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Math 175 - Syllabus

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Mathematics 175​   print version

COLLEGE ALGEBRA

Cuyamaca Community College

Fall Semester, 2016

 

Section 9782

Tues & Thurs 12:30 pm - 2:20 pm H-113

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Mary Touchet

mary.touchet@gcccd.edu

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Office Hours

Tues & Thurs 11:15 am - 12:15 pm,

or by appointment H-135

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4 hours lecture, 4 units

Total contact hours: 64-70

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Course Description

College level course in algebra for majors in science, technology, engineering, and mathematics: polynomial, rational, radical, exponential, absolute value, and logarithmic functions; systems of equations; theory of polynomial equations; and analytic geometry. Maximum of 7 units can be earned for successfully completing any combination of MATH 170, 175, 176.

 

Prerequisite

“C” grade or higher or “Pass” in MATH 110 or equivalent (MATH 103 does not meet the prerequisite)

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Required Materials

Text:  Functions Modeling Change: A Preparation for Calculus, Connally, 5th Edition

Graphing Calculator: Our Department highly recommends and supports the use of TI Graphing Calculators in our Math Classes.  For this class in particular, I would recommend that you use a TI-84 Calculator for your required graphing calculator.

 

Important Dates (Academic Calendar)

August 22...First day of regular semester classes

September 2...Last day to add, or drop classes (without a "W" on transcripts)

September 5...Holiday - Labor Day (No Classes)

September 23...Last day to apply for P/NP (CR/NCR)

October 14...Last day to apply for fall 2016 Degree/Certificate

November 10...Last day to drop semester length classes (with a "W")

November 11 - 12...Holiday - Veterans' Day (No Classes)

November 24 - 26...Holiday - Thanksgiving (No Classes)

December 12 - 17...Final Exam Schedule: No regular classes

December 13...Final Exam 12 PM - 2 PM

December 23 - January 2...College & District offices closed

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Course Schedule (Subject to Change)

Aug 23 & 25          Intro to the Course, 1.2, 1.5, and 1.6

Aug 30 & Sept 1    2.2, 2.3, and Review

Sept 6 & 8             2.4, 2.5, and 2.6 

Sept 13 & 15          3.1, 3.2, and Exam #1

Sept 20 & 22         4.1, 4.2, and 4.3

Sept 27 & 29          4.4, 4.5, and Review

Oct 4 & 6               5.1, 5.2, 5.3, and 5.4

Oct 11 & 13             6.1, 6.2, and Exam #2

Oct 18 & 20            6.3, 10.1, 10.2 and 10.3

Oct 25 & 27            11.1, 11.2, and Review

Nov 1 & 3               11.3, 11.4 and 11.5

Nov 8 & 10             12.1, and 12.2, Exam #3

Nov 15 & 17            12.3, 12.5, and Review

Nov 22                   13.1 and 13.2

Nov 24                   No Class - Thanksgiving

Nov 29 & Dec 1      14.2, and 14.3, Exam #4

Dec 6 & 8               14.4, and Final Review

Dec 13, Tues          Final Exam 12 PM - 2 PM

Dec 15                    Final Exam Schedule - No Class

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Course Requirements

  1. Track your grade on the Learning Management System (plan on using Canvas not Blackboard)​​

  2. Homework:  Homework problems will be assigned from each section of the text covered in class.  The homework problems are to be kept together and will be collected on the day of each test.  Each assignment should be neat with the first page labeled by the text section number and the problems assigned from that section.  Failure to meet these requirements or to submit work late will result in points deducted from those designated for the assignment.  Homework from previous chapters may not be submitted late once the test on that chapter has been returned to the student.

  3. Quizzes:  Quizzes will be given throughout the semester to determine students' learning.  Minimal or no notification may be given before a quiz. Always be ready to take a quiz at any time.  There are no makeups on quizzes, but I will drop the lowest 2 quizzes at the end of the semester.  Each quiz will count 10 points.

  4. Projects:  This may include writing, research, and in-class group work with more complex mathematical investigations.  Points will be deducted for incomplete work or late work.

  5. Tests:  There will be 4 in-class tests given throughout the semester, each worth 100 points.  The comprehensive final exam is also worth 100 points.  (Note you must earn at least a "D" on the final to earn a passing grade in this course.)

  6. Grading Scale (using a + and - scale):

A​      90% and above

B      80-89%

C      70-79%

D      60-69%

F      below 60%​

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Class Policies​

  • Attend every class, arrive on time and remain for the entire class.  Please notify me before class begins if you need to leave early or if you are expecting to be late (email is appropriate).  Remember that quizzes may be given at random and cannot be made up.

  • You may be dropped from the class for missing twice the number of hours the class meets per week. (more than 10 hours)

  • Please see the class schedule or connect with another student if you happen to miss a portion or all of class to be informed of changes to the schedule.

  • Cheating and other inappropriate behavior is not tolerated and could lead toward being dropped from the class. (Read #4 a-g on the link to understand what Academic Dishonesty is.)

  • Be courteous and discrete in drinking and snacking in class (if we hear or smell what you are consuming, you should plan on sharing it!)

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Course Prerequisite Skills

Without the following skills, competencies and/or knowledge, students entering this course will be highly unlikely to succeed:

  1. Identifying and/or simplifying:

    1. Linear, quadratic, rational, radical, absolute value, exponential and logarithmic equations

    2. Polynomial expressions

    3. Rational expressions

    4. Algebraic expressions involving radicals and/or rational exponents

    5. Logarithmic expressions

    6. Complex numbers

    7. Basic mathematical formulas from related disciplines

  2. Solving:

    1. Algebraic equations

    2. Logarithmic and exponential equations

    3. Systems of equations and inequalities

    4. Applications to a variety of disciplines

  3. Factoring polynomials

  4. Functions:

    1. Determine the domain and range

    2. Find the inverse

    3. Perform basic operations

  5. Graphing, transforming, and/or operating on the following:

    1. Polynomial, absolute value, exponential and logarithmic functions and their inverses

    2. Linear and quadratic inequalities

    3. Systems of equations and inequalities

  6. Mathematical reasoning and problem solving:

    1. Inductive and deductive reasoning

    2. Effective communication of mathematical arguments

 

Course Content

  1. Linear, quadratic, polynomial, rational, absolute value, exponential, logarithmic and piecewise-defined functions, their graphs and inverses

  2. Graphic, numeric and analytic methods to solve application problems including linear, quadratic, polynomial, rational, absolute value, exponential, logarithmic equations and systems of equations

  3. Polynomial and rational functions and equations including the use of graphing utilities and synthetic division to graph

  4. Graphic, numeric and analytical methods to solve linear and non-linear systems of equations and inequalities

  5. Matrices and determinants

  6. Sequences and series

  7. Binomial theorem

  8. Mathematical induction

  9. Conics

  10. Historical contributions of number and mathematical theories and concepts from diverse cultures

 

Course Objectives

Students will be able to:

  1. Analyze linear, quadratic, polynomial, rational, absolute value, exponential, logarithmic and piecewise-defined functions as well as inverse functions from a graphic, numeric and analytic perspective.

  2. Analyze and solve applied problems from various disciplines and involving a variety of equations including but not limited to: linear, quadratic, polynomial, rational, radical, absolute value, exponential and logarithmic equations as well as systems of equations.

  3. Apply critical thinking and mathematical reasoning skills necessary in collegiate-level algebraic problem solving in related disciplines such as science, business and engineering.

  4. Classify conic equations and construct graphs of conic sections.

  5. Observe, interpret and analyze the behavior of graphs of a wide variety of functions and statistical plots.

  6. Utilize sequences and series equations to solve theoretical and applied problems from various disciplines such as science, business and engineering.

  7. Select and apply appropriate technology including but not limited to computer programs and graphing utilities to model, analyze and interpret a collection of data or to solve real-world application problems requiring the use of collegiate-level mathematics.

 

Method of Evaluation

A grading system will be established by the instructor and implemented uniformly. Grades will be based on demonstrated proficiency in subject matter determined by multiple measurements for evaluation, one of which will be an essay exams, skills demonstration or, where appropriate, the symbol system.

  1. Exploration activities (both independent and group) which measure students’ ability to discover how different parameters affect the graphs or behaviors of linear, quadratic, polynomial, rational, absolute value, exponential, logarithmic and piecewise-defined functions as well as inverse functions and conic equations.

  2. Homework assignments which measure students’ ability to compute with and graph a variety of functions and conics, as well as construct a plan and carry out the plan to solve a diverse collection of real-world application problems.

  3. Exams, including a comprehensive final exam and quizzes which measure students’ ability to:

    1. Calculate and solve with linear, quadratic, polynomial, rational, absolute value, exponential, logarithmic and piecewise-defined functions as well as inverse functions.

    2. Sketch graphs of linear, quadratic, polynomial, rational, absolute value, exponential, logarithmic and piecewise-defined functions and inverse functions as well as discuss the functions’ domain and range; also sketch graphs of conics.

    3. Construct functions that models collected data or real-world application problems.

    4. Utilize sequence and series formula to solve for a sequence term, calculate a sum or solve a sequence related application problem.

 

Method of Instruction

  1. Lecture and discussion

  2. Teamwork

  3. Computer-facilitated instruction

 

Out-of-Class Assignments

  1. Problem sets

  2. Exploratory activities and/or projects

  3. Reading and/or writing assignments

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Exit Skills

Students having successfully completed this course exit with the following skills, competencies and/or knowledge:

  1. Identifying and/or performing:

    1. Range and domain of functions

    2. Operations on functions

    3. Inverses of functions

    4. Operations with complex numbers

  2. Solving:

    1. Algebraic and absolute value equations and inequalities

    2. Logarithmic and exponential functions

    3. nth order systems of equations and inequalities

    4. Applications from a variety of disciplines

  3. Analyzing and graphing:

    1. Algebraic and absolute value functions and inequalities

    2. Logarithmic and exponential functions

    3. Conic sections

    4. Family of curves

 

Student Learning Outcomes

Upon successful completion of this course, students will be able to:

  1. Analyze and investigate properties of functions;

  2. Apply transformations to the graphs of functions;

  3. Recognize the relationship between functions and their inverses graphically and algebraically;

  4. Solve rational, linear, polynomial, radical, absolute value, exponential, and logarithmic equations and solve linear, nonlinear, and absolute value inequalities;

  5. Solve systems of equations and inequalities;

  6. Apply techniques for finding zeros of polynomials and roots of equations;

  7. Apply functions and other algebraic techniques to model real world STEM applications;

  8. Analyze conics algebraically and graphically; and

  9. Use formulas to find sums of finite and infinite series.

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STEM Achievement Center

To support your efforts to succeed in this class, it is highly recommended that you utilize the free tutoring services available in the STEM Achievement Center or Academic Resource Center (ARC).  The hours of both centers are Monday through Thursday 9:00 am - 6:00 pm and Friday 9:00 am - 2:00 pm.  Please understand these hours are subject to budget restrictions and may change.

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Academic Accommodations

Academic accommodations are available for students with disabilities.  Please identify yourself to Disabled Students Programs and Services (DSP&S) staff so that the appropriate accommodations can be ensured.   Please show me your Authorized Academic Adjustment form to identify your accommodations.  If you suspect that you have a disability, or require services for any other type of disability please contact Disabled Student Programs & Services in the One Stop Center (A-113) or call at 619-660-4239.

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