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2023-24

Essential Objectives

Course Syllabus


Revision Date: 20-Jan-23
 

Spring 2023 | MAT-1330-VO01 - Pre-Calculus Mathematics


Online Class

Online courses take place 100% online via Canvas, without required in-person or Zoom meetings.

Location: Online
Credits: 4
Day/Times: Meets online
Semester Dates: 01-24-2023 to 05-08-2023
Last day to drop without a grade: 02-12-2023 - Refund Policy
Last day to withdraw (W grade): 03-26-2023 - Refund Policy
This course has started, please contact the offering academic center about registration

Faculty

Dan Lemay
View Faculty Credentials
View Faculty Statement
Hiring Coordinator for this course: Julie Dalley

General Education Requirements


This section meets the following VSC General Education Requirement(s) for Catalog Year 21-22 and later:
Mathematics
    Note
  1. Many degree programs have specific general education recommendations. In order to avoid taking unnecessary classes, please consult with additional resources like your program evaluation, your academic program catalog year page, and your academic advisor.
  2. Courses may only be used to meet one General Education Requirement.

Course Description

This course is a study of the functions used in calculus, including the exponential, logarithmic, and trigonometric functions. Students must take a math assessment for placement purposes prior to registration. Prerequisite: College Algebra or equivalent skills.


Essential Objectives

1. Solve systems of equations and inequalities.
2. Define and apply properties of linear, quadratic, polynomial, rational, and inverse functions.
3. Define and graph exponential and logarithmic functions.
4. Solve exponential and logarithmic equations and problems of growth and decay.
5. Define and graph trigonometric functions.
6. Simplify trigonometric expressions using trigonometric identities.
7. Use trigonometric identities and equations in application problems.
8. Recognize arithmetic and geometric sequences and associate corresponding key formulas.
9. Use the Principle of Mathematical Induction.
10. Employ the graphing calculator for the numerical and graphical solution of problems.
11.Demonstrate proficiency in understanding, interpreting, evaluating, and applying quantitative data and information.
12. Apply mathematical reasoning to analyze social justice problems in a variety of different contexts and consider whether these approaches are just and equitable.


Required Technology

More information on general computer and internet recommendations is available on the CCV IT Support page. https://support.ccv.edu/general/computer-recommendations/

Please see CCV's Digital Equity Statement (pg. 45) to learn more about CCV's commitment to supporting all students access the technology they need to successfully finish their courses.


Required Textbooks and Resources

This course only uses free Open Educational Resources (OER) and/or library materials. For details, see the Canvas Site for this class.


Methods

Each section we cover will have a set of lecture notes and an accompanying video for you to watch and see some worked examples. If this is your learning style, use it.

There are a set of recommended, ungraded paper based exercises from the textbook for you to choose to complete. I recommend doing them as getting that practice will speed along the graded online exercise sets.

The graded work will be an online set of exercises that you will need to complete each week. Sometimes, you have a correct answer but the online HW system does not recognize your answer as correct. Because of these errors, I grade HW practice exercise sets at full credit as long as you try every exercise and earn at least a 70%.

Most of the online exercises have an accompanying video help.

And I am available for approximately 18 hours of online office hour help via ZOOM. It is as good or even better as being in the same room as we do not have to look at the same computer screen. See the front page of the Canvas course for details.


Evaluation Criteria

Evaluation Criteria:

Forty Percent (40%) from 3 Exams. These exams will be two part exams, one with an online component that is auto graded and a second part that you will have to show work and get me a copy of your work. These exams are not cumulative.

Ten Percent (10%) from weekly online problem sets.

Each week you will have a set of online My Open Math style HW assignments to complete.

Ten Percent (10%) : Discussion Forums: Each week you are responsible to make at least two (2) attendance posts in the current week's discussion board.

Reading other peoples' questions and responding to them is what makes learning on line work. Neglecting to log on for more than a couple of days can lead to problems. I find students meet with difficulty in completing assignments and more importantly don’t master the material when they are not interactive. You will earn these points by asking/answering mathematical questions relevant to what we are studying or by “Going to the Board” and posting your solution (work and answer) to an unassigned exercise

Your first post must occur before Saturday night each week or you will be marked absent. You will also lose half of the attendance points for the week if you miss this deadline.

Forty Percent (40%) (11 @ 50 points each) Weekly quizzes.

Letter Grade Equivalents

A+ 98 - 100

B+ 88 - 89

C+ 78 - 79

D+ 68 - 69

A 93 - 97

B 83 - 87

C 73 - 77

D 63 - 67

S Satisfactory

A- 90 - 92

B- 80 - 82

C- 70 - 72

N Unsatisfactory

Grading Criteria

CCV Letter Grades as outlined in the Evaluation System Policy are assigned according to the following chart:

 HighLow
A+10098
A Less than 9893
A-Less than 9390
B+Less than 9088
B Less than 8883
B-Less than 8380
C+Less than 8078
C Less than 7873
C-Less than 7370
D+Less than 7068
D Less than 6863
D-Less than 6360
FLess than 60 
P10060
NPLess than 600


Weekly Schedule


Week/ModuleTopic  Readings  Assignments
 

1

Sections 1.1

Learning Targets

  • We will be able to look at the graph of a function and determine whether or not the graph is function using the vertical line test.

  • We will be able to look at a table of input output values and determine whether or not the values determine a function.

  • We will be able to look at the graph of a function and determine whether or not the graph is a one to one function using the horizontal line test.

  • We will be able to look at a table of input output values and determine whether or not the values determine a one-to-one function.

  • We will be able to evaluate a function for a specific value given the function in equation form, tabular form or in graphical form.

Section 1.2

Learning targets are:

  • We will be able to state the domain and range of functions in both interval notation and set builder notation given a function's equation or graph.

  • We will be able to work with piece-wise defined functions.

Section 1.3

Learning targets are:

  • We will be able to find the average rate of change of a function give representative table of values or a graph.

  • We will be able to judge when a function is increasing/decreasing, identify when it is concave up/down, identify inflection points and identify local maximum/minimum points.

  • Given a table of values, we will be able to determine when a function is concave up/down by examining rates of change.

Section 1.4

Learning targets:

We will be able to build functions from other functions provided a description of the component functions given in English, tabular, graphical and algebraic forms.

  

Lippman/Rasmussen Sections 1.1 through 1.4

  

Ungraded: Textbook exercises (See Canvas>Modules>Week 1) for what to do

Graded: MyOpenMath Exercises (See Canvas>Modules>Week 1)

Discussion Forum Posts (2) (See Canvas>Modules>Week 1 Overview)

 

2

Section 1.5

Learning targets:

  • We will be able to graph toolkit functions using transformations.

  • We will be able to identify even/odd functions from a graph and algebraically.

Section 1.6

· Learning target: We will learn to use properties of inverse functions

Sections 2.1 to 2.3: You will need to demonstrate mastery of these skills/concepts about linear functions.

Section 2.5

· Learning target: We will be able to solve absolute value equations and inequalities.

  

Lippmann/Rasmussen Sections 1/5, 1.6, 2.1-2.3 and 2.5

  

Quiz on last Week's work (See Canvas>Modules>Week 2)

Ungraded: Textbook exercises (See Canvas>Modules>Week 2) for what to do

Graded: MyOpenMath Exercises (See Canvas>Modules>Week 2)

Discussion Forum Posts (2) (See Canvas>Modules>Week 2 Overview)

 

3

New Learning

Section 3.1

Learning target:

  • We will be able to identify power functions given an equation or a graph.

  • We will be able to identify the coefficients, terms and degree of power functions

  • We will be able to describe long run and short run behavior of power functions

Section 3.2

Learning target:

  • We will be able to create an equation for a quadratic function given a graph or key features.

  • We will be able to find x -intercepts by factoring, using the quadratic formula and graphically

  

Lippmann/Rasmussen Sec 3.1 and 3.2

  

Exam on Week 1 and 2 work

Ungraded: Textbook exercises (See Canvas>Modules>Week 3 Overview) for what to do

Graded: MyOpenMath Exercises (See Canvas>Modules>Week 3)

Discussion Forum Posts (2) (See Canvas>Modules>Week 3 Overview)

 

4

Section 3.4

Learning targets:

· We will be able to perform long division and synthetic division of polynomials

· We will be able to apply the Remainder Theorem and the Factor Theorem

Section 3.5

Learning targets:

· We will be able to apply the Rational Roots Theorem

· We will be able to find real zeros of a polynomial analytically and graphically.

Section 3.6

Learning target:

· We will be able to work with Imaginary and Complex numbers along with finding ALL zeros of a polynomial

  

Lippmann/Rasmussen Sections 3.3 to 3.6

  

Quiz

Ungraded: Textbook exercises (See Canvas>Modules>Week 4) for what to do

Graded: MyOpenMath Exercises (See Canvas>Modules>Week 4)

Discussion Forum Posts (2) (See Canvas>Modules>Week 4 Overview)

 

5

Section 3.7

Learning target:

  • We will be able to write the equation of rational function given its graph

  • We will be able to find vertical and horizontal asymptotes of a rational function given its equation.

  • We will be able to sketch the graph of a rational function given its equation.

Section 3.8

Learning target:

  • We will be able to find inverses of functions by restricting domains as applicable.

  

Lippmann/Rasmussen Sec 3.7 and 3.8

  

Quiz on last Week's work (See Canvas>Modules>Week 5)

Ungraded: Textbook exercises (See Canvas>Modules>Week 5) for what to do

Graded: MyOpenMath Exercises (See Canvas>Modules>Week 5)

Discussion Forum Posts (2) (See Canvas>Modules>Week 5 Overview)

 

6

Section 4.1

Learning Target:

· We will recognize exponential growth/decay from equations and graphs

· We will find formulas which model exponential growth and decay.

· We will apply exponential growth/decay to financial models.

Section 4.2

Learning Target:

· We will be able to describe graphs of exponential functions using the language of transformations.

· W will be able to write formulas for transformed exponential functions give a graph of the function.

Section 4.3

Learning Target:

· We will be able to recognize common and natural logarithms.

· We will be able to rewrite exponential and logarithmic equations.

· We will learn how to use the change of base formula to solve exponential equations.

  

Lippmann/Rasmussen Sections 4.1 - 4.3

  

Quiz on Week 5 Work

Ungraded: Textbook exercises (See Canvas>Modules>Week 6) for what to do

Graded: MyOpenMath Exercises (See Canvas>Modules>Week 6)

Discussion Forum Posts (2) (See Canvas>Modules>Week 6 Overview)

 

7

Section 4.4

Learning Target:

· We will be able to rewrite logarithmic equations using the sum, difference and power log rules

· We will be able to solve equations using the log rules.

Section 4.5

Learning Target:

· We will be able to graph logarithmic functions using transformations.

· We will be able to write an equation given the graph of a logarithmic function.

Section 4.6

Learning Target

· We will be able to use exponential and logarithmic equations to model real life situations.

  

Lippmann/Rasmussen Sections 4.4, 4.5 and 4.6

  

Quiz on Week 6 work

Ungraded: Textbook exercises (See Canvas>Modules>Week 7) for what to do

Graded: MyOpenMath Exercises (See Canvas>Modules>Week 7)

Discussion Forum Posts (2) (See Canvas>Modules>Week 7 Overview)

 

8

An exam week. No new material to learn.

  

Review from Week 3 - 7

  

Two part Exam. See Week 8 in Canvas.

 

9

Section 5.1

Learning Target

  • We will be able to write equations of circles given information about the circle.

  • We will be able to use the equation of a circle to gain information about the circle (i.e. points on the circle, the radius).

  • We will be able to find the intersection(s) of a circle and a line.

Section 5.2

Learning Target

  • We will be able to convert between DMS and decimal degree notation

  • We will be able to convert between degree measure and radian measure

  • We will be able to calculate arc length and area of a sector.

  • We will be able to apply linear vs angular velocity.

Section 5.3

Learning Target

  • We will be able to calculate values based on the sine and cosine trigonometric ratios using the Unit Circle.

  • We will be able to calculate points on a circle using technology

  

Lippmann/Rasmussen Sections 5.1- 5.3

  

No Quiz this week.

Ungraded: Textbook exercises (See Canvas>Modules>Week 9) for what to do

Graded: MyOpenMath Exercises (See Canvas>Modules>Week 9)

Discussion Forum Posts (2) (See Canvas>Modules>Week 9 Overview)

 

10

Section 5.4

Learning Target

  • We will calculate values of all six trigonometric ratios given information about one of them.

  • We will simplify and verify trig identities.

Section 5.5

Learning Target

· We will solve application problems using right triangle trigonometry.

  

Lippmann/Rasmussen Sections 5.4 and 5.5

  

Quiz on Week 9 work

Ungraded: Textbook exercises (See Canvas>Modules>Week 10) for what to do

Graded: MyOpenMath Exercises (See Canvas>Modules>Week 10)

Discussion Forum Posts (2) (See Canvas>Modules>Week 10 Overview)

 

11

Section 6.1

Learning Target

  • We will be able to draw, by hand, accurate sketches of transformed sine and cosine functions.

  • We will be able to write a formula for a graphical or described sinusoidal function.

Section 6.2

Learning Target

  • We will be able to graph, by hand, sketches of Tangent, Cotangent, Secant and Cosecant functions

  • We will be able to write the equation of a transformed trigonometric function.

Section 6.3

Learning Target

  • We will be able to evaluate inverse trigonometric functions using unit circle values and technology.

  • We will be able to simplify both numerical and algebraic expressions containing inverse trigonometric functions.

  

Lippmann/Rasmussen Sections 6.1, 6.2 and 6.3

  

Quiz on Week 10 work

Ungraded: Textbook exercises (See Canvas>Modules>Week 11) for what to do

Graded: MyOpenMath Exercises (See Canvas>Modules>Week 11)

Discussion Forum Posts (2) (See Canvas>Modules>Week 11 Overview)

 

12

Section 6.4

Learning Target

· We will be able to solve trigonometric equations.

Section 6.5

Learning Targets

We will be able to

  • Model with trig equations
    Model with sinusoidal functions
    Solve right triangles for angles in degrees and radians

Section 7.1

Learning Target

· We will be able to solve trigonometric equations requiring trigonometric identities.

  

Lippmann/Rasmussen Sections 6.4, 6.5, 7.1 and parts of Section 7.2 and 7.3. Make sure to look at my additional instruction in the Week 12 module.

  

Quiz on Week 11 work

Ungraded: Textbook exercises (See Canvas>Modules>Week 12) for what to do

Graded: MyOpenMath Exercises (See Canvas>Modules>Week 12)

Discussion Forum Posts (2) (See Canvas>Modules>Week 12 Overview)

 

13

Section 8.1

Learning Target

· We will be able to solve non-right triangles to find missing angles and sides

Solving Systems of Equations

Learning Target

· There are two learning targets: We can solve linear systems of equations and solve non- linear systems of equations

  

Lippmann/Rasmussen Sec 8.1

Additional handouts in Canvas>Modules>Week 13 area.

  

Quiz on Week 12 work

Ungraded: Textbook exercises (See Canvas>Modules>Week 13) for what to do

Graded: MyOpenMath Exercises (See Canvas>Modules>Week 13)

Discussion Forum Posts (2) (See Canvas>Modules>Week 13 Overview)

 

14

Partial Fraction Decomposition

Learning Target

· We will be able to break a rational expression up to a sum or difference of two or more rational expressions.

Working with Sequences and Series

Learning Target:

· We will be able to work with geometric and arithmetic sequences and series.

  

Handouts in Canvas>Modules>Week 14

  

Quiz on Week 13 work

Ungraded: Textbook exercises (See Canvas>Modules>Week 14) for what to do

Graded: MyOpenMath Exercises (See Canvas>Modules>Week 14)

Discussion Forum Posts (2) (See Canvas>Modules>Week 14 Overview)

 

15

Proof by Mathematical Induction

· We will be able to perform a proof using mathematical induction.

  

Handouts in Canvas>Modules>Week 15

  

Discussion Post for Mathematical Induction

Third exam on the rest of the course since the last exam.

 

Attendance Policy

Regular attendance and participation in classes are essential for success in and are completion requirements for courses at CCV. A student's failure to meet attendance requirements as specified in course descriptions will normally result in a non-satisfactory grade.

  • In general, missing more than 20% of a course due to absences, lateness or early departures may jeopardize a student's ability to earn a satisfactory final grade.
  • Attending an on-ground or synchronous course means a student appeared in the live classroom for at least a meaningful portion of a given class meeting. Attending an online course means a student posted a discussion forum response, completed a quiz or attempted some other academically required activity. Simply viewing a course item or module does not count as attendance.
  • Meeting the minimum attendance requirement for a course does not mean a student has satisfied the academic requirements for participation, which require students to go above and beyond simply attending a portion of the class. Faculty members will individually determine what constitutes participation in each course they teach and explain in their course descriptions how participation factors into a student's final grade.


Participation Expectations

For CCV Attendance purposes you must do some work each week with in the current week's window. Online exercises or discussion board posts, quiz/exam. If you fail to complete any work, I mark you as absent for CCV. This can affect your financial aid eligibility.



Missing & Late Work Policy

If you miss the weekly discussion forum post deadlines, those cannot be made up. Once a deadline closes, you are talking in an empty room. If you miss a forum post because an unforeseen family emergency, email me privately.

For all other assignments, you will need prior approval to complete something late. Again if you miss a deadline due to an unforeseen family emergency, email me privately.

Each week runs from Midnight Tuesday morning through the next Monday night at midnight.


Accessibility Services for Students with Disabilities:


CCV strives to mitigate barriers to course access for students with documented disabilities. To request accommodations, please
  1. Provide disability documentation to the Accessibility Coordinator at your academic center. https://ccv.edu/discover-resources/students-with-disabilities/
  2. Request an appointment to meet with accessibility coordinator to discuss your request and create an accommodation plan.
  3. Once created, students will share the accommodation plan with faculty. Please note, faculty cannot make disability accommodations outside of this process.


Academic Integrity


CCV has a commitment to honesty and excellence in academic work and expects the same from all students. Academic dishonesty, or cheating, can occur whenever you present -as your own work- something that you did not do. You can also be guilty of cheating if you help someone else cheat. Being unaware of what constitutes academic dishonesty (such as knowing what plagiarism is) does not absolve a student of the responsibility to be honest in his/her academic work. Academic dishonesty is taken very seriously and may lead to dismissal from the College.