# The Ultimate Precalculus Course (+FREE Worksheets & Tests)

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## Precalculus Complete Course

### Real Numbers and Relation

- Real Numbers
- Real Numbers Line
- Coordinate Plane
- Relation
- Showing the relation in the coordinate plane
- Domain and Range of Relation
- Functions
- Identifying the function from the graph
- Graphs of Basic Functions

### Vectors in Two Dimension

- Introduction to Vectors: Vectors in Two Dimensions
- Equality of Vectors in Two Dimensions
- Scalar Multiplication
- Vector addition and subtraction
- Representation of Addition and Subtraction
- Length of a Vector
- Dot Product and Cross Product
- Parallel vectors
- Orthogonal Vectors
- Parametric Equations and Graphs
- Applications of Vectors

### Equations and Inequalities

- Solving Multi-Step Equations
- Slope and Intercepts
- Using Intercepts
- Transforming Linear Functions
- Solving Inequalities
- Graphing Linear Inequalities
- Solving Compound Inequalities
- Solving Absolute Value Equations
- Solving Absolute Value Inequalities
- Graphing Absolute Value Inequalities
- Solving Systems of Equations
- Solving Special Systems
- Systems of Equations Word Problems

### Functions

- Evaluating Functions: Function Notation
- Modeling Real-world Situations with Functions
- Adding and Subtracting Functions
- Multiplying and Dividing Functions
- Composite Functions
- Real Zeros
- Average Rate of Changes
- Codomain

### Polynomial and Rational Functions

- The Simplest Functions: Constant and Identity
- Polynomial Functions
- Graphing Polynomial Functions
- Writing Polynomials in Standard Form
- Simplifying Polynomials
- Factoring Trinomials
- Solving a Quadratic Equation
- Graphing Quadratic Functions
- Solving Quadratic Inequalities
- Graphing Quadratic Inequalities
- Rational Equations
- Multiplying and Dividing Rational Expressions
- Simplifying Rational Expressions
- Rational Functions
- Graphing Rational Expressions

### Exponential Functions and Logarithms

- Exponential Functions: Definition and Properties
- Solving Exponential Equations
- Logarithmic Functions: Definition and Properties
- Evaluating Logarithms
- Properties of Logarithms
- Natural Logarithms
- Solving Logarithmic Equations

### Radical and absolute value Functions

- Simplifying Radical Expressions
- Simplifying Radical Expressions Involving Fractions
- Adding and Subtracting Radical Expressions
- Multiplying Radical Expressions
- Radical Equations
- Solving Radical Inequalities
- Domain and Range of Radical Functions
- Graphing Radical Functions
- Absolute Value Functions
- Graphing Absolute Value Functions
- Absolute Value Properties
- Floor Value
- Floor Function
- Graphing Floor Function

### Functions Operations

- Positive, Negative, Increasing and Decreasing Functions on Intervals
- Transformations of Functions
- Function Symmetry: Even and Odd
- End Behavior of Polynomial Functions
- One-to-One Function
- Identifying the function one by one from the graph
- Onto (Surjective) Functions
- Function Inverses
- Inverse Function Graph
- Inverse Variation
- Piecewise-defined Functions

### Trigonometry

- Degrees, Radians, and Angle Conversions
- Coterminal and Reference Angles
- Angles of Rotation and Unit Circle
- Arc length and Sector Area
- Sine, Cosine, and Tangent
- Reciprocal Functions: Cosecant, Secant, and Cotangent
- Domain and Range of Trigonometric Functions
- Arcsine, Arccosine, and Arctangent
- Applications of Inverse Trigonometric Function
- Fundamental Trigonometric Identities
- Pythagorean Trigonometric Identities
- Co-Function, Even-Odd, and Periodicity Identities
- Double Angle and Half-Angle Formulas
- Sum and Difference Formulas
- Product-to-Sum and Sum-to-Product Formulas

### Trigonometric Functions and Graphs

- 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

### Trigonometric Equations

- Basic Techniques for Solving Trigonometric Equations
- Factoring and Simplifying Trigonometric Expressions
- Solving Equations with Multiple Angles

### Trigonometric Applications

- Law of Sines: Definition and Applications
- Law of Cosines: Definition and Applications
- Area of a Triangle Using Trigonometry

### Analytic Geometry

- Distance and Midpoint Formulas
- Circles
- Finding the Center and the Radius of Circles
- Parabolas
- Finding the Focus, Vertex, and Directrix of a Parabola
- Ellipses
- Hyperbolas
- Classifying a Conic Section (in Standard Form)
- Rotation of Axes and General Form of Conic Sections

### Complex Numbers

- Polar Coordinate System
- Converting Between Polar and Rectangular Coordinates
- Introduction to Complex Numbers
- Adding and Subtracting Complex Numbers
- Multiplying and Dividing Complex Numbers
- Rationalizing Imaginary Denominators
- Polar Form of Complex Numbers
- Multiplying and Dividing in Polar Form
- Powers and Roots in Polar Form
- Graphs of Polar Equations

### Matrices

- Introduction to Matrices
- Matrix Addition and Subtraction
- Scalar Multiplication
- Matrix Multiplication
- Determinants of Matrices
- Inverse of a Matrix
- Solving Systems of Equations with Matrices

### Sequences and Series

- Sequence
- Recursive Formula
- Write a Formula for a Recursive Sequence
- Arithmetic Sequences
- Geometric Sequences
- Sigma Notation
- Arithmetic Series
- Finite Geometric Series
- Infinite Geometric Series
- Convergent and Divergent Series
- The th Term Test for Divergence
- Introduction to the Integral Test
- Comparison, Ratio, and Root Tests
- Alternating Series and Absolute Convergence
- Pascal’s Triangle
- The Binomial Theorem

### Limits

- Limits and Function Values
- One-Sided Limits
- Properties of Limits
- Detecting Limits from Graphs
- Nonexistence of Limits
- Calculation of limits of functions
- Indeterminate Form and Vague Limits
- Vague Limits by Change of Function’s Value
- Infinite Limits
- Limits at Infinity
- More about Limits at Infinity
- Removing Ambiguity in Infinite Limits
- Limits Involving Floor and Absolute Value Functions
- The Squeeze Theorem
- Asymptotes: Vertical, Horizontal and Oblique

### Continuity

- Continuity at a Point
- Continuity over an Interval
- Types of Continuity
- Properties of Continuity
- Intermediate Value Theorem
- Integral
- Integral Properties
- Basic Integral Formulas
- Definite Integral

### Statistics

- Venn diagrams
- Organizing Data
- Types of Data
- Frequency Table and Histograms
- Bar Chart
- Pie Graph
- Scatter Plots
- Mean, Median, Mode, and Range of the Given Data
- Data Distribution
- Measures of Dispersion
- Central Limit Theorem and Standard Error
- Box-and-Whisker Plots

### Statistics and Probability

- Theoretical Probability
- Experimental Probability
- Mutually Exclusive Events
- Independent and Dependent Events
- Compound Events
- Permutations and Combinations
- Conditional and Binomial Probabilities
- Random Variables
- Probability Mass Function
- Probability Density Functions
- Expected value and a Random Variable

**A Perfect Book ****for Acing ****Precalculus** **Course**

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