Course Outline for Intermediate Algebra & Applications
Catalog description (2009-2012 Catalog): Topics
include function notation; linear,
quadratic, and absolute value functions and equations; rational expressions and
equations; rational
exponents and equations; radicals and radical equations; graphing of linear,
quadratic, and
polynomial functions; and inequalities. 4 lecture hours
Is course New, Revised, or Modified? Revised Spring 2009
Required texts/other materials:
1. Algebra for College Students, Dugopolski, 5th Ed.
2. Calculator: A graphing calculator such as the TI-83 or TI-84 is recommended,
especially for
students who need to take additional mathematics courses, but is not required.
Students must have
at least a scientific calculator. No calculator with a symbolic manipulator is
allowed.
Information resources: The Mercer County Community
College Library has close to 100
reference books that students may use and a collection of problems on CD.
Students are also
encouraged to utilize the Learning Centers for additional resources and/or
tutoring.
Other learning resources: The following are
additional resources that the publishers of the
text have made available for instructors and students.
Course Competencies/Goals:
Students will be able to demonstrate through tests, quizzes, homework, and
assigned projects the
ability to:
1. solve inequalities in one and two variables.
2. solve and graph both linear and quadratic equations.
3. factor a second degree polynomial and some special higher degree polynomials.
4. recognize and work with functions and function notation.
5. perform operations and solve equations involving
polynomial, radical and rational
expressions.
6. solve a system of two linear equations.
7. solve absolute value equations and inequalities
8 analyze graphs of polynomial functions.
9. recognize common graphs and graphing transformations
10. construct and/or analyze both linear and quadratic
models of real life phenomenon and
predict future data values from these models.
11. apply each of the above techniques in various real world applications.
Course-specific General Education Knowledge Goals and Core Skills:
General Education Knowledge Goals
Goal 1. Communication. Students will communicate
effectively in both speech and writing.
Goal 2. Mathematics. Students will use appropriate mathematical and
statistical concepts and
operations to interpret data and to solve problems.
Goal 4. Technology. Students will use computer systems or other
appropriate forms of
technology to achieve educational and personal goals.
MCCC Core Skills
Goal A. Written and Oral Communication in English.
Students will communicate effectively
in speech and writing, and demonstrate proficiency in reading.
Goal B. Critical Thinking and Problem-solving. Students will use critical
thinking and
problem solving skills in analyzing information.
Goal D. Information Literacy. Students will recognize when information is
needed and have the
knowledge and skills to locate, evaluate, and effectively use information for
college level work.
Goal E. Computer Literacy. Students will use computers to access, analyze
or present
information, solve problems, and communicate with others.
Units of study in detail:
Unit I – Linear Modeling: Equations, Inequalities, Slopes and Graphs (2.5 weeks)
The student will be able to:
• Define and solve linear equations in one variable. (Course
Goals 1 & 2, Gen Ed Goal 2, Core
Skill B)
•
Determine if a given number is a solution to a given linear equation. (Course
Goal 2, Gen Ed Goal 2, Core Skill B)
•
Define and solve linear inequalities in one variable. (Course Goal 1, Gen Ed
Goal 2, Core
Skill B)
•
Determine if a given number is a solution to a given linear inequality. (Course
Goal 1, Gen
Ed Goal 2, Core Skill B)
•
Graph solutions to linear inequalities on a real number line and express
solutions in interval
notation. (Course Goal 1, Gen Ed Goal 2, Core Skill B)
•
Define, solve, and graph solutions to compound linear inequalities, as well as
compound
linear inequalities using “and” & “or” terminology. (Course Goal 1, Gen Ed Goal
2, Core
Skill B)
•
Plot points and identify quadrants on the coordinate plane. (Course Goal 1, Gen
Ed Goal 2,
Core Skill B)
•
Define independent (x-variable) and dependent (y-variable) axes. (Course Goal 2,
Gen Ed
Goal 2, Core Skill B)
•
Read, interpret, and explain trends in graphs which model applications. (Course
Goals 10 &
11, Gen Ed Goals 1 & 2, Core Skills A& B)
•
Define, calculate and interpret slope, especially as a rate of change. (Course
Goals 2 & 11,
Gen Ed Goals 1 & 2, Core Skills A&B)
•
Determine relationship between slope and horizontal, vertical, parallel, and
perpendicular
lines. (Course Goal 2, Gen Ed Goals 1& 2, Core Skills A&B)
•
Define and graph linear equations in two variables. (Course Goals 2 & 10, Gen Ed
Goals 1&
2, Core Skills A&B)
•
Identify and graph x- and y-intercepts of a graph, and interpret them in
context. (Course Goals
2,10, & 11, Gen Ed Goals 1& 2, Core Skills A&B)
•
Express and graph linear equations in slope-intercept form. (Course Goals 2 &
10, Gen Ed
Goals 1& 2, Core Skills A&B)
•
Use linear modeling to find the equation of a line through two given points, or
a slope and y-
intercept. (Course Goals 2,10, & 11, Gen Ed Goals 1 & 2, Core Skills A, B, & D)
•
Find equations of lines that are horizontal, vertical, and
parallel/perpendicular to given lines.
(Course Goal 2, Gen Ed Goals 1& 2, Core Skills A&B)
•
Analyze and interpret application problems from other disciplines and/or
complete assigned
project(s). (Course Goals 2,10, & 11, Gen Ed Goals 1, 2, & 4, Core Skills A,B,D,
& E)
Unit II – Functions, Systems of Linear Equations, and Polynomials (4.5 weeks)
The student will be able to:
• Define relations and functions. (Course Goal 4, Gen Ed
Goal 2, Core Skill B)
•
Use function notation to evaluate outputs for given inputs. (Course Goal 4, Gen
Ed
Goal 2, Core Skill B)
•
Identify the domain and range of a function. (Course Goal 4, Gen Ed Goal 2, Core
Skill B)
•
Graph simple functions; apply the vertical line test. (Course Goals 2&4, Gen Ed
Goal 2,
Core Skill B)
•
Determine from its graph intervals on which a function is increasing, decreasing
or constant.
(Course Goal 8; Gen Ed Goal 2; Course Skill B)
•
Determine relative maximum and minimum values of polynomial functions. (Course
Goals
8&11, Gen Ed Goal 2: Course Skill B)
•
Recognize and use vertical and horizontal shifts, reflections and non-rigid
transformations to
graph functions. (Course Goals 8 & 9, Gen Ed Goal 2: Course Skill B)
•
Solve linear systems of equations having solutions. (Course Goal 6, Gen Ed Goal
2, Core
Skill B)
•
Define monomial and polynomial (and its degree). (Course Goal 5, Gen Ed Goal 2,
Core
Skill B)
•
Add and subtract polynomials. (Course Goal 5, Gen Ed Goal 2, Core Skill B)
•
Multiply monomials and binomials (using FOIL) and special products (squares of
binomials,
etc.) (Course Goal 5, Gen Ed Goal 2, Core Skill B)
•
Divide polynomials. (Course Goal 5, Gen Ed Goal 2, Core Skill B)
•
Factor the GCF from polynomials and expressions. (Course Goal 3, Gen Ed Goal 2,
Core
Skill B)
•
Factor polynomials by grouping. (Course Goal 3, Gen Ed Goal 2, Core Skill B)
•
Factor various trinomials. (Course Goal 3, Gen Ed Goal 2, Core Skill B)
•
Analyze and interpret application problems from other disciplines and/or
complete assigned
project(s). (Course Goals 2,8,10,11, Gen Ed Goals 1, 2, & 4, Core Skills A,B,D,
& E)
Unit III – Special Factoring, Rational Expressions & Equations, Radical
Expressions and
Rational Exponents (3.5 weeks)
The student will be able to:
• Factor the difference of two squares, and the
sum/difference of two cubes. (Course Goal 3,
Gen Ed Goal 2, Core Skill B)
•
Define and solve quadratic equations by the zero product property. (Course Goals
2 & 5, Gen
Ed Goal 2, Core Skill B)
•
Define rational expressions and identify where they are undefined. (Course Goal
5, Gen Ed
Goal 2, Core Skill B)
•
Simplify rational expressions. (Course Goal 5, Gen Ed Goal 2, Core Skill B)
•
Multiply and divide rational expressions. (Course Goal 5,
Gen Ed Goal 2, Core Skill B)
•
Find the LCD (least common denominator) for given rational expressions. (Course
Goal 5,
Gen Ed Goal 2, Core Skill B)
•
Add and subtract rational expressions. (Course Goal 5, Gen Ed Goal 2, Core Skill
B)
•
Solve rational equations. (Course Goal 5, Gen Ed Goal 2, Core Skill B)
•
Define and calculate square, cube, and nth root of a number. (Course Goal 5, Gen
Ed
Goal 2, Core Skill B)
•
Calculate and/or simplify expressions with radicals or rational exponents.
(Course Goal 5,
Gen Ed Goals 2 & 4, Core Skill B)
•
Find the distance between two given points in the coordinate plane. (Course
Goals 5 & 11,
Gen Ed Goal 2, Core Skill B)
•
Analyze and interpret application problems from other disciplines and/or
complete assigned
project(s). (Course Goals 5,10,& 11 , Gen Ed Goals 1, 2, & 4, Core Skills A,B,D,
& E)