MANOR COLLEGE

JENKINTOWN, PENNSYLVANIA

 

__Jane R. Zegestowsky________________                _____________________

          Instructor’s Name                                                        Semester / Year

 

Division Office:  Allied Health / Science / Math           Office: 215-885-2360 ext.223

Office Hours:___________________________        e-mail: __________________

 

Course Number / Title / Credit Hours:  MH 104 Algebra & Trigonometry I / 3 credits

 

Course Description:

            This course covers the real number system, imaginary and complex numbers.  It explores polynomial, rational, exponential and logarithmic functions, their characteristics, graph and applications using a graphing calculator.  It develops the unit circle and the trigonometric functions with their applications.

Pre-requisite:  Placement into College Level Math Course or passing grade on all required developmental math courses.

 

Philosophy of the Course:

            The study of calculus is now required or recommended for many students pursuing a four-year college degree.  In many fields, physics has also become a required course.  Mastery of the algebra of functions and trigonometric relationships is an essential step in this sequence of higher-level mathematics and sciences.  In addition to helping students make the transition from elementary mathematics to calculus, the study of trigonometry will develop students’ analytical and problem solving skills.

 

Course Content and Objectives:

By the end of this class students should be able to demonstrate the following skills:

 

Basic Skills ( pages 1 – 50)

The student should be able to:

1.      Add, subtract, multiply and divide positive and negative real numbers

2.      Find the absolute value of a numerical or algebraic expressions

3.      Apply the properties of real numbers

4.      Simplify expressions involving integral exponents using the rules of exponents

5.      Simplify expressions according to the order of operations

6.      Convert numerical expressions in standard form into scientific notation

7.      Perform calculations using scientific notation

8.      Add, subtract, multiply and divide polynomials

9.      Factor polynomials

10.  Find the square or cube root of an algebraic or numerical expression

11.  Simplify rational expressions

12.  Add, subtract, multiply and divide rational expressions

13.  Simplify complex rational expressions

14.  Determine meaningful replacements in rational expressions

15.  Simplify radical expressions

16.  Rationalize denominators

17.  Simplify rational exponents

18.  Determine meaningful replacements in radical expressions

TEST 1

 

Coordinate Geometry  (pages 51 – 164)

The student should be able to:

1.      Use correct terminology to describe the Cartesian Coordinate System

2.      Graph a given set of ordered pairs

3.      Determine if an ordered pair is a solution for an equation

4.      Determine the domain and range of a relation from a set of ordered pairs and from the graph

5.      Find the distance between 2 points on a graph using the distance formula

6.      Determine the midpoint of a line segment

7.      Use the distance formula to determine the equation of a circle

8.      Given the center and a point on a circle, determine the equation of the circle

9.      Define a relation

10.  Define a function

11.  Contrast relations and functions

12.  Evaluate a function

13.  Determine the domain and range of a function

14.  Graph a linear function

15.  Determine the slope of a line

16.  Determine the equation of a line, given the slope and a point on the line

17.  Determine the equation of a line given 2 points on the line

18.  Determine the x-intercept and y-intercept of a line

19.  Graph an equation in y = mx + b form

20.  Translate and reflect functions

21.  Determine when a function is increasing, decreasing or constant

22.  Determine relative maxima and minima on an interval

23.  Add, subtract, multiply and divide functions.

24.  Work with composite functions

25.  Define Symmetry

26.  Identify and Write new functions based on vertical and horizontal translations, reflections, stretching and shrinking.

MID-TERM

 

Equations and the Complex Number System (pages 166 – 241)

The student should be able to:

1.      solve simple equations and write the solution in set builder notation

2.      Describe or define an imaginary number

3.      Define a complex number

4.      Add, subtract, multiply and divide complex numbers

5.      Solve a quad equation by factoring, the quadratic formula or completing the square

6.      Determine the nature of roots using the discriminant

7.      Graph quadratic functions

8.      Solve rational equations

9.  Solve radical equations

10.  Solve inequalities

 

Polynomial Functions (pages 244 – 328)

The student should be able to:

1.        Describe a polynomial function, continuous function, the intermediate value and the turning point

2.        Find zeros of polynomial functions and use them to graph the function

3.        Divide polynomials using synthetic division

4.        Use the remainder theorem to determine if a given expression is a factor of a polynomial or if a given value is a root of the polynomial

5.        Given several values find a polynomial with those values as roots

6.        Use the rational root theorem to find the root of a polynomial

7.        Use Descartes’ Rule of Signs to aid in graphing a function

8.        Determine vertical, horizontal and/or oblique asymptotes of a rational function

9.        Define direct and indirect and joint variation

10.  Solve proportions using cross product or definition of direct or indirect variation

 

The Algebra of Functions (pages 330-390)

The student should be able to:

  1. Graph exponential and logarithmic functions
  2. Find the inverse of a function
  3. Apply properties of Logarithmic functions including common and natural logs.
  4.  Apply the algebra of function to the solution of applications.

PROJECT ON FUNCTION APPLICATIONS

 

Unit Circle and Trig Functions  ( selected sections between 412 – 474)

The student should be able to:

1.      Define a unit circle and graph points on a unit circle

2.      Graph sine and cosine functions

3.      Define six trigonometric functions

4.      Define angle and determine the measure of an angle in degrees and radians

5.      Define right, acute, obtuse, straight, complementary and supplementary angles

6.      Determine the trig, functions of angle rotations and reference angles

7.      Find function values for acute angles

8.Use trig functions in applications.

 

Additional Topics to be covered if time permits:

 

Trig Identities (pages 426 – 430)

The student should be able to:

1.  Simplify trigonometric expressions using basic and Pythagorean Identities

 

 

Proving Trig Identities (pages 448 – 456)

The student should be able to:

1.Prove trigonometric identities

 

Systems of Equations (pages 554 – 565)

The student should be able to:

1.    Solve systems of equations by graphing, substitution, linear comb./ matrices.

 

CUMULATIVE FINAL

This is a tentative schedule and follows the activities as they are outlined in the textbook.  Adjustments will be made based on the class and the needs of the individual students.

 

Student Outcomes

Outcome 1:  The student will demonstrate an understanding of the concept of functions and the ability to use this understanding to interpret and analyze situations mathematically.

Measure:  A student’s understanding will be judged by her/his performance on tests, class participation, and workbook and journal entries.

Standard:  70% of the students in the class will earn a “C” or better for the course.

 

Outcome 2:  Students will be able to use the internet to access and evaluate information related to a topic covered in this course.

Measure:  After selecting a topic and receiving approval from the instructor, the student will complete an internet search for information that supplements the course material on the selected topic.  The student will use this information to connect the course content to applications beyond those presented in class.  The results of this research and analysis will be included in the student’s journal.

Standard:  70% of the students will complete a clearly written, accurate, mathematically correct journal entry on his/her selected topic.  This entry will include a bibliography of researched sites, the supplemental nature of the material researched and a description of the possible applications.

 

Outcome 3:  The student will demonstrate the ability to think mathematically and discuss mathematical concepts in concise, precise language.

Measure:  This course requires collaboration and sharing of information among students in both a written and oral format.  Students will be required to submit written journal entries and give an oral presentation on a researched project.

Standard:  70% of the students will earn a “C” or better on the journal, presentation and participation components of this class.  Written and oral presentations must be concise, precise and mathematically accurate.

 

Approaches to Teaching:

         The material covered in this class will be presented in lecture format, coupled with directed activities and collaborative group work.

 

Procedures for Grading:

         Participation in classroom activities is essential to be successful in this course.  The grade will be determined by the following:

Test 1……………………….. 20%

Mid – Term ………………… 20%

Functions Project…………… 20%

Participation/Presentation……20%

Final………………………….20%

 

Letter grades have the following equivalents:

         0   -   59   =   F

         60  -  69   =   D

         70  -  79   =   C

         80  -  89   =   B

         90  -  100 =  A

 

Attendance:

    This is a collaborative class so your attendance is essential to academic success.  If you miss a class, you are responsible for the missed material and assignments.  IF YOU MISS A TEST, YOU MUST CONTACT ME BY THE END OF THE DAY OF THE TEST DATE.  IF YOU NO NOT, 10 POINTS WILL AUTOMATICALLY BE DEDUCTED FROM YOU TEST GRADE.

 

Materials Used: Graphing Calculator:  Preferably a TI -83          

Text:            Algebra and Trigonometry; Second Edition

                     By Beecher, Penna and Bittinger

                     Addison Wesley / Pearson Education, Inc.

                     ISBN :  0-321-15935-7

 

Academic Honesty College Policy:

            Manor College expects that its students will uphold the principles of truth and honesty in the performance of all academic work.  Plagiarism (the unacknowledged use of another person’s words or assistance) and academic cheating (falsifying data, submitting without instructor’s approval work in one course which was done for another, actually doing another student’s work, and/or the use of any unauthorized aid) are prohibited.

            Digital plagiarism (cutting, pasting and copying sections of an article written by another; downloading papers from a “paper mill” web site and submitting as work written by the student; utilizing any graphics or audio or video clips without permission; and submitting any work with an electronic source without correct citation) is strictly prohibited and a violation of fair use and intellectual property rights.

            The Academic Dean will be formally notified of any violations of the police.  The penalty for the first violation will be a grade of “F” for the assignment.  Any subsequent violations will result in a grade of “F” for the course and possible dismissal from the college.