Grade-by-Grade Information
 
Home / CTYOnline / Courses / Mathematics

Honors Precalculus with Trigonometry

Placement Test Available
Enroll in this Course

Prerequisites: Qualifying math score and completion of Algebra II or the equivalent

Course Format: Individually Paced

Course Length: Typically 6 months

Recommended School Credit: 1.0 credit

Course Code: PRE

Course Description

Description

This course provides a mathematically sound preparation for students who intend to study Advanced Placement (AP) Calculus. It also prepares students for the SAT II Math IIC Achievement Test. The course focuses on the study of functions and their graphical characteristics, and covers topics normally taught in high school precalculus

Topics include:

  • fundamentals of advanced algebra
  • functions and their graphs
  • polynomial and rational functions
  • exponential and logarithmic functions
  • trigonometric functions
  • analytic trigonometry
  • applications of trigonometry
  • systems of equations and inequalities
  • matrices
  • induction
  • sequences and series

Timelines

This course offers 9-month, 6-month, and 3-month timelines as guidelines for students to follow in order to finish within their desired time frame.

Materials Needed

Graphing calculator required, such as:

  • TI-83 PLUS*
  • TI-84 PLUS
  • TI-85
  • TI-86

* Recommended

List of Topics

Relations and Functions

  • Using the Cartesian System
  • Thinking Visually
  • Finding the Distance between Two Points
  • Finding the Second Endpoint of a Segment
  • Collinearity and Distance
  • Triangles
  • Finding the Center-Radius Form of the Equation of a Circle
  • Finding the Center and Radius of a Circle
  • Decoding the Circle Formula
  • Solving Word Problems Involving Circles
  • Graphing Equations by Locating Points
  • Finding the x- and y-Intercepts of an Equation
  • Functions and the Vertical Line Test
  • Identifying Functions
  • Function Notation and Finding Function Values
  • Determining Intervals Over Which a Function Is Increasing
  • Evaluating Piecewise-Defined Functions for Given Values
  • Solving Word Problems Involving Functions
  • Finding the Domain and Range of a Function
  • Domain and Range: One Explicit Example
  • Satisfying the Domain of a Function
  • An Introduction to Slope
  • Finding the Slope of a Line Given Two Points
  • Interpreting Slope from a Graph
  • Graphing a Line Using Point and Slope
  • Writing an Equation in Slope-Intercept Form
  • Writing an Equation Given Two Points
  • Writing an Equation in Point-Slope Form
  • Matching a Slope-Intercept Equation with Its Graph
  • Slope for Parallel and Perpendicular Lines
  • Constructing Linear Function Models of Data
  • Linear Cost and Revenue Functions
  • Graphing Some Important Functions
  • Graphing Piecewise-Defined Functions
  • Matching Equations with Their Graphs
  • The Greatest Integer Function
  • Graphing the Greatest Integer Function
  • Deconstructing the Graph of a Quadratic Function
  • Nice-Looking Parabolas
  • Using Discriminants to Graph Parabolas
  • Maximum Height in the Real World
  • Finding the Vertex by Completing the Square
  • Using the Vertex to Write the Quadratic Equation
  • Finding the Maximum or Minimum of a Quadratic
  • Graphing Parabolas
  • Shifting Curves along Axes
  • Shifting or Translating Curves along Axes
  • Stretching a Graph
  • Graphing Quadratics Using Patterns
  • Determining Symmetry
  • Reflections
  • Reflecting Specific Functions
  • Using Operations on Functions
  • Composite Functions
  • Components of Composite Functions
  • Finding Functions That Form a Given Composite
  • Finding the Difference Quotient of a Function

Polynomial and Rational Functions

  • Using Long Division with Polynomials
  • Long Division: Another Example
  • Using Synthetic Division with Polynomials
  • More Synthetic Division
  • The Remainder Theorem
  • More on the Remainder Theorem
  • The Factor Theorem and Its Uses
  • Factoring a Polynomial Given a Zero
  • Presenting the Rational Zero Theorem
  • Considering Possible Solutions
  • Finding Polynomials Given Zeros, Degree, and One Point
  • Finding all Zeros and Multiplicities of a Polynomial
  • Finding the Real Zeros for a Polynomial
  • Using Descartes' Rule of Signs
  • Finding the Zeros of a Polynomial from Start to Finish
  • Matching Graphs to Polynomial Functions
  • Sketching the Graphs of Basic Polynomial Functions
  • Understanding Rational Functions
  • Basic Rational Functions
  • Vertical Asymptotes
  • Horizontal Asymptotes
  • Graphing Rational Functions
  • Graphing Rational Functions: More Examples

Exponential and Logarithmic Functions

  • Understanding Inverse Functions
  • The Horizontal Line Test
  • Are Two Functions Inverses of Each Other?
  • Graphing the Inverse
  • Finding the Inverse of a Function
  • Finding the Inverse of a Function with Higher Powers
  • An Introduction to Exponential Functions
  • Graphing Exponential Functions: Useful Patterns
  • Graphing Exponential Functions: More Examples
  • Using Properties of Exponents to Solve Exponential Equations
  • Finding Present Value and Future Value
  • Finding an Interest Rate to Match Given Goals
  • e
  • Applying Exponential Functions
  • An Introduction to Logarithmic Functions
  • Converting between Exponential and Logarithmic Functions
  • Finding the Value of a Logarithmic Function
  • Solving for x in Logarithmic Equations
  • Graphing Logarithmic Functions
  • Matching Logarithmic Functions with Their Graphs
  • Properties of Logarithms
  • Expanding a Logarithmic Expression Using Properties
  • Combining Logarithmic Expressions
  • Evaluating Logarithmic Functions Using a Calculator
  • Using the Change of Base Formula
  • The Richter Scale
  • The Distance Modulus Formula
  • Solving Exponential Equations
  • Solving Logarithmic Equations
  • Solving Equations with Logarithmic Exponents
  • Compound Interest
  • Predicting Change
  • An Introduction to Exponential Growth and Decay
  • Half-Life
  • Newton's Law of Cooling
  • Continuously Compounded Interest

Special Topics

  • An Introduction to Conic Sections
  • An Introduction to Parabolas
  • Determining Information about a Parabola from Its Equation
  • Writing an Equation for a Parabola
  • An Introduction to Ellipses
  • Finding the Equation for an Ellipse
  • Applying Ellipses: Satellites
  • An Introduction to Hyperbolas
  • Finding the Equation for a Hyperbola
  • Applying Hyperbolas: Navigation
  • Identifying a Conic
  • Name That Conic
  • Using the Binomial Theorem
  • Binomial Coefficients
  • Understanding Sequence Problems
  • Solving Problems Involving Arithmetic Sequences
  • Solving Problems Involving Geometric Sequences
  • Proving Formulas Using Mathematical Induction
  • Examples of Induction
  • Solving Problems Involving Permutations
  • Solving Problems Involving Combinations
  • Solving for Probability and Odds: Dice Rolls
  • Solving for Probability and Odds: Decks of Cards

The Trigonometric Functions

  • Finding the Quadrant in Which an Angle Lies
  • Finding Coterminal Angles
  • Finding the Complement and Supplement of an Angle
  • Converting between Degrees and Radians
  • Using the Arc Length Formula
  • An Introduction to the Trigonometric Functions
  • Evaluating Trigonometric Functions for an Angle in a Right Triangle
  • Finding an Angle Given the Value of a Trigonometric Function
  • Using Trigonometric Functions to Find Unknown Sides of Right Triangles
  • Finding the Height of a Building
  • Evaluating Trigonometric Functions for an Angle in the Coordinate Plane
  • Evaluating Trigonometric Functions Using the Reference Angle
  • Finding the Value of Trigonometric Functions Given Information about the Values of Other Trigonometric Functions
  • Trigonometric Functions of Important Angles
  • An Introduction to the Graphs of Sine and Cosine Functions
  • Graphing Sine or Cosine Functions with Different Coefficients
  • Finding Maximum and Minimum Values and Zeros of Sine and Cosine
  • Solving Word Problems Involving Sine or Cosine Functions
  • Graphing Sine and Cosine Functions with Phase Shifts
  • Fancy Graphing: Changes in Period, Amplitude, Vertical Shift, and Phase Shift
  • Graphing the Tangent, Secant, Cosecant, and Cotangent Functions
  • Fancy Graphing: Tangent, Secant, Cosecant, and Cotangent
  • Identifying a Trigonometric Function from its Graph
  • An Introduction to Inverse Trigonometric Functions
  • Evaluating Inverse Trigonometric Functions
  • Solving an Equation Involving an Inverse Trigonometric Function
  • Evaluating the Composition of a Trigonometric Function and Its Inverse
  • Applying Trigonometric Functions: Is He Speeding?

Trigonometric Identities

  • Fundamental Trigonometric Identities
  • Finding All Function Values
  • Simplifying a Trigonometric Expression Using Trigonometric Identities
  • Simplifying Trigonometric Expressions Involving Fractions
  • Simplifying Products of Binomials Involving Trigonometric Functions
  • Factoring Trigonometric Expressions
  • Determining Whether a Trigonometric Function Is Odd, Even, or Neither
  • Proving an Identity
  • Proving an Identity: Other Examples
  • Solving Trigonometric Equations
  • Solving Trigonometric Equations by Factoring
  • Solving Trigonometric Equations with Coefficients in the Argument
  • Solving Trigonometric Equations Using the Quadratic Formula
  • Solving Word Problems Involving Trigonometric Equations
  • Identities for Sums and Differences of Angles
  • Using Sum and Difference Identities
  • Using Sum and Difference Identities to Simplify an Expression
  • familyirming a Double-Angle Identity
  • Using Double-Angle Identities
  • Solving Word Problems Involving Multiple-Angle Identities
  • Using a Cofunction Identity
  • Using a Power-Reducing Identity
  • Using Half-Angle Identities to Solve a Trigonometric Equation

Applications of Trigonometric

  • The Law of Sines
  • Solving a Triangle Given Two Sides and One Angle
  • Solving a Triangle (SAS): Another Example
  • The Law of Sines: An Application
  • The Law of Cosines
  • The Law of Cosines (SSS)
  • The Law of Cosines (SAS): An Application
  • Heron's Formula
  • An Introduction to Vectors
  • Finding the Magnitude and Direction of a Vector
  • Vector Addition and Scalar Multiplication
  • Finding the Components of a Vector
  • Finding a Unit Vector
  • Solving Word Problems Involving Velocity or Forces
  • Graphing a Complex Number and Finding Its Absolute Value
  • Expressing a Complex Number in Trigonometric or Polar Form
  • Multiplying and Dividing Complex Numbers in Trigonometric or Polar Form
  • Using DeMoivre's Theorem to Raise a Complex Number to a Power
  • Roots of Complex Numbers
  • More Roots of Complex Numbers
  • Roots of Unity
  • An Introduction to Polar Coordinates
  • Converting between Polar and Rectangular Coordinates
  • Graphing Simple Polar Equations

Systems of Equations and Matrices

  • An Introduction to Linear Systems
  • Solving a System by Substitution
  • Solving a System by Elimination
  • An Introduction to Linear Systems in Three Variables
  • Solving Linear Systems in Three Variables
  • Solving Inconsistent Systems
  • Solving Dependent Systems
  • Solving Systems with Two Equations
  • Investments
  • Solving with Partial Fractions
  • Solving Nonlinear Systems Using Elimination
  • Solving Nonlinear Systems by Substitution
  • An Introduction to Matrices
  • The Arithmetic of Matrices
  • Multiplying Matrices by a Scalar
  • Multiplying Matrices
  • Can They Multiply?
  • Using the Gauss-Jordan Method
  • Using Gauss-Jordan: Another Example
  • Evaluating 2x2 Determinants
  • Evaluating 3x3 Determinants
  • Applying Determinants
  • Using Cramer's Rule
  • Using Cramer's Rule in a 3x3 Matrix
  • An Introduction to Inverses
  • Inverses: 2x2 Matrices
  • Another Look at 2x2 Inverses
  • Inverses: 3x3 Matrices
  • Solving a System of Equations with Inverses
  • An Introduction to Systems of Inequalities
  • Graphing Systems of Inequalities
  • Graphing the Solution Set of a System of Inequalities
  • Solving for Maxima-Minima
  • Applying Linear Programming

Back to top

System Requirements

CTYOnline courses require a properly-maintained computer with Internet access and a recent-version web browser (such as Firefox, Safari, or Internet Explorer) with the Adobe Flash plugin. Students are expected to be familiar with standard computer operations (e.g. login, cut & paste, email attachments, etc).

This course requires high-speed Internet access (such as Cable or DSL) for online lesson videos. Your browser will need to allow javascript, login cookies, and popup windows from ctyjhu.org, bluejay.cty.jhu.edu, and any other course web sites.

You may also need the Java Runtime Environment.

9 Month, 6 Month, and 3 Month Timelines

Timelines

 Honors Precalculus - 9 Month Timeline

Week 1

  • 1.1.1 Using the Cartesian System
  • 1.1.2 Thinking Visually
  • 1.2.1 Finding the Distance between Two Points
  • 1.2.2 Finding the Second Endpoint of a Segment
  • 1.3.1 Collinearity and Distance
  • 1.3.2 Triangles
  • 1.4.1 Finding the Center-Radius Form of the Equation of a Circle
  • 1.4.2 Finding the Center and Radius of a Circle
  • 1.4.3 Decoding the Circle Formula
  • 1.4.4 Solving Word Problems Involving Circles
  • 1.5.1 Graphing Equations by Locating Points
  • 1.5.2 Finding the x- and y-Intercepts of an Equation
  • 1.6.1 Functions and the Vertical Line Test
  • 1.6.2 Identifying Functions
  • 1.6.3 Function Notation and Finding Function Values
  • 1.7.1 Determining Intervals Over Which a Function Is Increasing
  • 1.7.2 Evaluating Piecewise-Defined Functions for Given Values
  • 1.7.3 Solving Word Problems Involving Functions

Week 2

  • 1.8.1 Finding the Domain and Range of a Function
  • 1.8.2 Domain and Range: One Explicit Example
  • 1.8.3 Satisfying the Domain of a Function
  • 1.9.1 An Introduction to Slope
  • 1.9.2 Finding the Slope of a Line Given Two Points
  • 1.9.3 Interpreting Slope from a Graph
  • 1.9.4 Graphing a Line Using Point and Slope
  • 1.10.1 Writing an Equation in Slope-Intercept Form
  • 1.10.2 Writing an Equation Given Two Points
  • 1.10.3 Writing an Equation in Point-Slope Form
  • 1.10.4 Matching a Slope-Intercept Equation with Its Graph
  • 1.10.5 Slope for Parallel and Perpendicular Lines
  • 1.11.1 Constructing Linear Function Models of Data
  • 1.11.2 Linear Cost and Revenue Functions
  • 1.12.1 Graphing Some Important Functions
  • 1.12.2 Graphing Piecewise-Defined Functions
  • 1.12.3 Matching Equations with Their Graphs

Week 3

  • 1.13.1 The Greatest Integer Function
  • 1.13.2 Graphing the Greatest Integer Function
  • 1.14.1 Deconstructing the Graph of a Quadratic Function
  • 1.14.2 Nice-Looking Parabolas
  • 1.14.3 Using Discriminants to Graph Parabolas
  • 1.14.4 Maximum Height in the Real World
  • 1.15.1 Finding the Vertex by Completing the Square
  • 1.15.2 Using the Vertex to Write the Quadratic Equation
  • 1.15.3 Finding the Maximum or Minimum of a Quadratic
  • 1.15.4 Graphing Parabolas

Week 4

  • 1.16.1 Shifting Curves along Axes
  • 1.16.2 Shifting or Translating Curves along Axes
  • 1.16.3 Stretching a Graph
  • 1.16.4 Graphing Quadratics Using Patterns
  • 1.17.1 Determining Symmetry
  • 1.17.2 Reflections
  • 1.17.3 Reflecting Specific Functions
  • 1.18.1 Using Operations on Functions
  • 1.18.2 Composite Functions
  • 1.18.3 Components of Composite Functions
  • 1.18.4 Finding Functions That Form a Given Composite
  • 1.18.5 Finding the Difference Quotient of a Function
  • Chapter 1 Test

Week 5

  • 2.1.1 Using Long Division with Polynomials
  • 2.1.2 Long Division: Another Example
  • 2.2.1 Using Synthetic Division with Polynomials
  • 2.2.2 More Synthetic Division
  • 2.3.1 The Remainder Theorem
  • 2.3.2 More on the Remainder Theorem
  • 2.4.1 The Factor Theorem and Its Uses
  • 2.4.2 Factoring a Polynomial Given a Zero

Week 6

  • 2.5.1 Presenting the Rational Zero Theorem
  • 2.5.2 Considering Possible Solutions
  • 2.6.1 Finding Polynomials Given Zeros, Degree, and One Point
  • 2.6.2 Finding all Zeros and Multiplicities of a Polynomial
  • 2.6.3 Finding the Real Zeros for a Polynomial
  • 2.6.4 Using Descartes' Rule of Signs
  • 2.6.5 Finding the Zeros of a Polynomial from Start to Finish
  • 2.7.1 Matching Graphs to Polynomial Functions
  • 2.7.2 Sketching the Graphs of Basic Polynomial Functions

Week 7

  • 2.8.1 Understanding Rational Functions
  • 2.8.2 Basic Rational Functions
  • 2.9.1 Vertical Asymptotes
  • 2.9.2 Horizontal Asymptotes
  • 2.9.3 Graphing Rational Functions
  • 2.9.4 Graphing Rational Functions: More Examples
  • Chapter 2 Test

Week 8

  • 3.1.1 Understanding Inverse Functions
  • 3.1.2 The Horizontal Line Test
  • 3.1.3 Are Two Functions Inverses of Each Other?
  • 3.1.4 Graphing the Inverse
  • 3.2.1 Finding the Inverse of a Function
  • 3.2.2 Finding the Inverse of a Function with Higher Powers
  • 3.3.1 An Introduction to Exponential Functions
  • 3.3.2 Graphing Exponential Functions: Useful Patterns
  • 3.3.3 Graphing Exponential Functions: More Examples

Week 9

  • 3.4.1 Using Properties of Exponents to Solve Exponential Equations
  • 3.4.2 Finding Present Value and Future Value
  • 3.4.3 Finding an Interest Rate to Match Given Goals
  • 3.5.1 e
  • 3.5.2 Applying Exponential Functions
  • 3.6.1 An Introduction to Logarithmic Functions
  • 3.6.2 Converting between Exponential and Logarithmic Functions
  • 3.7.1 Finding the Value of a Logarithmic Function
  • 3.7.2 Solving for x in Logarithmic Equations
  • 3.7.3 Graphing Logarithmic Functions
  • 3.7.4 Matching Logarithmic Functions with Their Graphs

Week 10

  • 3.8.1 Properties of Logarithms
  • 3.8.2 Expanding a Logarithmic Expression Using Properties
  • 3.8.3 Combining Logarithmic Expressions
  • 3.9.1 Evaluating Logarithmic Functions Using a Calculator
  • 3.9.2 Using the Change of Base Formula
  • 3.10.1 The Richter Scale
  • 3.10.2 The Distance Modulus Formula
  • 3.11.1 Solving Exponential Equations
  • 3.11.2 Solving Logarithmic Equations
  • 3.11.3 Solving Equations with Logarithmic Exponents

Week 11

  • 3.12.1 Compound Interest
  • 3.12.2 Predicting Change
  • 3.13.1 An Introduction to Exponential Growth and Decay
  • 3.13.2 Half-Life
  • 3.13.3 Newton's Law of Cooling
  • 3.13.4 Continuously Compounded Interest
  • Chapter 3 Test

Week 12

  • 4.1.1 An Introduction to Conic Sections
  • 4.1.2 An Introduction to Parabolas
  • 4.1.3 Determining Information about a Parabola from Its Equation
  • 4.1.4 Writing an Equation for a Parabola
  • 4.2.1 An Introduction to Ellipses
  • 4.2.2 Finding the Equation for an Ellipse
  • 4.2.3 Applying Ellipses: Satellites

Week 13

  • 4.3.1 An Introduction to Hyperbolas
  • 4.3.2 Finding the Equation for a Hyperbola
  • 4.3.3 Applying Hyperbolas: Navigation
  • 4.4.1 Identifying a Conic
  • 4.4.2 Name That Conic
  • 4.5.1 Using the Binomial Theorem
  • 4.5.2 Binomial Coefficients

Week 14

  • 4.6.1 Understanding Sequence Problems
  • 4.6.2 Solving Problems Involving Arithmetic Sequences
  • 4.6.3 Solving Problems Involving Geometric Sequences
  • 4.7.1 Proving Formulas Using Mathematical Induction
  • 4.7.2 Examples of Induction
  • 4.8.1 Solving Problems Involving Permutations
  • 4.8.2 Solving Problems Involving Combinations
  • 4.8.3 Solving for Probability and Odds: Dice Rolls
  • 4.8.4 Solving for Probability and Odds: Decks of Cards

Week 15

  • Chapter 4 Test
  • Midterm Exam

Week 16

  • 5.1.1 Finding the Quadrant in Which an Angle Lies
  • 5.1.2 Finding Coterminal Angles
  • 5.1.3 Finding the Complement and Supplement of an Angle
  • 5.1.4 Converting between Degrees and Radians
  • 5.1.5 Using the Arc Length Formula

Week 17

  • 5.2.1 An Introduction to the Trigonometric Functions
  • 5.2.2 Evaluating Trigonometric Functions for an Angle in a Right Triangle
  • 5.2.3 Finding an Angle Given the Value of a Trigonometric Function
  • 5.2.4 Using Trigonometric Functions to Find Unknown Sides of Right Triangles
  • 5.2.5 Finding the Height of a Building

Week 18

  • 5.3.1 Evaluating Trigonometric Functions for an Angle in the Coordinate Plane
  • 5.3.2 Evaluating Trigonometric Functions Using the Reference Angle
  • 5.3.3 Finding the Value of Trigonometric Functions Given Information about the Values of Other Trigonometric Functions
  • 5.3.4 Trigonometric Functions of Important Angles

Week 19

  • 5.4.1 An Introduction to the Graphs of Sine and Cosine Functions
  • 5.4.2 Graphing Sine or Cosine Functions with Different Coefficients
  • 5.4.3 Finding Maximum and Minimum Values and Zeros of Sine and Cosine
  • 5.4.4 Solving Word Problems Involving Sine or Cosine Functions

Week 20

  • 5.5.1 Graphing Sine and Cosine Functions with Phase Shifts
  • 5.5.2 Fancy Graphing: Changes in Period, Amplitude, Vertical Shift, and Phase Shift
  • 5.6.1 Graphing the Tangent, Secant, Cosecant, and Cotangent Functions
  • 5.6.2 Fancy Graphing: Tangent, Secant, Cosecant, and Cotangent
  • 5.6.3 Identifying a Trigonometric Function from its Graph

Week 21

  • 5.7.1 An Introduction to Inverse Trigonometric Functions
  • 5.7.2 Evaluating Inverse Trigonometric Functions
  • 5.7.3 Solving an Equation Involving an Inverse Trigonometric Function
  • 5.7.4 Evaluating the Composition of a Trigonometric Function and Its Inverse
  • 5.7.5 Applying Trigonometric Functions: Is He Speeding?
  • Chapter 5 Test

Week 22

  • 6.1.1 Fundamental Trigonometric Identities
  • 6.1.2 Finding All Function Values
  • 6.2.1 Simplifying a Trigonometric Expression Using Trigonometric Identities
  • 6.2.2 Simplifying Trigonometric Expressions Involving Fractions
  • 6.2.3 Simplifying Products of Binomials Involving Trigonometric Functions
  • 6.2.4 Factoring Trigonometric Expressions
  • 6.2.5 Determining Whether a Trigonometric Function Is Odd, Even, or Neither

Week 23

  • 6.3.1 Proving an Identity
  • 6.3.2 Proving an Identity: Other Examples
  • 6.4.1 Solving Trigonometric Equations
  • 6.4.2 Solving Trigonometric Equations by Factoring
  • 6.4.3 Solving Trigonometric Equations with Coefficients in the Argument
  • 6.4.4 Solving Trigonometric Equations Using the Quadratic Formula
  • 6.4.5 Solving Word Problems Involving Trigonometric Equations

Week 24

  • 6.5.1 Identities for Sums and Differences of Angles
  • 6.5.2 Using Sum and Difference Identities
  • 6.5.3 Using Sum and Difference Identities to Simplify an Expression
  • 6.6.1 familyirming a Double-Angle Identity
  • 6.6.2 Using Double-Angle Identities
  • 6.6.3 Solving Word Problems Involving Multiple-Angle Identities

Week 25

  • 6.7.1 Using a Cofunction Identity
  • 6.7.2 Using a Power-Reducing Identity
  • 6.7.3 Using Half-Angle Identities to Solve a Trigonometric Equation
  • Chapter 6 Test

Week 26

  • 7.1.1 The Law of Sines
  • 7.1.2 Solving a Triangle Given Two Sides and One Angle
  • 7.1.3 Solving a Triangle (SAS): Another Example
  • 7.1.4 The Law of Sines: An Application

Week 27

  • 7.2.1 The Law of Cosines
  • 7.2.2 The Law of Cosines (SSS)
  • 7.2.3 The Law of Cosines (SAS): An Application
  • 7.2.4 Heron's Formula

Week 28

  • 7.3.1 An Introduction to Vectors
  • 7.3.2 Finding the Magnitude and Direction of a Vector
  • 7.3.3 Vector Addition and Scalar Multiplication
  • 7.4.1 Finding the Components of a Vector
  • 7.4.2 Finding a Unit Vector
  • 7.4.3 Solving Word Problems Involving Velocity or Forces

Week 29

  • 7.5.1 Graphing a Complex Number and Finding Its Absolute Value
  • 7.5.2 Expressing a Complex Number in Trigonometric or Polar Form
  • 7.5.3 Multiplying and Dividing Complex Numbers in Trigonometric or Polar Form
  • 7.6.1 Using DeMoivre's Theorem to Raise a Complex Number to a Power
  • 7.6.2 Roots of Complex Numbers

Week 30

  • 7.6.3 More Roots of Complex Numbers
  • 7.6.4 Roots of Unity
  • 7.7.1 An Introduction to Polar Coordinates
  • 7.7.2 Converting between Polar and Rectangular Coordinates
  • 7.7.3 Graphing Simple Polar Equations
  • Chapter 7 Test

Week 31

  • 8.1.1 An Introduction to Linear Systems
  • 8.1.2 Solving a System by Substitution
  • 8.1.3 Solving a System by Elimination
  • 8.2.1 An Introduction to Linear Systems in Three Variables

Week 32

  • 8.2.2 Solving Linear Systems in Three Variables
  • 8.2.3 Solving Inconsistent Systems
  • 8.2.4 Solving Dependent Systems
  • 8.2.5 Solving Systems with Two Equations

Week 33

  • 8.3.1 Investments
  • 8.3.2 Solving with Partial Fractions
  • 8.4.1 Solving Nonlinear Systems Using Elimination
  • 8.4.2 Solving Nonlinear Systems by Substitution

Week 34

  • 8.5.1 An Introduction to Matrices
  • 8.5.2 The Arithmetic of Matrices
  • 8.5.3 Multiplying Matrices by a Scalar
  • 8.5.4 Multiplying Matrices
  • 8.5.5 Can They Multiply?

Week 35

  • 8.6.1 Using the Gauss-Jordan Method
  • 8.6.2 Using Gauss-Jordan: Another Example
  • 8.7.1 Evaluating 2x2 Determinants
  • 8.7.2 Evaluating 3x3 Determinants
  • 8.7.3 Applying Determinants

Week 36

  • 8.8.1 Using Cramer's Rule
  • 8.8.2 Using Cramer's Rule in a 3x3 Matrix
  • 8.9.1 An Introduction to Inverses
  • 8.9.2 Inverses: 2x2 Matrices
  • 8.9.3 Another Look at 2x2 Inverses
  • 8.9.4 Inverses: 3x3 Matrices
  • 8.9.5 Solving a System of Equations with Inverses

Week 37

  • 8.10.1 An Introduction to Systems of Inequalities
  • 8.10.2 Graphing Systems of Inequalities
  • 8.10.3 Graphing the Solution Set of a System of Inequalities
  • 8.11.1 Solving for Maxima-Minima
  • 8.11.2 Applying Linear Programming

Week 38

  • Chapter 8 Test
  • Practice Exam

Week 39

  • Final Exam

Back to top

Honors Precalculus - 6 Month Timeline

Week 1

  • 1.1.1 Using the Cartesian System
  • 1.1.2 Thinking Visually
  • 1.2.1 Finding the Distance between Two Points
  • 1.2.2 Finding the Second Endpoint of a Segment
  • 1.3.1 Collinearity and Distance
  • 1.3.2 Triangles
  • 1.4.1 Finding the Center-Radius Form of the Equation of a Circle
  • 1.4.2 Finding the Center and Radius of a Circle
  • 1.4.3 Decoding the Circle Formula
  • 1.4.4 Solving Word Problems Involving Circles
  • 1.5.1 Graphing Equations by Locating Points
  • 1.5.2 Finding the x- and y-Intercepts of an Equation
  • 1.6.1 Functions and the Vertical Line Test
  • 1.6.2 Identifying Functions
  • 1.6.3 Function Notation and Finding Function Values
  • 1.7.1 Determining Intervals Over Which a Function Is Increasing
  • 1.7.2 Evaluating Piecewise-Defined Functions for Given Values
  • 1.7.3 Solving Word Problems Involving Functions
  • 1.8.1 Finding the Domain and Range of a Function
  • 1.8.2 Domain and Range: One Explicit Example
  • 1.8.3 Satisfying the Domain of a Function
  • 1.9.1 An Introduction to Slope
  • 1.9.2 Finding the Slope of a Line Given Two Points
  • 1.9.3 Interpreting Slope from a Graph
  • 1.9.4 Graphing a Line Using Point and Slope

Week 2

  • 1.10.1 Writing an Equation in Slope-Intercept Form
  • 1.10.2 Writing an Equation Given Two Points
  • 1.10.3 Writing an Equation in Point-Slope Form
  • 1.10.4 Matching a Slope-Intercept Equation with Its Graph
  • 1.10.5 Slope for Parallel and Perpendicular Lines
  • 1.11.1 Constructing Linear Function Models of Data
  • 1.11.2 Linear Cost and Revenue Functions
  • 1.12.1 Graphing Some Important Functions
  • 1.12.2 Graphing Piecewise-Defined Functions
  • 1.12.3 Matching Equations with Their Graphs
  • 1.13.1 The Greatest Integer Function
  • 1.13.2 Graphing the Greatest Integer Function
  • 1.14.1 Deconstructing the Graph of a Quadratic Function
  • 1.14.2 Nice-Looking Parabolas
  • 1.14.3 Using Discriminants to Graph Parabolas
  • 1.14.4 Maximum Height in the Real World

Week 3

  • 1.15.1 Finding the Vertex by Completing the Square
  • 1.15.2 Using the Vertex to Write the Quadratic Equation
  • 1.15.3 Finding the Maximum or Minimum of a Quadratic
  • 1.15.4 Graphing Parabolas
  • 1.16.1 Shifting Curves along Axes
  • 1.16.2 Shifting or Translating Curves along Axes
  • 1.16.3 Stretching a Graph
  • 1.16.4 Graphing Quadratics Using Patterns
  • 1.17.1 Determining Symmetry
  • 1.17.2 Reflections
  • 1.17.3 Reflecting Specific Functions
  • 1.18.1 Using Operations on Functions
  • 1.18.2 Composite Functions
  • 1.18.3 Components of Composite Functions
  • 1.18.4 Finding Functions That Form a Given Composite
  • 1.18.5 Finding the Difference Quotient of a Function
  • Chapter 1 Test

Week 4

  • 2.1.1 Using Long Division with Polynomials
  • 2.1.2 Long Division: Another Example
  • 2.2.1 Using Synthetic Division with Polynomials
  • 2.2.2 More Synthetic Division
  • 2.3.1 The Remainder Theorem
  • 2.3.2 More on the Remainder Theorem
  • 2.4.1 The Factor Theorem and Its Uses
  • 2.4.2 Factoring a Polynomial Given a Zero
  • 2.5.1 Presenting the Rational Zero Theorem
  • 2.5.2 Considering Possible Solutions
  • 2.6.1 Finding Polynomials Given Zeros, Degree, and One Point
  • 2.6.2 Finding all Zeros and Multiplicities of a Polynomial
  • 2.6.3 Finding the Real Zeros for a Polynomial
  • 2.6.4 Using Descartes' Rule of Signs
  • 2.6.5 Finding the Zeros of a Polynomial from Start to Finish

Week 5

  • 2.7.1 Matching Graphs to Polynomial Functions
  • 2.7.2 Sketching the Graphs of Basic Polynomial Functions
  • 2.8.1 Understanding Rational Functions
  • 2.8.2 Basic Rational Functions
  • 2.9.1 Vertical Asymptotes
  • 2.9.2 Horizontal Asymptotes
  • 2.9.3 Graphing Rational Functions
  • 2.9.4 Graphing Rational Functions: More Examples
  • Chapter 2 Test

Week 6

  • 3.1.1 Understanding Inverse Functions
  • 3.1.2 The Horizontal Line Test
  • 3.1.3 Are Two Functions Inverses of Each Other?
  • 3.1.4 Graphing the Inverse
  • 3.2.1 Finding the Inverse of a Function
  • 3.2.2 Finding the Inverse of a Function with Higher Powers
  • 3.3.1 An Introduction to Exponential Functions
  • 3.3.2 Graphing Exponential Functions: Useful Patterns
  • 3.3.3 Graphing Exponential Functions: More Examples
  • 3.4.1 Using Properties of Exponents to Solve Exponential Equations
  • 3.4.2 Finding Present Value and Future Value
  • 3.4.3 Finding an Interest Rate to Match Given Goals

Week 7

  • 3.5.1 e
  • 3.5.2 Applying Exponential Functions
  • 3.6.1 An Introduction to Logarithmic Functions
  • 3.6.2 Converting between Exponential and Logarithmic Functions
  • 3.7.1 Finding the Value of a Logarithmic Function
  • 3.7.2 Solving for x in Logarithmic Equations
  • 3.7.3 Graphing Logarithmic Functions
  • 3.7.4 Matching Logarithmic Functions with Their Graphs
  • 3.8.1 Properties of Logarithms
  • 3.8.2 Expanding a Logarithmic Expression Using Properties
  • 3.8.3 Combining Logarithmic Expressions
  • 3.9.1 Evaluating Logarithmic Functions Using a Calculator
  • 3.9.2 Using the Change of Base Formula

Week 8

  • 3.10.1 The Richter Scale
  • 3.10.2 The Distance Modulus Formula
  • 3.11.1 Solving Exponential Equations
  • 3.11.2 Solving Logarithmic Equations
  • 3.11.3 Solving Equations with Logarithmic Exponents
  • 3.12.1 Compound Interest
  • 3.12.2 Predicting Change
  • 3.13.1 An Introduction to Exponential Growth and Decay
  • 3.13.2 Half-Life
  • 3.13.3 Newton's Law of Cooling
  • 3.13.4 Continuously Compounded Interest
  • Chapter 3 Test

Week 9

  • 4.1.1 An Introduction to Conic Sections
  • 4.1.2 An Introduction to Parabolas
  • 4.1.3 Determining Information about a Parabola from Its Equation
  • 4.1.4 Writing an Equation for a Parabola
  • 4.2.1 An Introduction to Ellipses
  • 4.2.2 Finding the Equation for an Ellipse
  • 4.2.3 Applying Ellipses: Satellites
  • 4.3.1 An Introduction to Hyperbolas
  • 4.3.2 Finding the Equation for a Hyperbola
  • 4.3.3 Applying Hyperbolas: Navigation

Week 10

  • 4.4.1 Identifying a Conic
  • 4.4.2 Name That Conic
  • 4.5.1 Using the Binomial Theorem
  • 4.5.2 Binomial Coefficients
  • 4.6.1 Understanding Sequence Problems
  • 4.6.2 Solving Problems Involving Arithmetic Sequences
  • 4.6.3 Solving Problems Involving Geometric Sequences

Week 11

  • 4.7.1 Proving Formulas Using Mathematical Induction
  • 4.7.2 Examples of Induction
  • 4.8.1 Solving Problems Involving Permutations
  • 4.8.2 Solving Problems Involving Combinations
  • 4.8.3 Solving for Probability and Odds: Dice Rolls
  • 4.8.4 Solving for Probability and Odds: Decks of Cards
  • Chapter 4 Test
  • Review
  • Midterm Exam

Week 12

  • 5.1.1 Finding the Quadrant in Which an Angle Lies
  • 5.1.2 Finding Coterminal Angles
  • 5.1.3 Finding the Complement and Supplement of an Angle
  • 5.1.4 Converting between Degrees and Radians
  • 5.1.5 Using the Arc Length Formula
  • 5.2.1 An Introduction to the Trigonometric Functions
  • 5.2.2 Evaluating Trigonometric Functions for an Angle in a Right Triangle
  • 5.2.3 Finding an Angle Given the Value of a Trigonometric Function
  • 5.2.4 Using Trigonometric Functions to Find Unknown Sides of Right Triangles
  • 5.2.5 Finding the Height of a Building

Week 13

  • 5.3.1 Evaluating Trigonometric Functions for an Angle in the Coordinate Plane
  • 5.3.2 Evaluating Trigonometric Functions Using the Reference Angle
  • 5.3.3 Finding the Value of Trigonometric Functions Given Information about the Values of Other Trigonometric Functions
  • 5.3.4 Trigonometric Functions of Important Angles
  • 5.4.1 An Introduction to the Graphs of Sine and Cosine Functions
  • 5.4.2 Graphing Sine or Cosine Functions with Different Coefficients
  • 5.4.3 Finding Maximum and Minimum Values and Zeros of Sine and Cosine
  • 5.4.4 Solving Word Problems Involving Sine or Cosine Functions
  • 5.5.1 Graphing Sine and Cosine Functions with Phase Shifts
  • 5.5.2 Fancy Graphing: Changes in Period, Amplitude, Vertical Shift, and Phase Shift

Week 14

  • 5.6.1 Graphing the Tangent, Secant, Cosecant, and Cotangent Functions
  • 5.6.2 Fancy Graphing: Tangent, Secant, Cosecant, and Cotangent
  • 5.6.3 Identifying a Trigonometric Function from its Graph
  • 5.7.1 An Introduction to Inverse Trigonometric Functions
  • 5.7.2 Evaluating Inverse Trigonometric Functions
  • 5.7.3 Solving an Equation Involving an Inverse Trigonometric Function
  • 5.7.4 Evaluating the Composition of a Trigonometric Function and Its Inverse
  • 5.7.5 Applying Trigonometric Functions: Is He Speeding?
  • Chapter 5 Test

Week 15

  • 6.1.1 Fundamental Trigonometric Identities
  • 6.1.2 Finding All Function Values
  • 6.2.1 Simplifying a Trigonometric Expression Using Trigonometric Identities
  • 6.2.2 Simplifying Trigonometric Expressions Involving Fractions
  • 6.2.3 Simplifying Products of Binomials Involving Trigonometric Functions
  • 6.2.4 Factoring Trigonometric Expressions
  • 6.2.5 Determining Whether a Trigonometric Function Is Odd, Even, or Neither
  • 6.3.1 Proving an Identity
  • 6.3.2 Proving an Identity: Other Examples

Week 16

  • 6.4.1 Solving Trigonometric Equations
  • 6.4.2 Solving Trigonometric Equations by Factoring
  • 6.4.3 Solving Trigonometric Equations with Coefficients in the Argument
  • 6.4.4 Solving Trigonometric Equations Using the Quadratic Formula
  • 6.4.5 Solving Word Problems Involving Trigonometric Equations
  • 6.5.1 Identities for Sums and Differences of Angles
  • 6.5.2 Using Sum and Difference Identities
  • 6.5.3 Using Sum and Difference Identities to Simplify an Expression

Week 17

  • 6.6.1 familyirming a Double-Angle Identity
  • 6.6.2 Using Double-Angle Identities
  • 6.6.3 Solving Word Problems Involving Multiple-Angle Identities
  • 6.7.1 Using a Cofunction Identity
  • 6.7.2 Using a Power-Reducing Identity
  • 6.7.3 Using Half-Angle Identities to Solve a Trigonometric Equation
  • Chapter 6 Test

Week 18

  • 7.1.1 The Law of Sines
  • 7.1.2 Solving a Triangle Given Two Sides and One Angle
  • 7.1.3 Solving a Triangle (SAS): Another Example
  • 7.1.4 The Law of Sines: An Application
  • 7.2.1 The Law of Cosines
  • 7.2.2 The Law of Cosines (SSS)
  • 7.2.3 The Law of Cosines (SAS): An Application
  • 7.2.4 Heron's Formula

Week 19

  • 7.3.1 An Introduction to Vectors
  • 7.3.2 Finding the Magnitude and Direction of a Vector
  • 7.3.3 Vector Addition and Scalar Multiplication
  • 7.4.1 Finding the Components of a Vector
  • 7.4.2 Finding a Unit Vector
  • 7.4.3 Solving Word Problems Involving Velocity or Forces
  • 7.5.1 Graphing a Complex Number and Finding Its Absolute Value
  • 7.5.2 Expressing a Complex Number in Trigonometric or Polar Form
  • 7.5.3 Multiplying and Dividing Complex Numbers in Trigonometric or Polar Form

Week 20

  • 7.6.1 Using DeMoivre's Theorem to Raise a Complex Number to a Power
  • 7.6.2 Roots of Complex Numbers
  • 7.6.3 More Roots of Complex Numbers
  • 7.6.4 Roots of Unity
  • 7.7.1 An Introduction to Polar Coordinates
  • 7.7.2 Converting between Polar and Rectangular Coordinates
  • 7.7.3 Graphing Simple Polar Equations
  • Chapter 7 Test

Week 21

  • 8.1.1 An Introduction to Linear Systems
  • 8.1.2 Solving a System by Substitution
  • 8.1.3 Solving a System by Elimination
  • 8.2.1 An Introduction to Linear Systems in Three Variables
  • 8.2.2 Solving Linear Systems in Three Variables
  • 8.2.3 Solving Inconsistent Systems
  • 8.2.4 Solving Dependent Systems
  • 8.2.5 Solving Systems with Two Equations

Week 22

  • 8.3.1 Investments
  • 8.3.2 Solving with Partial Fractions
  • 8.4.1 Solving Nonlinear Systems Using Elimination
  • 8.4.2 Solving Nonlinear Systems by Substitution
  • 8.5.1 An Introduction to Matrices
  • 8.5.2 The Arithmetic of Matrices
  • 8.5.3 Multiplying Matrices by a Scalar
  • 8.5.4 Multiplying Matrices
  • 8.5.5 Can They Multiply?

Week 23

  • 8.6.1 Using the Gauss-Jordan Method
  • 8.6.2 Using Gauss-Jordan: Another Example
  • 8.7.1 Evaluating 2x2 Determinants
  • 8.7.2 Evaluating 3x3 Determinants
  • 8.7.3 Applying Determinants
  • 8.8.1 Using Cramer's Rule
  • 8.8.2 Using Cramer's Rule in a 3x3 Matrix

Week 24

  • 8.9.1 An Introduction to Inverses
  • 8.9.2 Inverses: 2x2 Matrices
  • 8.9.3 Another Look at 2x2 Inverses
  • 8.9.4 Inverses: 3x3 Matrices
  • 8.9.5 Solving a System of Equations with Inverses
  • 8.10.1 An Introduction to Systems of Inequalities
  • 8.10.2 Graphing Systems of Inequalities
  • 8.10.3 Graphing the Solution Set of a System of Inequalities
  • 8.11.1 Solving for Maxima-Minima
  • 8.11.2 Applying Linear Programming
  • Chapter 8 Test

Week 25

  • Chapter Make Up & Review

Week 26

  • Final Exam

Back to top

Honors Precalculus - 3 Month Timeline

Week 1

  • 1.1.1 Using the Cartesian System
  • 1.1.2 Thinking Visually
  • 1.2.1 Finding the Distance between Two Points
  • 1.2.2 Finding the Second Endpoint of a Segment
  • 1.3.1 Collinearity and Distance
  • 1.3.2 Triangles
  • 1.4.1 Finding the Center-Radius Form of the Equation of a Circle
  • 1.4.2 Finding the Center and Radius of a Circle
  • 1.4.3 Decoding the Circle Formula
  • 1.4.4 Solving Word Problems Involving Circles
  • 1.5.1 Graphing Equations by Locating Points
  • 1.5.2 Finding the x- and y-Intercepts of an Equation
  • 1.6.1 Functions and the Vertical Line Test
  • 1.6.2 Identifying Functions
  • 1.6.3 Function Notation and Finding Function Values
  • 1.7.1 Determining Intervals Over Which a Function Is Increasing
  • 1.7.2 Evaluating Piecewise-Defined Functions for Given Values
  • 1.7.3 Solving Word Problems Involving Functions
  • 1.8.1 Finding the Domain and Range of a Function
  • 1.8.2 Domain and Range: One Explicit Example
  • 1.8.3 Satisfying the Domain of a Function
  • 1.9.1 An Introduction to Slope
  • 1.9.2 Finding the Slope of a Line Given Two Points
  • 1.9.3 Interpreting Slope from a Graph
  • 1.9.4 Graphing a Line Using Point and Slope
  • 1.10.1 Writing an Equation in Slope-Intercept Form
  • 1.10.2 Writing an Equation Given Two Points
  • 1.10.3 Writing an Equation in Point-Slope Form
  • 1.10.4 Matching a Slope-Intercept Equation with Its Graph
  • 1.10.5 Slope for Parallel and Perpendicular Lines
  • 1.11.1 Constructing Linear Function Models of Data
  • 1.11.2 Linear Cost and Revenue Functions
  • 1.12.1 Graphing Some Important Functions
  • 1.12.2 Graphing Piecewise-Defined Functions
  • 1.12.3 Matching Equations with Their Graphs
  • 1.13.1 The Greatest Integer Function
  • 1.13.2 Graphing the Greatest Integer Function
  • 1.14.1 Deconstructing the Graph of a Quadratic Function
  • 1.14.2 Nice-Looking Parabolas
  • 1.14.3 Using Discriminants to Graph Parabolas
  • 1.14.4 Maximum Height in the Real World
  • 1.15.1 Finding the Vertex by Completing the Square
  • 1.15.2 Using the Vertex to Write the Quadratic Equation
  • 1.15.3 Finding the Maximum or Minimum of a Quadratic
  • 1.15.4 Graphing Parabolas
  • 1.16.1 Shifting Curves along Axes
  • 1.16.2 Shifting or Translating Curves along Axes
  • 1.16.3 Stretching a Graph
  • 1.16.4 Graphing Quadratics Using Patterns
  • 1.17.1 Determining Symmetry
  • 1.17.2 Reflections
  • 1.17.3 Reflecting Specific Functions
  • 1.18.1 Using Operations on Functions
  • 1.18.2 Composite Functions
  • 1.18.3 Components of Composite Functions
  • 1.18.4 Finding Functions That Form a Given Composite
  • 1.18.5 Finding the Difference Quotient of a Function
  • Chapter 1 Test

Week 2

  • 2.1.1 Using Long Division with Polynomials
  • 2.1.2 Long Division: Another Example
  • 2.2.1 Using Synthetic Division with Polynomials
  • 2.2.2 More Synthetic Division
  • 2.3.1 The Remainder Theorem
  • 2.3.2 More on the Remainder Theorem
  • 2.4.1 The Factor Theorem and Its Uses
  • 2.4.2 Factoring a Polynomial Given a Zero
  • 2.5.1 Presenting the Rational Zero Theorem
  • 2.5.2 Considering Possible Solutions
  • 2.6.1 Finding Polynomials Given Zeros, Degree, and One Point
  • 2.6.2 Finding all Zeros and Multiplicities of a Polynomial
  • 2.6.3 Finding the Real Zeros for a Polynomial
  • 2.6.4 Using Descartes' Rule of Signs
  • 2.6.5 Finding the Zeros of a Polynomial from Start to Finish
  • 2.7.1 Matching Graphs to Polynomial Functions
  • 2.7.2 Sketching the Graphs of Basic Polynomial Functions
  • 2.8.1 Understanding Rational Functions
  • 2.8.2 Basic Rational Functions
  • 2.9.1 Vertical Asymptotes
  • 2.9.2 Horizontal Asymptotes
  • 2.9.3 Graphing Rational Functions
  • 2.9.4 Graphing Rational Functions: More Examples
  • Chapter 2 Test

Week 3

  • 3.1.1 Understanding Inverse Functions
  • 3.1.2 The Horizontal Line Test
  • 3.1.3 Are Two Functions Inverses of Each Other?
  • 3.1.4 Graphing the Inverse
  • 3.2.1 Finding the Inverse of a Function
  • 3.2.2 Finding the Inverse of a Function with Higher Powers
  • 3.3.1 An Introduction to Exponential Functions
  • 3.3.2 Graphing Exponential Functions: Useful Patterns
  • 3.3.3 Graphing Exponential Functions: More Examples
  • 3.4.1 Using Properties of Exponents to Solve Exponential Equations
  • 3.4.2 Finding Present Value and Future Value
  • 3.4.3 Finding an Interest Rate to Match Given Goals
  • 3.5.1 e
  • 3.5.2 Applying Exponential Functions
  • 3.6.1 An Introduction to Logarithmic Functions
  • 3.6.2 Converting between Exponential and Logarithmic Functions
  • 3.7.1 Finding the Value of a Logarithmic Function
  • 3.7.2 Solving for x in Logarithmic Equations
  • 3.7.3 Graphing Logarithmic Functions
  • 3.7.4 Matching Logarithmic Functions with Their Graphs
  • 3.8.1 Properties of Logarithms
  • 3.8.2 Expanding a Logarithmic Expression Using Properties
  • 3.8.3 Combining Logarithmic Expressions

Week 4

  • 3.9.1 Evaluating Logarithmic Functions Using a Calculator
  • 3.9.2 Using the Change of Base Formula
  • 3.10.1 The Richter Scale
  • 3.10.2 The Distance Modulus Formula
  • 3.11.1 Solving Exponential Equations
  • 3.11.2 Solving Logarithmic Equations
  • 3.11.3 Solving Equations with Logarithmic Exponents
  • 3.12.1 Compound Interest
  • 3.12.2 Predicting Change
  • 3.13.1 An Introduction to Exponential Growth and Decay
  • 3.13.2 Half-Life
  • 3.13.3 Newton's Law of Cooling
  • 3.13.4 Continuously Compounded Interest
  • Chapter 3 Test
  • 4.1.1 An Introduction to Conic Sections
  • 4.1.2 An Introduction to Parabolas
  • 4.1.3 Determining Information about a Parabola from Its Equation
  • 4.1.4 Writing an Equation for a Parabola
  • 4.2.1 An Introduction to Ellipses
  • 4.2.2 Finding the Equation for an Ellipse
  • 4.2.3 Applying Ellipses: Satellites

Week 5

  • 4.3.1 An Introduction to Hyperbolas
  • 4.3.2 Finding the Equation for a Hyperbola
  • 4.3.3 Applying Hyperbolas: Navigation
  • 4.4.1 Identifying a Conic
  • 4.4.2 Name That Conic
  • 4.5.1 Using the Binomial Theorem
  • 4.5.2 Binomial Coefficients
  • 4.6.1 Understanding Sequence Problems
  • 4.6.2 Solving Problems Involving Arithmetic Sequences
  • 4.6.3 Solving Problems Involving Geometric Sequences
  • 4.7.1 Proving Formulas Using Mathematical Induction
  • 4.7.2 Examples of Induction
  • 4.8.1 Solving Problems Involving Permutations
  • 4.8.2 Solving Problems Involving Combinations
  • 4.8.3 Solving for Probability and Odds: Dice Rolls
  • 4.8.4 Solving for Probability and Odds: Decks of Cards
  • Chapter 4 Test
  • Review
  • Midterm Exam

Week 6

  • 5.1.1 Finding the Quadrant in Which an Angle Lies
  • 5.1.2 Finding Coterminal Angles
  • 5.1.3 Finding the Complement and Supplement of an Angle
  • 5.1.4 Converting between Degrees and Radians
  • 5.1.5 Using the Arc Length Formula
  • 5.2.1 An Introduction to the Trigonometric Functions
  • 5.2.2 Evaluating Trigonometric Functions for an Angle in a Right Triangle
  • 5.2.3 Finding an Angle Given the Value of a Trigonometric Function
  • 5.2.4 Using Trigonometric Functions to Find Unknown Sides of Right Triangles
  • 5.2.5 Finding the Height of a Building
  • 5.3.1 Evaluating Trigonometric Functions for an Angle in the Coordinate Plane
  • 5.3.2 Evaluating Trigonometric Functions Using the Reference Angle
  • 5.3.3 Finding the Value of Trigonometric Functions Given Information about the Values of Other Trigonometric Functions
  • 5.3.4 Trigonometric Functions of Important Angles
  • 5.4.1 An Introduction to the Graphs of Sine and Cosine Functions
  • 5.4.2 Graphing Sine or Cosine Functions with Different Coefficients
  • 5.4.3 Finding Maximum and Minimum Values and Zeros of Sine and Cosine
  • 5.4.4 Solving Word Problems Involving Sine or Cosine Functions

Week 7

  • 5.5.1 Graphing Sine and Cosine Functions with Phase Shifts
  • 5.5.2 Fancy Graphing: Changes in Period, Amplitude, Vertical Shift, and Phase Shift
  • 5.6.1 Graphing the Tangent, Secant, Cosecant, and Cotangent Functions
  • 5.6.2 Fancy Graphing: Tangent, Secant, Cosecant, and Cotangent
  • 5.6.3 Identifying a Trigonometric Function from its Graph
  • 5.7.1 An Introduction to Inverse Trigonometric Functions
  • 5.7.2 Evaluating Inverse Trigonometric Functions
  • 5.7.3 Solving an Equation Involving an Inverse Trigonometric Function
  • 5.7.4 Evaluating the Composition of a Trigonometric Function and Its Inverse
  • 5.7.5 Applying Trigonometric Functions: Is He Speeding?
  • Chapter 5 Test
  • 6.1.1 Fundamental Trigonometric Identities
  • 6.1.2 Finding All Function Values
  • 6.2.1 Simplifying a Trigonometric Expression Using Trigonometric Identities
  • 6.2.2 Simplifying Trigonometric Expressions Involving Fractions
  • 6.2.3 Simplifying Products of Binomials Involving Trigonometric Functions
  • 6.2.4 Factoring Trigonometric Expressions
  • 6.2.5 Determining Whether a Trigonometric Function Is Odd, Even, or Neither

Week 8

  • 6.3.1 Proving an Identity
  • 6.3.2 Proving an Identity: Other Examples
  • 6.4.1 Solving Trigonometric Equations
  • 6.4.2 Solving Trigonometric Equations by Factoring
  • 6.4.3 Solving Trigonometric Equations with Coefficients in the Argument
  • 6.4.4 Solving Trigonometric Equations Using the Quadratic Formula
  • 6.4.5 Solving Word Problems Involving Trigonometric Equations
  • 6.5.1 Identities for Sums and Differences of Angles
  • 6.5.2 Using Sum and Difference Identities
  • 6.5.3 Using Sum and Difference Identities to Simplify an Expression
  • 6.6.1 familyirming a Double-Angle Identity
  • 6.6.2 Using Double-Angle Identities
  • 6.6.3 Solving Word Problems Involving Multiple-Angle Identities
  • 6.7.1 Using a Cofunction Identity
  • 6.7.2 Using a Power-Reducing Identity
  • 6.7.3 Using Half-Angle Identities to Solve a Trigonometric Equation
  • Chapter 6 Test

Week 9

  • 7.1.1 The Law of Sines
  • 7.1.2 Solving a Triangle Given Two Sides and One Angle
  • 7.1.3 Solving a Triangle (SAS): Another Example
  • 7.1.4 The Law of Sines: An Application
  • 7.2.1 The Law of Cosines
  • 7.2.2 The Law of Cosines (SSS)
  • 7.2.3 The Law of Cosines (SAS): An Application
  • 7.2.4 Heron's Formula
  • 7.3.1 An Introduction to Vectors
  • 7.3.2 Finding the Magnitude and Direction of a Vector
  • 7.3.3 Vector Addition and Scalar Multiplication
  • 7.4.1 Finding the Components of a Vector
  • 7.4.2 Finding a Unit Vector
  • 7.4.3 Solving Word Problems Involving Velocity or Forces

Week 10

  • 7.5.1 Graphing a Complex Number and Finding Its Absolute Value
  • 7.5.2 Expressing a Complex Number in Trigonometric or Polar Form
  • 7.5.3 Multiplying and Dividing Complex Numbers in Trigonometric or Polar Form
  • 7.6.1 Using DeMoivre's Theorem to Raise a Complex Number to a Power
  • 7.6.2 Roots of Complex Numbers
  • 7.6.3 More Roots of Complex Numbers
  • 7.6.4 Roots of Unity
  • 7.7.1 An Introduction to Polar Coordinates
  • 7.7.2 Converting between Polar and Rectangular Coordinates
  • 7.7.3 Graphing Simple Polar Equations
  • Chapter 7 Test
  • 8.1.1 An Introduction to Linear Systems
  • 8.1.2 Solving a System by Substitution
  • 8.1.3 Solving a System by Elimination

Week 11

  • 8.2.1 An Introduction to Linear Systems in Three Variables
  • 8.2.2 Solving Linear Systems in Three Variables
  • 8.2.3 Solving Inconsistent Systems
  • 8.2.4 Solving Dependent Systems
  • 8.2.5 Solving Systems with Two Equations
  • 8.3.1 Investments
  • 8.3.2 Solving with Partial Fractions
  • 8.4.1 Solving Nonlinear Systems Using Elimination
  • 8.4.2 Solving Nonlinear Systems by Substitution
  • 8.5.1 An Introduction to Matrices
  • 8.5.2 The Arithmetic of Matrices
  • 8.5.3 Multiplying Matrices by a Scalar
  • 8.5.4 Multiplying Matrices
  • 8.5.5 Can They Multiply?

Week 12

  • 8.6.1 Using the Gauss-Jordan Method
  • 8.6.2 Using Gauss-Jordan: Another Example
  • 8.7.1 Evaluating 2x2 Determinants
  • 8.7.2 Evaluating 3x3 Determinants
  • 8.7.3 Applying Determinants
  • 8.8.1 Using Cramer's Rule
  • 8.8.2 Using Cramer's Rule in a 3x3 Matrix
  • 8.9.1 An Introduction to Inverses
  • 8.9.2 Inverses: 2x2 Matrices
  • 8.9.3 Another Look at 2x2 Inverses
  • 8.9.4 Inverses: 3x3 Matrices
  • 8.9.5 Solving a System of Equations with Inverses
  • 8.10.1 An Introduction to Systems of Inequalities
  • 8.10.2 Graphing Systems of Inequalities
  • 8.10.3 Graphing the Solution Set of a System of Inequalities
  • 8.11.1 Solving for Maxima-Minima
  • 8.11.2 Applying Linear Programming
  • Chapter 8 Test

Week 13

  • Review
  • Final Exam

Back to top

Demo

This demo requires the Flash plugin.

Precalculus Demo

Have a Question?

CTYOnline Catalog

View our Catalog