WENTWORTH INSTITUTE OF TECHNOLOGY
DEPARTMENT OF APPLIED MATHEMATICS AND SCIENCES
MATH 250 PRECALCULUS ONLINE
SUMMER 2010
Professors:
Amanda Hattaway
hattawaya@wit.edu
617-989-4368
Ira Allen 218
Anita Penta
pentaa@wit.edu
617-989-4351
Ira Allen 214
Office Hours:
These will be administered via webcam chat and in person if you live close to campus.
Introduction:
The class officially begins on May 15 but students can start as early as Friday, May 7. It is very
important that students get up and running with this course as quickly as possible once the
semester begins.
This is not a self-paced course. You will have to complete your homework assignments and
exams by specified dates. But homework and tests may be done ahead of schedule. The last
day to complete the final exam is by August 11. (More information about the exams is below in
the Exams and Proctoring Section.) If you plan to travel during the semester, we will expect you
to have convenient daily access to the internet while you are away or complete the assignments
and/or tests prior to your vacation.
This online course uses a mediated learning approach that includes both online and offline
activities in a student-centered learning environment. Online activities include: instruction that
uses our short online videos, homework assignments, practice exams, and conference (office)
hours via webcam chat. In addition, we will offer in-person conference hours here at
Wentworth; this is highly recommended if you are local. It is expected that you will watch the
videos before attempting the homework. The course lessons and homework will be available via
Mymathlab (see below.) Offline activities include: proctored exams and in-person conference
(office) hours.
The content of the course is the standard content for the Wentworth Math 250 course: a study
of functions, including: quadratic functions, exponential and logarithmic functions, trigonometric
and inverse trigonometric functions.
Text and Equipment:
1) Mymathlab (Student Access Kit) For Algebra and Trigonometry, by Sullivan (ISBN
0136150624). This system houses your e-book, your homework, our videos, and other relevant
course information. The course ID that you will need to type is penta22299.
2) A graphing calculator is encouraged. There will be some situations where it is appropriate and
others where it is not.
3) A laptop and internet access.
Prerequisite:
Math 205 College Math I or the equivalent.
Grading:
Exams 1 and 3 are each 20% of the grade.
The Midterm Exam and the Final Exam are each 30% of the grade.
Extra credit: If you complete between 60% and 100% of the HW then you will get between 0 – 4
extra points added to your final average. These points will be scaled according to your HW
average. If you do less than 60% of the HW then you will receive no extra credit points.
Grades are assigned on the following scale (refer to the Student Handbook):
A 96 - 100
B+ 88 - 91
C+ 76 - 79
D+ 64 - 67
A- 92 - 95
B 84 - 87
C 72 - 75
D 60 - 63
B- 80 - 83
C- 68 - 71
F
below 60
Course Calendar:
 Exam 1 and Unit 1 HWs: The Unit 1 HWs must be completed by June 1 and Exam 1 needs
to done by June 1 by an approved proctor or on campus.
 Exam 2 (Midterm) and Unit 2 HWs: The Unit 2 HWs must be completed by June 22 and
Exam 2 (Midterm Exam) needs to done by June 22 by an approved proctor or on campus.
 Summer Break: July 3 - July 11
 Exam 3 and Unit 3 HWs: The Unit 3 HWs must be completed by July 21and Exam 3 needs
to done by July 21 by an approved proctor or on campus
 Exam 4 (Final Exam) and Unit 4 HWs: The Unit 4 HWs must be completed by August 11
and Exam 4 (Final Exam) needs to done by August 11 by an approved proctor or on campus.
Exams and Proctoring:
Before each of the four exams, mentioned above, we will provide review tests that you can use
for practice. The review test is not a duplicate of the actual exam that you will take but the
concepts will be similar.
All exams may be taken at Wentworth but if you live outside of the Wentworth area then you
may have the exam given by a proctor at a location convenient to you.
You are responsible for finding a qualified proctor to administer exam by the exams. The
proctor must be a clergyman, teacher, professor, librarian or administrator in a nearby
secondary school, library, college, university, or testing center. Proctors cannot be family
members, friends, or co-workers. For assistance finding a proctor, you can contact a guidance
counselor or an academic advisor. The Consortium of College Testing Centers
(http://www.ncta-testing.org/cctc/) is an organization that has testing centers across the
country and abroad that provide proctoring services to distance students near their homes. Any
fees incurred are your responsibility.
You must send the proposed proctor’s name, title, phone number and email address to us via
email no later than 14 days prior to the first scheduled exam. A “Proctor Approval” Form is
available and will be emailed to you. Your course professor may contact your proposed proctor
and final approval of your proposed proctor is at the sole discretion of your course professor. All
proctoring arrangements will be approved by us at least 7 days prior to the date of the first
scheduled exam.
You will need to provide photo identification to your proctor when you arrive at each exam
whether taken away or at Wentworth. Your proctor will sign off on a form for each exam
indicating the type of identification presented. You must attach this form to each exam. An
exam without this form will not be graded.
Other Items:
1. Students with disabilities should be sure to contact the Counseling Center (617-989-4390
or counseling@wit.edu.) and appropriate accommodations can then be made.
2. Cheating is not tolerated and will result in failure. (Refer to the Student Handbook.)
3. If you are local, you are encouraged to attend our in-person conference hours at the
Wentworth campus. In addition, there is free tutoring available in the Center for
Teaching and Learning (CTL), which is located on the fourth floor of Beatty Hall. Check
the CTL website for hours.
4. If any changes to this outline are necessary then you will be informed of them by email.
COURSE OUTLINE AND OBJECTIVES
UNIT ONE – Functions and Their Graphs
Sec. 3.1 Functions
Objectives
1. Determine Whether a Relation Represents a Function. Find the
Domain and Range.
2. Find the Value of a Function.
3. Find the Domain of a Function.
Sec. 3.2 The Graph of Function
Objectives
1. Identify the Graph of a Function
2. Obtain Information from or about the Graph of a Function.
Sec. 3.3 Properties of Functions
Objectives
1. Use a Graph to Determine Where a Function is Increasing,
Decreasing or Constant and if it is Even or Odd.
2. Use a Graph to Locate Local Maxima and Local Minima.
3. Use a Graphing Utility to Analyze a Function.
Sec. 3.4 Library of Functions; Piecewise-defined Functions
Objectives
1. Graph the Functions Listed in the Library of Functions.
2. Graph Piecewise-defined Functions.
Sec. 3.5 Graphing Techniques: Transformations
Objectives
1. Graph Functions Using Vertical and Horizontal Shifts.
2. Graph Functions Using Compressions and Stretches.
3. Graph Functions Using Reflections about the x-Axis and the y-Axis.
Sec. 3.6 Mathematical Models: Building Functions
Objectives
1. Build and Analyze Functions.
All unit 1 homework and test 1 are to be done by June 1.
UNIT TWO- Systems of Equations; Polynomial and Rational Functions
Sec. 12.1 System of Linear Equations
Objectives
1. Solve Systems of Equations by Substitution.
2. Solve Systems of Equations by Elimination. Identify Inconsistent
Systems of Equations of Two Variables. Identify the Solution of a
System of Dependent Equations Containing Two Variables.
3. Solve Systems of Three Variables. Identify Inconsistent Systems.
Express the Solution of a System of Dependent Equations.
Sec. 12.2 Systems of Linear Equations: Matrices
Objectives
1. Write the Augmented Matrix of a System of Linea Equations.
Write the System of Equations from the Augmented Matrix.
2. Solve a System of Linear Equations Using Matrices on a Graphing
Utility.
Sec. 4.3 Quadratic Functions and Their Properties
Objectives
1. Graph Quadratic Functions Using Transformations. Write the
Equation of a Quadratic Function Given the Vertex and a Point.
2. Graph a Quadratic Function Using its Vertex, Axis and Intercepts.
3. Find the Maximum or Minimum Value of a Quadratic Function.
Sec. 4.4 Quadratic Models
Objectives
1. Solve Applied Problems Involving Quadratic Functions.
Sec. 5.1 Polynomial Functions
Objectives
1. Identify Polynomial Functions and Their Degree.
2. Graph Polynomial Functions Using Transformations.
Sec. 5.2 Properties of Rational Functions
Objectives
1. Find the Domain of a Rational Function.
2. Graph Rational Functions Using Transformations.
All unit 2 homework and the midterm (test 2) are to be done by June 22.
UNIT THREE – Exponential and Logarithmic Functions
Sec. 6.1 Composite Functions
Objectives
1. Form a Composite Function.
Sec. 6.2 One-to-One Functions; Inverse Functions
Objectives
1. Determine Whether a Function is One-to-One.
2. Determine the Inverse of a Function Defined by a Map or a Set of
Ordered Pairs. Obtain the Graph of the Inverse Function from the
Graph of the Function.
3. Find the Inverse of a Function Defined by an Equation.
Sec. 6.3 Exponential Functions
Objectives
1. Evaluate Exponential Expressions and Define e.
2. Graph Exponential Functions.
3. Solve Exponential Equations.
Se. 6.4 Logarithmic Functions
Objectives
1. Change Exponential Expressions to Logarithmic Expressions and
Logarithmic Expressions to Exponential Expressions. Evaluate
Logarithmic Expressions.
2. Determine the Domain of a Logarithmic Function. Graph
Logarithmic Functions.
3. Solve Logarithmic Equations.
Sec. 6.5 Properties of Logarithms
Objectives
1. Work with Properties of Logarithms, including the Change of Base
Formula.
2. Write a Logarithm Expression as a Sum or Difference of
Logarithms. Write a logarithmic Expression as a Single Logarithm.
Sec. 6.6 Logarithmic and Exponential Equations
Objectives
1. Solve Logarithmic Equations.
2. Solve Exponential Equations.
3. Solve Equations Using a Graphing Utility.
Sec. 6.7 Compound interest
Objectives
1. Determine the Future Value of a Lump Sum of Money.
2. Determine the Rate of Interest or Time Required to Double a Lump
Sum of Money.
Sec. 6.8 Exponential Growth and Decay Models; Newton’s Law;
Objectives
1. Find and Solve Equations of Quantities that Obey the Law of
Uninhibited Growth and the Law of Decay
2. Use Newton’s Law of Cooling (and Heating) and Logistic Models.
All unit 3 homework and test 3 are to be done by July 21.
UNIT FOUR – Trigonometric Functions and Analytic Trigonometry
Sec. 7.1 Angles and Their Measure
Objectives
1. Review the Definition of Radian Measure. Review Converting
Degrees to Radians and Radians to Degrees.
Sec. 7.3 Computing the Values of Trigonometric Functions of Acute Angles
Objectives
1. Review the Exact Values of First Quadrant Special Angles.
2. Review the Use of a Calculator to Approximate the Values of the
Trigonometric Functions of Acute Angles.
Sec. 7.4 Trigonometric Functions of General Angles
Objectives
1. Review the Exact Values of Trigonometric Functions of an Angle
Using Reference Angles.
Sec. 7.6 Graphs of the Sine and Cosine Functions
Objectives
1. Understand the Sinusoidal Graphs.
2. Determine the Amplitude and Period of Sinusoidal Functions.
3. Graph Sinusoidal Functions Using Key Points.
4. Find an Equation for a Sinusoidal Graph.
Sec. 7.8 Phase Shift
Objectives
1. Graph Sinusoidal Functions with Phase Shifts.
Sec. 7.7 Graphs Of Tangent and Cotangent
Objectives
1. Graph Tangent and Cotangent Functions.
Sec. 8.1 The Inverse Sine, Cosine and Tangent Functions
Objectives
1. Find the Exact Value of Inverse Sine, Cosine and Tangent Functions.
2. Find the Inverse Sine, Cosine and Tangent Functions Using a
Calculator. Use the Properties of Inverse Functions to Find Exact
Values of Certain Composites.
Sec. 8.3 Trigonometric Identities
Objectives
1. Use Algebra to Simplify Trigonometric Expressions.
2. Establish Identities.
Sec. 8.7 Trigonometric Equations I
Objectives
1. Solve Equations using a Single Trigonometric Function.
2. Solve Equations Using a Graphing Utility.
All unit 4 homework and the final exam (test 4) are to be done by August
11.