math182.summer

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Academic Enhancement Center

Course SyllabusSummer Term 2010

Name of Instructor: Steven DiazPhone: 305-628-6643 (office); 786-546-2415 (Cell)Email:[email protected]: CafeRicoIM: kaferico (Google & Yahoo)Office Hours:

Monday-Friday 8 - 9 AM & T-Th 1:30 3 PM

Course Description:

This course is designed for those students whose majors require Calculus I, Calculus II or anyadvanced mathematics. Topics include: Trigonometric functions, it relations and graphs, radianmeasures, functions of compound angles, solution of right and oblique triangles, solution oftrigonometric equations, fundamentals problems of analytic geometry, circles, parabolas,ellipses and hyperbolas, polar coordinates and parametric equations.

Pre-requisite: MAT 181

Course Competencies

Basic Planar Trigonometry and Angles

1. Understand and operate with angles and their measures.2. Translate different units of measurement of angles.3. Calculate the length of the arc, the sector area, and the angular speed.4. Review properties of triangles and how to classify them. Congruent and Similar triangles.

Ratios and proportions.5. Trigonometric ratios in right triangles. Pythagorean Theorem.6. The laws of Sine and Cosine. Generalized Pythagorean Theorem.7. Solve right triangles and apply them to real-life examples.

Reviewing basic properties of functions and operations on functions

8. Understand the concept of function.9. Do algebraic operations with functions.10. Symmetric properties of functions: Even and odd functions, translations, mirror images,

rotations, squeezing and stretching.11. Domain and range of a function. Basic elements of graphing.

Course # Course Name Credit Class Schedule

MAT 182Pre-Calculus &Trigonometry

3 Credits M-W-F 1 to 2:45 PMScience &

Technology105
mailto:[email protected]:[email protected]:[email protected]:[email protected]


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Trigonometric functions

12. Understand the concept of periodic functions.13. Identify the graphs of basic trigonometric functions: Sine, Cosine, Tangent, and

Cotangent.14. Identify trigonometric functions of any angle.15. Graphing trigonometric functions by using transformations.16. Identify the concepts of amplitude, wavelength, frequency, and phase shift.

17. Explain how wave intensity is measured and its relationship to the decibel scale.Logarithms and trigonometric functions.

18. Modeling with trigonometric functions.

Trigonometric Identities and Equations

19. Identify trigonometric identities.20. Identify trigonometric functions of multiple angles, sum and difference of angles, and

semi-angles.21. Proof trigonometric identities.22. Understand and identify inverse trigonometric functions.23. Solve trigonometric equations.

Trigonometry, Complex Numbers, and Vectors

24. Complex numbers review. Addition, multiplication and division of complex numbers.Powers and radical of complex numbers.

25. Relate trigonometric functions with complex numbers.26. Understand the concept of vectors and operate algebraically with them. Construct vector

sums by graphical means. Resolve a vector into mutually perpendicular components.27. Absolute value of a vector and its relationship with the concept of distance. Dot product

and cross product. The use of matrices and determinants in vector algebra.28. Vectors and applications.

Conics, Planar curves and Polar coordinates

29. Identify the equation of the Parabola. Determine all geometrical points associated withthis curve. Determine the line tangent to a parabola. Determine the line crossing aparabola and the crossing points.

30. Identify the equation of the Circle and the Ellipse. Determine all geometrical pointsassociated with these curves. Determine the line tangent to a circle and/or an ellipse.Determine the line crossing a circle and the crossing points.

31. Identify the equation of the Hyperbola. Determine all geometrical points associated withthis curve. Determine the line tangent to a hyperbola. Determine the line crossing ahyperbola and the crossing points.

32. Apply the equations of the parabola, ellipse and hyperbola to real-life situations.

33. Understand the concept of polar coordinates and how to represent planar curves in polarcoordinates.

34. An overview of the most common planar curves.


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Course Text & Materials: Pre-Calculus,3rd edition by Beecher, Penna, and Bittinger; Pearson/Addison Wesley:

ISBN 0321460065

MyMathLab Online Course for Precalculus. ISBN: 0321465474

Student-Centered Learning Environment

Students must take the initiative and responsibility to use all the available resources to activelylearn the course content. Instructional time will be spent less on listening class lectures and

more on learning by doing and reflecting.

Taking into considerationour diverse population of students and to ensure they are involved asmuch as possible in the learning process, this course will be based on a blended learningapproach. In a blended course, students complete 50% of the learning activities online (i.e.Blackboard and MyMathLab), and the other learning activities (50%) takes place in the face-to-face classroom. Here is what students should expect in this course:

Face-to-Face Meetings: Class will meet 3 times a week in the classroom, wherestudents ask questions to clarify what they did not understand from the course readingsand e-Lectures. Students will also demonstrate and discuss how to work problems fromthe course textbook that will count toward their participation grade. Finally, students take

the scheduled tests during the class meetings. Computer assisted instruction: A learning and assessment web-based system (i.e.

MyMathLab or MML) is used to help students grasp and master the course content.Students receive immediate feedback for their performance in the interactive practicesets. They will have access to SHOW ME HOW tools that assist them learning coursecontent.

Online Learning Resources: MML provides detailed explanations and demonstrationsof the concepts and skills covered in the course. It also provides supplementaryresources such as videos, animations, Power Point presentations, and the coursetextbook (i.e. e-book). In addition, students have access in Blackboard of additionalinstructor-made resources (i.e. handouts, Power Points, screencasts, etc.) and mathlinks to other Internet sites that provide tutorials, virtual manipulatives, and multimedia

materials. Available Assistance: Students have many alternatives to seek assistance to succeed

in this course: (a) Visit the math center to get individual assistance from the instructor(see office hours info); (b) Visit the math center during business hours to sign up for atutoring session; (c) Ask questions using the Question thread in the discussion board ofBlackboard (questions will be answered within 24 hours); and (d) Class discussions area great opportunity to learn collaboratively the course content.

Reflection Journals: Students will post a reflection in the Bb discussion board on whatthey have learned in the course. These reflections are based on instructors guidedquestions.

Bb Quizzes: Students will watch e-lectures in Bb and take an online quiz based on thecontent.


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Grading Policy:

A= 100 95 % B+= 89 87 % C+= 79 77 % D+= 69 65 %A- = 94 90 % B = 86 83 % C = 76 73 % D = 64 60 %

B-= 82 80 % C-= 72 70 % F = less than 60 %

Course Grading Criteria:

Your grade for this course will be based on the following criterion:

Grading Categories

Class Participation 20%

MML Practice Sets 20%

Tests 40%

Bb Quizzes 10%

Reflection Journals 10%

TOTAL 100%

Course Outline/Schedule:

Week Item/Subject Readings Assignments

1

Course Introduction

Intro to Graphing

Review of BasicConcepts of Geometry

1.1 1.2

Appendix

Watch e-Lectures Bb Qz 1 Discussion Board CW Set

2

Trigonometric Functionsof Acute Angles

Applications of Right

Triangles

5.1 - 5.2

Watch e-Lectures Bb Qz 2 CW Set MML Practice Set

3

Trigonometric Functionsof Any Angle

Radians, Arc Length,and Angular Speed

5.3 5.4

Watch e-Lectures Bb Qz 3 CW Set MML Practice Set

4 Law of Sines Law of Cosines 7.1 7.2

Watch e-Lectures Discussion Board CW Set Test 1: Wks 1-4 (Fri.)

5

More on Functions The Algebra of Functions Symmetry and

Transformations 1.5 1.7

Watch e-Lectures Bb Qz 4 CW Set

MML Practice Set

6

Circular Functions:Graphs & Properties

Graphs of TransformedSine and CosineFunctions

5.5 5.6


MML Practice Set


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7

Identities: Pythagoreanand Sum and Difference

Identities: Cofunction,Double-Angle, and Half-Angle

6.1 6.2


MML Practice Set

8 Proving Trigonometric

Identities 6.3

Watch e-Lectures Discussion Board

CW Set Test 2: Wks 5-8 (Fri.)

9

Inverses ofTrigonometric Functions

Solving TrigonometricEquations

6.4 6.5


MML Practice Set

10

The Complex Numbers Complex Numbers:

Trigonometric Form 7.3 & 2.2


MML Practice Set

11

The Parabola The Circle and the

Ellipse The Hyperbola

9.1 9.3

Watch Video Lectures Bb Qz 9 CW Set

MML Practice Set

12 Polar Coordinates and

Graphs 7.4

Watch e-Lectures CW Set Discussion Board

Test 3: Wks 9-12 (Fri.)


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COURSE POLICIES

1 Practice Problem Sets and TestsThere are 2 types of practice problem sets: Classwork sets and MyMathLab (MML) sets. Classwork setare problems from the course textbook that will be discussed during the classroom meetings. Studentsparticipation grade is based on their performance working the classwork sets (see rubric in thidocument). MML sets are interactive problems sets done in MyMathLab. Students grade is based othe number of problems they got correct out of the total number of problems. MML sets are scheduled tobe on Fridays class meetings at the computer lab of the Academic Enhancement Center.

Scheduled tests are taken only in the classroom (Fridays). There are no make up for tests.

2 AttendanceEducational research has proven there is a positive connection between attendance and academisuccess, so students are strongly urged to attend classes regularly. Face-to-Face attendance imandatory. Students who miss a third of the class sessions will automatically earn a failing (Fgrade. Contact immediately the instructor to find out how to make up an absence.

3 Use of ComputersComputers and network systems offer powerful tools for communications among members of the StThomas community and of communities outside St. Thomas. When used appropriately, these tools caenhance dialogue, education, and communications. Unlawful or inappropriate use of these toolshowever, can infringe on the rights of others. Activities that are expressively forbidden on St. Thomascomputers include but are not limited to the viewing, downloading or use of inappropriate materialsvandalism, virus propagation and installation of unauthorized materials. In addition, you are expected tact as a professional and use the equipment only when directed or appropriate to classroom activities. Alack of compliance with any of these directives could result in disciplinary action and dismissed of clasor course.

4 Expected Classroom BehaviorStudents have a responsibility to maintain both the academic and professional integrity of the schooand to meet the highest standards of academic and professional conduct. Students are expected to dtheir own work on examinations, class preparation and assignments and to conduct themselveprofessionally when interacting with fellow students, faculty and staff. Academic and/or professionamisconduct is subject to disciplinary action including course failure and/or probation of dismissal. Nfood allowed in the classroom. Dress appropriately to attend class. For additional clarificationplease see Student Code of Conduct as stated in the Student Handbook.

5 Cell Phones and CalculatorsCell phones must be turned off or in vibrating mode. If a student must answer a phone call then thstudents must leave the classroom without disrupting the flow of the class. Students who spend considerable amount of time attending a phone call outside the classroom will be considered absentCalculators are permitted during class and tests. Access to a graphing calculator is recommended.

6 Assistance and TutoringStudents should take advantage of the individualized assistance from the instructor during his officehours at the Math Center (Academic Enhancement Center). One of the keys to pass this course is toask questions without hesitation. In addition, students can sign up for tutoring sessions at the AcademiEnhancement Center. Visit the center for additional info.

7 Incomplete GradeStudents will be granted an incomplete grade only on extenuating circumstances (instructor s discretionand if they have a passing grade by the last week of the course. An incomplete grade grants the studenanother week to complete pending assignments. Request for an incomplete grade must be done iperson, not phone calls or e-mails.


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Rubrics

Rubrics are a list of expectations for the different assignments in MAT 181. It is a scoring guidethat seeks to evaluate a student's performance based on the sum of a full range of criteria(expectations). Students should use the rubrics when working on the assignments since theirscores are based on the expectations presented in this scoring guide. In addition, studentsshould use the rubrics to review and analyze their assignments by comparing the earned scoreswith the list of expectations. Rubrics help students understand the meaning behind their grades,and it helps them to improve their performance.

The following rubric will be used for participation:

Score Label Description

5Exemplary

responses

Correct solutions and appropriate strategies are shown or explained,and the solutions are shown with correct labels or descriptions ifnecessary; communicates effectively to the identified audience;shows full understanding of the problem's mathematical ideas andprocesses; identifies all the important elements of a problem; mayinclude examples and counterexamples; presents strong supportingarguments.

4Competent

responses

Complete and appropriate strategies are shown or explained, butincorrect solutions are given due to simple computational or carelesserrors; communicates effectively to the identified audience; showsfull understanding of the problem's mathematical ideas andprocesses; identifies the most important elements of the problems;presents solid supporting arguments.

3Serious Flaws

But NearlySatisfactory

Completes the problems satisfactorily, but the explanations may bemuddled; argumentations may be incomplete; communication issomewhat vague or difficult to interpret; shows limitedunderstanding of the underlying mathematical ideas; identifies thefew important elements of the problems; presents weak supporting

arguments.

2Serious Flaws

And NotSatisfactory

Begins the problems appropriately but may fail to complete or mayomit significant parts of the problems; may fail to show fullunderstanding of mathematical ideas and processes; may make majorcomputational errors; may misuse or fail to use mathematical terms;communication is vague or difficult to interpret.

1Unable to

BeginEffectively

Shows some work or explanation beyond re-copying data, but workould not lead to correct solutions; one or more incorrect

approaches attempted or explained; shows no understanding of theproblem situations; major computational errors; communicatesineffectively.

0 No AttemptMade

No work or solution shown or explained.


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The following rubric will be used to score test items.

Points Expectation

1-pointCorrect answer. Work or process to support answer is logical andneatly organized. It reveals student understanding of conceptsand skills.

1 1 2 3, , ,

4 2 3 4or - point

Incorrect answer. Work or process to support answer is logicaland neatly organized. It reveals student understanding ofconcepts and skills. Minor computational or careless mistakes.

0-pointCorrect or Incorrect answer. Work or process to support answeris not logical or shown. It reveals students misunderstanding ofconcepts and skills. Major computational mistakes.

The following rubric will be used to grade students reflection posts in the discussion board :

Score Criteria

5

Response is coherent and well structured. Mathematical ideas are communicatedclearly and concisely. Student demonstrates full understanding of the mathematicalideas and processes. Student identifies all the key points of the activity and presentsstrong supporting arguments. Response includes examples and counterexamples.

4

Response is coherent and adequately structured. Mathematical ideas are communicatedfairly well. Student demonstrates sufficient understanding of the mathematical ideasand processes. Student identifies most of the key points of the activity and presentsgood supporting arguments.

2

Response is somewhat coherent and structured. Mathematical ideas are vaguelycommunicated. Difficult to make sense students explanation or reasoning. Studentdemonstrates limited understanding of the underlying mathematical ideas andprocesses. Student identifies few key points of the activity and presents weak

supporting arguments.

1Response is incomplete. Ideas are incoherent. Ideas are written in fragments;therefore, student omits most key points of the activity. Student fails to proveunderstanding of the mathematical ideas and processes.

0 No response or ideas are completely irrelevant and inadequate.


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Become an Active Learner

An active learner takes control and ownership of the learning process to meet the coursesgoals and expectations. Active learners decide why, what and how of their learning. They do notwait for learning to happen; instead, they make it happen. The instructional model of this courserequires students to become active learners to meet successfully the course objectives. Thefollowing traits are typical of active learners:

1. Identify personal goals and the steps necessary to achieve the goals.

2. Use resources. Identify the people and tools available to aid in goal pursuit.

3. Learn how to solve almost any problem they ever have to face.

4. Look at situations objectively.

5. Ask the right questions.

6. Use time well. They organize and set priorities.

7. Apply good reading, studying, and questioning skills to course materials.

8. Apply good listening skills in the classroom.

9. Find patterns and take effective notes to organize materials for studying.

10. Assess progress along the way and revise their plans.

Source: http://www.lafayettehigh.org/Course%20Guide/becoming_an_active_learner.htm

English Second Language Learners

For students who do not speak English as their first language, the following suggestions may behelpful to succeed in this course:

1. Bring a dictionary that translates from the students native language to English and vice

versa. If a student does not have a dictionary, the following website provides word andtext translation:http://www.foreignword.com/.2. Find a classmate or group of students who speak English fluently to study for the class

and to gain proficiency with the English language.3. If there is a classmate that speaks the same native language, students can ask for

clarification or assistance using their native language as long it does not disrupt theclassroom learning experience.

4. The instructor of this course is bilingual (English-Spanish) and welcome students tospeak Spanish during office hours or before-after class. In addition, there are manylanguages that have words which are pronounced and written similarly. Therefore, theinstructor encourages students to sometimes use words in their native language tocommunicate ideas, concerns, or questions.

5. If students learned different ways or methods for simplifying or solving math problems intheir countries, the instructor encourages these students to share their methods withhim.
http://www.foreignword.com/http://www.foreignword.com/http://www.foreignword.com/http://www.foreignword.com/


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Students with Disabilities

Please note that students requiring accommodations as a result of a disability must contactMaritza Rivera (e-mail:[email protected] phone number: 305-628-6563) at the AcademicEnhancement Center.

Note for Changes: The instructor reserves the right to change this syllabus at any time duringthe term in order to better meet the needs of this particular class group.
mailto:[email protected]:[email protected]:[email protected]:[email protected]

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