Intermediate Algebra

CATALOG COURSE DESCRIPTION:

Prerequisite:

High School Algebra II with a grade of C or higher
and placement by the Counseling Department, or
completion of Elementary Algebra with a grade of C or
higher.

Corequisite: None

A continuation of algebra containing topics such as factoring;
operations with rational expressions, absolute value; exponents,
radicals and roots; complex numbers; linear and quadratic equations
and linear inequalities; graphs; systems of equations; and
functions, all with applications throughout the course. Certain
sections of this course will use the Academic Systems teaching
software; such sections will occur in an automated and interactive
environment. Meets 3 hours of elective credit for the A.A. degree.

General Education Requirements - Associate of Arts Degree, meets Area(s):
General Education Requirements - Associate in Science Degree, meets Area(s):

UNIT TITLES:

1. Factoring Polynomials
2. Algebraic Fractions and Equations
3. Selected Linear Equations and Inequalities
4. Rational Exponents, Radicals, and Complex Numbers
5. Quadratic Equations and Inequalities in One Variable
6. Linear Equations and Inequalities in Two Variables
7. Introduction to Functions

I. Course Overview:

Upon successful completion of this course, the students should be
able to demonstrate a knowledge of skills necessary to enter
college-level Mathematics courses such as MAC 1105, STA 2023,
MGF 1106 or MGF 1107.

II. Units:

Unit 1. Factoring Polynomials

General Outcome:

1.0 The students should be able to factor polynomials.

Specific Learning Outcomes:

Upon successful completion of this unit, the students
should be able to:

1.1 Factor out the greatest common factor.

1.2 Factor the difference of two squares.

1.3 Factor trinomials, including perfect square
trinomials.

1.4 Factor by grouping using pairs.

1.5 Factor the sum and difference of two cubes.

Unit 2. Algebraic Fractions and Equations

General Outcome:

2.0 The students should be able to simplify rational
expressions and complex fractions; and solve rational
equations, literal equations and applied problems.

Specific Learning Outcomes:

Upon successful completion of this unit, the students
should be able to:

2.1 Identify when a rational expression is undefined.

2.2 Write rational expressions in lowest terms.

2.3 Multiply and divide rational expressions, including
long division of polynomials.

2.4 Add and subtract rational expressions.

2.5 Simplify complex fractions.

2.6 Solve literal equations involving rational
expressions.

2.7 Solve equations involving rational expressions.

2.8 Solve applied problems involving rational expressions.

Unit 3. Selected Equations and Inequalities.

General Outcome:

3.0 The students should be able to solve equations and
inequalities in one variable.

Specific Learning Outcomes:

Upon successful completion of this unit, the students
should be able to:

3.1 Solve absolute value equations of the form
|ax + b| = k

3.2 Express the union and intersection of intervals in
simplest interval form.

3.3 Solve compound linear inequalities in one variable,
and express the solutions in interval notation.

Unit 4. Rational Exponents, Radicals, and Complex Numbers

General Outcome:

4.0 The students should be able to simplify expressions
using the rules of exponents and radicals, and perform
operations with complex numbers.

Specific Learning Outcomes:

Upon successful completion of this unit, the students
should be able to:

4.1 Simplify expressions involving rational exponents.

4.2 Simplify radical expressions.

4.3 Add and subtract radical expressions.

4.4 Multiply and divide radical expressions.

4.5 Rationalize the denominator of radical expressions.

4.6 Solve radical equations including those which have
more than one radical.

4.7 Perform operations with complex numbers, including
powers of i.

Unit 5. Quadratic Equations and Inequalities in One Variable

General Outcome:

5.0 The students should be able to solve quadratic
equations and inequalities, and related applied
problems.

Specific Learning Outcomes:

Upon successful completion of this unit, the students
should be able to:

5.1 Solve quadratic equations by factoring.

5.2 Solve quadratic equations using the square root
property.

5.3 Solve quadratic equations by completing the square.

5.4 Solve quadratic equations by using the quadratic
formula.

5.5 Solve equations quadratic in form.

5.6 Solve applied problems involving quadratic equations.

5.7 Solve quadratic inequalities, graph the solution set,
and express the solution set in interval notation.

Unit 6. Linear Equations and Inequalities in Two Variables

General Outcome:

6.0 The students should be able to graph linear equations
and inequalities in two variables, solve and graph
systems of linear equations and inequalities in two
variables, and solve related applied problems.

Specific Learning Outcomes:

Upon successful completion of this unit, the students
should be able to:

6.1 Find the distance between two points.

6.2 Find the midpoint of a line segment.

6.3 Find the x- and y- intercepts of a line.

6.4 Find the slope of a line.

6.5 Determine if two lines are parallel, perpendicular, or
neither.

6.6 Graph a linear equation.

6.7 Find an equation of a line.

6.8 Solve a system of two linear equations in two unknowns
graphically and algebraically, and solve related
applied problems.

6.9 Graph the solution set for a system of linear
inequalities.

Unit 7. Introduction to Functions

General Outcome:

7.0 The students should be able to identify the
characteristics of a function of the form y= f(x).

Specific Learning Outcomes:

Upon successful completion of this unit, the students
should be able to:

7.1 Specify the domain and range of a relation.

7.2 Determine whether a relation is a function.

7.3 Find the value of a function for a given value of the
domain.