CATA LOG DESCRIPTION
This course is a functional approach to algebra that incorporates the use of
appropriate
technology. Emphasis will be placed on the study of functions and their graphs,
(linear,
quadratic, piece-wise defined, rational, polynomial, exponential, and
logarithmic
functions) as well as inequalities. Systems of equations (linear and nonlinear)
will be
solved using matrices and/or algebraic techniques. Non-function parabolas and
circles
will be studied as shifted graphs. Appropriate applications will be included.
EXPECTED EDUCATIONAL RESULTS
As a result of completing this course, students will be able to:
1. Understand the definition of a function.
2. Determine the domain, range, and where a function is increasing, decreasing
or
constant for each type of function studied in the course.
3. Students will be able to inter pret the slope and y- intercept of a line as an
average
rate of change and an initial amount, respectively. Students will be able to
interpret and apply these ideas in applied settings.
4. Model linear and non-linear functions from data.
5. Graph transformations (vertical and horizontal shifts, vertical stretching
and
compressions, and reflections) of basic functions.
6. Graph quadratic functions of the form y = a x^2 + b x + c by determining the
vertex and intercepts . Students will be able to interpret and apply these ideas
in
applied settings.
7. Identify and graph power functions, transformations of power functions, and
polynomial functions where the polynomial is factorable. Students will be able
to
describe the end behavior of polynomials and the relationship between end
behavior and the degree of the polynomial. Students will be able to determine
intercepts of factorable polynomials exactly. Students will be able to use
technology to approximate x-intercepts and turning points of polynomials.
8. Identify and graph transformations of y = 1/x and y = 1/x^2. Students will be
able
to recognize and determine vertical and horizontal asymptotes, end behavior, and
behavior near vertical asymptotes.
9. Relate algebraic solutions to the fol lowing types of
equations to the graphs of
corresponding functions and applications:
a. Linear
b. Quadratic
c. Factorable polynomial
d. Rational
e. Radical (involving only one radical)
f. Equations of the form x^n = k
10. Graph piece-wise defined functions.
11. Students will be able to determine the symmetry of functions algebraically
and
graphically
12. Compose two functions and determine the domain of the composite function.
13. Define an inverse function, get a rule for an inverse function, and graph an
inverse
function.
14. Graph exponential functions of the form y = a^x and their transformations.
Students should also be able to graph the inverse function of y = a ^ x.
15. Solve simple exponential equations both graphically and using logarithms.
16. Apply exponential functions to problems involving exponential growth or
decay.
17. Define a logarithm, convert between logarithmic and exponential form, and
understand the inverse relationship between logarithmic and exponential
functions.
18. Use properties of logarithms to solve logarithmic equations and use
logarithms in
application problems.
19. Use function graphs to determine solutions to the following types of
inequalities
and apply these solutions to concepts related to functions and other
applications:
a. Linear
b. Quadratic
c. Factorable Polynomial
d. Rational
e. Exponential
20. Solve non-linear systems of equations analytically and graphically.
21. Solve linear systems of equations using Gaussian elimination and matrices.
22. Graph parabolas and circles whose equations are given in general form by
completing the square .
GENERAL EDUCATION OUTCOMES
I. This course addresses the general education outcome relating to communication
by providing additional support as follows:
A. Students improve their listening skills by taking part in general class
discussions and in small group activities.
B. Students improve their reading skills by reading and discussing the text
and other materials. Reading mathematics requires skills somewhat
different from those used in reading materials for other courses, and
these are discussed in class.
C. Unit tests, examinations, and other assignments provide
opportunities for
students to practice and improve mathematical writing skills. Mathematics
has a specialized vocabulary that students are expected to use correctly.
II. This course addresses the general education outcome of demonstrating
effective
individual and group problem-solving and critical skills as follows:
A. Students must apply mathematical concepts to non-template problems and
situations.
B. In applications, students must analyze problems, often through the use
of multiple representations, develop or select an appropriate mathematical
model, utilize the model, and interpret results.
III. This course addresses the general education outcome of using mathematical
concepts to interpret, understand, and communicate quantitative data as follows:
A. Students must demonstrate proficiency in problem solving including
applications of linear, quadratic, exponential, and logarithmic functions.
B. Students must be familiar with simple data analysis tools for building
linear and non-linear models.
IV. This course addresses the general education outcome of organizing
information
through the use of computer software packages as follows:
A. Students are required to use a graphing calculator to graph functions,
determine intercepts, and determine turning points of graphs.
B. Students will use simple data analysis tools for building linear and
nonlinear
models.
COURSE CONTENT
1. Linear Functions
2. Quadratic Functions
3. Other Basic Functions.
4. Polynomial Functions
5. Rational Functions.
6. Composition and Inverse Functions
7. Exponential and Logarithmic Functions
8. Systems of Equations
ENTRY-LEVEL COMPETENCIES
Before enrolling in this course, the student is expected to be able to:
1. Use algebraic symbols and notation to make meaningful statements
2. Solve applications for which linear equations, quadratic equations, and
systems
are mathematical models
3. Solve the following equations algebraically:
a. Quadratic with real and non -real solutions
b. Absolute value of the form : |ax + b| = constant
c. Fractional leading to a quadratic
d. Polynomial of degree higher than two by factoring
e. Radical leading to linear or quadratic
4. Solve inequalities algebraically, write the solution
set in interval notation, and
graph the solution set on a number line for the following types of inequalities:
a. Factorable quadratic
b. |ax + b| < or > constant
c. Factorable polynomial of degree higher than two
5. Solve a system of two linear equations in two variables (having no, one, or
many
solutions) by graphing, substitution, or elimination
6. Perform operations with complex numbers (excluding division)
7. Apply properties of exponents with integral and rational exponents
8. Perform the four basic operations with radicals (excluding rationalizing)
9. Solve problems where students have to display comprehension of basic
geometric
concepts including the Pythagorean Theorem, formulas for area and perimeter of
rectangles, squares, and triangles
10. Perform the following activities with lines:
a. Use the distance and midpoint formula
b. Graph equations in standard form and slope-intercept form
c. Compute the slope given two points
d. State the slope given an equation
e. State if lines are parallel or perpendicular from given information
f. Write the equation of a line given information
11. Use a graphing calculator
12. Understand function notation
13. Graph parabolas using a table of values and plotting points
ASSESSMENT OF EXPECTED EDUCATIONAL RESULTS
A. COURSE GRADE
The course grade will be determined by the individual instructor using a variety
of
evaluation methods. A portion of the course grade will be determined through the
use of
frequent assessment using such means as tests, quizzes, projects, or homework as
developed by the instructor. Some of these methods will require the student to
demonstrate ability in problem solving and critical thinking as evidenced by
explaining
and interpreting solutions. A comprehensive final examination is required which
must
count at least one-fifth and no more than one-third of the course grade.
B. DEPARTMENTAL ASSESSMENT
This course will be assessed every three years. The next assessment will occur
during
spring semester, 2008. The assessment instrument will be administered as a
portion of
the final exam and will be administered in all sections of the course. The
instrument will
consist of ten to fifteen multiple-choice questions. Each of the eight course
content areas
and each of the General Education Outcomes addressed by the course will be
measured
by at least one exam question.
C. USE OF ASSESSMENT FINDINGS
The Math 1111 committee, or a special assessment committee appointed by the
Academic Group, will analyze the results of the assessment and determine
implications
for curriculum changes. An item analysis will be done for each exam question. If
the
mean success rate on any assessment item is below 60%, the committee will make a
recommendation to address the area of weakness. The committee will prepare a
report
for the Academic Group summarizing its finding.
