Problem Solving in Algebra I, Part II

Course Description

Description

CTY's Problem Problem Solving and Enrichment Math courses sharpen investigative skills, broaden mathematical understanding of concepts, and enhance reasoning skills. Designed around performance objectives that reflect national and state mathematical standards, these courses demonstrate how mathematical issues arise out of real-life situations. Concepts are assessed through challenging quizzes and module tests. With the guidance of their instructors, students typically select enrichment or supplementary math courses of the appropriate level in between their accelerated courses to ensure a solid foundation and mastery of math concepts at each level.

In Problem Solving in Algebra I, Part II, students apply advanced algebraic concepts using a variety of techniques. Topics include concepts typically covered in second semester algebra, such as:

• applications of the real number system
• powers and polynomials
• quadratic equations
• functions
• first and second degree equations
• linear best-fit graphs
• rational expressions

Students refine and expand their skills through interactions, practice problems, and workout questions. This course provides a solid foundation for students who will be advancing into Algebra II.

Materials Needed

There are no required materials for this course.

List of Topics

Module 1: The Real Number System

Rational and Irrational Numbers

• Defining the Real Numbers
• Working with Radicals
• The Square Root Function

Module 2: Powers and Polynomials

Polynomial Arithmetic

• Working with Powers
• Adding and Subtracting Polynomial Expressions
• Multiplying Polynomials

Factoring Polynomials

• Finding Common Factors
• Factoring Quadratic Trinomials
• Special Cases

Module 3: Quadratic Functions & Equations

Graphing Quadratic Functions and Equations

• Graphing Parabolas
• Analyzing Properties of Parabolas
• Solving Quadratic Equations by Graphing

Solving Quadratic Equations Using Algebra

• Factoring and the Zero Product Theorem
• The Square Root Method and Completing the Square
• The Quadratic Formula

Module 4: Algebraic Expressions & Functions

Radical Equations and Functions

• Solving Radical Equations
• The Inverse of the Square Root Function

Rational Functions and Equations

• Rational Operations
• Rational Functions
• Rational Equations

Module 5: Describing Data

Statistical Displays

• Stem-and-Leaf Plots and Box Plots
• Scatter Plots and Best-Fit Curves

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System Requirements

CTYOnline courses require a properly-maintained computer with Internet access and a recent-version web browser (such as Firefox, Safari, or Internet Explorer) with the Adobe Flash plugin. Students are expected to be familiar with standard computer operations (e.g. login, cut & paste, email attachments, etc).

This course requires high-speed Internet access (such as Cable or DSL) for online lesson videos. Your browser will need to allow javascript, login cookies, and popup windows from ctyjhu.org, bluejay.cty.jhu.edu, and any other course web sites.

This course uses an online mathematical whiteboard for individual or group discussions with the instructor. The whiteboard web site requires cookies, popup windows, and the Java Runtime Environment. (Note: iOS & Android devices cannot run Java applets.)