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Precalculus
Online precalculus video lessons to help students with the notation, theory, and problems to improve their math problem solving skills so they can find the solution to their Precalculus homework and worksheets.
Conic Sections
- Introduction to Conic Sections
- The Circle
- The Ellipse
- The Hyperbola
- Transformations of a Hyperbola
- Conic Section Formulas
Sequences and Series
- Introduction to Sequences
- Series and Summation Notation
- Arithmetic Sequences
- Arithmetic Series
- Geometric Sequences
- Geometric Series
- Recursion Sequences
- Mathematical Induction
Equations of Lines, Parabolas and Circles
- Parallel and Skew Lines
- Parallel Planes and Lines
- Converse of Parallel Lines Theorem
- Constructing the Perpendicular Bisector
- Introduction to Parabolas
- Finding the Vertex of a Parabola by Completing the Square
- Finding Intercepts, Domain, Range and Vertex of a Parabola
- The Circle
- Computing Difference Quotients
Polynomial and Rational Functions
- Power Functions
- Integer Power Functions
- Polynomial Functions
- Graphing Polynomial Functions
- Graphing Polynomial Functions with Repeated Factors
- Find an Equation of the Polynomial Function
- Finding Maximum and Minimum Values
- Finding Zeros of a Polynomial Function
- Using the Conjugate Zeros Theorem
- The Reciprocal Transformation
- Introduction to Rational Functions
- Limits of Rational Functions
- Limits at a Glance
- Graphing Rational Functions, n less than m
- Graphing Rational Functions, n=m
- Graphing Rational Functions, n>m
- Graphs with Holes
Exponential and Logarithmic Functions
- Exponential Functions and their Graphs
- Solving Exponential Equations with the 'Same' Base
- Introduction to Logarithms
- Solving Simple Logarithmic Equations
- Function Notation with Logs and Exponentials
- Graph of Logarithmic Functions
- Product Rule of Logarithms
- Quotient Rule of Logarithms
- Power Rule of Logarithms
- Expanding Logarithms
- Condensing Logarithms
- Common and Natural Logarithms
- Change of Base Formula
- Solving Exponential Equations with the Different Bases
- Solving a Logarithmic Equation
- Solving a Logarithmic Equation with Multiple Logs
- Compound Interest (Finite Number of Calculations)
- Compound Interest (Continuously)
- Evaluating a Logarithmic Expression in terms of Known Quantities
- Exponential Functions
- Logarithmic Functions
- Properties of Logarithms
- The Number e and the Natural Logarithm
- Exponential Growth and Decay
Basic Trigonometry
- Trigonometric Ratios: Sine
- Trigonometric Ratios: Cosine
- Trigonometric Ratios: Tangent
- Inverse Trigonometric Functions
- Angle of Elevation and Depression
- Using Sine to Calculate the Area of a Triangle
- The Law of Sines
- The Law of Cosines
Trigonometric Functions
- Radian Measure of Angles
- The Definitions of Sine and Cosine
- Evaluating Sine and Cosine at Special Acute Angles
- Evaluating Sine and Cosine at Other Special Angles
- Graphs of the Sine and Cosine Functions
- Transforming the Graphs of Sine and Cosine
- More Transformations of Sine and Cosine
- Find an Equation for the Sine or Cosine Wave
- The Tangent Function
- Evaluating the Tangent Function
- Graph of the Tangent Function
- Transforming the Tangent Graph
- Intercepts and Asymptotes of Tangent Functions
- Trigonometric Identities
- The Reciprocal Trigonometric Functions
- Graphing the Reciprocal Trigonometric Functions
- Using Trigonometric Identities
- Transforming the Cotangent Graph
- Transforming Secant and Cosecant
- Asymptotes of Secant, Cosecant, and Cotangent
Advanced Trigonometry
- The Inverse Sine Function
- The Inverse Cosine Function
- The Inverse Tangent Function
- Using the Inverse Trigonometric Functions
- Solving Trigonometric Equations
- Trigonometric Equations that Require Factoring
- The Cosine Addition Formulas
- The Sine Addition Formulas
- Using the Sine and Cosine Addition Formulas to Prove Identities
- The Double-Angle Formulas
- Other Forms of the Cosine Double-Angle Formula
- The Half-Angle Identities
- Angle Inclination of a Line
Vectors and Parametric Equations
- The Geometric Representation of Vectors
- Adding Vectors
- The Resultant of Two Forces
- Components of a Force
- Navigation Problems
- Algebraic Representation of Vectors
- Addition and Scalar Multiplication of Vectors
- Unit Vectors
- The Vector Equation of a Line
- Motion Along a Line
- Parametric Equations and Motion
- Parametrizing a Line Segment
- Parametrizing a Circle
- The Dot Product of Vectors
- The Angle Between Vectors
- Introduction to the 3D Coordinate System
- Vector Operations in 3D
- The Midpoint and Distance Formulas in 3D
- Lines in 3D
- Perpendicular, Parallel and Skew Lines in Space
- Introduction to Planes
- Vectors and Planes
- The Angle Between Planes
Polar Coordinates and Complex Numbers
- Introduction to Polar Coordinates
- Converting from Rectangular Coordinates to Polar
- Converting from Polar Coordinates to Rectangular
- The Distance Formula in Polar Coordinates
- Lines in Polar Coordinates
- Symmetry of Polar Graphs
- Graphing Polar Equations
- Families of Polar Curves: Circles, Cardiods, and Limacon
- Families of Polar Curves: Roses
- Families of Polar Curves: Conic Sections
- The Complex Plane
- Trigonometric Form of Complex Numbers
- Converting Complex Numbers From Trigonometric Form to Rectangular
- Converting Complex Numbers From Rectangular Form to Trigonometric
- Multiplying Complex Numbers
- Dividing Complex Numbers
- DeMoivre's Theorem
- The Euler Formula
- Finding the Roots of a Complex Number
- More Roots of Complex Numbers
Systems of Linear Equations and Matrices
- Square Matrices
- The Identity Matrix
- The Inverse of a Square Matrix
- Solving Linear Systems Using Matrix Algebra
- 2x2 Determinants
- 3x3 Determinants
- Simplifying Determinants
- Cramer's Rule
- Area With Determinants
- The Cross Product of Vectors
- Area With the Cross Product
- Invertible Square Matrices and Determinants
Topics in Discrete Math
- Pascal's Triangle
- Binomial Theorem
- Introduction to Probability
- Fundamental Counting Principal
- Permutations
- Combinations
- Combinations vs. Permutations
- Probability of Multiple Events
- Probability of Independent Events
- Using the Complement to Calculate Probability
- Probability of Dependent Events
- Conditional Probability
Linear Equations and Inequalities
- Solving and Graphing Compound Inequalities
- Graphing 2 Variable Inequalities
- Solving Linear Equations
- Solving for a Parameter in a Linear Equation
- Applied Linear Equations: Geometry Problem
- Applied Linear Equations: Mixture Problem
- Applied Linear Equations: Investment Problem
- Applied Linear Equations: Tax Problem
- Applied Linear Equations: Distance Problem
- Applied Linear Equations: Collection Problem
- Applied Linear Equations: Consecutive Numbers
- Solving Linear Inequalities
- Solving a Three-part Linear Inequality
- Applied Linear Inequalities
- Set Operation: Union
- Set Operation: Intersection
- Solving "Greater Than" Absolute Value Inequalities
- Solving "Less Than" Absolute Value Inequalities
Introduction to Functions
- Computing Difference Quotients
- Seven Elementary Functions and Their Graphs
- Finding the Domain of a Function
- Graphing the Transformation y = a f(x) + k
- Graphing the Transformation y = f(x - h)
- Domain Restrictions and Functions Defined Piecewise
- The Reflection y = f(-x)
- Symmetry of Graphs: Odd and Even Functions
- The Greatest Integer Function
- The Transformation y = f(bx)
