General PreCalculus Resources

Animated Precalculus – TextBook

• Video: Slope Formula – An Overview
• Video: Slope Formula
• Video: Find the Slope of a Line Given Two Points
• Video: Write the Equation of a Line Given a Point and the Slope
• Video: Graph a Line Given the Intercept and the Slope
• Video: Slope-Intercept Form
• Video: Use Slope to Identify Parallel and Perpendicular Lines

• Video: Determine Whether Relations between Two Variables Are Functions
• Video: Determine Whether Relations between Two Variables Are Functions
• Video: Use Function Notation and Evaluate a Function
• Video: Evaluate a Piecewise-Defined Functions
• Simulation: Piecewise Defined Functions
• Video: Find Domain and Range of a Function
• Video: Use Functions to Model and Solve Real-Life Problems
• Video: Difference Quotient of a Quadratic

• Video: Determine Domain and Range from a Graph
• Video: Apply the Vertical Line Test
• Video: Determine Intervals on Which Functions Are Increasing or Decreasing
• Video: Find Relative Minima and Relative Maxima
• Video: Graphing a Step Function
• Video: Graph Piecewise Functions
• Video: Identify Even and Odd Functions
• Video: Identify Even and Odd Functions
• Video: Identify Even and Odd Functions

• Video: Identify Graphs of Basic Functions
• Video: Use Vertical and Horizontal Shifts to Sketch Graphs of Functions
• Video: Use Vertical and Horizontal Shifts to Sketch Functions
• Simulation: Transformations of Graphs and Functions
• Video: Use Reflections to Sketch Graphs of Functions
• Video: Nonrigid Transformations

• Video: Operations with Functions
• Video: Find the Composition of Two Functions
• Simulation: Algebra of Functions

• Video: Verify Inverse Functions
• Video: The Graph of an Inverse Function
• Video: Determine Whether a Function Is One-to-One
• Video: Find the Inverse of a Function

• Video: Make a Scatter Diagram, Visually Estimate Degree of Linear Correlation
• Video: Scatter Plots and Correlation
• Simulation: Linear Modeling with Least Squares Regression
• Simulation: Linear Modeling with Least Squares Regression
• Video: Finding a Linear Regression Using a Graphing Utility
• Video: Finding a Correlation Coefficient Using a Graphing Utility

• Video: Graph a Quadratic Function
• Simulation: Transformations of Graphs and Functions
• Video: Write the Equation of a Parabola
• Video: Finding a Parabolic Equation Given Its Vertex and a Point
• Video: Applications Problems- Solving Minimum and Maximum Problems
• Simulation: Finding the Maximum or Minimum Value of a Quadratic Function

• Simulation: Advanced Techniques for Graphing Polynomial Functions
• Video: Characteristics of Higher Degree Polynomials
• Video: Determine Right-Hand and Left-Hand Behavior of Functions
• Video: Find the Zeros of a Polynomial Equation
• Simulation: Finding Zeros of Polynomial Functions
• Video: Find a Polynomial with Given Zeros
• Video: Sketching the Graph of a Polynomial Function
• Video: Use the Intermediate Value Theorem to Help Locate Zeros of Polynomial Functions

• Video: Divide Polynomials Using Long Division
• Video: Use Synthetic Division to Factor Polynomials
• Video: Apply the Remainder Theorem
• Video: Apply the Factor Theorem
• Video: Apply the Rational Zeros Theorem
• Video: Apply Descartes Rule of Signs
• Video: Apply the Upper- and Lower-Bound Theorems

• Video: Use the Imaginary Unit i to Write Complex Numbers
• Video: Add and Subtract Complex Numbers
• Video: Multiply Complex Numbers
• Simulation: Finding Products of Complex Conjugates
• Video: Complex Conjugates
• Video: Divide Complex Numbers
• Video: Plot Complex Numbers in the Complex Plane

• Video: Apply the Fundamental Theorem of Algebra
• Video: Apply the Factorization Theorem
• Video: Finding Complex Zeros of a Polynomial Function
• Video: Find Conjugate Pairs of Complex Zeros
• Video: Find All Zeros of a Cubic by Factoring Given a Complex Zero – Part A
• Video: Find All Zeros of a Cubic by Factoring Given a Complex Zero – Part B

• Video: Introduction to Asymptotes
• Video: Determine Asymptotes of Rational Equations
• Video: Application Problems- Graphing Rational Equations
• Simulation: Graphs of Rational Functions

• Video: Use Asymptotes to Graph Rational Equations
• Simulation: The Domain and Slant Asymptotes of a Rational Function
• Video: Sketch Graphs of Rational Functions That Have Slant Asymptotes
• Simulation: Graphs of Rational Functions

• Video: Determine the Function Type That Will Best Model Data
• Video: Choosing between a Linear and a Quadratic Regression
• Simulation: Quadratic Modeling with Least Squares Regression

• Video: Recognize and Evaluate Exponential Functions with Base a
• Simulation: Exponential Functions
• Video: Graph Exponential Functions
• Video: Transformations of Exponential Functions
• Video: Evaluate and Graph Natural Exponential Functions
• Video: Evaluate and Graph Natural Exponential Functions
• Simulation: Exponential Functions
• Video: Compound Interest

• Video: Write Equivalent Exponential and Logarithmic Equations and Evaluate Logarithms
• Video: Write Equivalent Exponential and Logarithmic Equations and Evaluate Logarithms
• Video: Write Equivalent Exponential and Logarithmic Equations and Evaluate Logarithms
• Video: Graph Logarithmic Functions
• Simulation: Graphs and Properties of Logarithms
• Video: Evaluate Natural Logarithms and Graph Natural Logarithm Functions
• Video: Evaluate Natural Logarithms and Graph Natural Logarithm Functions
• Video: Find the Domain of a Logarithmic Function

• Video: Apply Change of Base to Evaluate Logarithms
• Video: Evaluate Logarithms Using the Properties of Logarithms
• Video: Rewrite, Expand, and Condense Logarithmic Expression – Part A
• Video: Rewrite, Expand, and Condense Logarithmic Expression – Part B

• Video: Solve Basic Exponential Equations
• video: Solve Basic Logarithmic Equations
• Simulation: Exponential and Logarithmic Equations
• Video: Solve Exponential Equations
• Video: Solve Logarithmic Equations
• Video: Application Problems- Solving Exponential and Logarithmic Equations
• Simulation: Exponential and Logarithmic Equations

• Video: Recognize the Five Most Common Types of Models Involving Exponential and Logarithmic Functions
• Video: Use Exponential Growth and Decay to Model Real-Life Situations
• Simulation: Exponential and Logarithmic Models
• Video: Use Exponential Growth and Decay to Model Real-Life Situations
• Video: Gaussian Models
• Video: Logistic Growth Models
• Video: Logarithmic Models

• Video: Classifying a Scatter Plot as Exponential or Logarithmic
• Simulation: Using Regression to Find Exponential and Logarithmic Models
• Simulation: Using Regression to Find Exponential and Logarithmic Models
• Video: Fitting Data to Quadratic, Cubic, and Exponential Models – Part A
• Video: Fitting Data to Quadratic, Cubic, and Exponential Models – Part B
• Video: Modeling with an Exponential Function – Part A
• Video: Modeling with an Exponential Function – Part B

• Video: Describe Angles
• Video: Use Radian Measure
• Video: Convert between Degree and Radian Measures
• Video: Use Angles to Model and Solve Real-Life Problems

• Video: Definition of Sine and Cosine
• Simulation: Defining the Trigonometric Functions Using the Unit Circle
• Video: Identify a Unit Circle and Its Relationship to Real Numbers
• Video: Evaluate Sine and Cosine at Standard Angles
• Video: Evaluating Trigonometric Functions with a Calculator- Unit Circle
• Video: Use the Domain and the Period to Evaluate Sine and Cosine Functions

• Video: Evaluate Trigonometric Functions of Acute Angles
• Video: Use the Fundamental Trigonometric Identities
• Video: Use Trigonometric Functions to Model and Solve Real-Life Problems

• Video: Evaluate Trigonometric Functions of Any Angle
• Simulation: Trigonometric Functions of Any Angle
• Video: Use Reference Angles to Evaluate Trigonometric Functions
• Video: Evaluate Trigonometric Functions of Real Numbers

• Video: Sketch the Graphs of Basic Sine and Cosine Functions
• Video: Sketch the Graphs of Basic Sine and Cosine Functions
• Simulation: Graphing Sine and Cosine Functions
• Video: Use Amplitude and Period to Help Sketch the Graphs of Sine and Cosine Functions
• Video: Use Amplitude and Period to Help Sketch the Graphs of Sine and Cosine Functions
• Video: Sketch Translations of the Graphs of Sine and Cosine Functions
• Simulation: Graphing Sine and Cosine Functions
• Simulation: Finding a Trigonometric Model for Data

• Video: Sketch the Graphs of Tangent Functions
• Video: Sketch the Graphs of Cotangent Functions
• Video: Sketch the Graphs of Secant and Cosecant Functions
• Video: Sketch the Graphs of Secant and Cosecant Functions
• Video: Sketch the Graphs of Secant and Cosecant Functions
• Simulation: Graphing the Secant and Cosecant Functions
• Video: Sketch the Graphs of Damped Trigonometric Functions
• Simulation: Damped Trigonometric Graphs

• Video: Evaluate the Inverse Sine Function
• Video: Evaluate the Inverse Sine Function
• Video: Evaluate the Inverse Sine Function
• Simulation: Inverse Sine Function
• Video: Evaluate the Other Inverse Trigonometric Functions
• Video: Evaluate the Compositions of Trigonometric Functions

• Video: Right Triangle Trigonometry
• Video: an Application with the Tangent Function
• Video: Solve Real-Life Problems Involving Right Triangles
• Video: Solve Real-Life Problems Involving Directional Bearings
• Video: Solve Real-Life Problems Involving Directional Bearings

• Video: Use the Fundamental Trigonometric Identities – Part A
• Video: Use the Fundamental Trigonometric Identities – Part B

• Video: Plan a Strategy for Verifying Trigonometric Identities
• Video: Verify Trigonometric Identities

• Video: Use Standard Algebraic Techniques to Solve Trigonometric Equations
• Video: Solve Trigonometric Equations of Quadratic Type
• Video: Solve Trigonometric Equations Involving Multiple Angles
• Simulation: Solving Trigonometric Equations

• Video: Use Sum and Difference Formulas

• Video: Use Multiple-Angle formulas to Rewrite and Evaluate Trigonometric Functions
• Video: Use Half-Angle formulas to Rewrite and Evaluate Trigonometric Functions
• Video: Use Product-to-Sum and Sum-to-Product Formulas

• Video: Use the Law of Sines to Solve Oblique Triangles (AAS or ASA)
• Video: Use the Law of Sines to Solve Oblique Triangles (AAS or ASA)
• Video: Use the Law of Sines to Solve Oblique Triangles (SSA)
• Simulation: Law of Sines

• Video: Use the Law of Cosines to Solve Oblique Triangles (SSS or SAS)
• Simulation: Law of Cosines

• Video: Represent Vectors as Directed Line Segments
• Video: Write the Component forms of Vectors
• Video: Vector Operations
• Simulation: Vectors in the Plane
• Video: Write Vectors As Linear Combinations of Unit Vectors
• Video: Find the Direction Angles of Vectors
• Video: Use Vectors to Model and Solve Real-Life Problems
• Video: Use Vectors to Model and Solve Real-Life Problems
• Simulation: Using Unit Vectors

• Video: the Dot Product of Two Vectors
• Video: Find the Angle between Two Vectors and Determine Whether Two Vectors Are orthogonal
• Video: Find the Angle between Two Vectors and Determine Whether Two Vectors Are orthogonal
• Simulation: Finding Vector Components
• Video: Write a Vector as the Sum of Two Vector Components
• Video: Scalar Projection of a Vector
• Video: Scalar Projection of a Vector
• Video: Scalar Projection of a Vector
• Video: Use Vectors to Find the Work done by a Force
• Video: Vectors- Application-Work

• Video: Absolute Value of a Complex Number
• Video: Write the Trigonometric Forms of Complex Numbers
• Video: Multiply and Divide Complex Numbers Written in Trigonometric Form
• Video: Use DeMoivre’s Theorem to Find Powers of Complex Numbers
• Video: Find nth Roots of Complex Numbers

• Video: Solve a System of Linear Equations in Two Variables by the Substitution Method
• Video: Use the Method of Substitution to Solve Systems with No Solution or Infinitely Many Solutions
• Video: Solve a System of Linear Equations in Two Variables by Graphing
• Simulation: Solving Systems of Linear Equations in Two Variables
• Video: Find Break-Even Points

• Video: Solve a System of Two Linear Equations in Two Variables by the Addition Method
• Video: Use a Coordinate System to Solve Systems of Linear Equations Graphically
• Video: Construct a System of Linear Equations from an Application Problem

• Video: Solve Systems of Equations in Three Variables Written in Row Echelon form
• Video: Solve Systems of Linear Equations in Three Variables by Gaussian Elimination
• Video: A System of Three Variables with Infinitely Many Solutions
• Video: Three-Dimensional Coordinate System
• Video: Three-Dimensional Coordinate System
• Video: Three-Dimensional Coordinate System
• Video: Find Partial Fraction Decompositions of Rational Expressions
• Video: Partial Fractions Decomposition- Distinct Linear Factors
• Video: Find a Quadratic Equation Given Three Solution Points Using Systems of Linear Equations

• Video: Identify the order of Matrices
• Video: Write Augmented and Coefficient Matrices
• Video: Use Matrices and Gaussian Elimination to Solve Systems of Linear Equations
• Video: Use Matrices to Solve Systems of Linear Equations with Nonunique Solutions
• Video: Use Matrices to Solve Systems of Linear Equations with Nonunique Solutions
• Video: Use Matrices and Gauss-Jordan Elimination to Solve Systems of Linear Equations

• Video: Equality of Matrices
• Video: Add and Subtract Matrices
• Video: Multiply a Matrix by a Scalar
• Video: Multiply Two Matrices
• Video: Use Matrix Operations to Model and Solve Real-Life Problems
• Simulation: Matrix Equations and Systems of Linear Equations

• Video: Verify That Two Matrices Are Inverses of Each Other
• Video: Find Inverse Matrices
• Video: Find Inverse Matrices
• Simulation: the Inverse of a Square Matrix
• Video: Use Inverse Matrices to Solve Systems of Linear Equations

• Video: Determinant of a 2 by 2 Matrix
• Video: Evaluate Determinants
• Video: the Determinant of a Square Matrix
• Simulation: Determinants
• Video: Finding the Determinant of a Triangular Matrix

• Video: Area of a Triangle
• Video: Lines in a Plane
• Video: Solve Systems of Linear Equations in Two Variables by Using Cramer’s Rule
• Video: Solve Systems of Linear Equations in Three Variables by Using Cramer’s Rule
• Video: Cryptography
• Video: Cryptography

• Video: Write the Terms of a Sequence
• Video: Use Factorial Notation
• Video: Use Summation Notation to Write Sums
• video: Evaluate a Series
• Video: Finding an Elementary Infinite Sum

• Video: Find the nth Term of an Arithmetic Sequence
• Video: Evaluate an Arithmetic Series, Partial Sum
• Simulation: Arithmetic Sequences and Series

• Video: Finding the Common Ratio of a Geometric Sequence
• Video: Find the nth Term of a Geometric Sequence
• Video: Calculate Finite Geometric Series
• Video: Calculate Infinite Geometric Series
• Simulation: Geometric Sequences and Series
• Video: Application Problems- Geometric Series

• Video: Introduction to Mathematical Induction
• Video: Introduction to Mathematical Induction- a way of proving math statements for all integers
• Video: Use Mathematical Induction to Prove a Statement
• Simulation: Sums of Powers of Integers and Finite Differences
• Simulation: Sums of Powers of Integers and Finite Differences

• Video: Expand a Binomial to a Power Using the Binomial theorem
• Simulation: Binomial Expansions
• Video: Find Binomial Coefficients Using Pascal’s Triangle

• Video: Simple Counting Problems
• Video: Use the Fundamental Counting Principle to Solve Counting Problems
• Video: Use Permutations to Solve Counting Problems
• Video: Use Combinations to Solve Counting Problems

• Video: Understand the Definition of Probability
• Video: Calculate the Probability of a Simple Event
• Video: Mutually Exclusive Events
• Video: Compute the Probability That Two or More Independent Events Will Occur
• Video: the Complement of an Event

• Video: Recognize the Four Basic Conics
• Video: Write Equations of Circles
• Video: Write Equations of Parabolas
• Video: Analyze Parabolas
• Video: Analyze Parabolas
• Video: Analyze Parabolas
• Video: Reflective Property of Parabolas

• Video: Introduction to Ellipses and Elliptical Equations
• Simulation: Ellipses Centered at (0, 0)
• Video: Write Equations of Ellipses
• Simulation: Ellipses and Hyperbolas Centered at (h, k)
• Video: Application Problems – Ellipses
• Video: Eccentricity of an Ellipse

• Video: Introduction to Hyperbolas
• Simulation: Hyperbolas Centered at (0, 0)
• Video: Graph a Hyperbola with Center at (h, k)
• Video: Graph a Hyperbola with Center at (h, k)

• Video: Use the Discriminant to Classify a Conic
• Simulation: Solving Nonlinear Systems of Equations

• Video: Plane Curves
• Video: Evaluate a Set of Parametric Equations
• Video: Sketch the Curve that is Represented by a Set of Parametric Equations
• Video: Rewrite a Set of Parametric Equations as a Single Rectangular Equation

• Video: Plot Points on the Polar Coordinate System
• Video: Plot Points on the Polar Coordinate System
• Simulation: Polar Coordinates
• Video: Convert Points from Rectangular to Polar and Vice-Versa
• Video: Convert Equations from Rectangular to Polar and Vice Versa
• Video: Convert Equations from Rectangular to Polar and Vice Versa

• Video: Graph Polar Equations by Point Plotting
• Video: Graph Polar Equations by Point Plotting
• Video: Preparing a Table of Polar Coordinates
• Video: Use Symmetry to Sketch Graphs of Polar Equations
• Video: Use Zeros and Maximum r-Values to Sketch Graphs of Polar Equations
• Video: Recognize Special Polar Graphs
• Video: Graphing Polar Equations with a Calculator

• Video: Define Conics in Terms of Eccentricity
• Video: Eccentricity of an Ellipse
• Simulation: Polar Equations of Conics
• Video: Polar Equations of Conics
• Simulation: Polar Equations of Conics

• Video: Three-Dimensional Coordinate System
• Video: Three-Dimensional Coordinate System
• Video: Plot Points in Space
• Video: Plot Points in Three Dimensional Space
• Video: Three-Dimensional Coordinate System
• Video: Find Distances between Points in Space and Find Midpoints of Line Segments in Space
• Video: Find Distances between Points in Space and Find Midpoints of Line Segments in Space
• Video: Write the Standard Forms of the Equations of Spheres
• Video: Write the Standard Forms of the Equations of Spheres
• Video: Sketch the Coordinate Plane Traces of Spheres

• Video: Vectors – Introduction
• Video: Use Points in Space to Describe Vectors
• Video: Vector Length
• Video: The Dot Product
• Video: Parallel and Orthogonal Vectors
• Simulation: Vectors in Space

• Video: The Cross Product
• Video: Cross Product of Vectors
• Video: Geometric Properties of the Cross Product
• Video: Geometry of the Cross Product of Vectors- an Overview
• Video: the Triple Scalar Product

• Video: Vectors – Parametric and Symmetric Equations for the Line
• Video: Lines in Space
• Video: Vectors – Find Parametric Equation for a Line through a Point and Parallel to a Line
• Video: Sketch Planes in Space
• Video: Vectors- Find Distance from Point to Plane
• Video: Distance between a Point and a Plane

• Video: Formal Definition of a Limit
• Video: Formal Definition of a Limit
• Video: Find Limits of Functions Graphically and Numerically
• Video: Recognize Unbounded Behavior of Functions
• Video: Recognize Unbounded Behavior of Functions
• Video: Recognize Unbounded Behavior of Functions
• Video: Use the Properties of Limits to Evaluate Limits of Functions
• Video: Properties of Limits
• Video: Finding Limits with the Rules of Limits
• Video: Limits of Polynomial and Rational Functions

• Video: Approximate Limits That Produce Indeterminate Forms
• Video: Finding Limits by Simplifying
• Video: Finding Limits by Simplifying
• Video: Evaluate One-Sided Limits
• Simulation: Identifying a Composition of Functions and Finding a Difference Quotient

• Video: Approximate the Slopes of Tangent Lines to Graphs at Points
• Video: Slope of Tangent Lines to a Point on a Curve
• Video: Tangents, Secants, and Rate of Change
• Video: Tangent Line with Slope m – Part A
• Video: Tangent Line with Slope m – Part B
• Video: A Limit from Calculus
• Video: Use the Limit Definition to Find the Derivatives of Functions

• Video: Find the Horizontal Asymptotes of Functions and Find Limits at Infinity
• Video: Properties of Limits at Infinity
• Video: Evaluation of Limits at Infinity for a Rational Function
• Video: Find the Horizontal Asymptotes of Functions and Find Limits at Infinity
• Video: Limits at Infinity
• Simulation: Evaluating a Limit at Infinity
• Video: Determine the Convergence or Divergence of

• Video: Using Sigma Notation
• Video: Summation Notation
• Video: Summation Formulas
• Video: Approximation of the Area under a Curve Using Rectangles
• Video: Area of a Region in the Plane
• Video: Area from Riemann Sums – Part A
• Video: Area from Riemann Sums – Part B