Detailed Course Information

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

• 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

• 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

• 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

• 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?

• 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

• 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

• 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

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