MATH ANALYSIS

Course Syllabus

MR. DOHERTY

SY 2004-2005

COURSE TITLE: MATH ANALYSIS

TEACHER: David D. Doherty (room B1.17)

E-MAIL: David_Doherty@eu.odedea.edu

COURSE DESCRIPTION:

This course will involve students with functions and equations, circular functions, vectors, applications of matrices, recursion, advanced proof ideas, rates and areas, algebra and algorithms. Connections will be made of graphs with equations with real world situations. Reasoning in trigonometry, probability, discrete math, mathematical structure and the conceptual underpinnings of calculus is a major emphasis in the course.

COURSE GOALS/OBJECTIVES/STANDARDS:

Upon successful completion of this course, the student should be able to:

-Describe the sum, difference, product, quotient and composite of two given functions

-Graph polynomial, exponential, rational, and hybrid functions

-Recognize and graph reflections and transformations of functions

-Justify properties of factors of integers or factors of polynomials

-Solve realistic problems involving conic sections

-Use trig identities to express values of trig functions in terms of rational numbers and radicals

-Find the value of selected trig circular functions by applying them to triangles

-Verify trigonometric identities

-Solve problems using the Law of Sines and the Law of Cosines

-Solve equations involving trig and inverse trig functions

-Use computers or calculators to determine linear, exponential, power, and logarithmic regression lines of a set of data

-Use an appropriate experimental design to conduct a study of biological or scientific phenomena

-Solve a counting problem using the Multiplicative Counting Principle or the Binomial Theorem

-Use matrix theory with graphics calculators to solve systems of equations, problems involving coordinate transformations, and finite function

-Apply vector geometry to solve real world problems

SCOPE AND SEQUENCE:

Fall Semester

Chapter 1 Linear Relations and Functions 6 classes

Chapter 2 Systems of Equations and Inequalities 7 classes

Chapter 5 The Trigonometric Functions 6 classes

Chapter 6 Graphs and Inverses of the Trig Functions 7 classes

Chapter 7 Trig Identities and Equations 7 classes

Chapter 8 Vectors and Parametric Equations 6 classes

Chapter 9 Polar Coordinates and Complex Numbers 5 classes

Spring Semester

Chapter 10 Conics (Parabola, Ellipse, Hyperbola) 7 classes

Chapter 11 Exponential and Logarithmic Functions 6 classes

Chapter 12 Sequences and Series 8 classes

Chapter 17 Limits, Derivatives and Integrals 7 classes

Chapter 3 The Nature of Graphs 7 classes

Chapter 4 Polynomial and Rational Functions 6 classes

The rational for having Chapters 3 and 4 at the end is they are not difficult and the concepts are in large part a review. If students need to accelerate, these two chapters can pretty much be done independently.

CONTINOUS SCHOOL IMPROVEMENT:

AFNORTH International High School’s Continuous School Progress (CSP) goal is,

“All students will improve their written communication skills across the curriculum.” The 6 + 1 Traits is the model selected to improve school-wide writing in all subject areas. The 6 + 1 Trait writing framework is a powerful way to learn and use a common language to refer to characteristics of writing as well as establish a common vision of what strong writing looks like. Teachers and students will use the 6 + 1 Trait model to identify areas of strength and weakness as they continue to strive towards continued writing improvement. Success of all students requires that the 6 + 1 trait become a consistent and integral component of each course taught at AFNORTH International High School.

All tests (4 to 5 per semester) will contain at least one problem in which the student will be required to write a paragraph detailing how they would solve and check that problem. Those problems will be scored based on a rubric involving content, student understanding and use of one of the 6 + 1 traits. Students will receive in class training and practice in writing the above paragraphs.

COURSE GRADING AND ASSESSMENT:

Students will be evaluated on completing given assignments, participating in class activities, and completing the computations and measurements in written tests. Formal tests will normally be administered at the middle and completion of a chapter, midyear and at the end of the semester. Open-ended questions and projects are utilized throughout the course to assess student’s abilities to solve problems, reason and communicate about mathematics.

Grading Scale:

A+ 97 – 100%

A 93 - 96

A- 90 -92

B+ 87 - 89

B 83 - 86

B- 80 - 82

C+ 77 - 79

C 73 – 76

C- 70 - 72

D+ 67 - 69

D 63 - 66

D- 60 - 62

F Below 60%

Quarter grades are determined by:

Class Participation approx. 15 % +/-

Daily Practice approx. 20 % +/-

Quizzes (15) approx. 10 % +/-

Chapter Tests (6) approx. 20 % +/-

Cumulative Tests (5) approx. 20 % +/-

Mid-Term or End-Term Exam (1) approx. 15 % +/-

The final semester grade is calculated using 80% of the average of the two-quarter grades plus 20% of the exam grade.

COURSE EXPECTATIONS/CONSEQUENCES:

It is expected that all students come to class prepared and with a willingness to learn. Students needing to use the restroom or get a drink of water should do so during the very generous 10-minute passing period. Classroom time is to be used for learning Algebra only. Behavior should never interfere with learning or teaching. Students will be expected to enter the room quietly and respectfully and maintain that decorum the entire time they are in the classroom.

· Students are not to bring gum, candy, snacks, food or drink of any kind into the classroom.

· Hats and head covers of any kind (including bandanas, hair nets, sweat bands, etc.) not to be worn inside the classroom by students.

· No electronic devices of any kind are to be visible or used in the classroom by students at any time except when instructed to use calculators.

Since math skills are built one upon another and cumulative in nature, any gap in skill mastery will impact future learning and performance. Therefore,

· Late work will be awarded no (zero) points,

· Make-up work must be completed in a timely manner in accordance with the policies set forth in the AFNorth HS Handbooks,

· Students will not be allowed to take a quiz until all of the daily practice for all of the sections covered on the quiz have been completed,

· Students will not be allowed to take a chapter test until all of the quizzes for that chapter have been completed,

· Students will not be allowed to take a chapter test unless they have passed the prior test with a 70% or higher or have been retested on the prior chapter.

· Students may not be re-tested until they have attended a tutoring / re-teaching session either with an AIS Academic Coach (on Wednesdays after school in the library) or by appointment with their Algebra teacher.

Students will be expected to put forth whatever effort is required for them to master the Algebra skills presented to them. Since every student has a different level of mathematical talent and ability as well as prior skill, the amount of effort required for each individual student to master the course material may vary significantly. “Trying” will never be an acceptable alternative for “doing”.

FALURE IS NOT AN OPTION. All students who do not earn a C- (70%) or higher on a chapter test will be required to attend after school and/or seminar tutoring / re-teaching sessions that will be offered the week following the exam. The student will then be required to take another chapter test following the tutoring / re-teaching session. The two chapter test scores will then be averaged and that average will be posted into the grade book.

SUCCESS IS ALWAYS ENCOURAGED. Any student who earned a 70% or higher on the 1^st chapter test is welcome to attend the tutoring / re-teaching sessions in attempt to raise their test score. The two chapter test scores will then be averaged and that average will be posted into the grade book.

TEXTBOOK: Advanced Mathematical Concepts – Precalculus with Applications, Glencoe McGraw-Hill, New York, 1999.

SUPPLIES:

Please come to class prepared with the following materials:

· 3-ring Binder with lined paper

· Spiral Notebook for notes, daily practice, and math journal (that can be secured into the 3-ring binder)

· Graph paper

· Plastics zip pocket with the following: pencils, large eraser, fine RED tip marker or pen (for correcting assignments)

· Tissues (personal use)

The student will have a textbook to keep at home. A class set of textbooks and calculators will be available for the student to use in class.

The following items should be part of your supplies at home:

· TI-83 Plus calculator

HOMEWORK POLICY:

1. Work must be turned in on time. NO POINTS WILL BE AWARDED FOR LATE ASSSIGNMENTS

2. Independent, individual practice is essential for Algebra skill mastery.

a. Daily practice may be begun in class but will usually require time at home as well to complete the assignment.

b. It is recommended that students do half of the unfinished assignment the night of class then complete it the following evening. DO NOT WAIT UNTIL THE LAST MINUTE TO COMPLETE THE DAILY PRACTICE.

c. If no specific assignment has been given, then the student is expected to study Algebra in general at least 30 minutes every school day evening.

3. Work must be neat and directions followed correctly.

a. Organize your work and label your paper WITH FIRST AND LAST NAME properly.

b. SHOW your work. NO WORK? NO CREDIT! Answers along will not be awarded points.

MAKE-UP WORK POLICY:

Mathematics is a challenging subject. One topic builds on another. Daily participation is a must. Many of our math activities will involve group work, graphing calculators and the use of manipulatives. These activities cannot be made up at home, so class attendance is extremely important. If it is necessary for you to miss class please ask for the work that you miss.

You have one class period to make-up any missed work. If a test or quiz is assigned for the day you return and it is listed on your assignment sheet, you will have to take it. Any missed test or quiz must be made-up within ONE week.

EXTRA HELP:

Please feel free to come see me during seminar period if you feel that you need extra help. I am also available after school by appointment. PLEASE ASK.