# Precalculus Help Directory

## Our Clients love our Services!

Sindu is always patient and accommodating. We would recommend her and will be using her services again! My son really enjoyed the tutoring lessons for his precalc!  – Jennifer Singer, Ohio       Read More

## How our Tutoring Works?

How are the Lessons conducted?
Lessons are conducted through Zoom video calling software, similar to Skype. If you can make video calls, then don’t hesitate to give it a try. It is very comfortable…

## PreCalculus Course Description

This course is designed to cover topics in Algebra ranging from polynomial, rational, and exponential functions to conic sections.  Trigonometry concepts such as Law of Sines and Cosines will be introduced.  Students will then begin analytic geometry and calculus concepts such as limits, derivatives, and integrals.  This class is important for any student planning to take a college algebra or college pre-calculus class.

## PreCalculus Syllabus

Complex Numbers

• What are the imaginary numbers?: Complex numbers
• What are the complex numbers?: Complex numbers
• The complex plane: Complex numbers
• Adding and subtracting complex numbers: Complex numbers
• Distance and midpoint of complex numbers: Complex numbers
• Multiplying complex numbers: Complex numbers
• Complex conjugates and dividing complex numbers: Complex numbers
• Identities with complex numbers:Complex numbers
• Absolute value and angle of complex numbers: Complex numbers
• Polar form of complex numbers: Complex numbers
• Multiplying and dividing complex numbers in polar form: Complex numbers\

Polynomials

• Adding and subtracting polynomials: two variables
• The binomial theorem
• The fundamental theorem of algebra
• Polynomial division
• Solving equations by graphing

Composite functions

• Composing functions
• Modeling with composite functions
• Verifying inverse functions by composition
• Invertible functions

Trigonometry

• Inverse trigonometric functions
• Sinusoidal equations
• Sinusoidal models
• Trigonometric identities
• Angle addition identities
• Using trigonometric identities

Vectors

• Vectors introduction
• Magnitude of vectors
• Scalar multiplication
• Vector addition and subtraction
• Combined vector operations
• Unit vectors
• Magnitude and direction form of vectors
• Component form of vectors
• Adding vectors in magnitude and direction form
• Vectors word problems

Matrices

• Introduction to matrices
• Representing linear systems of equations with augmented matrices
• Elementary matrix row operations
• Row-echelon form and Gaussian elimination
• Adding and subtracting matrices
• Multiplying matrices by scalars
• Properties of matrix addition & scalar multiplication
• Multiplying matrices by matrices
• Properties of matrix multiplication
• Matrices as transformations
• The determinant of a 2×2 matrix
• Introduction to matrix inverses
• Finding the inverse of a matrix using its determinant
• Practice finding the inverses of 2×2 matrices
• Solving equations with inverse matrices
• Model real-world situations with matrices

Series

• Arithmetic sequences
• Geometric sequences
• Geometric series
• Geometric series (with summation notation)
• Arithmetic series

Conic sections

• Introduction to conic sections
• The features of a circle
• Standard equation of a circle
• Expanded equation of a circle
• Center and radii of an ellipse
• Foci of an ellipse
• Focus and directrix of a parabola
• Introduction to hyperbolas
• Foci of a hyperbola
• Hyperbolas not centered at the origin
• Identifying conic sections from their equations

Probability and combinatorics

• Basic probability
• Venn diagrams and the addition rule
• Compound probability of independent events using diagrams
• Compound probability of independent events using the multiplication rule
• Dependent events
• Permutations
• Combinations
• Probability using combinatorics

## PreCalculus Readiness Test

The following are online open text (i.e. free) resources:

Websites with free video lectures

## PreCalculus Practice Tests

Here is a website where you can download free practice tests for PreCalculus, I will upload more tests soon. http://pages.duneland.k12.in.us/mr-berry-chs/practice-tests

## PreCalculus Tutoring

We also provide 1-1 private math tutoring for students.

You can book a free consultation and demo lesson to know more.

## Our Clients love our Services!

Sindu is always patient and accommodating. We would recommend her and will be using her services again! My son really enjoyed the tutoring lessons for his precalc!  – Jennifer Singer, Ohio       Read More

## How our Tutoring Works?

How are the Lessons conducted?
Lessons are conducted through Zoom video calling software, similar to Skype. If you can make video calls, then don’t hesitate to give it a try. It is very comfortable…