MTH207: Continuing Algebra

This list is representative of the materials provided or used in this course. Keep in mind that the actual materials used may vary, depending on the school in which you are enrolled, and whether you are taking the course as Independent Study.

For a complete list of the materials to be used in this course by your enrolled student, please visit MyInfo. All lists are subject to change at any time.

Scope & Sequence : Scope & Sequence documents describe what is covered in a course (the scope) and also the order in which topics are covered (the sequence). These documents list instructional objectives and skills to be mastered. K12 Scope & Sequence documents for each course include:

Course Overview

In this course, students build on what they learned in Developmental Algebra to complete their knowledge of all topics associated with a deep understanding of Algebra I. They learn about relations and functions, radicals and radical expressions, polynomials and their graphs, factoring expressions and using factoring to solve equations, solving quadratics, rational expressions, and logic and reasoning.

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Course Length

Two Semesters

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Prerequisites

MTH107: Developmental Algebra (or equivalent)

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Course Outline

SEMESTER 1

Continuing Algebra I A, Unit 1: Relations and Functions, Part 1

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 if you put any valid input into a function, you will get a single result out of it.

  • Semester Introduction
  • Foundations
  • Foundations Wrap-Up
  • Relations
  • Relations Wrap-Up
  • Functions
  • Functions Wrap-Up
  • Function Equations, Part 1
  • Function Equations, Part 1 Wrap-Up
  • Function Equations, Part 2
  • Function Equations, Part 2 Wrap-Up
  • Absolute Value Functions
  • Absolute Value Functions Wrap-Up
  • Unit Review
  • Unit Test

Continuing Algebra I A, Unit 2: Relations and Functions, Part 2

How can you tell if two things are related mathematically? If you look closely at the numbers, you might see a pattern as to how one set of numbers changes in relation to the other set of numbers. In mathematics, this is called variation.

  • Foundations
  • Foundations Wrap-Up
  • Direct Variation, Part 1
  • Direct Variation, Part 1 Wrap-Up
  • Direct Variation, Part 2
  • Direct Variation, Part 2 Wrap-Up
  • Quadratic Variation
  • Quadratic Variation Wrap-Up
  • Inverse Variation
  • Inverse Variation Wrap-Up
  • Unit Review
  • Unit Test

Continuing Algebra I A, Unit 3: Irrationals and Radicals, Part 1

Are rational numbers very level-headed? 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
  • Foundations Wrap-Up
  • Rational Numbers
  • Rational Numbers Wrap-Up
  • Terminating and Repeating Numbers
  • Terminating and Repeating Numbers Wrap-Up
  • Square Roots, Part 1
  • Square Roots, Part 1 Wrap-Up
  • Square Roots, Part 2
  • Square Roots, Part 2 Wrap-Up
  • Irrational Numbers
  • Irrational Numbers Wrap-Up
  • Unit Review
  • Unit Test

Continuing Algebra I A, Unit 4: Irrationals and Radicals, Part 2

Expressions that have radicals can sometimes be simplified. Using what you know about simplifying radicals and like terms, you can simplify a variety of radical expressions.

  • Foundations
  • Foundations Wrap-Up
  • Estimating Square Roots
  • Estimating Square Roots Wrap-Up
  • Radicals with Variables, Part 1
  • Radicals with Variables, Part 1 Wrap-Up
  • Radicals with Variables, Part 2
  • Radicals with Variables, Part 2 Wrap-Up
  • Using Square Roots to Solve Equations
  • Using Square Roots to Solve Equations Wrap-Up
  • Pythagorean Theorem
  • Pythagorean Theorem Wrap-Up
  • Unit Review
  • Unit Test

Continuing Algebra I A, Unit 5: Working with Polynomials, Part 1

Just as a train is built from linking rail cars together, a polynomial is built by bringing terms together and linking them with plus or minus signs. You can perform basic operations on polynomials in the same way that you add, subtract, multiply, and divide numbers.

  • Foundations
  • Foundations Wrap-Up
  • Overview of Polynomials
  • Overview of Polynomials Wrap-Up
  • Adding and Subtracting Polynomials
  • Adding and Subtracting Polynomials Wrap-Up
  • Multiplying Monomials
  • Multiplying Monomials Wrap-Up
  • Unit Review
  • Unit Test

Continuing Algebra I A, Unit 6: Working with Polynomials, Part 2

Some polynomials have one term, while other polynomials have two or more terms. Learning how to multiply polynomials with one or more terms is an important step toward understanding polynomials.

  • Foundations
  • Foundations Wrap-Up
  • Multiplying Polynomials by Monomials
  • Multiplying Polynomials by Monomials Wrap-Up
  • Multiplying Polynomials
  • Multiplying Polynomials Wrap-Up
  • The FOIL Method
  • The FOIL Method Wrap-Up
  • Unit Review
  • Unit Test

Continuing Algebra I A, Unit 7: Semester Review and Test

  • Semester Review
  • Semester Test

SEMESTER 2

Continuing Algebra I B, Unit 1: Factoring Polynomials, Part 1

Polynomials are similar to numbers. You can add, subtract, multiply, and divide with polynomials just as you can with numbers. Polynomials even have factors, just as numbers do.

  • Foundations
  • Foundations Wrap-Up
  • Factoring Integers
  • Factoring Integers Wrap-Up
  • Properties of Exponents
  • Properties of Exponents Wrap-Up
  • Dividing Monomials
  • Dividing Monomials Wrap-Up
  • Dividing Polynomials by Monomials
  • Dividing Polynomials by Monomials Wrap-Up
  • Unit Review
  • Unit Test

Continuing Algebra I B, Unit 2: Factoring Polynomials, Part 2

A polynomial is an expression that has variables that represent numbers. A number can be factored, so you should be able to factor a polynomial, right? Sometimes you can, and sometimes you can’t. Finding ways to write a polynomial as a product of factors can be quite useful.

  • Foundations
  • Common Factors of Polynomials
  • Common Factors of Polynomials Wrap-Up
  • Factoring Perfect Squares
  • Factoring Perfect Squares Wrap-Up
  • Factoring Differences of Squares, Part 1
  • Factoring Differences of Squares, Part 2
  • Factoring Differences of Squares Wrap-Up
  • Factoring Quadratic Trinomials
  • Factoring Quadratic Trinomials Wrap-Up
  • Finding Roots of a Polynomial
  • Finding Roots of a Polynomial Wrap-Up
  • Unit Review
  • Unit Test

Continuing Algebra I B, Unit 3: Quadratic Equations, Part 1

Solving equations can help you find answers to many kinds of problems in your daily life. Linear equations usually have one solution, but what about quadratic equations? How can you solve them, and what do the solutions look like?

  • Foundations
  • Foundations Wrap-Up
  • Solving Perfect Square Equations
  • Solving Perfect Square Equations Wrap-Up
  • Completing the Square
  • Completing the Square Wrap-Up
  • The Quadratic Formula
  • The Quadratic Formula Wrap-Up
  • The Discriminant
  • The Discriminant Wrap-Up
  • Unit Review
  • Unit Test

Continuing Algebra I B, Unit 4: Quadratic Equations, Part 2

There are many different ways to solve a quadratic equation. How can quadratic equations be used to model problems, and how can their solutions be used to solve problems?

  • Foundations
  • Solving Quadratic Equations
  • Solving Quadratic Equations Wrap-Up
  • Equations and Graphs: Roots and Intercepts
  • Equations and Graphs: Roots and Intercepts Wrap-Up
  • Applications: Area Problems
  • Applications: Area Problems Wrap-Up
  • Applications: Projectile Motion
  • Applications: Projectile Motion Wrap-Up
  • Unit Review
  • Unit Test

Continuing Algebra I B, Unit 5: 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 with fractions. Fractions with variable expressions in the numerator and denominator can help you solve many kinds of problems.

  • Foundations
  • Foundations Wrap-Up
  • Simplifying Rational Expressions
  • Simplifying Rational Expressions Wrap-Up
  • Multiplying Rational Expressions
  • Multiplying Rational Expressions Wrap-Up
  • Dividing Rational Expressions
  • Dividing Rational Expressions Wrap-Up
  • Adding and Subtracting Rational Expressions, Part 1
  • Adding and Subtracting Rational Expressions, Part 2
  • Adding and Subtracting Rational Expressions Wrap-Up
  • Unit Review
  • Unit Test

Continuing Algebra I B, Unit 6: 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. Once you have mastered the uses of inductive and deductive reasoning, you will be able to make and understand arguments in many areas.

  • Foundations
  • Foundations Wrap-Up
  • Hypothesis and Conclusion
  • Hypothesis and Conclusion Wrap-Up
  • Reasoning and Arguments
  • Reasoning and Arguments Wrap-Up
  • Inductive and Deductive Reasoning
  • Inductive and Deductive Reasoning Wrap-Up
  • Algebraic Proof
  • Algebraic Proof Wrap-Up
  • Unit Review
  • Unit Test

Developmental Algebra I B, Unit 7: Semester Review and Test

  • Semester Review
  • Semester Test
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K12 Scope & Sequence documents for each course include:

  • Course Overview (as seen above)
  • Course Outline
  • Lesson Time and Scheduling