MATH IV ( Pre-Calculus) Course Syllabus
Dutchtown High School
2013 - 2014
Teachers
Mrs. Teresa Jackson
teresa.jackson@henry.k12.ga.us
Mr. Srinvas Garlapati
srinvas.garlapati@henry.k12.ga.us
Room #213
Room # 324
School Phone: (770) 515.7510
School Web Page: www.henry.k12.ga.us/dh
Text: Pre-calculus Glencoe McGraw-Hill © 2011
Online Resources: www.georgiastandards.org
Prerequisite: Completion of Math III
Supplies:
 2 Dry Erase Markers Monthly/Dry Erase Board
 Pencils (no pens! Prefer mechanical pencils)
 1 2” Three Ring Binders and Notebook paper with 8 notebook dividers
 TI-84 Graphing Calculator ($109-$129)
 Graph paper, ruler, index cards, pack of colored pencils
Course Description / Content:
This is the fourth course in a sequence of courses designed to provide students with a rigorous
program of study in mathematics. It includes sample statistics such as the central limit theorem, confidence
intervals, and sampling distributions, sequences and series, rational functions, and trigonometry (functions,
graphs, and identities). GPS standards are attached.
Concepts will be presented in multiple ways such as concrete/pictorial, verbal/written,
numeric/data-based, graphical and symbolic. Periodically, online assignments/assessments will be given.
These assignments will be completed outside the classroom environment.
1st Semester
Unit 1: How Confident Are You?
Unit 2: Sequences and Series
Unit 3: Rational Functions
Unit 7: Extended Trigonometry
Grading Procedure:
Homework
Practice (Tasks/CW/Quizzes)
Unit Assessments
2nd Semester
Unit 4: Introduction to Trigonometry
Unit 5: Investigating Trigonometry Graphs
Unit 6: Trigonometric Identities
Unit 8: Investigations of Functions
10%
40%
50%
Total
100%
Final Grade = .85 of 100%(total) = 85% + Final Exam Grade = 15%
Grading Scale:
A = 90-100
B = 80-89
C = 74-79
D = 70-73
F = 0-69
Grading:
Tasks/Classwork/Quiz (40%) & Homework (10%)
Assignments will be made daily and are designed to help students understand, practice and
apply the standards prior to being formally assessed. In order to ensure mastery, successful
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completion of assignments and proof that standards have been met are required for students to
participate in unit assessments.
 Homework Checks. Homework is assigned primarily for reinforcement and
independent practice. Homework quizzes will be given weekly.
 Quizzes. These will be about every week and may or may not be announced.
Unit Assessments (50%)
Unit tests over multiple standards will be given about every three weeks. There will be
approximately 8 unit assessments.
Semester Exam (15%)
At the end of each semester, all students will take an exam covering units 1 -4 from first
semester and units 5 -8 from second semester.
Infinite Campus:
Grades are uploaded to the Infinite Campus in real time. Parents will be contacted by their child’s teacher
when his/her math grade falls below 74. Parents may contact the school’s counseling office to set up a parentteacher conference.
Make-up Procedure: (Per student handbook)
It is the student’s responsibility to make arrangements for make-up work. The number of days
allowed to complete make-up work will be one day for each day absent, unless determined otherwise by the
principal. Failure to comply with this make-up procedure will result in a zero (0) being given for work and
graded assignments missed during an excused absence. Students with an unexcused absence will not be
allowed to make up work and graded assignments missed during the unexcused absence. Students with
excused absences may arrange with the teacher for extra help if an extended absence is unavoidable.
Students who have an absence on the day of a test should come prepared to take that test the day they return
to school. In addition, if the student was informed prior to the absence date of a test, the student is required
to take the test upon return. Tests may be made up before or after regular school hours at the Bulldog
Learning Center (room 204).
Tutoring:
Tutoring provided by a certified math teacher is available on Monday -Thursday from 3:25 P.M. to
4:00 P.M. in the Bulldog Learning Center (room 204). Students may request a study or make-up session with
their teacher on a needs basis. Teachers will not be responsible for transporting students. Tutorial will not be
available for students who choose to be otherwise occupied during the initial teaching of the lesson.
Classroom Rules:
1. Be on time.
2. Be respectful.
3. Be prepared for class.
4. Follow all school and classroom rules.
5. No food or beverages in the classroom.
Procedure for enforcing class, school, and county rules:
(For definitions of Section I, II, and III offenses see student handbook.)
1) For any offense of classroom rules: 4-step process
First offense:
conference with student
Second offense: parental contact/30 minute detention
Third offense:
parental contact/1 hour detention
Fourth offense: referral to administration
2) For any offense that falls into SECTION I, II, or III:
First offense:
Referral to administration
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How to pass this class: Doing the following items will help you be successful in this class:
1. Do assigned reading and practice promptly.
2. Use a planner.
3. Be present on a daily basis. If you are sick, make up work in a timely manner when you return. If
absent for more than one day, arrange for your work to be brought to you (by a classmate).
4. Keep your notebook up to date.
5. Complete your own assignments.
6. Study for tests (start reviewing for a test at least three nights before a test).
7. Ask questions when you do not understand.
Grades are not “given” by an instructor. Your grades are the record of the standards assessments
assigned over the duration of the course.
Keep this in the front of your Math Portion of your Notebook
Disclaimer: This syllabus is subject to change at the instructor’s request
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Math IV Syllabus
“I understand the course requirements and expectations outlined in the course syllabus. I understand
that I may contact the instructor at Dutchtown High School with any questions or concerns that I
might have. I also understand that attendance in a mathematics based class is critical to success.”
The signed syllabus should be kept in the notebook at all times, and a second copy will be maintained
by your teacher.
Student Signature
Student Name (printed)
Date
Student Parent/Guardian Signature
Parent/Guardian (printed)
Date
Period
4
Gradebook Code
MM4A1a (domain)
MM4A1a (range)
MM4A1a (zeros)
MM4A1a (points of
discontinuity)
MM4A1a (increase/decrease)
MM4A1a (rates of change)
MM4A1a (extrema)
MM4A1a (symmetry)
MM4A1a (asymptotes)
MM4A1a (end behavior)
MM4A1b
MM4A1c (equations)
MM4A1c (inequalities)
MM4A2a
MM4A2b
MM4A2c
MM4A2d
MM4A2e
MM4A3a
MM4A3b (amplitude)
MM4A3b (period)
MM4A3b (phase shift)
MM4A3b (vertical shift)
MM4A3b (domain)
MM4A3b (range)
MM4A3b (zeros)
MM4A3b (extrema)
MM4A3b (points of
discontinuity)
MM4A3b (increase/decrease)
MM4A3b (rates of change)
MM4A3c
MM4A3d
MM4A4a
MM4A4b
MM4A4c
MM4A5 (establish)
Math IV Standards
Description of the Georgia Performance Standard
Algebra
Investigate and explain domain of rational functions
Investigate and explain range of rational functions
Investigate and explain zeros of rational functions
Investigate and explain points of discontinuity of rational functions
Investigate and explain intervals of increase or decrease of rational functions
Investigate and explain rates of change of rational functions
Investigate and explain extrema of rational functions
Investigate and explain symmetry of rational functions
Investigate and explain asymptotes of rational functions
Investigate and explain end behavior of rational functions
Find inverses of rational functions, discussing domain and range, symmetry and function
composition
Solve rational equations analytically, graphically and by using appropriate technology
Solve rational inequalities analytically, graphically and by using appropriate technology
Define and understand angles measured in degrees and radians, including but not limited to 0°, 30°,
45°, 60°, 90°, their multiples and equivalences
Understand and apply the six trigonometric functions as functions of general angles in standard
position
Find values of trigonometric functions using points on the terminal sides of angles in standard
position
Understand and apply the six trigonometric functions as functions of arc length on the unit circle
Find values of trigonometric functions using the unit circle
Understand and apply the six basic trigonometric functions as functions of real numbers (graphing)
Investigate and explain amplitude of the six basic trigonometric functions and their transformations
Investigate and explain period of the six basic trigonometric functions and their transformations
Investigate and explain phase shift of the six basic trigonometric functions and their
transformations
Investigate and explain vertical shift of the six basic trigonometric functions and their
transformations
Investigate and explain domain of the six basic trigonometric functions and their transformations
Investigate and explain range of the six basic trigonometric functions and their transformations
Investigate and explain zeros and intercepts of the six basic trigonometric functions and their
transformations
Investigate and explain extrema of the six basic trigonometric functions and their transformations
Investigate and explain points of discontinuity of the six basic trigonometric functions and their
transformations
Investigate and explain intervals of increase or decrease of the six basic trigonometric functions and
their transformations
Investigate and explain rates of change of the six basic trigonometric functions and their
transformations
Graph transformations of trigonometric functions including changing period, amplitude, phase shift
and vertical shift
Apply graphs of trigonometric functions in realistic contexts involving periodic phenomena
Compare and contrast properties of functions within and across the following types: linear,
quadratic, polynomial, power, rational, exponential, logarithmic, trigonometric and piecewise
Investigate transformations of functions
Investigate characteristics of functions built through sum, difference, product, quotient and
composition
Students will establish the following identities: 𝑡𝑎𝑛𝜃 =
1
𝑠𝑖𝑛𝜃
𝑠𝑖𝑛𝜃
𝑐𝑜𝑠𝜃
, 𝑐𝑜𝑡𝜃 =
𝑐𝑜𝑠𝜃
𝑠𝑖𝑛𝜃
, 𝑠𝑒𝑐𝜃 =
1
𝑐𝑜𝑠𝜃
, 𝑐𝑠𝑐𝜃 =
,
𝑠𝑖𝑛2 𝜃 + 𝑐𝑜𝑠 2 𝜃 = 1,
𝑐𝑜𝑡 2 𝜃 + 1 = 𝑐𝑠𝑐 2 𝜃,
sin(α ± β) = sinαcosβ ± cosαsinβ ,
cos(𝛼 ± 𝛽) = 𝑐𝑜𝑠𝛼𝑐𝑜𝑠𝛽 ∓ 𝑠𝑖𝑛𝛼𝑠𝑖𝑛𝛽, sin(2𝜃) = 2𝑠𝑖𝑛𝜃𝑐𝑜𝑠𝜃, cos(2𝜃) = 𝑐𝑜𝑠 2 𝜃 − 𝑠𝑖𝑛2 𝜃
MM4A5 (simplify)
𝑠𝑖𝑛𝜃
𝑐𝑜𝑠𝜃
1
1
Students will simplify the following identities: 𝑡𝑎𝑛𝜃 =
, 𝑐𝑜𝑡𝜃 =
, 𝑠𝑒𝑐𝜃 =
, 𝑐𝑠𝑐𝜃 =
,
𝑐𝑜𝑠𝜃
𝑠𝑖𝑛𝜃
𝑐𝑜𝑠𝜃
𝑠𝑖𝑛𝜃
𝑠𝑖𝑛2 𝜃 + 𝑐𝑜𝑠 2 𝜃 = 1,
𝑐𝑜𝑡 2 𝜃 + 1 = 𝑐𝑠𝑐 2 𝜃,
sin(α ± β) = sinαcosβ ± cosαsinβ ,
cos(𝛼 ± 𝛽) = 𝑐𝑜𝑠𝛼𝑐𝑜𝑠𝛽 ∓ 𝑠𝑖𝑛𝛼𝑠𝑖𝑛𝛽, sin(2𝜃) = 2𝑠𝑖𝑛𝜃𝑐𝑜𝑠𝜃, cos(2𝜃) = 𝑐𝑜𝑠 2 𝜃 − 𝑠𝑖𝑛2 𝜃
5
MM4A5 (verify)
MM4A6a
MM4A6b
MM4A6c
MM4A6c
MM4A7
MM4A8a
MM4A8b
MM4A9a (recursive)
MM4A9a (explicit)
MM4A9b (arithmetic)
MM4A9b (geometric)
MM4A9c
MM4A9d
MM4A10a
MM4A10b
MM4A10c (add)
MM4A10c (subtract)
MM4A10c (scalar multiples)
MM4A10d
MM4D1
MM4D2
MM4D3
𝑠𝑖𝑛𝜃
𝑐𝑜𝑠𝜃
1
1
Students will verify the following identities: 𝑡𝑎𝑛𝜃 =
, 𝑐𝑜𝑡𝜃 =
, 𝑠𝑒𝑐𝜃 =
, 𝑐𝑠𝑐𝜃 =
,
𝑐𝑜𝑠𝜃
𝑠𝑖𝑛𝜃
𝑐𝑜𝑠𝜃
𝑠𝑖𝑛𝜃
𝑠𝑖𝑛2 𝜃 + 𝑐𝑜𝑠 2 𝜃 = 1,
𝑐𝑜𝑡 2 𝜃 + 1 = 𝑐𝑠𝑐 2 𝜃,
sin(α ± β) = sinαcosβ ± cosαsinβ ,
cos(𝛼 ± 𝛽) = 𝑐𝑜𝑠𝛼𝑐𝑜𝑠𝛽 ∓ 𝑠𝑖𝑛𝛼𝑠𝑖𝑛𝛽, sin(2𝜃) = 2𝑠𝑖𝑛𝜃𝑐𝑜𝑠𝜃, cos(2𝜃) = 𝑐𝑜𝑠 2 𝜃 − 𝑠𝑖𝑛2 𝜃
Solve trigonometric equations over a variety of domains, using technology as appropriate
Use the coordinates of a point on a terminal side of an angle to express x as 𝑟𝑐𝑜𝑠𝜃 and y as 𝑟𝑠𝑖𝑛𝜃
Apply the law of sines
Apply the law of cosines
Verify and apply ½ ab sin C to find the area of a triangle
Find values of inverse sine, inverse cosine and inverse tangent functions using technology as
appropriate
Determine characteristics of the inverse trigonometric functions and their graphs
Use and find recursive formulae for the terms of sequences
Use and find explicit formulae for the terms of sequences
Recognize and use simple arithmetic sequences
Recognize and use simple geometric sequences
Find and apply the sums of finite and, where appropriate, infinite arithmetic and geometric
sequences
Use summation notation to explore series
Represent vectors algebraically and geometrically
Covert between vectors expressed using rectangular coordinates and vectors expressed using
magnitude and direction
Add vectors
Subtract vectors
Compute scalar multiples of vectors
Use vectors to solve realistic problems
Data Analysis
Using simulation, develop the idea of the central limit theorem
Using student generated data from random samples of at least 30 members, determine the margin of
error and confidence interval for a specified level of confidence
Use confidence intervals and margin of error to make inferences from data about a population
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