## Course Content

The textbook is: **Precalculus,** 7th edition, by Larson, Hostetler.

##### The final exam is comprehensive.

### Exam 1 | Exam 2 | Exam 3

##### Chapters 1 and 2.1, 2.3, 2.4 and 2.5

Section 1.1 - Rectangular Coordinates
Section 1.2 - Graphs of Equations
Section 1.3 - Linear Equations in Two Variables
Section 1.4 - Functions
Section 1.5 - Analyzing Graphs of Functions
Section 1.6 - A Library of Parent Functions
Section 1.7 - Transformations of Functions
Section 1.8 - Combinations of Functions
Section 1.9 - Inverse Functions
Section 2.1 - Quadratic Functions and Models
Section 2.3 - Polynomials and Synthetic Division
Section 2.4 - Complex Numbers
Section 2.5 - Zeros of Polynomial Functions

- The Cartesian Plane
- Plotting Points in the Cartesian Plane
- Sketching a Scatter Plot
- The Pythagorean Theorem
- The Distance Formula
- Verifying a Right Triangle
- The Midpoint Formula
- Finding a Line Segment's Midpoint
- Translating Points in the Plane
- Using a Geometric Formula

- Determining Solutions
- Sketching the Graph of an Equation
- Finding x- and y- Intercepts
- Symmetry
- Testing for Symmetry
- Using Symmetry as a Sketching Aid
- Circles
- Finding the Equation of a Circle

- Using Slope
- The Slope-Intercept Form of the Equation of a Line
- Graphing a Linear Equation
- Finding the Slope of a Line
- Writing Linear Equations in Two Variables
- Parallel and Perpendicular Lines
- Using Slope as a Rate of Change

- Introduction to Functions
- Four Ways to Represent a Function
- Testing for a Function
- Function Notation
- Evaluating a Function
- A Piecewise-Defined Function
- The Domain of a Function
- The Range of a Function
- Difference Quotients

- The Graph of a Function
- Finding the Domain and Range of a Function
- Vertical Line Test for Functions
- Zeros of a Function
- Increasing and Decreasing Functions
- Definition of Relative Minimum and Maximum
- Average Rate of Change
- Even and Odd Functions

- Linear and Squaring Functions
- Constant Function
- Identity Function
- Cubic Functions
- Square Root Functions
- Reciprocal Functions
- Step Functions
- Piecewise-Define Functions
- Evaluating a Step Function
- Graphing a Piecewise-Defined Function

- Shifting Graphs
- Vertical and Horizontal Shifts
- Reflecting Graphs
- Nonrigid Transformations

- Arithmetic Combinations of Functions
- Find the Domains of Quotients of Functions
- Compositions of Functions
- Finding the Domain of a Composite Function
- Decomposing a Composite Function

- Finding Inverse Functions Informally
- Definition of Inverse Function
- Verifying Inverse Functions
- The Graph of an Inverse Function
- Finding Inverse Functions Graphically
- One-To-One Functions
- Applying the Horizontal Line Test
- Finding Inverse Functions Algebraically
- Finding an Inverse Function

- The Graph of a Quadratic Function
- Definition of a Quadratic Function
- Sketching Graphs of Quadratic Functions
- The Standard Form of a Quadratic Function
- Finding the Vertex and x-Intercepts of a Parabola
- Writing the Equation of a Parabola

- Long Division of Polynomials
- Synthetic Division of Polynomials
- The Remainder and Factor Theorems

- The Imaginary Unit i
- Definition of a Complex Number
- Operations with Complex Numbers
- Adding and Subtracting Complex Numbers
- Multiplying Complex Numbers
- Complex Conjugates
- Writing a Quotient of Complex Numbers in Standard Form
- Complex Solutions of Quadratic Equations

- The Fundamental Theorem of Algebra
- The Rational Zero Test
- Using the Rational Zero Test
- Conjugate Paris
- Factoring a Polynomial
- Using Descarte's Rule of Signs to Find the Zeros of a Polynomial

### Exam 2 | Exam 1 | Exam 3

##### Section 2.6, Chapters 3, 7 and 8

Section 2.6 - Rational Functions
Section 3.1 - Exponential Functions and their Graphs
Section 3.2 - Logarithmic Functions and their Graphs
Section 3.3 - Properties of Logarithms
Section 3.4 - Exponential and Logarithmic Equations
Section 3.5 - Exponential and Logarithmic Models
Section 7.1 - Linear and Nonlinear Systems of Equations
Section 7.2 - Two-Variable Linear Systems
Section 7.3 - Multivariable Linear Systems
Section 7.4 - Partial Fractions
Section 8.1 - Matrices and Systems of Equations
Section 8.2 - Operations with Matrices
Section 8.3 - The Inverse of a Square Matrix

- Finding the Domain of a Rational Function
- Horizontal and Vertical Asymptotes
- Analyzing Graphs of Rational Functions
- Sketching the Graphs of Rational Functions
- Rational Functions with Common Factors in the Numerator and Denominator
- Holes of a Rational Function

- Exponential Functions
- Evaluating Exponential Functions
- Graphs of Exponential Functions
- Transformation of Graphs of Exponential Functions
- The Nature Base e
- Compound Interest
- Radioactive Decay

- Logarithmic Functions
- Definition of Logarithmic Functions with Base e
- Evaluating Logarithmic Functions
- Properties of Logarithmic Functions
- Sketching the Graph of a Logarithmic Function
- Shifting Graphs of Logarithmic Functions
- The Natural Logarithmic Function
- Evaluating the Natural Logarithmic Function
- Find the Domains of Logarithmic Functions

- Change of Base
- Changing Bases Using Common Logarithms
- Changing Bases Using Natural Logarithms
- Properties of Logarithms
- Rewriting Logarithmic Expressions
- Condensing Logarithmic Expressions

- Solving Simple Equations
- Solving Exponential Equations
- Solving Logarithmic Equations

- Exponential Growth Model
- Exponential Decay Model
- Gaussian Model
- Logistic Growth Model
- Logarithmic Models
- Exponential Growth and Decay
- Modeling Populations Growth
- Carbon Dating

- Method of Substitution
- Solving a System by Substitution
- Graphical Approach to Finding Solutions

- The Method of Elimination
- Solving System of Equations Using Elimination
- Graphical Interpretation of Solutions

- Row-Echelon Form and Back-Substitution
- Using Back-Substitution in Row-Echelon Form
- Gaussian Elimination
- Using Gaussian Elimination to Solve a System of Equations Inconsistent System
- System with Infinite Solutions
- Nonsquare Systems
- Data Analysis: Curve Fitting

- Decomposition of Rational Expressions into Partial Fractions
- Repeated Linear Factors
- Distinct Linear and Quadratic Factors
- Repeated Quadratic Factors

- Matrices
- Order of Matrices
- Writing an Augmented Matrix
- Elementary Row Operations
- Row-Echelon Form and Reduced Row-Echelon Form
- Gaussian Elimination with Back-Substitution
- Gauss-Jordan Elimination

- Equality of Matrices
- Matrix Addition and Scalar Multiplication
- Properties of Matrix Addition and Scalar Multiplication
- Matrix Multiplication
- Finding the Product of Two Matrices
- Solving a System of Linear Equations Using Matrices

- The Inverse of a Matrix
- Finding Inverse Matrices
- The Inverse of a 2 x 2 Matrix
- Systems of Linear Equations
- Solving a System Using an Inverse

### Exam 3 | Exam 1 | Exam 2

##### Chapters 4, 5 and 6

Section 4.1 - Radian and Degree Measure
Section 4.2 - Trigonometry Functions: The Unit Circle
Section 4.3 - Right Triangle Trigonometry
Section 4.4 - Trigonometric Functions of Any Angle
Section 4.5 - Graphs of Sine and Cosine Functions
Section 4.6 - Graphs of Other Trigonometric Functions
Section 4.7 - Inverse Trigonometric Functions
Section 4.8 - Applications and Models
Section 5.1 - Using Fundamental Identities
Section 5.2 - Verifying Trigonometric Identities
Section 5.3 - Solving Trigonometric Equations
Section 5.4 - Sum and Difference Formulas
Section 5.5 - Multiple Angle and Product-to-Sum Formulas
Section 6.1 - Law of Sines
Section 6.2 - Law of Cosines

- Angles
- Radian Measure
- Coterminal Angles
- Complementary Angles
- Supplementary Angles
- Degree Measure
- Conversions Between Radian and Degree Measures
- Finding Arc Length
- Finding Linear Speed
- Finding Angular Speed
- Finding Area of a Circle

- The Unit Circle
- Sine Function
- Cosine Function
- Tangent Function
- Cosecant Function
- Secant Function
- Cotangent Function
- Evaluating Trigonometric Functions
- Domain and Period of Sine and Cosine Functions
- Definition of Periodic Function
- Even and Odd Trigonometric Functions

- The Six Trigonometric Functions
- Right Angle Definitions of Trigonometric Functions
- Right Triangles
- Right Triangles
- Trigonometric Identities
- Applying Trigonometric Identities

- Definition of Trigonometric Functions of Any Angle
- Trigonometric Functions of Quadrant angles
- Reference Angles
- Finding Reference Angles
- Trigonometric Functions of Real Numbers

- Basic Sine and Cosine Curves
- Amplitude and Period
- Vertical Shrinking and Stretching
- Period of Sine and Cosine Functions
- Horizontal Stretching
- Translations of Sine and Cosine Curves
- Horizontal Translations
- Vertical Translations
- Mathematical Modeling

- Graph of Tangent Functions
- Graphs of Reciprocal Functions
- Damped Trigonometric Graphs

- Inverse Sine Function
- Definition of Inverse Sine Function
- Evaluating the Inverse Sine Function
- Graphing the Inverse Sine Function
- Inverse Cosine Function
- Definition of Inverse Cosine Function
- Evaluating the Inverse Cosine Function
- Graphing the Inverse Cosine Function
- Inverse Tangent Function
- Definition of Inverse Tangent Function
- Evaluating the Inverse Tangent Function
- Graphing the Inverse Tangent Function
- Composition of Trigonometric Functions

- Solving a Right Triangle
- Finding the Side of a Right Triangle
- Finding an Acute Angle of a Right Triangle
- Trigonometry and Bearings
- Harmonic Motion

- Using Identities to Evaluate a Function
- Simplifying a Trigonometric Expression
- Factoring Trigonometric Expressions
- Rewriting Trigonometric Expressions
- Trigonometric Substitution

- Guidelines
- Working With Each Side Separately

- Factoring
- Equations of a Quadratic Type
- Converting to a Quadratic Type
- Using Inverse Functions

- Evaluating Trigonometric Functions
- Proving a Cofunction Identity
- Deriving Reduction Formulas
- Solving Trigonometric Equations

- Multiple-Angle Formulas
- Solving a Multiple-Angle Equation
- Using Double-Angle Formulas to Analyze Graphs
- Evaluating Functions Involving Double Angles
- Deriving a Triple-Angle Formula
- Reducing a Power
- Half-Angle Formulas
- Using a Half-Angle Formula
- Solving a Trigonometric Function Using Half-Angle Formulas
- Writing Products as Sums
- Using Sum-to-Product Formula

- Angle-Angle-Side (AAS)
- Angle-Side-Angle (ASA)
- The Ambiguous Case (SSA)
- Area of an Oblique Triangle

- Three Sides of a Triangle (SSS)
- Two Sides and The Included Angle (SAS)
- Heronís Area Formula