Absolute Value Functions
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213
Graphing Techniques Transformation III - Sketching Absolute Value Functions
BONUS - Graphing Techniques Special Transformation
BONUS - Graphing Techniques Conics
BONUS - Graphing Techniques Rational Functions
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221
Graphing Techniques Rational Functions I - Standard Question Solving Techniques
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222
Graphing Techniques Rational Functions I - Example (Non-Sketching Questions)
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223
Graphing Techniques Rational Functions II - Using Discriminant
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224
Graphing Techniques Rational Functions II - Example 1 (Involving discriminant)
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225
Graphing Techniques Rational Functions III - Example 2 (involving discriminant)
BONUS - Inequalities
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Course details
Lectures
226
Assignments
18
Level
Beginner
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