|
MASTER SYLLABUS |
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| INTERMEDIATE AND
COLLEGE ALGEBRA DSPM0850 / MATH 1130 |
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| Class Hours: 3.0 | Credit Hours: 6.0 | ||||||||
| Laboratory Hours: 0.0 | Revised: Fall 05 | ||||||||
| Catalog Course Description: | |||||||||
| College
algebra
for students who are not in university parallel/transfer programs of
science,
mathematics, engineering or computer science. Topics include
linear,
polynomial, rational, exponential and logarithmic functions, their
graphs
and applications; linear and nonlinear regression models. |
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| Entry Level Standards: | |||||||||
| Students
must
be able to read at the college level. |
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| Prerequisites: | |||||||||
| Two
years of
high school algebra and ACT math score of at least 19; or DSPM0850 or
equivalent
math placement score. |
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| Textbook(s) and Other Course Materials: | |||||||||
| Textbook: Lial, Margaret, John Hornsby, David I. Schneider. College Algebra, Ninth Edition. Addison-Wesley, Reading, MA, 2005. References: Bittinger, Marvin L., Judith A. Beecher, David Ellenbogen, and Judith A. Penna. College Algebra: Graphs and Models., 3rd Ed. Addison-Wesley, Reading, MA, 2001. Blitzer, Robert. College Algebra Essentials. Pearson Prentice Hall, Upper Saddle River, NJ, 2004. Larson, Roland E., Robert P. Hostetler, and Bruce Edwards. College Algebra: A Graphing Approach, 4th Ed. Houghton Mifflin Company, Boston, MA, 2005. Required Supplements: Student Solutions Manual; Graphing Calculator fold-out; DVD set for MATHXL unlimited practice; Digital Video Tutor set of lessons; and A Review of Algebra by Heidi Howard. Technology Requirement: A non-symbolic graphing calculator is required; the TI-83 or TI-83 Plus is preferred. |
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| I. Week/Unit/Topic Basis: | |||||||||
| Included in the topics listed below are projects which students may be asked to complete individually or in groups. Some instructors may use other projects. The selection, timing and manner of presentation of the projects is to be determined by the instructor. AR = A Review of Algebra supplemental text. | |||||||||
| Week | Topic | ||||||||
| 1 | Introduction,
Real Number System, AR Chapter 1; Integer exponents and Laws of
Exponents,
AR 3.1; Scientific Notation, Addition and Subtraction of Polynomials,
AR
3.2 |
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| 2 | Multiplication
of Polynomials AR 3.3; Review; Unit 1 Test; Intro to Factoring, AR 3.4 |
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| 3 | More
Factoring,
AR 3.5; Applications; Review; Unit 2 Test |
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| 4 | Calculator
Intro,
1.1, 1.2; Graphs of Equations, 2.1; Functions 2.2; Linear Functions 2.3; |
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| 5 | Writing
the Equation
of a Line, 2.4; Curve Fitting 2.4; Solving Linear Equations AR 2.2;
Review;
Unit 3 Test; |
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| 6 | Quadratic
Functions,
3.1; Quadratic Regression and Models 3.1; Solving Quadratic Equations
by
Factoring and Graphing Calculator, 1.3; Evaluating Roots AR 5.1; |
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| 7 | Multiplication
and Division of Radicals AR 5.2; Addition and Subtraction of Radicals
AR
5.3; Solving Quadratics by Inverse and Quadratic Formula, 1.4;
Quadratic
Inequalities, 1.7; Review; Unit 4 Test |
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| 8 | Properties
of
Functions, 2.5; Graphing Techniques 2.6; Polynomial
Functions,
3.4; Review; Unit 5 Test |
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| 9 | Properties
of
Rational Functions, 3.5; Simplifying, Multiplying and Dividing Rational
Expressions,
AR 4.1, 4.2; Adding and Subtracting Rational Expressions, AR 4.1, 4.3 |
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| 10 | Adding
and Subtracting
Rational Expressions, AR 4.3; Solving Rational Equations; Applications
of
Rational Equations, 3.5; Review; Unit 6 Test |
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| 11 | Function Operations and Composition 2.7; Inverse Functions, 4.1; Exponential Functions, 4.2; Logarithmic Functions, 4.3 | ||||||||
| 12 | Change
of Base
Theorem, 4.4; Properties of Logarithms 4.3; Log and Exponential
Equations,
4.5; Review |
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| 13 | Unit 7 Test; Difference Quotient, 2.7; Interest Applications, 4.6; | ||||||||
| 14 | Growth
and Decay
Applications, 4.6; Review; Unit 8 Test; Review for Final |
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| 15 | Final
Exam |
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| II. Course Objectives*: | |||||||||
| A. | Find
appropriate
regression equations to model real data using statistical
analysis.
VI.1-6 |
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| B. | Master
the use
of a graphing utility to solve problems and to check solutions.
VI.1-6 |
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| C. | Construct
and
analyze graphs of linear, quadratic, polynomial, rational, radical,
exponential
and logarithmic functions. VI.1-6 |
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| D. | Construct
appropriate
mathematical models to solve applications. VI.1-6 |
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| E. | Interpret
and
apply functional notation and concepts. VI.1-6 |
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| F. | Analyze
and explore
linear, quadratic, polynomial, piecewise, rational, radical,
exponential
and logarithmic functions and their applications. VI.1-6 |
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| G. | Solve
and check
the solutions of linear, absolute value, piecewise, quadratic,
polynomial,
rational, radical, exponential and logarithmic equations analytically
and
graphically. VI.1-6 |
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| H. | Solve
and check
variation application problems. VI.1-6 |
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| *Roman numerals after course objectives reference TBR's general education goals. | |||||||||
| III. Instructional Processes*: | |||||||||
| Students will: | |||||||||
| 1. | Use a
graphing
utility to analyze properties of functions and to solve equations and
check
solutions. Technological Literacy Outcome, Numerical Literacy
Outcome, Transitional Strategy, Active Learning Strategy |
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| 2. | Engage
in collaborative
activities, e.g. modeling projects, group work and/or other activities
that
use mathematics to solve real world applications. Problem
Solving
and Decision Making Outcome, Numerical Literacy Outcome, Communications
Outcome,
Transitional Strategy, Active Learning Strategy |
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| 3. | Demonstrate
personal
integrity and ethical behavior by being punctual, dependable,
considerate,
and cooperative. Personal Development Outcome |
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| 4. | Use
multiple
approaches – physical, symbolic, graphical, and verbal – to solve
application
problems in business, finance, and the sciences. Numerical
Literacy
Outcome, Transitional Strategy |
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| *Strategies and outcomes listed after instructional processes reference TBR's goals for strengthening general education knowledge and skills, connecting course work to experiences beyond the classroom, and encouraging students to take active and responsible roles in the educational process. | |||||||||
| IV. Expectations for Student Performance*: | |||||||||
| Upon successful completion of this course, the student should be able to: | |||||||||
| 1. | Determine
the slope of a line and explain its meaning numerically, graphically
and
analytically. A, C, F |
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| 2. | Determine
the equations of horizontal and vertical lines numerically, graphically
and
analytically. C, F |
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| 3. | Determine
the equations of parallel and perpendicular lines numerically,
graphically
and analytically. C, F |
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| 4. | Determine
equations of lines using the point-slope or slope-intercept
equations.
F |
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| 5. | Determine
if a relation is a function. C, E |
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| 6. | Work
with functional notation; find and simplify the difference quotient for
a
polynomial function of degree one, two, or three. E |
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| 7. | Sketch
careful graphs of functions by hand: linear, absolute value,
piecewise,
quadratic, radical, rational, exponential, and logarithmic. C |
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| 8. | Find
suitable windows to create comprehensive graphs of functions on a
graphing
utility: linear, absolute value, piecewise, quadratic,
polynomial,
radical, rational, exponential, and logarithmic. A, B, C |
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| 9. | Find
the real zeros of functions analytically and graphically. B, C, E |
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| 10. | Analytically
and graphically analyze graphs of linear, absolute value, piecewise,
quadratic,
polynomial, rational, radical, exponential, and logarithmic
functions:
determine domain, range, intercepts, extrema, increasing/decreasing
intervals,
continuity, end behavior, and asymptotes. B, C |
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| 11. | Use
linear, piecewise, quadratic, polynomial, rational, exponential, and
logarithmic
models to solve applications. D |
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| 12. | Use
transformations to build new functions from basic functions; determine
domain
and range of new functions. B, C, E |
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| 13. | Use
statistical regression on a graphing utility to find linear, quadratic,
cubic,
quartic, exponential, and logarithmic models and use them to make
meaningful
predictions. A, B, D |
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| 14. | Use
the quadratic formula to get exact solutions to quadratic
equations.
F |
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| 15. | Use
the discriminant to determine number and nature of the roots of a
quadratic
equation. F |
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| 16. | Optimize
quadratic functions. B, F |
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| 17. | Make
a reasonable sketch of a polynomial function based on an analysis of
its
degree, leading coefficient, zeros and end behavior. C |
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| 18. | Determine
the real zeros and their multiplicities for a polynomial
function.
E, F |
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| 19. | Write
a polynomial function given its real zeros and their
multiplicities.
E |
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| 20. | Find
the equations of the horizontal and vertical asymptotes of rational
functions.
C |
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| 21. | Solve
linear, quadratic, polynomial, and rational inequalities analytically
and
graphically. B, C |
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| 22. | Use
the zeros of a function and its graph to solve related
inequalities.
B, C |
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| 23. | Solve
direct, indirect, and joint variation problems and applications.
B,
C |
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| 24. | Determine
if a function is one-to-one and find formulas for inverses of
one-to-one
functions. E |
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| 25. | Use
the graph of a one-to-one function to draw the graph of its inverse
function.
B, C |
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| 26. | Convert
between exponential and logarithmic notation. E |
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| 27. | Find
common and natural logarithms on a graphing utility. B |
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| 28. | Use
the change of base formula to evaluate logarithms. B |
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| 29. | Use
the properties of logarithms to rewrite and simplify expressions. E, F |
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| 30. | Solve
equations analytically: linear, absolute value, quadratic,
rational,
radical, special polynomials, exponential, and logarithmic. G |
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| 31. | Solve
equations on a graphing utility using the intersection of graphs
method.
B |
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| 32. | Solve
exponential growth and decay applications analytically using
statistical
regression or algebraic methods. A, B, D |
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| *Letters after performance expectations reference the course objectives listed above. | |||||||||
| V. Evaluation: | |||||||||
| A. Testing Procedures: | |||||||||
| Students
are evaluated primarily on the basis of tests, projects, homework,
quizzes,
and a comprehensive final exam. A minimum of four major exams is
recommended. |
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| B. Laboratory Expectations: | |||||||||
| As
assigned by instructor |
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| C. Field Work: | |||||||||
| As
assigned by instructor |
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| D. Other Evaluation Methods: | |||||||||
| As
assigned by instructor |
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| E. Grading Scale: | |||||||||
| 93-100%
A 88-92 B+ 83-87 B 78-82 C+ 70-77 C 60-69 D Below 60 F |
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| VI. Policies: | |||||||||
| A. Attendance Policy: | |||||||||
| Regular
attendance is essential for the successful completion of this course,
and
absences will be recorded daily. Pellissippi State Technical
Community
College expects students to attend all scheduled instructional
activities.
As a minimum, students in all courses must be present for at least 75 %
of
their scheduled class and laboratory meetings in order to receive
credit
for the course. Individual departments/programs/disciplines, with
the
approval of the Vice President of Academic and Student Affairs, may
have
requirements that are more stringent. |
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| B. Academic Dishonesty: | |||||||||
| Academic
dishonesty in any form is prohibited and will be dealt with
severely.
Penalties range from an F or a zero for the specific project or
examination
to automatic failure for the course for all students involved.
Individual
instructors must distribute their policy on academic dishonesty during
the
first week of class. |
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| C. Accommodations for disabilities: | |||||||||
| If you need accommodations because of a disability, if you have emergency medical information to share, or if you need special arrangements in case the building must be evacuated, please inform the instructor immediately. Please see the instructor privately after class or in his/her office. Students must present a current accommodation plan from a staff member in Services for Students with Disabilities (SSWD) in order to receive accommodations in this course. Services for Students with Disabilities may be contacted by going to Goins 127 or 131 or by phone: 694-6751(Voice/TTY) or 539-7153. | |||||||||