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
Chapter 4: Quadratics
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
Chapter 14: Radicals
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

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What our parents say

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

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AGES 13 - 17
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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.

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