Precalculus

Precalculus

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Course Description

Complex numbers

What are the imaginary number ?
what are the complex number ?
The complex plane
Adding and subtracting complex number
Distance and midpoint of complex number
Multiplying complex number
complex conjugates and dividing complex number
Identities with complex number
Absolute value and angle of complex number
polar from a complex number
Multiplying and dividing a complex number  in a polar form

Polynomials

Adding and subtracting polynomials :two variable
The binomial theorem
The fundamental theory of algebra
polynomial division
solving equation by graphing
Composite functions
Composite function
Modeling with composite function
verifying inverse function by composite
Invertible function

Trigonometry

Inverse trigonometry function
Sinusoidal function
Sinusoidal model
trigonometry identities
angle addition identities
using trigonometry identities

Vectors

Vector introduction
Magnitude of vector
Scalar multiplication
vector addition and subtracting
combined vector operation
Unit vector
Magnitude and direction form of vector
component form of vector
Adding vector in magnitude and direction form
vector word problem

Matrices

Introduction to matrices
Representing linear system of equation with augmented
Elementary matrices row operation
Row-echelon from and Gaussian elimination
Adding and subtracting matrices
Multiply matrices by scalars
Properties of matrices addition &scalar multiplications
Multiplying matrices by matrices
properties of matrices multiplication
matrices as transformation
The determine of a 2×2 matrices
solving equation  with inverse matrices
Model real word situations with matrices

Series

Arithmetic sequence
Geometric sequence
Geometric series
Geometric series (with summation rotation )
Arithmetic series

Conic sections

Introduction to conic section
The feature of a circle
Standard equation of a circle
Expand Equation of a circle
center and radii of an ellipse
Foci of an ellipse
focus and directrix  of a parabola
Introduction to hyperbola
Foci of hyperbola
Hyperbola is not centered at origin
Identifying conic section  from their equation
Challenging conic section problem (IIT JEE)

Probability and combinatorics

Basic probability
Venn diagram and additional rule
Compound probability of independent event using diagram
Compound probability of independent event using multiple
Dependent event
Permutations
Combinations

Probability using combinatorics

COURSE CHALLENGE

Test your knowledge of the skills in this course. Have a test coming up? The Course challenge can help you understand what you need to review.

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