Details
Course Overview
In this course, students explore the tools of algebra. Students learn to identify the structure and properties of the real number system; complete operations with integers and other rational numbers; work with square roots and irrational numbers; graph linear equations; solve linear equations and inequalities in one variable; solve systems of linear equations; use ratios, proportions, and percentages to solve problems; use algebraic applications in geometry, including the Pythagorean theorem and formulas for measuring area and volume; complete an introduction to polynomials; and understand logic and reasoning. This is the second semester of MTH122.
Course Outline
SEMESTER TWO
Algebra I B, Unit 1: Relations and Functions
A solar cell is a little machine that takes in solar energy and puts out electricity. A mathematical function is a machine that takes in a number as an input and produces another number as an output. There are many kinds of functions. Some have graphs that look like lines, while others have graphs that curve like a parabola. Functions can take other forms as well. Not every function has a graph that looks like a line or a parabola. Not every function has an equation. The important thing to remember is that any valid input into a function, results in a single result out of it.
 Semester Introduction
 Foundations
 Relations
 Functions
 Function Equations 1
 Function Equations 2
 Absolute Value Functions
 Direct Linear Variation 1
 Direct Linear Variation 2
 Quadratic Variation
 Inverse Variation
 Unit Review
 Unit Test
Algebra I B, Unit 2: Rationals, Irrationals, and Radicals
Are rational numbers very levelheaded? Are irrational numbers hard to reason with? Not really, but rational and irrational numbers have things in common and things that make them different.
 Foundations
 Rational Numbers
 Terminating and Repeating Numbers
 Square Roots 1
 Square Roots 2
 Irrational Numbers
 Estimating Square Roots
 Radicals with Variables 1
 Radicals with Variables 2
 Using Square Roots to Solve Equations
 The Pythagorean Theorem
 Unit Review
 Unit Test
Unit 3: Working with Polynomials
Just as a train is built from linking railcars together, a polynomial is built by bringing terms together and linking them with plus or minus signs. Basic operations on polynomials work the same way as adding, subtracting, multiplying, and dividing numbers.
 Foundations
 Overview of Polynomials
 Adding and Subtracting Polynomials
 Multiplying Monomials
 Multiplying Polynomials by Monomials
 Multiplying Polynomials
 The FOIL Method
 Unit Review
 Unit Test
Unit 4: Factoring Polynomials
A polynomial is an expression that has variables that represent numbers. A number can be factored, but what about a polynomial? Sometimes yes and sometimes no. Finding ways to write a polynomial as a product of factors can be quite useful.
 Foundations
 Factoring Integers
 Properties of Exponents
 Dividing Monomials
 Dividing Polynomials by Monomials
 Common Factors of Polynomials
 Factoring Perfect Squares
 Factoring Differences of Squares 1
 Factoring Differences of Squares 2
 Factoring Quadratic Trinomials
 Finding Roots of Polynomials
 Unit Review
 Unit Test
Unit 5: Quadratic Equations
Solving equations can help answer many kinds of problems. Linear equations usually have one solution, but what about quadratic equations? How many solutions can a quadratic equation have and what do the solutions look like?
 Foundations
 Solving Perfect Square Equations
 Completing the Square
 The Quadratic Formula
 The Discriminant
 Solving Quadratic Equations
 Equations and Graphs: Roots and Intercepts
 Applications: Area Problems
 Applications: Projectile Motion
 Unit Review
 Unit Test
Unit 6: Rational Expressions
A fraction always has a number in the numerator and in the denominator. However, those numbers can actually be expressions that represent numbers, which means you can do all sorts of interesting things can happen with fractions. Fractions with variable expressions in the numerator and denominator can help solve many kinds of problems.
 Foundations
 Simplifying Rational Expressions
 Multiplying Rational Expressions
 Dividing Rational Expressions
 Adding and Subtracting Rational Expressions 1
 Adding and Subtracting Rational Expressions 2
 Unit Review
 Unit Test
Unit 7: Logic and Reasoning
Professionals use logical reasoning in a variety of ways. Just as lawyers use logical reasoning to formulate convincing arguments, mathematicians use logical reasoning to formulate and prove theorems.
 Foundations
 Hypothesis and Conclusion
 Reasoning and Arguments
 Forms of Conditionals
 Inductive and Deductive Reasoning
 Analyzing and Writing Proofs
 Counterexample
 Unit Review
 Unit Test
Unit 8: Semester Review and Test
 Semester Review
 Semester Test
To use this course, you'll need a computer with an Internet connection. Some courses require additional free software programs, which you can download from the Internet.
Hardware and Browsers (Minimum Recommendations)
Windows OS

CPU: 1.8 GHz or faster processor (or equivalent)

RAM: 1GB of RAM

Browser: Microsoft Internet Explorer 9.0 or higher, Mozilla Firefox 10.0 versions or higher, Chrome 17.0 or higher
 At this time our users are encouraged not to upgrade to Windows 10 or Edge (the new browser)
Mac OS

CPU: PowerPC G4 1 GHz or faster processor; Intel Core Duo 1.83 GHz or faster processor

RAM: 1GB of RAM

Browser: Firefox 10.0 versions or higher, Chrome 17.0 or higher (Safari is not supported!)
Internet Connections
It is highly recommended that a broadband connection be used instead of dial up.