# Honors Immediate Algebra

**CATALOG DESCRIPTION
Brief Course Description**

Honors Intermediate Algebra builds on the material from Honors Beginning Algebra.

The course begins with a review of the real number system and solutions of linear

equations and inequalities. Students learn to solve equations and inequalities involving

absolute value. Following this, graphs of linear equations are reviewed and students

learn additional material about functions and variation. After a review of solutions to 2x2

systems, students learn how to solve 3x3 and 4x4 systems of linear equations.

Operations on polynomials, including factoring , are covered, along with rational

expressions. Radical expressions are reviewed, and students learn to solve equations

involving several radical expressions. Students learn to apply the quadratic formula to

equations that are quadratic in type, and they investigate solutions to quadratic and

rational inequalities . Beginning with a general study of inverse functions, students learn

the basic properties of exponential and logarithmic functions and apply them to realworld

problems. Finally, the course concludes with an introduction to arithmetic series,

geometric series, and the binomial theorem.

**Pre-Requisites: **Required: Honors Beginning Algebra

**TEXTS AND SUPPLEMENTAL INSTRUCTIONAL MATERIALS
**

**Supplemental Instructional Materials (please describe)**

Education Program for Gifted Youth (EPGY) Intermediate Algebra course. EPGY offers

students mathematics courses by presenting the material on personal computers, in a

way that aims to replicate the classroom environment as closely as possible. Students

complete lessons which include multimedia lectures, online exercises, and derivations.

Derivation exercises ask students to justify their steps in an interactive workshop

environment.

**COURSE CONTENT**

A. Course Purpose.

A. Course Purpose.

Honors Intermediate Algebra requires that students master the following specific topics:

• Algebraic Expressions

• The Real Number System, The Order of Operations , Properties of Real Number

• Linear Equations and Inequalities

• Linear Equations and Inequalities, Absolute Value Equations and Inequalities,

Graphing

• Linear Equations, Relations, Functions, Variation

• Systems of Linear Equations

• Solving 2x2, 3x3 and 4x4 Systems of Equations with Applications

• Polynomial Functions

• operations on Polynomials, Polynomial Long Division, Factoring, Special

Factorizations,

• Solving Equations by Factoring, Applications

• Rational Functions

• Operations on Rational Expressions, Graphing Rational Functions, Applications

Radical Functions

• Operations on Radical Expressions, Graphing Radical Expressions, Complex

Numbers, Applications

• Exponential and Logarithmic Functions

• Inverse Functions, Exponential Functions, Exponential Equations, Logarithmic

• Functions, Evaluating Logarithms, Logarithmic Equations, Exponential Growth and

Decay, The Change-of-base Formula

**B. Course Outline.**Detailed description of topics covered. Show examples of how the

text or readings are incorporated into the topics covered.

Lesson Number Concepts Covered

Textbook Section

• Sets; real numbers; order of operations; properties of real number

• Linear equations and inequalities in one variable; applications

• Absolute value; equations involving absolute value; applications

• Set operations; interval notation; solving compound inequalities

• Solving absolute value inequalities; applications

• Slope and the equation of a line; 2x2 systems of linear equations

• Systems of linear inequalities in two variables; variation

• Solving 2x2 systems of linear equations

• Solving 3x3 and 4x4 systems of linear equations; applications

• Relations and functions; domain and range; vertical line test

• Linear functions; operations on functions; composition of functions

• Identifying linear, quadratic, polynomial, and square root functions

• Polynomial functions; adding, subtracting , and multiplying polynomials

• Factoring: by grouping, trinomials, special factorizations

• Adding, subtracting, multiplying, and dividing rational expressions

• Rational Expressions and Functions

• Appendix C Polynomial long division; synthetic division

• Graphing rational functions; applications: proportions, work, distance-rate-time

• Adding, subtracting, multiplying, and dividing radical expressions; graphs

• Solving equations involving radical expressions; complex numbers

• Solving quadratic equations: completing the square and the quadratic formula

• The discriminant; use of the discriminant to analyze quadratic equations

• Solving equations quadratic in form; applications: area, quadratic functions, etc.

• Solving quadratic and rational inequalities

• Inverse functions; horizontal line test; finding the inverse of a function

• Exponential functions; solving exponential equations; exponential growth/decay

• Logarithmic functions; graphs; solving logarithmic equations

• Properties of logarithms; simplifying logarithmic expressions

• Common logarithms ; natural logarithms

• Exponential and logarithmic equations; compound interest, exponential growth

• The change-of-base formula

• Sequences and series; finding general terms; evaluating series

• Sigma notation

• Arithmetic sequences; general term; finite sums of arithmetic sequences

• Geometric sequences; general term; finite/infinite sums of geometric sequences

• The Binomial Theorem; Pascal’s triangle; finding terms of binomial expansions

• Additional Graphs of Functions

• The Circle and the Ellipse

• The Hyperbola and Functions defined by Radicals

• Nonlinear Systems of Equations

• Second-Degree Inequalities and Systems of Inequalitites

**B. Key Assignments:**

Homework - The homework assignments are picked from the textbook and submitted to

the instructor. The homework assignments are used as a tool for reinforcing the material

presented and discussed in class.

Software lessons and quizzes - The software lessons further the students

understanding and depths of the material. The software EPGY offers presents the

material on personal computers, in a way that aims to replicate the classroom

environment as closely as possible. Students complete lessons which include

multimedia lectures, online exercises, and derivations. Derivation exercises ask

students to justify their steps in an interactive workshop environment.The software is

interactive and gives students feedback on problems they missed. The student's work is

sent through the software and processed by the Stanford servers.

Chapter Exams - The students take chapter exams in the course software.

Midterm and Final Exams - The students take comprehensive proctored midterm and

final exams during the course of the semester.

**D. Instructional Methods and/or Strategies**

The classroom time is used to present new information, discuss homework assignments

that students had difficulty with, and present more challenging problems. The EPGY

software is used as a tool to enhance student understanding of the material. In the

software, students complete lessons which include multimedia lectures, online

exercises, and derivations. Derivation exercises ask students to justify their steps in an

interactive workshop environment. The software gives students feedback on the

problems they missed.

**E. Assessment Methods and/or Tools**

The assessments tools include: EPGY software lessons, quizzes, chapter exams,

proctored comprehensive midterm exams, and a proctored comprehensive final exam.

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