Description and Objectives

The course Algebra II is a two semester course covering all of the traditional studies. The course can be broken down into the following four general topics: Basic algebra (a review of Algebra I), Polynomial functions, Exponential and Logarithmic functions and basic Trigonometry with Geometry permeating the entire course.

Outline of Topics Covered

• Basic Algebra I Review

Objective: To make sure the students recall how to solve linear equations, inequalities and systems of each and how to graph solution sets of such equations, inequalities and systems. Next the discussion turns to quadratics of the form and piece-wise linears . After this, factoring is employed as a tool in graphing.

• Functions

Objective: This topic covers basic functions theory: relations vs. functions, inverses and the concept of one-to-one. Here we re-iterate the notions from Algebra I with an eye on increasing the library of functions with which the student is familiar.

• Polynomials

Objective: We continue to increase the degree of the polynomial having already looked at linear and quadratic functions. Some mention will be made to the Fundamental Theorem of Algebra but most of our analysis will be graphical.

• Rational functions

Objective: Having already discussed polynomials, it is now time to discuss the quotient of polynomials – namely rational functions. We will limit ourselves to simple rational functions and make much use of the Chart of Signs to discuss the qualitative graphs of these functions.

• Trigonometry

Objective: The students learn of the basic trigonometric functions and their origin. Use of the unit circle and reference triangle is emphasized. The students are also introduced to the proofs of trigonometric identities from the basic odd/even and Pythagorean identities. This helps to prepare the student for the notion of proof given in Geometry the following year.

• Exponential functions

Objective: Here we introduce having variable exponents instead of bases: bx. This is then used as a springboard to a discussion of inverses of functions and specifically to the definition of logarithm.

Textbooks

Intermediate Algebra, Kaufmann, 1996.

Course Requirements

This course integrates nicely with the course Algebra I typically offered in Grade 8. Here we hope to not only review the material already learned but to go deeper in scope and understanding. As far as new material is concerned, this will be the first time the student is exposed to the concept of an exponential function. In addition to this, we expand the understanding of trigonometry which will be revisited in Geometry next school year and in Precalculus the following year. The time allocation to each of these general topics is as follows: approximately 2 months are necessary for the basic algebra review and the definition of function, another 2 months on polynomial functions and their graphs, 2 months on trigonometry, and 5-6 weeks on the exponential and logarithmic functions.

Homework is given daily and comprises a large part of the overall grade. Quizzes are given every 1-2 weeks. Each semester there are typically 4 full period exams (roughly 2 per quarter) and an hour-and-a-half Midterm/Final exam.

Successful Students

Students may ask questions any time. Office hours are plentiful and include before school every day, lunch hour most days and after school by appointment. Students are encouraged to make use of the instructor’s email address: jmaloney@heights.edu or his extension on campus 301.365.0227 ext. 141

Summer Assignment

2021 Algebra 2 Summer Assignment