ALGEBRA 2

Mr. P. Nelson

pnelson0502@yahoo.com

General Course Description

In Algebra 2, students will continue to study, further develop, and extend on the ideas formulated in Algebra 1. The study of linear and quadratic equations will be extended to higher-degree polynomials over the set of complex numbers as opposed to just the real numbers. Furthermore, the properties of functions and relations will be studied in greater depth. Topics of focus include graphical transformations and the inverses of power functions and exponential functions with applications. In addition, the theory of basic algebra and geometry will serve as prerequisites to the development of trigonometry. Finally, the course will conclude with some statistical concepts. In essence, Algebra 2 is also a survey course that introduces concepts that students will encounter in higher-level mathematics.

Materials Needed

• Notebook paper

• Graph paper

• #2 pencils

• Scientific calculator

Desmos Scientific Calculator: https://www.desmos.com/scientific

Desmos Graphing Calculator: https://www.desmos.com/calculator

Course Content

In Algebra 1, it is expected that students were introduced to the real number system, functions and relations on the Cartesian plane, and polynomials. Computations were performed over the real numbers, and linear, exponential, and quadratic functions were studied in particular. In Algebra 2, we pick up with quadratic equations and extend the study of quadratics over the complex numbers. We then extend this study to polynomial functions of higher degree, examining the structure and properties of specific polynomial and power functions. Special attention will be paid to the study of the roots of polynomial equations with emphasis on the Fundamental Theorem of Algebra, the Remainder Theorem, and the Factor Theorem. This study of polynomials is extended to rational functions (the quotients of polynomials). Then, we examine the inverses of functions of interest, inviting us to study the relationship betwen exponential and logarithmic functions with applications. Finally, we plunge into trigonometry using the skills we have acquired in algebra and geometry. If time permits, we will delve into introductory statistics with emphasis on the Normal Distribution.

Course Material

The lecture summaries should not be used as a substitute for participating in class. Students should still take their own notes.

Handouts

• Coordinate Grids

• Properties of the Real Numbers

• Guidelines for Factoring Completely

• Completing the Square Procedure

• Perfect Squares and Square Roots to Remember & Memorize

• Graphical Transformations

• Twelve Basic Functions

• Review of Polynomial Terms with Examples

• Polynomial Functions: Important Terms, Definitions, Theorems, Corollaries to Know

• Graphs of Rational Functions

• Review Handout: Exponent Rules

• Significant Figures

• Properties of Logarithms

• Summary of Sequences and Series

• Sequences and Series Formula Sheet

• Triangle Trigonometry

• Derivation of Hero's Formula

• Special Angles and Trig Values

• Blank Unit Circle

• Trigonometric Graphs and Identities

• Trigonometry Formula Sheet

• General Solutions for Arcsine, Arccosine, Arctangent

• Table for Standard Normal Distribution

Lecture Summaries

Semester 1:

• Complex Numbers and the Cartesian Plane

• Solving and Graphing Quadratic Functions

• Quadratics and the Golden Ratio

• Absolute Value, Piecewise-Defined Functions, and Graphical Transformations

• Functions

• The Theory of Polynomial Equations

• Polynomial Inequalities

• Rational Functions, Equations, and Applications

Semester 2:

• Inverse Relations and Functions

• Radical Equations

• Fractional Exponents

• Logarithmic Equations with Applications

• Sequences and Series

• The Binomial Theorem

• Proof by Mathematical Induction

• Trigonometric Functions and Triangle Trigonometry

• Trigonometric Graphs, Identities, Equations, and Applications

• The Normal Distribution