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 & Planes

  Parallel Lines, Skew Lines & Planes
  Proving Parallel Lines

• 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

  Parent Functions & their Graphs
  Transformation of Linear Functions
  Transformation of Quadratic Functions
  
  Horizontal & Vertical Graph Transformations
  Horizontal & Vertical Graph Stretches & Compressions
  Reflective Transformations
  Examples of Graph Transformations

• 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

• 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

  Series and Summation
  Arithmetic Series I
  Arithmetic Series II
  
  Geometric Series I
  Geometric Series II
  Infinite Geometric Series
  

• Mathematical Induction

  Mathematical Induction
  Examples of Mathematical Induction I
  Examples of Mathematical Induction II

• 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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