Algebra 2A 2B

Textbook: “Intermediate Algebra”, by Richard Rusczyk and Mathew Crawford, the Art of Problem Solving series, ISBN-13: 978-1-934124-04-8

For the upcoming semester (Fall 2019), we are teaching Algebra 2A.

Course Introduction:

Algebra 2 covers complex numbers, quadratic equations, conics, polynomials, functions, logarithms, cleaver factorizations and substitutions, systems of equations, sequences and series, symmetric sums, advanced factoring methods, classical inequalities, functional equations, and more. This course goes beyond what you would find in a typical honors Algebra II curriculum, as it covers topics found in honors Algebra II and Precalculus classes, as well as many topics no found in most other curricula. This is a one-year course and is divided into two parts to be taught in two semesters, Algebra 2A and Algebra 2B.

Algebra 2A covers complex numbers, conics, polynomial division, polynomial roots, factoring multivariable polynomials, sequences and series. Algebra 2B covers identities, induction, inequalities, exponents and logarithms, radicals, special classes of functions, and piecewise defined functions.

This course is intended for high-performing students and will focus on problem solving skills. Students will learn via practicing solving problems in the classroom. Each class will have 3 hours where after being introduced with the new material, students spend the rest of the classroom time practicing the new skills.

Who Should Take Algebra 2A:

Students should have a mastery of basic algebra up through and including quadratic equations before taking this course. Typically this class follows our “Algebra 1B” class. Students who have completed typical Algebra 1 may be ready for this class.

An entrance exam should be taken to evaluate student’s readiness.

Who Should Take Algebra 2B:

Students should have a mastery of basic algebra up through and including polynomials, sequences and series, advanced factoring before taking this course. Typically this class follows our “Algebra 2A” class.

An entrance exam should be taken to evaluate student’s readiness.

Requirements for Students Registering for Algebra 2A or Algebra 2B

In general, students in grade 8 – 10 are eligible to register for either one of Algebra 2 courses. All students interested in take any of these courses should pass the corresponding evaluation test. The test must be taken and submitted before the specified deadline posted by the school web site. The tests are posted on the school web site as well. Please check the class schedule at the school web site.

Teaching Plan

Algebra 2A
Lesson 1 Ch 3. Complex Numbers

3.1 Arithmetic of Complex Numbers

3.2 The Complex Plane

Lesson 2 3.3 Real and Imaginary Parts

3.4 Graphing in the Complex Plane

3.5 Summary

Lesson 3 Ch 5. Conics

5.1 Parabolas

5.2 Problem Solving With Parabolas

5.3 Maxima and Minima of Quadratics

Lesson 4 5.4 Circles

5.5 Ellipses

Lesson 5 5.6 Hyperbolas

5.7 Summary

Lesson 6 Ch 6. Polynomial Division

6.1 Polynomial Review

6.2 Introduction to Polynomial Division

Lesson 7 6.3 Synthetic Division

6.4 The Remainder Theorem

6.5 Summary

Lesson 8 Ch 7. Polynomial Roots, Part 1

7.1 The Factor Theorem

7.2 Integer Roots

Lesson 9 7.3 Rational Roots

7.4 Bound

Lesson 10 7.5 Graphing and Fundamental Theorem of Algebra

7.6 Algebraic Applications of the Fundamental Theorem

7.7 Summary

Lesson 11 Ch 8. Polynomial Roots, Part 2

8.1 Irrational Roots

8.2 Nonreal Roots

Lesson 12 8.3 Vieta’s Formulae

8.4 Using Roots to Make Equations

8.5 Summary

Lesson 13 Ch 9. Factoring Multivariable Polynomial

9.1 Grouping

9.2 Sums and Differences of Powers

Lesson 14 9,3 The Factor Theorem of Multivariable Polynomial

9.4 Summary

Lesson 15 Ch 10. Sequences and Series

10.1 Arithmetic Sequences

10.2 Arithmetic Series

Lesson 16 10.3 Geometric Sequences

10.4 Geometric Series

 

Algebra 2B
Lesson 1 10.5 Sequence, Summation, and Product Notation

10.6 Nested Sums and Products

10.7 Summary

Lesson 2 Ch 11. Identities, Manipulations, and Induction

11.1 Brute Force

11.2 Ratios

Lesson 3 11.3 Induction

11.4 Binomial Theorem

11.5 Summary

Lesson 4 Ch 12. Inequalities

12.1 Manipulating Inequalities

12.2 The Trivial Inequality

Lesson 5 12.3 AM-GM Inequality with Two Variables

12.4 AM-GM Inequality with More Variables

Lesson 6 12.5 The Cauchy-Schwarz Inequality

12.6 Maxima and Minima

12.7 Summary

Lesson 7 Ch 13. Exponents and Logarithms

13.1 Exponential Function Basics

13.2 Introduction to Logarithms

Lesson 8 13.3 Logarithmic Identity

13.4 Using Logarithm Identity

Lesson 9 13.5 Switching Between Logarithms and Exponents

13.6 Natural Logarithm and Exponential Decay

13.7 Summary

Lesson 10 Ch 14. Radicals

14.1 Raising Radicals to Powers

14.2 Evaluating Expressions with Radicals

Lesson 11 14.3 Radical Conjugates

14.4 Summary

Lesson 12 Ch 15. Special Classes of Functions

15.1 Rational Functions and Their Graphs

15.2 Rational Function Equations and Inequalities

Lesson 13 15.3 Even and Odd Functions

15.4 Monotonic Functions

15.5 Summary

Lesson 14 Ch 16. Piece-wise Defined Functions

16.1 Introduction to Piece-wise Defined Functions

16.2 Absolute Value

Lesson 15 16.3 Graphing Absolute Value

16.4 Floor and Ceiling

Lesson 16 16.5 Problem Solving with the Floor Functions

16.6 Summary

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