PreCalculus



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Explore our rich collection of videos, games, activities and worksheets that are suitable for the study, practice or review of PreCalculus.

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.

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 I Inverse of 2x2 Matrix II
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  


Probabilty 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 I Components of a Vector II
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├žon, 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
 






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