__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:
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
Addison Wesley / Pearson Education, Inc.
ISBN : 0-321-15935-7
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.