Thursday, September 25, 2008

AP Exam Review

AP Booklet Test #1 Complete by midterm exam
Turn is essays based upon schedule located on the board in the classrom.

Final Exam Report Card Grade
AP grade of 5 will be recorded as an A on the report card.
AP grade of 4 will be recorded as a B on the report card.
AP grade of 3 will be recorded as a C on the report card.
AP grade of 2 will be recorded as a D on the report card.
AP grade of 1 will result in an F appearing on the report card.

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Note: Practice integration every day.

Tuesday, August 12, 2008

Higher Level students must decide upon their paper three option of Statistics or Analysis(differential Equations) by the end of October.
The instructor reserves the right to alter this syllabus.
Course: AP/BC AND AB CALCULUS
AB STUDENTS You Start At This Point
Length: 18 weeks broken into two 9 week semester under a Block Schedule
Block Schedule: Classes meet from Aug. - December for 90 minutes each school day

Flash Cards of formulas are suggested.

Labs and Portfolios : Story format, two copies, typed or black non-erasable ink all five areas of interaction with technology unless otherwise instructed.

Journals are required to be continued : Students answer each day :” What are you grateful for learning in math today? This journal acts as a review book of the AP syllabus just prior to them sitting to take the test.

Notebooks are not required but are recommended in the following format: Each notebook should contain a formula , vocabulary, homework, example, essays and practice problem section. Additional section appropriate with school board policy are allowed . The note book will be graded.

Textbooks and Supplements:

Calculus Larson Hostetler Edwards from Houghton Mifflin
Calculus and Analytic Geometry Thomas/Finney from Addison Wesley
Calculus Concepts and Application Foerster by Key Curriculum
Calculus Problems for a New Century from MAA editor Fraga
Mathematics Vertical Teams Toolkit College Board
Old AP released exams from 1987 to present
Investigating Change by Barnes from Curriculum Corporation
Advance Placement Mathematics by Best & Lux from Venture Publishing
Multiple Choice & Free Response Question by Lederman from D & S Marketing
AP College Board Calculus internet site
MAPLE software
CBL units

[NOTE BC Students Only: Students have all had AP/AB the first term of the previous year Aug. - Dec.
Thus it is necessary to review all of AP/AB material as soon as possible. The first 1-5 weeks is spent doing this. Time is strictly determined on student recall and is not limited to a specific section. The instructor keeps the syllabus handy and marks off topics covered and needing additional review. As we journey into BC material infinite series are introduced slowly to develop more theory and work on remediating those silly algebra errors.
Students are usually 12 graders taking either the Methods or Higher Level test of the IB program. Since students are in the AP/BC class the instructor still must meet their in depth theory questions that exceed the boundaries of College Board.]

Midterm Exam: An actual AP test is administered with the AP grade calculated.
Report card exam column has a modified scaling as not all concepts may have been presented.

Final Exam is based upon a complete AP test graded according to AP standards
5- A , 4- B, 3-C, 2-D, 1-F

AB Calculus and BC Review
The rate of Change of a Function
Introduction
Coordinates
Increments
Slopes of a straight line
Equations of a straight line : Standard , Point Slope, Slope Intercept and Double Intercept.
Functions and graphs
Domain, Range, Intercepts, Concavity,Increasing , decreasing, zeros, maximum and minimum values of domain and range,
slopes at points from a Calculator aspect for discovery of info for next chapter. Continuity from the “Driving on the Road” aspect.
Derivative of a function both formal and short cut using simple polynomials and rational functions
Velocity and rates
Properties of Limits

Formal Differentiation
“Litany” Graphing functions using Calculus concepts involving limits/formulas and interpreting by naming the y’ line, y” line, Summarizing what each one does. Confirm by the second derivative test.
Continuation of limit First Principles” into epsilon delta definition
Rational and polynomials functions with irrational and rational coefficients and their derivatives
Inverse functions and their derivatives
The increment of a function ( intro to Riemann sums from an algebraic Perspective)
Newton’s Method for solving Equations
Trig functions Review with appropriate identities
Derivatives of Sine and Cosine
Composite functions and their derivatives
L’Hopitals Rule for limits using differentiation formulas
Derivatives of Secant, Cosecant , Tangent and Cotangent
Formal Continuity
Differentials
Use of various derivative notation of for differentiation
Euler's Method via a lab activity
Application
Sign of the first derivative as it compares to the graph of the function
Implicit Differentiation
(Two methods dy/dx versus ( dy and dx).
Related Rates
Sign change of the second derivative as it relates to the graph of f(x) and f’(x)
Curve plotting from both an algebraic standpoint and calculator. Emphasis on when to use Calculator and when to rely on algebra skills
Average Rate of Change
Slope Fields
Rolle’s Theorem
Mean Value Theorem
L’Hopital’s Rule from a formal presentation and its indeterminate forms.
Extension of the Mean Value Theorem
Applications of the Mean Value Theorem
Integration
Review of summation notation
Riemannian Sums Major Lab using both Technology Programs and simple Geometry/Algebra. Students are required to discover a relationship from the following areas under the curve of a quadratic and cubic:
Upper, Lower , Midpoint, Trapezoidal Rule, Simpson’s rule include an error analysis after third day of working with this topic.

The indefinite integral
Applications of indefinite integration
Integration of sine and cosine
Area under a curve by Calculus and technology
Area between curves using the definite integral


Application of the Definite Integral
Continue with area between curves involving trig functions and polynomials for use of the calculator.
Distance
Volumes
slices: Disk, isosceles right triangles, equilateral triangles
shell
washer
Length of a plane curve
Area of surface of revolution
Average value of a function
The Theorems of Pappus Donut Lab during FCAT testing of 10Th graders
Work Problems

Solving differential equations by separation of variables ( More growth and decay)

During the Application of the definite Integral include
Derivatives of inverse function and apply the “litany of graphing”
Derivatives of natural log and logarithmic functions and apply the “litany of graphing.”
Derivatives of exponential functions au and hyperbolic sine and apply the “ litany of graphing”

Note: The “Litany” is a comprehensive look at the function from domain through concavity using the second derivative test.
Compound interest
Exponential Growth

Methods of Integration with a constant spiral back into applications involving derivatives
Basic Formulas
Powers of Trig. Functions
Even powers of trig functions
Integrals involving radicals TRIG Substitution
Integrals involving ax2 + bx + c
Integration by partial fractions
Integration by Parts
Integration of rational functions and appropriate trig. functions
Improper Integrals

Polar Graphs
The polar coordinate system
Graphs of polar functions by hand and by calculator.
Polar equations of the conic sections and other curves
The angle between the radius vector and tangent line
Plane areas in polar graphs.

Vectors and Parametric Equations
Vector components and the unit vector
parametric equations in kinematics
Parametric equations in Analytic Geometry
The derivative of the vector function
Tangential vectors
Curvature and normal vectors
Tangential and normal components of the velocity and acceleration vectors
Polar Graphs
BC Curriculum
INFINITE SERIES Will be taught slowly and be intermixed with the AP/AB review through vectors. After this is completed we use another textbook and do the chapter on INFINITE SERIES from start to finish with no spiraling to AB/AP curriculum unless needed for one of the test for convergence or divergence.
Infinite Series
Introduction using graphing calculator and MAPLE software
limits that arise frequently
Infinite series ( arithmetic and geometric)
Test for convergence of series with nonnegative terms
Absolute convergence
Alternating series
Conditional convergence
Power Series for functions Taylor and Mac laurin
Taylor’s Theorem with Remainder
Sine, Cosine, ex
Binomial Series
Lagrange’s Form
Further computations
Logarithms, arctangent, π
Indeterminate forms
Convergence of power series
integration and differentiation

Solving differential equations
First order : Variables separable
First order : Homogeneous
First order : Linear
First order: Exact


Complete old AP exams are administrated during the course.
Practice exams from various authors are also included.
Students need to recognize when to use the calculator appropriately.
All responses should be in story format with appropriate calculus documentation.

January to testing day
Individual Review from journal, internet, exams in class
6:30 A.M to 7:15 A.M. review first come first serve with instructor
County Saturday Review
Special appointment with instuctor
Mu Alpha Theta competitions Calculus individual and Calculus Team
Mu Alpha Theta after school practices
Honor Society tutoring


Courses: Honors Geometry / IB, Calculus AB , BC , IB

Instructor: T Lambert

Description: Each course above will meet the criteria for the State of Florida
Standards , AP curriculum and all Pre-IB/ IB courses will cover the requirements of the IB curriculum as well. A list of topics can be found in your course curriculum guide.
Grading Policy: In accordance with the Broward county Public School System the following grading scale is in effect.
A 90-100 C+ 77-79 D+ 67-69
B+ 87-89 C 70 - 76 F 0 - 59
B 80-86 D 67 - 69
Points are awarded to each activity based upon teacher discretion.
If an activity carries a weight higher point value then usual students are notified verbally.

IB/Pre_IB Portfolios:Students are required to complete special individual math portfolios assigned by the instructor. These portfolios must be turned in in multiple copies 2 for testing year and 3 for MYP. All work is to be done in non erasable black ink. Each portfolio must be in story format with graphs and/or pictures included with the worded reference. All calculator / math programs must be documented by printing the screen(s). Only math notation is acceptable!! No programming language is allowed. All work must be done by the IB student and turned in on the assigned day/time. There are no redo’s for portfolios/projects!!! Your MYP program forms the foundation for your external evaluation.

Student Rights and Responsibilities
1.To be given the opportunity to learn and receive a full period of meaningful instruction.
2.To be treated with respect by all individuals within the teaching environment.
3.To respect self and others through action, words and deeds.
4.To be willing to try and try again until the task meets the set criteria.
5.To abide by all rules as set down in the Student Conduct Code.
6.To try all assignments and document their efforts in writing / tape recording.
7. To obtain at least two phone numbers from his/her classmates so as to keep abreast of materials and topics that were covered during an absence.


How to Study for a Math Test
1.Rewrite your notes each day.
2.Complete all portions of your notebook. Write down the definitions and formulas.
3.Attempt the examples that are related to your assigned work that appear in your textbook.
4.Try out the problems in the book that have answers.
5.As you gain confidence attempt the homework problems. Making sure not to erase your attempts ( unless you know it is absolutely wrong). This will enable your tutor to see how you were thinking at the time of a potential error.
7.If a formula or vocabulary word is not easily remembered then make a flash card out of it. Use an index card
Side one: A = Special Area of an Equilateral Formula then

Side two would be: Area of an equilateral triangle where s is the measure of a side of the triangle ( Sorry that not all symbols are transfering.)
8. Review the stack of flash cards every two days making two piles the ones you study every day and the ones you study every week. Parents please work the flash cards with your student, so that you can be made aware of their progress.

9.As you do problems either from the textbook or other correct assignments generate your own test questions and practice problems each day. So before a major test you will have a practice test with the correct methods within your grasp.


Major Tests: Must be made up.

Quizzes and some test are both written and oral
You will be required to present your work on the WHITEBOARD. Bring your markers.

Extra Credit: Earned by 1. Winning a Math Bee Competition in class
or
2. A classroom activity deemed appropriate by the
teacher.

Writing Skills across the curriculum
Journal: Calculus students must make a journal entry six days a week. ENTRIES WILL RELATE A MATHEMATICAL CONCEPT APPROPRIATE TO THE LEVEL. Journals will be collected at any time. Students are therefore required to bring their journal to class every day.

Student Notebook: Students are required to submit their notebook
on Aug.-Dec. students the second Tuesday of December
or
for Jan.- May students the first Tuesday of May
during their respective class periods.

Contents will include and not limited to separate sections for
1. List of definitions ( Hand written in complete sentence form.)
2. List of conjectures / theorems ( Hand written)
3. Order and labeled correctly investigations.
4. Evaluations such as quizzes and test
5. Formula Section ( Hand written )
continuation from previous courses

6. Homework assignments dated and page from book that have been returned.
7.Math Vocabulary from all courses.( Hand written in complete sentences)
continuation from previous courses
8.Portfolio section for the IB Program ( Special projects)
9.Technology section- labs and calculator information
10. Journal entries seven times a week.
(What are you grateful for with respect to what you learned in math today? )

All assigned problems, investigations and definitions must be organized so that they can easily be found within your notebook. Outside evaluators will use a given rubric to evaluate your notebook. No computer generated notebooks are allowed for evaluation. Additional sections can be included in the notebook.

Example of an evaluation. Award only five points if the student has completed at least two of the following sections
pg 34 solution to problem 23 is A = 34 in2.
or pg 122 solution to problem 16 must be 18 cm
or pg 165 Investigation 4.3.2 ( Must have drawn the shape and labeled as line j.)


All Algebra Presentations will be vertically presented!!!!!!!
Example: 3x + 6 - 2( x+1 ) = 9
3x + 6 -2x -2 = 9
3x - 2x + 6 -2 = 9
x + 4 = 9
x = 9 - 4
x = 5

All Classes Special Projects are assigned at various times during the year. If students are working within a group they are responsible to get their part of the project to a group member prior to the time that the project is due. If a student is unable to do this please post mark their material to the instructor at the school.



Teacher rights and responsibilities:
1.To work in an environment conducive to teaching , learning and discovering.
2.To be provided with a safe teaching environment. ( Book bags out of aisles.)
3.To work in an environment where all individuals are treated with respect.
4.To teach students proper classroom and small group behavior.
5.To provide a complete period of meaningful instruction each day with respect to the subject matter and the relationship it has across the curriculum.
6.To be a good role model by adhering to school board policy.