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
  • 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
Section 1.2 - Graphs of Equations
  • 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
Section 1.3 - Linear Equations in Two Variables
  • 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
Section 1.4 - Functions
  • 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
Section 1.5 - Analyzing Graphs of Functions
  • 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
Section 1.6 - A Library of Parent 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
Section 1.7 - Transformations of Functions
  • Shifting Graphs
  • Vertical and Horizontal Shifts
  • Reflecting Graphs
  • Nonrigid Transformations
Section 1.8 - Combinations of Functions
  • 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
Section 1.9 - Inverse Functions
  • 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
Section 2.1 - Quadratic Functions and Models
  • 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
Section 2.3 - Polynomials and Synthetic Division
  • Long Division of Polynomials
  • Synthetic Division of Polynomials
  • The Remainder and Factor Theorems
Section 2.4 - Complex Numbers
  • 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
Section 2.5 - Zeros of Polynomial Functions
  • 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
  • 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
Section 3.1 - Exponential Functions and their Graphs
  • Exponential Functions
  • Evaluating Exponential Functions
  • Graphs of Exponential Functions
  • Transformation of Graphs of Exponential Functions
  • The Nature Base e
  • Compound Interest
  • Radioactive Decay
Section 3.2 - Logarithmic Functions and their Graphs
  • 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
Section 3.3 - Properties of Logarithms
  • Change of Base
  • Changing Bases Using Common Logarithms
  • Changing Bases Using Natural Logarithms
  • Properties of Logarithms
  • Rewriting Logarithmic Expressions
  • Condensing Logarithmic Expressions
Section 3.4 - Exponential and Logarithmic Equations
  • Solving Simple Equations
  • Solving Exponential Equations
  • Solving Logarithmic Equations
Section 3.5 - Exponential and Logarithmic Models
  • Exponential Growth Model
  • Exponential Decay Model
  • Gaussian Model
  • Logistic Growth Model
  • Logarithmic Models
  • Exponential Growth and Decay
  • Modeling Populations Growth
  • Carbon Dating
Section 7.1 - Linear and Nonlinear Systems of Equations
  • Method of Substitution
  • Solving a System by Substitution
  • Graphical Approach to Finding Solutions
Section 7.2 - Two-Variable Linear Systems
  • The Method of Elimination
  • Solving System of Equations Using Elimination
  • Graphical Interpretation of Solutions
Section 7.3 - Multivariable Linear Systems
  • 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
Section 7.4 - Partial Fractions
  • Decomposition of Rational Expressions into Partial Fractions
  • Repeated Linear Factors
  • Distinct Linear and Quadratic Factors
  • Repeated Quadratic Factors
Section 8.1 - Matrices and Systems of Equations
  • 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
Section 8.2 - Operations with Matrices
  • 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
Section 8.3 - The Inverse of a Square Matrix
  • 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
  • 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
Section 4.2 - Trigonometry Functions: The Unit 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
Section 4.3 - Right Triangle Trigonometry
  • The Six Trigonometric Functions
  • Right Angle Definitions of Trigonometric Functions
  • Right Triangles
  • Right Triangles
  • Trigonometric Identities
  • Applying Trigonometric Identities
Section 4.4 - Trigonometric Functions of Any Angle
  • Definition of Trigonometric Functions of Any Angle
  • Trigonometric Functions of Quadrant angles
  • Reference Angles
  • Finding Reference Angles
  • Trigonometric Functions of Real Numbers
Section 4.5 - Graphs of Sine and Cosine Functions
  • 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
Section 4.6 - Graphs of Other Trigonometric Functions
  • Graph of Tangent Functions
  • Graphs of Reciprocal Functions
  • Damped Trigonometric Graphs
Section 4.7 - Inverse Trigonometric Functions
  • 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
Section 4.8 - Applications and Models
  • Solving a Right Triangle
  • Finding the Side of a Right Triangle
  • Finding an Acute Angle of a Right Triangle
  • Trigonometry and Bearings
  • Harmonic Motion
Section 5.1 - Using Fundamental Identities
  • Using Identities to Evaluate a Function
  • Simplifying a Trigonometric Expression
  • Factoring Trigonometric Expressions
  • Rewriting Trigonometric Expressions
  • Trigonometric Substitution
Section 5.2 - Verifying Trigonometric Identities
  • Guidelines
  • Working With Each Side Separately
Section 5.3 - Solving Trigonometric Equations
  • Factoring
  • Equations of a Quadratic Type
  • Converting to a Quadratic Type
  • Using Inverse Functions
Section 5.4 - Sum and Difference Formulas
  • Evaluating Trigonometric Functions
  • Proving a Cofunction Identity
  • Deriving Reduction Formulas
  • Solving Trigonometric Equations
Section 5.5 - Multiple Angle and Product-to-Sum Formulas
  • 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
Section 6.1 - Law of Sines
  • Angle-Angle-Side (AAS)
  • Angle-Side-Angle (ASA)
  • The Ambiguous Case (SSA)
  • Area of an Oblique Triangle
Section 6.2 - Law of Cosines
  • Three Sides of a Triangle (SSS)
  • Two Sides and The Included Angle (SAS)
  • Heronís Area Formula
Page last modified: 13 Oct 2011, 02:28 PM