Download MAT 127 Precalculus Module 3 - www7

UCC/UGC/YCC
Proposal for New Course
1. Effective BEGINNING of what term and year?:
Winter 2012
See effective dates calendar.
2. College: Engineering, Forestry
& Natural Sciences
4. Course subject and number:
3. Academic Unit: Mathematics & Statistics
MAT 127
5. Units: 1
6. Long course title: Precalculus Module 3
(max 100 characters including spaces)
7. Short course title: Precalculus Module 3
(max. 30 characters including spaces)
8. Catalog course description (max. 60 words, excluding requisites):
Trigonometry. Content covered in Module 3 of MAT 125. Available only to students who have
completed Modules 1 and 2 of MAT 125. May and Winter sessions only. Audit only.
Prerequisite: Instructor’s consent.
9. Grading option:
Letter grade
Pass/Fail
Students will be required to register as auditors.
Both
10a. UGC approval date*:
10. Co-convened with:
(For example: ESE 450 and ESE 550)
*Must be approved by UGC before UCC submission, and both course syllabi must be presented
11. Cross-listed with:
(For example: ES 450 and DIS 450)
Please submit a single cross-listed syllabus that will be used for all cross-listed courses.
12. May course be repeated for additional units?
Yes
No
12a. If yes, maximum units allowed?
12b. If yes, may course be repeated for additional units in the same term?
Yes
No
13. Prerequisites:
Instructor’s consent.
Instructor’s consent will be based on student’s successful completion of Module 1 and Module
2 while enrolled in MAT 125.
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1
14. Co requisites:
15. Is this course in any plan (major, minor or certificate) or sub plan (emphasis or concentration)?
Yes
No
If yes, describe the impact and attach written responses from the affected academic units prior
to college curricular submission.
16. Is there a related plan or sub plan proposal being submitted?
If no, explain.
Yes
No
17. Does this course include combined lecture and lab components?
Yes
If yes, note the units specific to each component in the course description above.
No
18. Does this course duplicate content of existing courses?
Yes
No
If yes, list the courses with duplicate material. If the duplication is greater than 20%,
explain why NAU should establish this course.
The content of MAT 127 duplicates one-third of the content of MAT 125. As described in the
justification section below, MAT 127 provides students who have had partial success with the
material in MAT 125, the opportunity to complete the remaining material more quickly and via
an alternate mode of delivery.
19. Names of the current faculty qualified to teach this course:
Amy Rushall, Robert
Daugherty, Barbara
Boschmans
20. Justification for new course.
In sections of MAT 125 Precalculus (4) that are delivered via the modular approach, the
course material is divided into 3 modules, and taught in a regular classroom environment (not
online). A student must successfully complete each module in turn before moving on to the
next, and must complete all three modules and pass a comprehensive Exit Exam in order to
earn a passing grade in the course. A student who completes only two of the three modules
in a given semester receives a grade of Incomplete in MAT 125, which will convert to a
passing grade upon successful completion of Module 3 and the Exit Exam while enrolled in
MAT 125 as an auditor a subsequent semester.
MAT 127 is designed to provide an alternate, quicker path for such students to complete
Module 3 of MAT125. MAT 127 provides a structured environment in which students can
complete Module 3 online during winter or summer pre-session without having to register for
an additional 4 credit hour offering of MAT 125 in the subsequent semester.
The advantage to a student in taking MAT 127 is that if successful in MAT 127 the student
can complete MAT 125 before the start of the next regular semester and move on in their
academic career without “retaking” MAT 125 and possibly delaying their progress toward
degree.
MAT 127 has been offered three times under the MAT 199X Topics course number (Winter
2010, Summer Pre-Session 2011, and Winter 2011). A total of 30 students have taken the
course of which 19 (63%) have successfully completed the material and earned credit in MAT
125.
Answer 21-22 for UCC/YCC only:
21. Is this course being proposed for Liberal Studies designation?
Yes
If yes, forward this form along with the appropriate supporting documentation to the
Revised 06/22/2011
No
2
Liberal Studies Committee.
22. Is this course being proposed for Diversity designation?
Yes
If yes, forward this form along with the appropriate supporting documentation to the
Diversity Committee
Scott Galland
Reviewed by Curriculum Process Associate
No
01/30/2012
Date
Approvals:
Department Chair/ Unit Head (if appropriate)
Date
Chair of college curriculum committee
Date
Dean of college
Date
For Committee use only:
UCG/UGC/YCC Approval
Date
:
Approved as submitted:
Yes
No
Approved as modified: Yes
No
:
:
Please attach proposed Syllabus in approved university format.
Revised 06/22/2011
3
College of Engineering, Forestry & Natural Sciences
Department of Mathematics & Statistics
MAT 127 Precalculus Module 3
SYLLABUS AND COURSE INFORMATION
Course: MAT 127: Precalculus Module 3
Semester Offered: Winter and Summer pre-session only
Clock and credit hours: asynchronous, 1 credit hour
Instructor: Amy Rushall
Office: Adel Mathematics Building Room 171
Office Hours: By appointment.
Email Address: [email protected]
Phone: 928.523.0660
Credit Hours: 1 credit (Audit Only)
Course Prerequisites: Instructor consent only. Instructor consent is based on a student having successfully completed Module
1 and Module 2, but not Module 3 of MAT 125 in a previous semester.
Course Structure/Approach: This is an asynchronous online course. The course is an Audit Only course. The course may not
be taken for a letter grade.
Course Outline:
Module 3: Trigonometric Functions and Their Applications
We will cover Chapter 5, Chapter 6, Section 7.1 and Section 7.2 of the Dugopolski text.
Required Text: Precalculus, Dugopolski, (3rd Edition) Custom Edition for Northern Arizona University bundled with a My Math
Lab Access code. You may also decide to buy only the access code which includes the on-line text.
Assessment of Student Learning Outcomes:
Your grade for this module will be determined by the following:
1. Exit Exam (Paper and Pencil)
60%
2. Homework (My Math Lab)
20%
3. Quizzes (My Math Lab)
20%
Grading System:
In order to pass Module 3, you must
1. Earn at last 60% on the Exit Exam for Module 3.
2. Have at least a 70% overall grade for the Module 3 based on the above distributions.
Calculators: You will need a scientific calculator for Module 3. A graphing calculator is also fine.
Homework: All of your homework will be done online through My Math Lab. You may continue to work on Homework in
MML after the deadline with a 20% penalty on problems completed after the due date. COURSE ID: rushallXXXXX
Quizzes: There is a My Math Lab Quiz for each section covered in Module 3. You will get 10 attempts at each Quiz. These
Quizzes contain 3-6 problems each and will count as 20% of your overall grade. When you reattempt a quiz, you may be given
different questions that address the learning objectives.
Exit Exam: Friday, January 13, 2012 @ Adel Mathematics or Another Approved Proctored Site
You must earn at least 60% on the Exit Exam (and have at least a 70% overall) to pass this module. There are no make-ups for
Exit Exams. The Exit Exam is a 50-minute paper and pencil in-class test. The Exit Exam is cumulative: 25% from Module 1
content, 25% from Module 2 content, 50% from Module 3 content.
Challenge Exam: Saturday, January 14, 2012 @ Adel Mathematics or Another Approved Proctored Site
If you do not make at least a 60% on the Exit Exam or if you do not have a 70% overall grade, you may take the Challenge Exam
as an alternative way to pass the module. The Challenge Exam is 32 questions in My Math Lab. You will have 120 minutes to
take the exam. If you make at least 70% on the Challenge Exam, you will pass this module regardless of the other grades you
have earned for this module. The Challenge Exam grade will be your Module 3 grade.
Successful Behaviors for Students in Online Courses: Students should be prepared to work on this course for at least an hour
every day. The most successful students will spend at least two hours per day on the course. Successful students will seek
additional learning opportunities through the videos embedded in BbLearn. These are labeled so that you can find a helpful,
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efficient supplement to the MML video lesson. Successful students will complete the homework and quiz for the day’s lesson
by the end of the scheduled day (see the Course Calendar in BbLearn). Successful students will contact the instructor for
clarification of course content or course expectations.
*All Exit and Challenge Exams will be taken at the Adel Mathematics Building or at another approved, prearranged proctored
site. If you are unable to take your Exit Exam in Flagstaff, please contact your instructor immediately to make alternate
arrangements.
Student Learning Outcomes
5.1: Angles: Degrees & Radians

Draw and label angles in standard position using both radian and degree measure.

Convert angle measure from degrees to radians or from radians to degrees.

Label “nice” angles on the unit circle in both degrees and radians.

What are coterminal angles?

Determine if two angles are coterminal.

Find an angle that is coterminal with a given angle.
5.2: Sine and Cosine

Definition of sine and cosine using the unit circle.

What are reference angles? Determine the reference angle for any given angle.

The Sine and Cosine of angles with reference angles of 30○, 45○, 60○.

Use reference angles to determine the sine and cosine of a given “nice” angle
5.3: Graphing the Sine and Cosine Functions

Use the five important points method to graph y = sin(x).

Use the five important points method to graph y = cos(x).

Transformations of sine and cosine: Phase Shift, Vertical Shift, Amplitude

Transformations of sine and cosine: Change the Period

Give domain, range, amplitude, period of a given sine function or graph.
5.4: Other Trigonometric Functions

Evaluate the other trigonometric functions at given angles

Be able to identify the graphs of the functions and the domain and range of each.

Be able to graph basic transformations of these trigonometric functions
5.5: Inverse Trig Functions

Know the graphs (including domain and range) of inverse sine, inverse cosine and inverse tangent.

DO NOT study inverse cotangent, inverse cosecant, or inverse secant.

Evaluate these inverse functions for given numbers in the domain.

Evaluate compositions of these functions and the trigonometric functions
5.6: Right Triangle Trigonometry

Given some information about a triangle, find some of the missing parts.

Solve a triangle given some of the sides and/or angles.

Application word problems.
6.1: Basic Identities

Use the Trigonometric Identities Sheet to simplify trigonometric expressions.

Perform algebra with trigonometric expressions: multiply binomials, FOIL, factor expressions that are quadratic in form, etc.

Use identities to find exact values of trigonometric functions evaluated at other angles.
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5
6.2: Verifying Identities

Use the quotient and reciprocal identities found on your Trigonometric Identities Sheet to simplify verify trigonometric
identities.

Use the following strategies to verify trigonometric identities:
o Work on ONLY ONE SIDE of the identity.
o Rewrite everything in terms of sine and cosine.
o Substitute known identities.
o Multiply numerator and denominator by the conjugate of either the numerator or denominator as appropriate.
o Split a fractional expression into multiple terms.
o Combine fractional expressions (by first getting common denominators)
6.3: Sum and Difference Identities

Use the sum and difference identities found on your Trigonometric Identities Sheet to simplify trigonometric expression,
verify trigonometric identities, and find exact values of trigonometric functions.
6.4: Double-Angle and Half-Angle Identities

Use the double-angle and half-angle identities found on your Trigonometric Identities Sheet to simplify trigonometric
expression, verify trigonometric identities, and find exact values of trigonometric functions.
6.5: Product and Sum Identities

Use the product and sum identities found on your Trigonometric Identities Sheet to simplify trigonometric expression, verify
trigonometric identities, and find exact values of trigonometric functions.
6.6: Conditional Trigonometric Equations

Find all real numbers that satisfy a trigonometric equation.

Find all real numbers on a specified interval that satisfy a trigonometric equation.
7.1: Law of Sines

Solve a triangle given some parts.

Determine the number of triangles with the given parts

Find the area of a triangle using law of sines.
7.2: Law of Cosines

Solve a triangle given some parts.

Determine the number of triangles with the given parts.
Schedule:
Week 1:
Angles and Their Measure, Graphs of Sine and Cosine, The Other Four Trigonometric Functions
Week 2:
Inverse Trigonometric Functions, Right Triangle Trigonometry, Basic Trigonometric Identities, Verifying Identities
Week 3:
Sum and Difference Identities, Double-Angle and Half-Angle Identities, Product and Sum Identities, Conditional
Trigonometric Equations
Week 4:
Law of Sines, Law of Cosines
Course Policies not Addressed Above:
University policies – Students are responsible for the following policies: Safe Environment, Students with Disabilities,
Institutional Review Board, Academic Integrity, and Academic Contact Hour. A copy of these policies may be downloaded from
the web site: http://www4.nau.edu/avpaa/UCCPolicy/plcystmt.html.
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