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# Algebra I, Core Level, Part 2 (MTH122B)

## Quick Overview

In this high school math 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; and use ratios, proportions, and percentages to solve problems. This is the second semester of MTH122.

Teacher-Led Course (one-time payment)   \$450.00

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Price as configured: \$0.00

## 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
• 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
• 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
• 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
• Finding Roots of Polynomials
• Unit Review
• Unit Test

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 Discriminant
• 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

Course Length 4 Months
Prerequisites N/A
Course Materials

Many K12 courses utilize physical materials in addition to the online content.  These materials may include the following.

K12
Standard Kits

STANDARD kits contain K12 course materials that are required for completion of the course.  These kits include K12 authored materials and/or difficult to procure materials that a student needs to complete a course. Printed reference guides are not included in Standard kits.

Consumable
Materials

CONSUMABLE kits contain only those materials from the standard kit that are intended for one time use. Families who purchase a Standard kit for Child A could later purchase a Consumable kit for Child B to complete the same course.

Materials

Offered for added convenience, ADDITIONAL kits contain easily obtained materials needed for the course which a family may already have in their home.

Learning
Coach and/or Student Reference Guides are available for purchase with some courses.  Electronic versions of these reference guides are also available within digital courses.

Course Start Date

### Courses Taught by a K12 Teacher

Courses with a teacher have designated start dates throughout Fall, Spring, and Summer. Full-year courses last 10 months and semester courses last 4 months. Courses are taught by teachers in K12 International Academy. For details on start dates, click here.

Teacher Assisted Yes, this course is taught by a K12 International Academy teacher. If you are looking for a teacher-supported option with additional flexibility and year-round start dates, click here to learn about the Keystone School, another K12 online private schooling option.
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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.