There are two tables that comprise the lecture videos and practice quiz questions for each course:
(i) table for pure and pre-calculus mathematics courses and (ii) table for advanced mathematics courses.
TABLE FOR PURE AND PRE-CALCULUS MATHEMATICS LECTURE VIDEOS.
- ARITHMETIC PROCESSES.
Definition of Number , Types And Factors of a number.
Fractions, Types, Maths Operations, Directed, Binary And Standard Form Numbers.
Word Problems In Numbers And Numerations.
Highest Common Factor And Lowest Common Factor.
- ALGEBRAIC PROCESSES.
Algebraic Simplification(Non-Fraction And Fraction).
Substitution Method At The End Of Above Algebraic Simplification (1:37:00).
Algebraic Equations With Fractions, Undefined And Zeros Of Expressions Or Equations.
Algebraic Factorisation
- INEQUALITY
Linear Inequality
Systems Of Inequalities.
Linear and Non-Linear Systems of Equations By Substitution Method
Two Variable Linear Systems.
Multi-Variable Linear Systems.
Linear Programming.
SURDS (Addition, Subtraction, Multiplication, Division And Other Operations).
TRIANGLES
Triangle – Law of Sine (Length, Area And Angle Mensuration).
Triangle – Law of Cosine (Length And Angle Mensuration).
Quadratic Equation 2 – Identification And Solving It By Algebraic Method with Real-Life Problem.
Quadratic Equation – Identification And Solving It By Graphical Method.
Transformation of Quadratic Functions.
- POLYNOMIAL EXPRESSIONS. FUNCTIONS AND EQUATIONS.
Parents Functions And Transformations.
Polynomial Function 1 – Identify And Sketch The Graph.
Polynomial Function 2 – Use Of End Behaviour To Interprete And Describe The Graph.
Polynomial Function 3 – Graphing with Table of values of x.
Analyzing the Graph of Polynomial Functions (Part 1).
Analysing The Graph Of Polynomial Functions (Part 2).
Transformation of Polynomial Functions.
Division Of Polynomial Functions – Factor And Remainder Theorems.
Addition, Subtraction, Multiplication And Factoring Polynomials By Pascal Triangle.
Finding The Zeros And Solutions of Polynomial Functions And Equations.
Fundamental Theorem of Algebra And Descarte´s Rule of sign.
- RATIONAL AND RADICAL FUNCTIONS AND EQUATIONS.
nTh Root of Rational Exponents.
Properties of Rational and Radical Exponents.
Variable Expressions With Rational and Radical Exponents.
Radical Functions And Graphic Representations.
Graphing Parabolic Circle.
Rational Functions And Graphic Representations.
Addition And Subtraction of Rational Expressions (Section 1).
Addition And Subtraction of Rational Expressions (Section 2).
Multiplication and Division of Rational Expressions (Section 1).
Multiplication and Division of Rational Expressions (Section 2).
Solving Rational Equations and With Complex Fractions.
Inverse of Functions.
Performing Function Operations(Part 2).
Exponential Growth And Decay Functions.
- LOGARITHM OF NUMBERS, FUNCTIONS AND EQUATIONS.
Logarithm of Numbers Greater Than One.
Logarithm of Numbers Less Than One.
Logarithms And Logarithmic Functions (Part 1).
Logarithms And Logarithmic Functions (Part 2).
Logarithms And Logarithmic Functions (Part 3).
Properties of Logarithms.
Natural Base e, Equations and Graphing its Functions.
Transformation of Logarithmic and Exponential Functions.
Solving Exponential and Logarithmic Equations.
Modelling With Exponential And Logarithmic Functions.
- TRIGONOMETRY.
Right Triangle Trigonometry.
Trigonometric Functions of Any Angle.
Graphing Sine and Cosine Functions (Section1).
Graphing Sine and Cosine Functions (Section 2).
Graphing Other Trigonometric Functions (Section 1).
Graphing Other Trigonometric Functions (Section 2).
Modelling With Trigonometric Functions.
Using Trigonometric Identities.
Using Sum and Difference Formulas.
Multiple-Angle And Product-To-Sum Formulas.
Solving Trigonometric Equations.
Trigonometric Form Of Complex Numbers.
Powers Of Complex Numbers (De Moivre´s Theorem).
- ANGLES AND RADIAN MEASURES.
- CIRCLE GEOMETRY (SECTION 1).
- CIRCLE GEOMETRY (SECTION 2)
- EQUATION OF AN ELLIPSE (Conversion from general to standard form and so on).
- SEQUENCES AND SERIES.
Defining Arithmetic Sequence and Series.
Analyzing Arithmetic Sequences and Series.
Analyzing Geometric Sequences and Series.
Finding Sums of Infinite Geometric Series.
- INTRODUCTION TO STATISTICS.
Displaying Quantitative Data With Graph.
Describing Quantitative Data With Numbers.
Identifying Outliers.
Describing Location In A Distribution.
Density Curves And Normal Distributions.
Scatter Plots And Correlations.
Least-Square Regression.
Sampling And Surveys.
Experiments.
Using Studies Wisely.
Randomness, Simulation And Probability.
Probability Rules.
Venn Diagram.
Conditional Probability And Independence.
Discrete And Continuous Random Variables.
Transforming And Combining Random Variables.
Binomial And Geometric Random Variables.
- STATISTICS (SECTION 2)
Tables, Charts And Measures Of Center.
Measure Of Dispersion
(Variance, S.D, Range, Quartiles, Interquartile Range And so on).
Deciles And Percentiles.
TABLE FOR ADVANCED MATHEMATICS VIDEO CLASSES.
Solving Questions Involving Circle Theorem.
BINOMIAL THEOREM FOR EXPANSION OF FUNCTIONS/EQUATIONS AND FOR PROBABILITY (Introduction).
FINDING DISTANCE, MID-POINT AND DIVISION IN THE RATIO P : 1 OF TWO POINT CO-ORDINATES.
FINDING THE EQUATIONS OF TANGENT AND NORMAL TO A LINE OR CURVE.
CALCULIS.
Derivative Of Functions.
INTRODUCTION TO INTEGRATION: Substitution, Partial Fraction And Decomposition Method.
Integration By Trigonometric Identities, Parts And Applications.
Introduction To Inverse Trigonometric Functions.
FUNDAMENTAL OF MATRIX.
HOW TO USE CRAMER´S RULE AND GAUSS-JORDAN MATRIX METHOD To Solve Systems Of Linear Equations (Part1).
HOW TO USE CRAMER´S RULE AND GAUSS-JORDAN MATRIX METHOD To Solve Systems Of Linear Equations And Find The Rank (Part2).
How To Find The Adjoint Of A Given 3×3 Matrix (Part 1).
How To Find The Adjoint Of A Given 3×3 Matrix (Part 2).
How To Find The Inverse Of A Given 3×3 Matrix.
How To Find The Inverse Of Matrix And Use It To Solve Systems Of Linear Equations.
VECTORS IN THE PLANE (Section 1).
Writing Linear Combination of A Unit Vector i and j (Section 2).