Study well.
Precalculus
Preliminaries:
Interval and Set NotationIntercepts
Part 1 - An Introduction to Functions
Relations
What is a Function?
Functions: A Graphical View
Function Notation
1.2 - More With Functions
Six Basic Functions
Operations on Functions
What is a Zero of a Function?
Symmetry
Even and Odd Functions
1.3 - Graphs of Functions
Piecewise Functions
Increasing, Decreasing, and Constant
Absolute and Local Extrema
1.4 - Translations of Graphs
Horizontal and Vertical Translations
Reflecting Graphs
Vertically Stretching and Shrinking Graphs
1.5 - Linear Functions
Slope
Horizontal and Vertical Lines
Slope-Intercept Form of a Line
Point-Slope Form of a Line
Finding Equations of Lines
Part 2 - Polynomial, Rational, and Radical Functions
Quadratic Functions
The Vertex Formula
The Quadratic Formula
The Discrminant
2.2 Reading Graphs, Absolute Value Equations and Inequalities, and Quadratic Inequalities
Reading Graphs to Determine the Solutions of Equations and Inequalities
Absolute Value Equations and Inequalities - Part 1
Absolute Value Equations and Inequalities - Part 2
Quadratic Inequalities
2.3 - Introduction to Polynomial Functions
Definition of a Polynomial Function
End Behavior of a Polynomial Function
Recall - What is a Zero of a Function?
Repeated Zeros
2.4 - The Remainder and Factor Theorems
Synthetic Division
The Remainder and Factor Theorems
2.5 - Zeros of Polynomial Functions
Complex Zeros
Finding the Zeros of a Polynomial Function
2.6 - Rational Functions
Rational Functions
Asymptotes of Rational Functions
Graphing Rational Functions
2.7 - Rational Equations and Inequalitites
Rational Equations
Rational Inequalities
2.8 - Radical Equations and Inequalities
Radical Functions
Radical Equations
Part 3 - Exponential and Logarithmic Functions
Composition of Functions
One-to-One Functions
Inverse Functions
3.2 - Exponential and Logarithmic Functions
Exponential Functions
Definition of Logarithm
Properties of Logarithms
Change of Base Formula
Logarithmic Functions
3.3 - Exponential and Logarithmic Equations
Exponential Equations
Logarithmic Equations
Compound Interest
Exponential Growth and Decay
Million, Billion, Trillion
Part 4 - Matrices
The General Idea of a Matrix
Matrices - Row Operations - Part 1
Matrices - Row Operations - Part 2
Matrices - Row Operations - Part 3
Matrices - Row Operations - Part 4
4.2 - Properties of Matrices
Properties of Matrices
Matrix Multiplication
Determinants
Inverse of a 2x2 Matrix
4.3 - Partial Fractions
Partial Fractions - Part 1
Partial Fractions - Part 2
Part 5 - Conic Sections
5.1 - Circles
Circles - Part 1
Circles - Part 2
5.2 - Parabolas
Parabolas - Part 1
Parabolas - Part 2
Parabolas - Part 3
Parabolas - Part 4
5.3 - Ellipses
Ellipses - Part 1
Ellipses - Part 2
5.4 - Hyperbolas
Hyperbolas - Part 1
Hyperbolas - Part 2
Hyperbolas - Part 3
5.5 - The General Equation of Conic Sections and Eccentricity
The General Equation of Conic Sections and Eccentricity
Part 6 - The Foundations of Trigonometry
6.1 - Angles, Radians, and Arc Length
Angles
Radians
Arc Length
6.2 - Definition of Trigonometric Functions and Fundamental Identities
Definition of Trigonometric Functions
Fundamental Trigonometric Identities
6.3 - Right Triangle Trigonometry
The Definition of Trigonometric Functions for Right Triangles
Trigonometric Function Values of Special Angles
Reference Angles
6.4 - Graphs of Sine and Cosine Functions
An Introduction to Graphing to Sine and Cosine
Graphs of Sine and Cosine - Part 1
Graphs of Sine and Cosine - Part 2
Graphs of Sine and Cosine - Part 3
6.5 - Verifying Trigonometric Identities
Verifying Trigonometric Identities
6.6 - More Trigonometric Identities
Derivation of Sum and Difference Identities for Cosine and Sine
Sum and Difference Identities
Double Angle Identities
Half-Angle Identities
6.7 - Inverse Trigonometric Functions
Inverse Trigonometric Functions
6.8 - Trigonometric Equations
Trigonometric Equations - Part 1
Trigonometric Equations - Part 2
Part 7 - Applications of Trigonometry
7.1 - The Law of Sines and The Law of Cosines
The Law of Sines - Part 1
The Law of Sines - Part 2
The Law of Cosines
7.2 - An Introduction to Vectors
An Introduction to Vectors - Part 1
An Introduction to Vectors - Part 2
An Introduction to Vectors - Part 3
7.3 - The Polar (Trigonometric) Form of Complex Numbers
The Polar Form of Complex Numbers
Powers and Roots of Complex Numbers
7.4 - Polar Equations
Polar Equations
Graphing Polar Equations
7.5 - An Introduction to Parametric Equations
An Introduction to Parametric Equations
