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.
- Lines & Planes
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Functions
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 & Odd Functions I
Even & Odd Functions II
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 - Transformation of Graphs
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Polynomials
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 & Minimum Values of Polynomial Functions
Find the Zeros of a Polynomial Function I
Find the Zeros of a Polynomial Function II
Conjugate Zeros Theorem
Reciprocal of a Function -
Graphs of Rational Functions
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 & 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
Introduction to Complex Numbers I
Introduction to Complex Numbers II
Adding & Subtracting Complex Numbers
Multiplying Complex Numbers
Dividing Complex Numbers
Trigonometric or Polar Form of Complex Numbers
Converting Complex Numbers between Trigonometric Form & Rectangular
Multiplying & Dividing Complex Numbers in Trigonometric or Polar Form
DeMoivre’s Theorem & Euler Formula
Roots of a Complex Number
Complex Quadratic Equations I
Complex Quadratic Equations II
Simplify Complex Rational Expressions -
Exponential Functions
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
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Logarithmic Functions
Introduction to Logarithmic Functions
Exponential & 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 & Expanding Logarithmic Expressions
Solving Logarithmic Equations I
Solving Logarithmic Equations II
Graphs of Logarithmic Functions -
Conic Sections
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 & Graph Conic Sections -
Matrices
Introduction to Matrices
Matrix Addition & Subtraction I
Matrix Addition & 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 & a Polygon
Cross Product of Vectors & Determinants - area of triangles and parallelograms -
Sequences
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
- Mathematical Induction
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Probability & Combinatorics
Introduction to Probability I
Introduction to Probability II
Fundamental Counting Principles
Permutations I
Permutations II
Permutations III
Combinations I
Combinations II
Permutations & Combinations
Probability using Permutations & 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 & the Binomial Theorem
Binomial Theorem I
Binomial Theorem II -
Advanced Trigonometry
Inverse Trigonometric Functions I
Inverse Trigonometric Functions II
Factoring Trigonometric Equations
Trig Identities cofunctions, reciprocal, quotient, ratio, Pythagorean, & even/odd
Sum & Difference Identities I
Sum & 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 & Double Angle Examples -
Vectors & Parametric Equations
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 & Scalar Multiplication
Vector Magnitude & 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 & Motion
Parameterize a Line Segment & 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
Introduction to Polar Coordinates
Conversion between Polar Coordinates & Rectangular Coordinates
Polar Coordinates Distance Formula
Equations of Lines in Polar Coordinates
Convert between Polar Equations & Rectangular Equations
Symmetry of Polar Graphs
Graphing Polar Equations
Families of Polar Curves: Circles, Cardiods, Limacon, Roses & Conic Sections -
IIT JEE Questions
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 & Algebra
IIT JEE Complex Numbers
IIT JEE Differentiability & Boundedness
IIT JEE Integral with Binomial Expansion
IIT JEE Symmetric & Skew-Symmetric Matrices
IIT JEE Trace & 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, & Line Segments,
Absolute Value Expressions & Equations,
Radical Expressions & Equations,
Rational Expressions & Equations,
Polynomial & Rational Functions,
Factoring Polynomials, Conic Sections,
Exponential & Logarithmic Functions,
Trigonometry, Analytic Trigonometry,
Inequalities, Linear Equations,
Systems of Equations, Quadratic Equations
Matrices, Sequences & Series,
Analytic Geometry in Rectangular Coordinates,
Analytic Geometry in Polar Coordinates,
Limits & an Introduction to Calculus,
Vectors, Number Sets
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