# Mathematics

Question 1

In a class where the exam averages are normally distributed, the mean score is 75 and the standard deviation is 10. If you want to find out the probability that a randomly picked student has scored 85 or above, what is the z value that you should look up on the normal distribution table?

Question 2

According to a report by Scarborough Research, the average monthly household cellular phone bill is $73. Suppose local monthly household cell phone bills are normally distributed with a standard deviation of $11.

a. What is the probability that a randomly selected monthly cell phone bill is less than $95?

b. What is the probability that a randomly selected monthly cell phone bill is between $62 and $84?

Question 3

A Travel Weekly International Air Transport Association survey asked business travelers about the purpose for their most recent business trip. Nineteen percent responded that it was for an internal company visit. Suppose 950 business travelers are randomly selected.

a. What is the probability that more than 20% of the business travelers say that the reason for their most recent business trip was an internal company visit?

b. What is the probability that between 18% and 21% of the business travelers say that the reason for their most recent business trip was an internal company visit?

Barton Community College

Course Syllabus Fall 2016

I. GENERAL COURSE INFORMATION

Course Number: MATH 1831

Course Title: Business Calculus

Credit Hours: 3

Prerequisites: MATH 1828 College Algebra with a grade of C or better OR MATH 1826

College Algebra with Review with a grade of C or better OR appropriate placement score

Division/Discipline: Academics/Mathematics and Science

Course Description: A condensed study of differential and integral calculus with an emphasis

on applications in the area of business and economics.

II. INSTRUCTOR INFORMATION

Instructor Name: Brian Howe

Contact Data:

Email: howeb@bartonccc.edu

Office Location: Great Bend campus – C116

Office Phone: 620-792-9254

III. COLLEGE POLICIES

Students and faculty of Barton Community College constitute a special community engaged

in the process of education. The College assumes that its students and faculty will

demonstrate a code of personal honor that is based upon courtesy, integrity, common sense,

and respect for others both within and outside the classroom.

Plagiarism on any academic endeavors at Barton Community College will not be tolerated.

The student is responsible for learning the rules of, and avoiding instances of, intentional or

unintentional plagiarism. Information about academic integrity is located in the Student

Handbook.

The College reserves the right to suspend a student for conduct that is determined to be

detrimental to the College educational endeavors as outlined in the College Catalog, Student

Handbook, and College Policy & Procedure Manual. [Most up-to-date documents are

available on the College webpage.]

Any student seeking an accommodation under the provisions of the Americans with

Disability Act (ADA) is to notify Student Support Services via email at

disabilityservices@bartonccc.edu.

IV. COURSE AS VIEWED IN THE TOTAL CURRICULUM

Business Calculus is an approved general education course at Barton Community College,

which can be used to fulfill degree requirements as a fundamental mathematics course.

Business Calculus is designed to provide business and economic majors with a basic

understanding of differential and integral calculus and its applications in business and

economics. Students needing calculus but who are not business majors or are uncertain of

their major should enroll in the 5 credit Calculus I, MATH 1832. Any student whose major

program requires two or more calculus courses should also take MATH 1832 since it is a

more in-depth study of differential and integral calculus.

This course transfers well to most of the regent universities as a three credit hour

Basic/Business Calculus. However, requirements vary among institutions, and even within

departments, and often without much notification. Thus, it is the student’s responsibility to

be in contact with the transfer institution throughout his/her tenure at Barton Community

College to insure that the student is enrolling in the most appropriate set of courses for the

transfer program. http://bartonccc.edu/transfer/schools

V. ASSESSMENT OF STUDENT LEARNING

Barton Community College is committed to the assessment of student learning and to quality

education. Assessment activities provide a means to develop an understanding of how

students learn, what they know, and what they can do with their knowledge. Results from

these various activities guide Barton, as a learning college, in finding ways to improve

student learning.

Course Outcomes, Competencies, and Supplemental Competencies

A. Utilize the definition of a limit to compute and interpret the nature of a function.

1. Evaluate the limit of a function at a point both algebraically and graphically.

2. Evaluate the limit of a function at infinity both algebraically and graphically.

3. Determine the continuity of a function using the definition of a limit.

4. Distinguish between average and instantaneous rates of change.

5. Differentiate a function using the limit definition of a derivative.

B. Apply the patterns of differentiation to find the derivative of a given function.

1. Compute a derivative of a function involving powers, exponents and sums.

2. Calculate a derivative of a function involving products and quotients.

3. Produce the derivative of a function involving compositions of functions.

4. Find the derivative of a function involving exponential and logarithmic functions.

5. Differentiate a function that is defined implicitly.

C. Compile and synthesize information concerning a function using derivation to sketch the

graph of a function.

1. Detect the critical point(s) of a function using the first derivative.

2. Determine the inflection point(s) for a function using the second derivative.

3. Find the intervals of increasing and decreasing and local extrema using the first

derivative.

4. Determine the concavity of a function using the second derivative.

5. Sketch the graph of a function using information gathered from the first and second

derivatives.

6. Identify vertical and horizontal asymptotes of a function.

7. Analyze the graph of a function.

D. Apply differentiation to theoretical and practical situations and interpret the results.

1. Use the derivative to find the marginal profit, marginal revenue and marginal cost.

2. Use the derivative to find the equation of a tangent line to a curve at a given point.

3. Use optimization techniques to find maximum revenue, minimum average cost and

maximum profit in business applications.

4. Solve related rate problems.

5. Use differentials to estimate change of profit, cost and revenue as production

changes.

6. Compute the elasticity of demand.

E. Utilize the definition of an antiderivative to perform integration and interpret the nature of

a function.

1. Evaluate definite integrals using the Fundamental Theorem of Calculus.

2. Integrate indefinite integrals.

3. Integrate algebraic and exponential functions.

4. Evaluate integrals of the form ∫ 1

𝑢 𝑑𝑢

VI. INSTRUCTOR’S EXPECTATIONS OF STUDENTS IN CLASS

MATH1831 Business Calculus is designed in weekly (9-week session) units. Students must

complete any graded assignments by the due date of each lesson. In the event of computer or

network problems, it is the responsibility of the student to contact the Canvas Helpdesk

(helpdesk@bartonline.org -or- 1-844-711-0949) for technical assistance and email the

instructor of the situation.

Failure to complete a graded assignment before the deadline will result in a late penalty on

that assignment. The penalty applies regardless of reason (e.g. computer or network

problems, personal situations, work conflicts, etc.), so plan to complete graded assignments

before the deadline in order to leave yourself some time for unforeseen circumstances.

Failure to complete a graded assignment prior to the end of the course will result in a

score of zero (0).

Courteous, professional conduct on the Internet is mandatory. Disruptive and/or offensive

behavior will result in dismissal from the course.

All students are required to produce their own work on ALL assignments. Evidence of

cheating will result in at least a zero for that assignment. Additionally, the instructor may,

without cause, require the use of Panopto web-cam video recording for all remaining

assignments for an individual student or the class as a whole.

VII. TEXTBOOKS AND OTHER REQUIRED MATERIALS

Barnett, Raymond. Calculus for Business, Economics, Life Sciences & Social Sciences 13/e.

Pearson Prentice Hall, 2014.

Scientific or Graphing Calculator

Webcam and Microphone (most new laptops have them already embedded/installed)

VIII. REFERENCES

None

IX. METHODS OF INSTRUCTION AND EVALUATION

HOMEWORK SETS

It is really important to practice the mathematics. The homework sets for each section can be

found embedded within the course. You need to score a minimum of 50% on each homework

set in order for the Unit Quiz/Test to open. Make sure that you complete the homework sets

in plenty of time before the due date for the Unit Quiz/Test. A 20% deduction will be made

on any Homework Set completed within a week after the due date. After one week, the score

will be and remain a zero.

SHOW WORK

There is also a Show Work problem set that is a cross-section of the entire unit. In the Show

Work problem set, not only must you input your answer correctly but you must show your

work for each problem like you would if a teacher was collecting your written work in a face-

to-face class and looking at your steps to solve a problem.

You can show your work two major ways. (1) Upload a picture of your handwritten work

onto the whiteboard. This is the recommended way of showing your work. Please make sure

that your picture is clear (not fuzzy) so that your handwriting can be clearly read. (2) Write

on the whiteboard. Each Show Work question has a whiteboard and “pens” that you can write

with on it.

In order for the weekly tests to open, you have to score a 50% on the Show Work assignment

too. The Show Work assignment has to be graded by your instructor personally. Since the

instructor is not constantly in the course there may be a delay. The instructor will

communicate with you concerning the days and times they will be entering the course to

grade the Show Work questions. Make sure that you have them completed by one of those times otherwise you may not get access to the test.

QUIZZES AND TESTS

There will be at least one Unit Quiz/Test over each chapter and a Final. All of these

assignments can be found in My Math Lab. The final exam is comprehensive. You should

complete each quiz/test by the end of the corresponding chapter/unit; quizzes/exams may be

completed after the chapter/unit but will receive a late penalty of 20% and must be completed

within a week of the due date. After a week, the score will be a zero and there is no chance of

making up the assignment. A score of zero (0) is recorded for all quizzes/tests not completed

by the end of the course.

All Unit Quizzes and Tests must be proctored using the Panopto software. Failure to do so

will result in a zero.

THREADED DISCUSSIONS

Threaded discussions include the muddiest points. Grading will be based on participation,

completion and quality of the posts. You must post a question and respond to two others.

PRE TEST and POST TEST

Every student must complete the pretest and post test. A student earns full credit for

attempting the Pre-Test. The Post Test will be graded on the correctness of the responses.

FINAL EXAM There is a comprehensive final exam for this course. The final exam must be proctored using

the Panopto software. Failure to do so will result in a zero.

Orientation Week 5%

Muddiest Point/Threaded Discussions 5 %

Homework Sets 10%

Show Work 10%

Quizzes/Tests 50 % Post Test 5 %

Final Exam 15%

Letter grades will be determined using the following scale:

90-100% A

80-89.99% B

70-79.99% C

60-69.99% D Below 60% F

X. ATTENDANCE REQUIREMENTS

The Barton Community College Course Attendance Policy is available online for student

reference. The Barton Community College Grade and Attendance Reporting Policy is also

available online for student reference. Students should read both documents to familiarize

themselves with the official attendance and grade reporting policies of the college.

Class attendance in Barton distance learning classes is measured primarily by completion of

assignments and participation. I will measure your participation by you having: (1)

successfully logged in each lesson, (2) completed all assignments by the end of the lesson,

and (3) emailed questions when you are having difficulty.

XI. COURSE OUTLINE

WEEK 1: ORIENTATION MODULE

Orientation Lecture

Orientation Quiz

Academic Integrity Quiz

Introduction Thread

Pre-Test

WEEK 2: MODULE 1

Homework Sets

Functions (Section 1.1)

Elementary Functions: Graphs and Transformations (Section 1.2)

Linear and Quadratic Functions (Section 1.3)

Polynomial and Rational Functions (Section 1.4)

Exponential Functions (Section 1.5)

Logarithmic Functions (Section 1.6) Show Work – Functions and Graphs

Discussion Thread

Unit Test – Functions and Graphs

WEEK 3: MODULE 2

Homework Sets

Introduction to Limits (Section 2.1)

Infinite Limits and Limits at Infinity (Section 2.2)

Continuity (Section 2.3)

The Derivative (Section 2.4) Show Work – Limits

Discussion Thread

Unit Quiz – Limits

WEEK 4: MODULE 3

Homework Sets

Basic Differentiation Properties (Section 2.5)

Differentials (Section 2.6)

Marginal Analysis in Business and Economics (Section 2.7) Show Work – Limits and the Derivative

Discussion Thread Unit Test – Limits and the Derivative

WEEK 5: MODULE 4

Homework Sets

The Constant e and Compounding Interest (Section 3.1)

Derivatives of Exponential and Logarithmic Functions (Section 3.2)

Derivatives of Products and Quotients (Section 3.3)

The Chain Rule (Section 3.4) Show Work – Derivative Rules

Discussion Thread

Unit Quiz – Derivative Rules

WEEK 6: MODULE 5

Homework Sets

Implicit Differentiation (Section 3.5)

Related Rates (Section 3.6)

Elasticity of Demand (Section 3.7) Show Work – Additional Derivative Topics

Discussion Thread

Unit Test – Additional Derivative Topics

WEEK 7: MODULE 6

Homework Sets

First Derivative and Graphs (Section 5.1)

Second Derivative and Graphs (Section 5.2)

L’Hôpital’s Rule (Section 5.3)

Curve-Sketching Techniques (Section 5.4)

Absolute Maxima and Minima & Second Derivative Test (Section 5.5)

Optimization (Section 5.6) Show Work – Graphing and Optimization

Discussion Thread

Unit Test – Graphing and Optimization

WEEK 8: MODULE 7

Homework Sets

Antiderivatives and Indefinite Integrals (Section 5.1)

Integration by Substitution (Section 5.2)

Differential Equations; Growth and Decay (Section 5.3)

The Definite Integral (Section 5.4)

The Fundamental Theorem of Calculus (Section 5.5) Show Work – Integration

Discussion Thread

Unit Test – Integration

WEEK 9: FINAL

Post Test Final Exam