# The Ultimate Precalculus Course

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

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Thousands of people taking Precalculus exams use this Precalculus course, along with additional Effortless Math Education products every year so they can do better on the test.

It covers core topics, renews math skills, and helps individuals learn areas in which they are strong or weak before the test. Then they can get a great score on the day of the test.

**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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