# The Ultimate Precalculus Course

**The best complete course to help you review Precalculus topics!**

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**Learning happens at your own pace and without worries about late papers! **Each lesson includes notes, along with examples, exercises, and other activities, so you will learn everything you need and be able to understand it easily.

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## Precalculus Mathematics Complete Course

### Complex Numbers

- The Complex Plane
- Identities of Complex Numbers
- Distance and Midpoint of Complex Numbers
- Multiplying and Dividing Complex Numbers
- Modulus (Absolute Value) and Argument (Angle) of Complex Numbers
- Polar Form of Complex Numbers
- Multiplying and Dividing Complex Numbers in Polar Form
- The Fundamental Theorem of Algebra

### Rational Functions

- End Behavior of Rational Functions
- Discontinuities of Rational Functions
- Adding and Subtracting Rational Expressions
- Multiplying Rational Expressions
- Dividing Rational Expressions
- Reducing Rational Expressions to the Lowest Terms
- Graphing Rational Functions

### Conic Sections

- Conic Sections
- Classifying a Conic Section (in Standard Form)
- Hyperbola in Standard Form and Vertices, Co– Vertices, Foci, and Asymptotes of a Hyperbola
- Equation of Each Ellipse and Finding the Foci, Vertices, and Co– Vertices of Ellipses

### Vectors

- Vectors Introduction
- Vector Components
- Magnitude of Vectors
- Scalar Multiplication of Vectors
- Addition and Subtraction of Vectors
- Direction of Vectors

### Probability and Combinatorics

- Venn Diagrams and the Addition Rule
- Multiplication Rule for Probabilities
- Permutations and Combinations
- Theoretical and Empirical Probability Distributions
- Expected Value of a Random Variable
- Probability Distribution

### Limits

- Properties of Limits
- Define Limits Analytically Using Correct Notation
- Estimating Limit Values from the Graph
- Determining Limits Using Algebraic Manipulation
- Selecting Procedures for Determining Limits
- Determining Limits Using the Squeeze Theorem
- Finding continuity at a point
- Discontinuous Function
- Removing Discontinuities
- Infinite Limits and Vertical Asymptotes
- Connecting Limits at Infinity and Horizontal Asymptotes
- Working with the Intermediate Value Theorem

### Trigonometry

- The Law of Sines
- The Law of Cosines
- Apply Trigonometry to General Triangles
- Inverse Trigonometric Functions
- Sum and Difference of Trigonometric Functions Formulas

### Function Composition

### Matrices

- Adding and Subtracting Matrices
- Matrix Multiplication
- Scalar Multiplication of Matrices
- Transformation Using Matrices
- Representing Systems of Linear Equations Using Matrices
- Introduction to Matrix Inverse
- Inverse of 2×2 Matrix

### Sequences

- Solving Finite Geometric Series
- Solving Infinite Geometric Series
- Sigma Notation
- The Binomial Theorem

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