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 |