# The Ultimate College Mathematics Placement Course (+FREE Worksheets & Tests)

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## College Mathematics Complete Course

### Integers and Order of Operations

- Adding and Subtracting Integers
- Multiplying and Dividing Integers
- Translate Phrases into an Algebraic Statement
- Order of Operations
- Integers and Absolute Value
- Proportional Ratios
- Similarity and Ratios
- Percent Problems
- Percent of Increase and Decrease
- Discount, Tax, and Tip
- Simple Interest
- The Distributive Property
- Approximating Irrational Numbers

### Exponents and Variables

- Multiplication Property of Exponents
- Division Property of Exponents
- Zero and Negative Exponents
- Powers of Products and Quotients
- Negative Exponents and Negative Bases
- Scientific Notation
- Addition and Subtraction in Scientific Notation
- Multiplication and Division in Scientific Notation

### Expressions and Equations

- Simplifying Variable Expressions
- Evaluating One Variable
- Evaluating Two Variables
- One-Step Equations
- Multi-Step Equation
- Finding Midpoint
- Finding Distance of Two Points

### Linear Functions

- Point-Slope Form
- Finding Slope
- Writing Linear Equations
- Graphing Linear Inequalities
- Finding the x-Intercept
- Finding the y-Intercept
- Write an Equation from a Graph
- Properties of the Horizontal Line
- Properties of the Vertical Lines
- Parallel and Perpendicular Lines

### Inequalities and System of Equations

- One-Step Inequalities
- Multi-Step Inequalities
- Linear Inequalities
- Systems of Equations
- Systems of Equations with Substitution
- Systems of Equations Word Problems
- Number of Solutions in a System of Equations
- Systems of Linear Inequalities

### Quadratic Functions and Equations

- Quadratic Function
- Solving a Quadratic Equation
- Graphing Quadratic Functions
- Solving a Quadratic Equation by Completing the Square
- Solving a Quadratic Equation by Factoring
- Finding Discriminant of Quadratic Equation
- Transformations of Quadratic Equations

### Complex Numbers

- Complex Plane
- Adding and Subtracting Complex Numbers
- Multiplying and Dividing Complex Numbers
- Rationalizing Imaginary Denominators
- Complex Roots of the Quadratic Equation

### Matrices

- Using Matrices to Represent Data
- Adding and Subtracting Matrices
- Matrix Multiplication
- The Inverse of a Matrix
- Solving Systems with Matrix Equations
- Finding Determinants of a Matrix

### Polynomial Operations

- Writing Polynomials in Standard Form
- Simplifying Polynomials
- Adding and Subtracting Polynomials
- Multiplying and Dividing Monomials
- Multiplying a Polynomial and a Monomial
- Multiplying Binomials
- Factoring Trinomials
- Choosing a Factoring Method for Polynomials
- Factoring by GCF
- Factors and Greatest Common Factors
- Operations with Polynomials
- Even and Odd Function
- End behavior of polynomial functions
- Remainder and Factor Theorems
- Polynomial Division (Long Division)
- Polynomial Division (Synthetic Division)
- Finding zeros of polynomials
- Polynomial identities

### Complex Numbers

- Adding and Subtracting Complex Numbers
- Multiplying and Dividing Complex Numbers
- Rationalizing Imaginary Denominators

### Functions Operations

- Function Notation
- Adding and Subtracting Functions
- Multiplying and Dividing Functions
- Composition of Functions
- Writing Functions
- Parent Functions
- Function Inverses
- Inverse Variation
- Graphing Functions
- Domain and Range of Function
- Piecewise function
- Positive, negative, increasing and decreasing functions on intervals
- Finding Average Rate of Change of a Function

### Exponential Functions

### Logarithms

- Properties of Logarithms
- Evaluating Logarithms
- Natural Logarithms
- Solving Logarithmic Equations
- The Change of Base Formula for Logarithms

### Radical Expressions

- Simplifying Radical Expressions
- Simplifying Radical Expressions Involving Fraction
- Multiplying Radical Expressions
- Adding and Subtracting Radical Expressions
- Domain and Range of Radical Functions
- Radical Equations
- Solving Radical Inequalities

### Rational and Irrational Expressions

- Rational and Irrational Numbers
- Simplifying Rational Expressions
- Graphing Rational Expressions
- Multiplying Rational Expressions
- Dividing Rational Expressions
- Adding and Subtracting Rational Expressions
- Rational Equations
- Simplifying Complex Fractions
- Maximum and Minimum Points
- Solving Rational Inequalities
- Irrational Functions
- Direct, Inverse, Joint, and Combined Variation
- Rational Exponents
- Rational Exponents and Radicals

### Conics

- Equation of Parabola
- Finding the Focus, Vertex, and Directrix of a parabola
- Standard Form of a Circle
- Finding the Center and the Radius of Circles
- Equation of Each Ellipse and Finding the Foci, Vertices, and Co– Vertices of Ellipses
- Hyperbola in Standard Form and Vertices, Co– Vertices, Foci, and Asymptotes of a Hyperbola
- Classifying a Conic Section (in Standard Form)

### Sequences and Series

- Arithmetic Sequences
- Geometric Sequences
- Arithmetic Series
- Finite Geometric Series
- Infinite Geometric Series
- Pascal’s Triangle
- Binomial Theorem
- Sigma Notation (Summation Notation)
- Alternate Series

### Trigonometric Functions

- Trig Ratios of General Angles
- Trigonometric Ratios
- Right-Triangle Trigonometry
- Angles of Rotation
- Unit Circle
- The Reciprocal Trigonometric Functions
- Function Values of Special Angles
- Function Values from the Calculator
- Reference Angles and the Calculator
- Coterminal Angles and Reference Angles
- Periodic Function
- Angles and Angle Measure
- Evaluating Trigonometric Function
- Missing Sides and Angles of a Right Triangle
- Arc length and Sector Area
- Inverse of Trigonometric Functions
- Solving Trigonometric Equations

### More Topics Trigonometric Functions

- Pythagorean Identities
- Domain and Range of Trigonometric Functions
- Cofunctions
- Law of Sines
- Law of Cosines
- Fundamental Trigonometric Identities
- Sum and Difference Identities
- Double Angle Identities
- Half-Angle Identities
- Using the Law of Cosines to Find Angle Measure

### Graphs of Trigonometric Functions

- Graph of the Sine Function
- Graph of the Cosine Function
- Amplitude, Period, and Phase Shift
- Writing the Equation of a Sine Graph
- Writing the Equation of a Cosine Graph
- Graph of the Tangent Function
- Graph of the Cosecant Function
- Graph of the Secant Function
- Graph of the Cotangent Function
- Graph of Inverse of the Sine Function
- Graph of Inverse of the Cosine Function
- Graph of Inverse of the Tangent Function
- Sketching Trigonometric Graphs

### Statistics

- Frequency and Histograms
- Box-and-Whisker Plots
- Measures of Dispersion
- Organizing Data
- Data Distribution
- Central Limit Theorem and Standard Error

### Probability

- Independent and Dependent Events
- Compound Events
- Conditional and Binomial Probabilities
- Theoretical Probability
- Experimental Probability

**The Absolute Best Books for College Mathematics Placement Course**

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