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# Intermediate Algebra

(Formerly called Algebra 3) Algebraic subjects covered include advanced quadratics, polynomials, conics, general functions, logarithms, clever factorizations and substitutions, systems of equations, sequences and series, symmetric sums, advanced factoring methods, classical inequalities, functional equations, and more.

This course is University of California a-g approved. Click here for more details.

24 weeks

#### Diagnostics

ARE YOU READY? DO YOU NEED THIS?

SYLLABUS
24 weeks

### AoPS Holidays

There are no classes May 29 or July 4.

### Who Should Take?

Students should have a mastery of basic algebra up through and including quadratic equations before taking this course. Typically this class follows our Introduction to Geometry class.

This course goes beyond what you would find in a typical honors Algebra curriculum. Algebra courses vary widely in their definitions, but our Intermediate Algebra class covers topics typically found in honors Algebra 2 and Precalculus classes, as well as many topics that are not found in most other curricula. Students who have completed a typical honors Algebra 2 course elsewhere may be ready for Intermediate Algebra.

### Lessons

 Lesson 1 Review and Overview Lesson 2 Functions Review Lesson 3 Complex Numbers Lesson 4 Quadratic Equations and Graphing Parabolas Lesson 5 Minima, Maxima, and Circles Lesson 6 Conics Lesson 7 Polynomial Division, the Remainder Theorem, the Factor Theorem Lesson 8 Integer and Rational Roots Lesson 9 Proof by Contradiction and Irrational Roots Lesson 10 Vieta's Formulas Lesson 11 Multivariable Polynomials Lesson 12 Advanced Strategies for Polynomials Lesson 13 Arithmetic and Geometric Sequences and Series Lesson 14 Advanced Sequences and Series Lesson 15 Induction Lesson 16 Exponents and Logarithms Lesson 17 Radicals, Monotonic, and Even and Odd Functions Lesson 18 Rational Functions and Partial Fractions Lesson 19 Piecewise Functions, Absolute Value, Integer and Fractional Part Lesson 20 Inequalities Lesson 21 Mean Inequality Chain Lesson 22 Cauchy-Schwarz Inequality Lesson 23 Functional Equations Lesson 24 More Functional Equations and Challenging Problems

### Required Textbook

 Intermediate Algebra By Richard Rusczyk and Mathew Crawford A comprehensive textbook covering Algebra 2 and topics in Precalculus. This book is the follow-up to the acclaimed Introduction to Algebra textbook. In addition to offering standard Algebra 2 and Precalculus curriculum, the text includes advanced topics such as those problem solving strategies required for success on the AMC and AIME competitions.

This was the first AoPS class I have taken, and I feel like it was lots of fun and the instructor was very helpful without giving away too many hints. The class also opened my eyes up to a lot of new possibilities and kind of made me feel very small in the sense that there is a vast amount of problem solving techniques and mathematics branches that I have yet to even hear about, much less learn or master. It was also my first online class, and I loved the flexibility it gave me in doing homework and keeping up with class.

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