Sets
Numbers
- The Evolution of Numbers
- Prime and Composite Numbers
- Fundamental Theorem of Arithmetic
- Whole Numbers and Integers
- Rational Numbers
- Irrational Numbers
- Rational Numbers and Irrational Numbers
- Real Numbers
- Imaginary Numbers
- Complex Numbers
- Adding and Subtracting Complex Numbers
- Multiplying and Dividing Complex Numbers
- Absolute Value of Complex Numbers
- The Complex Plane
- Common Number Sets
Inequalities
- Introduction to Inequalities
- Properties of Inequalities
- Solving Inequalities
- Absolute Value Inequalities
- Solving Rational Inequalities
- Solving Inequality Word Questions
- Intervals
Exponents
- Exponents
- Variables with Exponents
- Using Exponents in Algebra
- Squares and Square Roots
- Squares and Square Roots in Algebra
- nth Root
- Fractional Exponents
- Laws of Exponents
- Exponents of Negative Numbers
Polynomials
- What is a Polynomial?
- Types of Polynomials
- Monomials, Binomials, and Polynomials
- Adding Polynomials
- Subtracting Polynomials
- Dividing Polynomials
- Multiplying Binomials
- Polynomials – Long Division
- Degree (of an Expression)
- Special Binomial Products
- Multiplying Binomials
- Difference of Two Cubes
- Polynomial Remainder Theorem
- Factoring in Algebra
- Factorization of Polynomials Using Factor Theorem
- How do you use the factor theorem?
- How to factorise a polynomial by splitting the middle term?
- Review Factoring Polynomials
- Zeros of a Polynomial Function
- Factors and Coefficients of a Polynomial
- Roots of Polynomials: Sums and Products
- Rational Expressions
- Using Rational Expressions
- Review Factoring Polynomials
- Solving Polynomial Equations of Higher Degree
- Examining Graphs of Polynomial Equations of Higher Degree
Graphing Polynomials
- How Polynomials Behave
- Polynomials: The Rule of Signs
- Polynomials: Bounds on Zeros
Equations
- Equations and Formulas
- Solving Equations
- Simplify
- Solving Word Questions
- Zero Product Property
- Implication and Iff
- Theorems, Corollaries, Lemmas
Graphs
- Cartesian Coordinates
- Pythagoras’ Theorem
- Distance Between 2 Points
- Graph of an Equation
- Finding Intercepts From an Equation
- Symmetry in Equations
Linear Equations
- Equation of a Straight Line
- Linear Equations
- Point-Slope Equation of a Line
- Equation of a Line from 2 Points
- Midpoint of a Line Segment
- Parallel and Perpendicular Lines
Functions
- What is a Function?
- Domain, Range and Codomain
- Evaluating Functions
- Increasing and Decreasing Functions
- Maxima and Minima of Functions
- Even and Odd Functions
- Set-Builder Notation
- Common Functions Reference:
- Square Function
- Square Root Function
- Cube Function
- Reciprocal Function
- Absolute Value Function
- Floor and Ceiling Function
- Function Transformations
- Operations with Functions
- Composition of Functions
- Finding Domains of Composite Functions
- Inverse Functions
Equations of Second Degree
- Quadratic Equations
- Factoring Quadratics
- Solving A Quadratic Equation By Factoring
- Completing the Square
- Solving a Quadratic Equation by Completing the Square
- Derivation of Quadratic Formula
- Graphing Quadratic Equations
- A Summary of the Methods of Solving Quadratic Equations
- Quadratic Equations in the Real World
- Circle Equations
Solving
- Mathematical Models and Mathematical Models 2
- Approximate Solutions
- Intermediate Value Theorem
- Solving Radical Equations
- Change of Variables
- Algebra Mistakes
Solving Inequalities
- Solving Inequalities
- Graphing Linear Inequalities
- Inequality Grapher
- Solving Quadratic Inequalities
- Solving Rational Inequalities
- Absolute Value in Algebra
- Absolute Value Equations
Exponents and Logarithms
- Introduction to Logarithms
- Exponents, Roots and Logarithms
- Working with Exponents and Logarithms
- Logarithmic Equations
- Exponential Function
- Logarithmic Function
- Exponential Growth and Decay
Systems of Linear Equations
- Systems of Linear Equations
- Solving Systems Of Equations By Elimination Method
- Solving Systems Of Equations By Substitution Method
- Cross Multiplication Method For Solving Equations
- Graphical Method Of Solving Linear Equations In Two Variables
- Matrices
- Special Types of Matrices
- Scalar, Vector, Matrix and Vectors
- Dot Product
- Cross Product
- How to Multiply Matrices
- Determinant of a Matrix
- Inverse of a Matrix:
- Using Elementary Row Operations (Gauss-Jordan)
- Using Minors, Cofactors and Adjugate
- Solving Systems of Linear Equations Using Matrices
- Solving Linear Quadratic Systems Algebraically
- Solving Linear Systems Algebraically Using Substitution
- Solving a Linear Quadratic System Graphically
- Solving Linear Systems Graphically
Probability
- Probability
- Probability – Types of Events
- The Basic Counting Principle
- Probability and Permutations
- Combinations and Permutations
Sequences, Series and Partial Sums
Finally
These last few subjects use what you have learned above.
- Partial Fractions
- Mathematical Induction
- Pascal’s Triangle
- Binomial Theorem
- Binomial Theorem for any Index