# Algebra

This class will build on concepts learned in the Pre-Calculus and Introduction to Calculus courses. Students will learn advanced concepts that include polynomials, inequality, radicals, and functions. This class is designed to expand on the Algebra and Pre-Calculus curriculum to introduce students to the problem solving strategies required for success on the AMC and AIME competitions.

###### Chapter 1: Basic Techniques for Solving Equations
Solving system of equations by substitution and elimination
###### Chapter 2: Functions Review
Definition of functions, graph of functions, composition, and inverse functions
###### Chapter 3: Complex Numbers
Arithmetics of complex numbers, complex plane
Factoring, Vieta’s formulae, discriminant, quadratic inequalities
###### Chapter 5: Conics
Parabolas, Circles, Ellipses, Hyperbolas
###### Chapter 6: Polynomial Division
Division, synthetic division, remainder theorem
###### Chapter 7: Polynomial Roots I
Factor Theorem, Fundamental Theorem of Algebra
###### Chapter 8: Polynomial Roots II
Irrational and complex roots, Vieta’s Formula
###### Chapter 9: Factoring Multivariable Polynomials
Grouping, sums and differences of powers
###### Chapter 10: Sequences and series
Arithmetic series and sequences, geometric series and sequences, summation and product notation
###### Chapter 11: Identities, Manipulations, and Induction
Brute Force, Induction, Binomial Theorem
###### Chapter 12: Inequalities
Trivial and AM-GM inequality, Cauchy Schwarz inequality
###### Chapter 13: Exponents and Logarithms
Exponential Functions, Properties of Logarithm
Working with expressions with radicals, conjugates
###### Chapter 15: Special Classes of Functions
Rational Function, even and odd functions, monotonic functions
###### Chapter 16: Piecewise Defined Functions
Piecewise functions, absolute value, floor and ceiling
###### Chapter 17: More Sequences and series
Recursive Sequences, Telescoping series
###### Chapter 18: More Inequalities
Rearrangement Inequality
###### Chapter 19: Functional Equations
Solving functional equations with substitution, separation
###### Chapter 20: Some advanced strategies
Solving problems by exploiting the symmetry in the problem, substitution, using undetermined coefficients

## Learn from the best

Passion for tech. Unmatched expertise. Personality that brings out the absolute best in your child. We know there's no replacement for the best teacher. It's no surprise that iconic companies like Google, Amazon, Microsoft, and Disney hire the same talent we do. Our Geek Certified instructors possess the whole package of skills that inspires students for the Tech World!

Recruited from top universities and leading IT companies
Rigorous background and reference checks
Geekedu Certified professional level
Verified teaching experience

## What our parents say

This course is for students who have completed our Introduction to Algebra course.

Level:
AGES 13 - 17
Online 1-on-1 Private Sessions

This course typically takes 3-6 months to complete. This depends on the student's experience and how fast they can master the concepts and the knowledge. Our instructors move at the pace of the student, it may take extra time for some students to reinforce what they have learned.

### You Might Also Be Interested In Our Elective Courses

##### Python Level 1
AGES 10 - 15

Designed for beginners, this level is designed to teach the basic fundamentals and design principles of Python, with the help of Turtle graphics and PyGame. This includes: variables, conditional statements, loop basics, and functions.

These concepts are transferable to any other programming language. Throughout the way, students will create projects in order to apply the concepts they have learned, and to solidify their knowledge.

##### Python Level 2
AGES 10 - 15

Level 2 dives deeper into the basics of Python for a more thorough understanding and introduces advanced topics. Students will build on knowledge from Level 1 and work with data structures, advanced loops, algorithms, and object-oriented programming, and create games based on what they learn.

Students will complete the course with a solid understanding of Python fundamentals.

##### Java Level 1
AGES 10 - 15

This beginner-friendly course serves as an introduction to the Java programming language. Students will learn the fundamentals of Java along with core computer science concepts.