#### Precalculus

### 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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