# FUNDAMENTALS OF ALGEBRA

## VIII. COURSE OUTLINE

A. Unit One: (Chapter Two) ** Equations Inequalities and
Problem Solving**

**1. Unit Objectives:** Upon successful completion of this unit the student
will be able to do the following:

a. Identify terms , like terms, and unlike terms

b. Combine like terms

c. Use the distributive property to remove parentheses

d. Write word phrases as algebraic expressions

e. Define linear equation in one variable and equivalent equations

f. Use the addition property of equality to solve linear equations

g. Write word phrases as algebraic equations

h. Use the multiplication property of equality to solve linear equations

i. Use both the addition and multiplication properties of equality to
solve linear equations

j. Apply the general strategy for solving a linear equation

k. Solve equations containing fractions or decimals

l. Recognize identities and equations with no solution

m. Solve problems involving direct translations

n. Solve problems involving relationships among unknown quantities

o. Solve problems involving consecutive integers

p. Use formulas to solve problems

q. Solve a formula or equation for one of its variables

r. Solve percent equations

s. Solve discount and mark-up problems

t. Solve percent increase and percent decrease problems

u. Solve mixture problems

v. Define linear inequality in one variable

w. Graph solution sets on a number line and use interval notation

x. Solve linear inequalities

y Solve compound inequalities

z. Solve inequality applications

**2. Learning Activities:**

a. Classroom lecture/discussion (F5, F6, F7, F8)

b. Reading/homework assignments (F1, F2, F7, F8, F9, F10, F11, F12)

c. Computer Laboratory/Computer Tutor (F2, F7, F8, F9, F10, F11, F12)

**3. Unit Outline:**

a. Section 2.1 Simplifying Algebraic Expressions

b. Section 2.2 The Addition Property of Equality

c. Section 2.3 The Multiplication Property of Equality

d. Section 2.4 Solving Linear Equations

e. Section 2.5 An Introduction to Problem Solving

f. Section 2.6 Formulas and Problem Solving

g. Section 2.7 Percent and Mixture Problem Solving

h. Section 2.8 Further Problem Solving

i. Section 2.9 Solving Linear Inequalities

B. Unit Two: (Chapter Three)** Graphing**

**1. Unit Objectives: **Upon successful completion of this unit the student
will be able to do the following:

a. read bar and line graphs

b. Define the rectangular coordinate system and plot ordered pairs of
numbers

c. Graph paired data to create a scatter diagram

d. Determine whether an ordered pair is a solution of an equation in two
variables

e. Find the missing coordinate of an ordered pair solution, given one
coordinate of the pair

f. Identify linear equations

g. Graph a linear equation by finding and plotting ordered pair solutions

h. Identify intercepts of a graph

i. Graph a linear equation by finding and plotting intercepts

j. Identify and graph vertical and horizontal lines

k. Find the slope of a line given two points of the line

l. Find the slope of a line given its equation

m. Find the slopes of horizontal and vertical lines

n. Compare the slopes of parallel and perpendicular lines

o. Slope as a rate change

p. Use the slope-intercept form to write an equation of a line

q. Use the slope-intercept form to graph a linear equation

r. Use the point-slope form to find an equation of a line given its

slope and a point of the line

s. Use the point-slope form to find an equation of a line given two points
of the line

t. Find equations of vertical and horizontal lines

u. Use the point-slope form to solve problems

v. Identify relations, domains, and ranges

w. Identify functions

x. Use the vertical line test

y. Use function notation

**2. Learning Activities:**

a. Classroom lecture/discussion (F5, F6, F7, F8)

b. Reading/homework assignments (F1, F2, F7, F8, F9, F10, F11, F12)

c. Computer Laboratory/Computer Tutor (F2, F7, F8, F9, F10, F11, F12)

**3. Unit Outline:**

a. Section 3.1 Reading Graphs and the Rectangular Coordinate System

b. Section 3.2 Graphing Linear Equations

c. Section 3.3 Intercepts

d. Section 3.4 Slope and Rate of Change

e. Section 3.5 Equations of Lines

f. Section 3.6 Functions

C. Unit Three: (Chapter Four)** Solving Systems of Linear
Equations and Inequalities**

**1. Unit Objectives:** Upon successful completion of
this unit the student will be able to do the following:

a. Determine if an ordered pair is a solution of a system of equations in
two variables

b. Solve a system of linear equations by graphing

c. Without graphing, determine the number of solutions of a system

d. Use the substitution method to solve a system of linear equations

e. Use the addition method to solve a system of linear equations

f. Use a system of equations to solve problems

g. Graph a linear inequality in two variables

h. Solve a system of linear inequalities

i. Solve a system of three linear equations in three variables

2**. Learning Activities:**

a. Classroom lecture/discussion (F5, F6, F7, F8)

b. Reading/homework assignments (F1, F2, F7, F8, F9, F10, F11, F12)

c. Computer Laboratory/Computer Tutor (F2, F7, F8, F9, F10, F11, F12)

**3. Unit Outline:**

a. Section 4.1 Solving Systems of Linear Equations by Graphing

b. Section 4.2 Solving Systems of Linear Equations by Substitution

c. Section 4.3 Solving Systems of Linear Equations by Addition

d. Section 4.4 Systems of Linear Equations and Problem Solving

e. Section 4.5 Graphing Linear Inequalities

f. Section 4.6 Systems of Linear Inequalities

g. Section 4.7 Solving Systems of Linear Equations in Three Variables
(handout)

D. Unit Four: (Chapter Five) **Exponents and Polynomials**

**1. Unit Objectives: Upon successful completion of this unit the student will
be able to do the following:**

a. Evaluate exponential expressions

b. Use the product rule for exponents

c. Use the power rule for exponents

d. Use the power rules for products and quotients

e. Use the quotient rule for exponents, and define a number raised to the
0 power

f. Decide which rule(s) to use to simplify an expression

g. Define polynomial, monomial, binomial, trinomial, and degree

h. Find the value of a polynomial given replacement values for the
variables

i. Simplify a polynomial by combining like terms

j. Add and subtract polynomials

k. Use the distributive property to multiply polynomials

l. Multiply polynomials vertically

m. Multiply two binomials using the FOIL method

n. Square a binomial

o. Multiply the sum and difference of two terms

p. Simplify expressions containing negative exponents

q. Use all the rules and definitions for exponents to simplify exponential
expressions

r. Write numbers in scientific notation

s. Convert numbers from scientific notation to standard form

t. Divide a polynomial by a monomial

u. Use long division to divide a polynomial by another polynomial

**2. Learning Activities:**

a. Classroom lecture/discussion (F5, F6, F7, F8)

b. Reading/homework assignments (F1, F2, F7, F8, F9, F10, F11, F12)

c. Computer Laboratory/Computer Tutor (F2, F7, F8, F9, F10, F11, F12)

**3. Unit Outline:
**a. Section 5.1 Exponents

b. Section 5.2 Adding and Subtracting Polynomials

c. Section 5.3 Multiplying Polynomials

d. Section 5.4 Special Products

e. Section 5.5 Negative Exponents and Scientific Notation

f. Section 5.6 Dividing Polynomials

E. Unit Five: (Chapter Six) ** Factoring Polynomials **

**1. Unit Objectives: **Upon successful completion of
this unit the student will be able to do the following:

a. Find the greatest common factor of a list of integers

b. Find the greatest common factor of a list of terms

c. Factor out the greatest common factor from a polynomial

d. Factor a polynomial by grouping

e. Factor trinomials of the form x^2 + bx + c

f. Factor out the greatest common factor and then factor a trinomial of
the form x^2 + bx + c

g. Factor trinomials of the form ax^2 + bx + c, where a ≠ 1

h. Factor out the greatest common factor and then factor a trinomial of
the form ax^2 + bx + c

i. Factor perfect square trinomials

j. Factor trinomials of the form ax^2 + bx + c by grouping

k. Factor the difference of two squares

l. Factor the sum or difference of two cubes

m. Solve quadratic equations by factoring

n. Solve equations with degree greater than 2 by factoring

o. Find the x-intercepts of the graph of a quadratic equation in two
variables.

p. Solve problems that can be modeled by quadratic equations

**2. Learning Activities:**

a. Classroom lecture/discussion (F5, F6, F7, F8)

b. Reading/homework assignments (F1, F2, F7, F8, F9, F10, F11, F12)

c. Computer Laboratory/Computer Tutor (F2, F7, F8, F9, F10, F11, F12)

**3. Unit Outline:**

a. Section 6.1 The Greatest Common Factor and Factoring by Grouping

b. Section 6.2 Factoring Trinomials of the Form x^2 + bx + c

c. Section 6.3 Factoring Trinomials of the Form ax^2 + bx + c and Perfect
Square Trinomials

d. Section 6.4 Factoring Trinomials of the Form ax^2 + bx + c by Grouping

e. Section 6.5 Factoring Binomials

f. Section 6.6 Solving Quadratic Equations by Factoring

g. Section 6.7 Quadratic Equations and Problem Solving

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