PreCalculus

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The topics covered are: Lines and Planes, Functions and Transformation of Graphs, Polynomials, Rational Functions, Limits of a Function, Complex Numbers, Exponential Functions, Logarithmic Functions, Conic Sections, Matrices, Sequences and Series, Probability and Combinatorics, Advanced Trigonometry, Vectors and Parametric Equations, and Polar Coordinates.

Related Topics:
PreCalculus Worksheets
Math Worksheets
Algebra II lessons

Lines and Planes Videos

Parallel Lines, Skew Lines and Planes

Proving Parallel Lines

Functions and Transformation of Graphs Videos

Difference Quotient of Function I	Difference Quotient of Function II
Domain of a Function	Greatest Integer Function I
Greatest Integer Function II	Piece-Wise Functions I
Piece-Wise Functions II	Piece-Wise Functions III
Even and Odd Functions I	Even and Odd Functions II
Parent Functions and their Graphs	Transformation of Linear Functions
Transformation of Quadratic Functions	Horizontal and Vertical Graph Transformations
Horizontal And Vertical Graph Stretches and Compressions	Reflective Transformations
Examples of Graph Transformations	Composite Functions I
Composite Functions II	Composite Functions III
One-to-one Functions	Inverse of a Function I
Inverse of a Function II	Finding the Inverse of a Function or Showing One Does not Exist

Polynomials Videos

Power Functions	Polynomial Functions
Graphing Polynomial Functions I	Graphing Polynomial Functions II
Families of Polynomials	Graphing Polynomials with Repeated Factors
Finding the Equation of a Polynomial Function	Finding Maximum and Minimum Values of Polynomial Functions
Finding the Zeros of a Polynomial Function I	Finding the Zeros of a Polynomial Function II
Conjugate Zeros Theorem	Reciprocal of a Function

Rational Functions Videos

Introduction to Rational Functions	Limits of Rational Functions
Graphing Rational Functions I	Graphing Rational Functions II
Horizontal Asymptotes I	Horizontal Asymptotes II
Vertical Asymptotes	Vertical and Horizontal Asymptotes
Oblique or Slant Asymptotes	Find all Asymptotes of a Rational Function
Graphing Rational Functions with Holes	Rational Function Problems

Limits of a Function

Introduction to Limits of Functions	Limits of Rational Functions
Examples to Learn about Limits	Calculating Limits using Different Techniques I
Calculating Limits using Different Techniques II	Limit Laws to Evaluate a Limit
One Sided Limits	Squeeze Theorem for Limits
The Limit definition of Continuity

Complex Numbers Videos

Introduction to Complex Numbers I	Introduction to Complex Numbers II
Adding and Subtracting Complex Numbers	Multiplying Complex Numbers
Dividing Complex Numbers	Trigonometric or Polar Form of Complex Numbers
Converting Complex Numbers between Trigonometric Form and Rectangular	Multiplying and Dividing Complex Numbers in Trigonometric or Polar Form
DeMoivre's Theorem and Euler Formula	Roots of a Complex Number
Complex Quadratic Equations I	Complex Quadratic Equations II
Simplify Complex Rational Expressions

Exponential form to find complex roots
Complex Conjugates
Complex Determinant Example

Exponential Function Videos

Introduction to Exponential Functions	Graphing Exponential Functions I
Graphing Exponential Functions II	Applying Exponential Functions I
Applying Exponential Functions II	Solving Exponential Equations with the Same Base
Solving Exponential Equations with Different Bases I	Solving Exponential Equations with Different Bases II
Solving Exponential Equations with Different Bases III

Logarithmic Function Videos

Introduction to Logarithmic Functions	Exponential and Logarithmic Functions
Logarithm Review Product Rule	Logarithm Review Product & Quotient Rules
Logarithm Review Power Rule	Logarithm Review Change of Base Rule
Properties of Logarithms (or Rules of Logarithms)	Proof of Logarithm Properties
Expanding Logarithmic Expressions	Simplifying (or Condensing) Logarithmic Expressions
Simplifying and Expanding Logarithmic Expressions	Solving Logarithmic Equations I
Solving Logarithmic Equations II	Graphs of Logarithmic Functions

Conic Sections Videos

Introduction to Conic Sections	Conic Sections - Circles I
Conic Sections - Circles II	Conic Sections - Ellipses I
Conic Sections - Ellipses II	Conic Sections - Parabolas
Conic Sections - Hyperbolas I	Conic Sections - Hyperbolas II
Conic Sections - Hyperbolas III	Conic Sections Summary
Identify and Graph Conic Sections

Matrices Videos

Introduction to Matrices	Matrix Addition and Subtraction I
Matrix Addition and Subtraction II	Matrix Scalar Multiplication
Matrix Multiplication I	Matrix Multiplication II
Matrix Multiplication III	Identity Matrix
Determinant of a 2x2 Matrix	Determinant of a 3x3 Matrix I
Determinant of a 3x3 Matrix II	Simplifying Determinant
Inverse of 2x2 Matrix	Inverse of 3x3 Matrix
Singular Matrix - A Matrix with no Inverse	Solving a 2x2 System of Equations Using a Matrix Inverse I
Solving a 2x2 System of Equations Using a Matrix Inverse II	Solving a 3x3 System of Equations Using a Matrix Inverse
Using Gauss-Jordan to Solve a System of Three Linear Equations	Row Reducing a Matrix to solve a System of Equations
Solving a System of Equations using Matrix Row Transformations	Cramer's Rule
Using Determinant to find the Area of a Parallelogram	Using Determinant to find the Area of a Triangle and a Polygon
Cross Product of Vectors and Determinants(area of triangle and parallelogram)

Sequences and Series Videos

Introduction to Sequences	Arithmetic Sequences I
Arithmetic Sequences II	Arithmetic Sequences Finding the nth Term
Geometric Sequences I	Geometric Sequences II
Geometric Sequences Finding the nth Term	Recursion Sequences
Series and Summation	Arithmetic Series I
Arithmetic Series II	Geometric Series I
Geometric Series II	Infinite Geometric Series
Mathematical Induction	Examples of Mathematical Induction I
Examples of Mathematical Induction II

Probability and Combinatorics Videos

Introduction to Probability I	Introduction to Probability II
Fundamental Counting Principles	Permutations I
Permutations II	Permutations III
Combinations I	Combinations II
Permutations and Combinations	Probability using Permutations and Combinations
Probability of Multiple Events	Probability of Independent Events
Probability of Dependent Events	Probability of Complementary Events
Conditional Probability I	Conditional Probability II
Conditional Probability III	Pascal's Triangle and the Binomial Theorem
Binomial Theorem I	Binomial Theorem II

Advanced Trigonometry Videos

Inverse Trigonometric Functions I	Inverse Trigonometric Functions II
Factoring Trigonometric Equations	Trig Identities cofunctions, reciprocal, quotient, ratio, Pythagorean, and even/odd
Sum and Difference Identities I	Sum and Difference Identities II
Sine and Cosine Addition Formulas (Proofs)	Double Angle Identities I
Double Angle Identities II	Power Reducing Identities
Half Angle Identities	Half Angle and Double Angle Examples

Vectors and Parametric Equations Videos

Geometric Representation of Vectors	Algebraic Representation of Vectors
Components of a Vector
Adding Vectors Graphically or Head-to-Tail Method	Adding Vectors using Components I
Adding Vectors using Components II	Vector Addition and Scalar Multiplication
Vector Magnitude and Direction	The Resultant of Two Forces
Components of a Force	Solve Navigation Problems using Vectors
Unit Vectors I	Unit Vectors II
Vector Equation of a Line	Parametric Equations and Motion
Parameterize a Line Segment and a Circle	Parametric Equations
Dot Product of Vectors	Angle between Two Vectors
Vectors in Three Dimensions	Lines in 3D Coordinate Systems
Vectors and Planes I	Vectors and Planes II

Polar Coordinates Videos

Introduction to Polar Coordinates	Conversion between Polar Coordinates & Rectangular Coordinates
Polar Coordinates Distance Formula	Equations of Lines in Polar Coordinates
Convert between Polar Equations and Rectangular Equations	Symmetry of Polar Graphs
Graphing Polar Equations	Families of Polar Curves: Circles, Cardiods, Lima?on, Roses & Conic Sections

IIT JEE Questions

Questions from previous IIT JEE 2010

IIT JEE Trigonometry Problem IIT JEE Perpendicular Planes	IIT JEE Complex Root Probability IIT JEE Position Vectors
ITT JEE Matrix Equations	IIT JEE Integral Limit IIT JEE Algebraic Manipulation IIT JEE Function Maxima IIT JEE Diameter Slope
IIT JEE Hairy Trig and Algebra	IIT JEE Complex Numbers IIT JEE Differentiability and Boundedness
IIT JEE Integral with Binomial Expansion IIT JEE Symmetric and Skew-Symmetric Matrices IIT JEE Trace and Determinant IIT JEE Divisible Determinants	IIT JEE Circle Hyperbola Intersection IIT JEE Circle Hyperbola Common Tangent
IIT JEE Trigonometric Constraints IIT JEE Trigonometric Maximum Vector Triple Product Expansion (very optional) IIT JEE Lagrange's Formula	Tangent Line Hyperbola Relationship (very optional) 2010 IIT JEE Paper 1 Problem 50 Hyperbola Eccentricity Normal vector from plane equation Point distance to plane Distance Between Planes
Periodic Definite Integral Complex Determinant Example Series Sum Example Trigonometric System Example Simple Differential Equation Example

PreCalculus Calculator with step by step solutions
Relations, Functions,
Operations on Functions,
Points, Lines, and Line Segments,
Absolute Value Expressions and Equations,
Radical Expressions and Equations,
Rational Expressions and Equations,
Polynomial and Rational Functions,
Factoring Polynomials, Conic Sections,
Exponential and Logarithmic Functions,
Trigonometry, Analytic Trigonometry,
Inequalities, Linear Equations,
Systems of Equations, Quadratic Equations
Matrices, Sequences and Series,
Analytic Geometry in Rectangular Coordinates,
Analytic Geometry in Polar Coordinates,
Limits and an Introduction to Calculus,
Vectors, Number Sets

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