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Connie McCullough > AP Calculus Syllabus

Greer High School

AP Calculus AB Syllabus

Teacher: Mrs. Connie McCullough

Room: 241

Email: cmccullo@greenville.k12.sc.us

Tutoring: mornings 7:50-8:15 by appointment

Textbook: James Stewart. Calculus. California: Brooks/Cole – Thompson Learning, INC., 2003.

Class Description:

This course is for the mathematically gifted student capable of the college level. The course outline reflects the content currently recommended by the College Entrance Examination Board. Students enrolled in the course are required to take the Advanced Placement Calculus Examination administered by CEEB in the spring. Most colleges grant one semester of credit to students who complete this course successfully and pass the examination. There will be a practice examination given on a Saturday in April in which your participation is strongly encouraged.

Grading and Assessment Procedures:

Grades will include major tests in a 60% category and minor tests in a 40% category.

Major tests will cover an entire chapter or a large number of sections within the chapter and will be cumulative. A review sheet will be given prior to the test on most occasions. The quarter test and the portfolio given at the end of each quarter will count as a major test.

Minor tests will include quizzes (announced, unannounced, and cumulative), free response assignments, and any other graded assignments.

***If you are absent on the day of a quiz (except for cumulative quizzes), there will be no make up. The grade that you receive on the corresponding section of the following major test will also count as your missing quiz grade. If you know in advance that you are going to be absent, you may take the quiz the day before outside of class time. ***A cumulative quiz will be given every Monday covering any material that we have discussed since the beginning of the year. You should constantly be studying your notes from the first of the year to the present to be prepared for these quizzes.

***If you are absent on the day of a major test or a cumulative quiz, there will be no make up. The grade that you receive on the quarter test will also count as your missing major test and/or cumulative quiz grade. If you are not absent for any of the major tests, the quarter test may replace the single lowest major test grade if the quarter test is higher. If you are absent for any of the major tests, you forfeit the opportunity to have the quarter test replace any other major tests other than those for which you were absent.

***Free response assignments must be done on white paper with all work shown on the front only. Free response assignments will have a 25 point deduction for each day that they are turned in late.

***Homework will not be counted as a grade unless it is checked for accuracy. Since this is a college level course, the student should have the maturity and logical foresight to realize that working the homework assignments is absolutely imperative in order to succeed or possibly even pass.

There will also be a portfolio test given at the end of each nine weeks except for the fourth quarter. This test will cover any material that has been studied prior to the test. The questions are actual AP questions from previous College Board exams, and they are in both the multiple choice and free response format. This test will count as one of the major tests.

Class Routine:

Each day will begin with the answers to the previous day’s homework on the overhead. You are to check your work as soon as you enter the classroom. After 5 minutes, I will remove the answers and begin the notes for the new section. The remaining 15 minutes will be reserved for discussing any questions from the previous day’s assignment.

We must move at a fast and steady pace in order to complete all of the objectives prior to the AP exam. If you find that you are having trouble and need extra help, please set up an appointment to come for morning tutoring. I am more than happy to help you; it is my goal to have you succeed in this course.

Materials Needed:

You will need a large 3-ring notebook, notebook paper, lineless white paper (computer paper), pencils, highlighter, and a graphing calculator (TI-83, TI-83 plus, or TI-89 calculator*). I will be using a TI-83 plus for demonstrations. *I cannot help you if you do not know how to operate your TI-89, but you are welcome to use it on a restricted basis. It performs some calculus functions that I and the AP guidelines expect you to do without any calculator assistance, therefore when I am assessing these objectives, you will have to use one of my TI-83 calculators.

Grading Scale:

A: 93-100 B: 85-92 C: 77-84 D: 70-76 F: below 70

***Note for IB students:

You will have additional portfolios and Practice Papers to prepare for Paper 1 and Paper 2. The deadlines for these assignments will be strictly enforced.

Classroom Expectations:

The following guidelines will help ensure your success:

1. Respect everyone – I will respect you, and I expect the same

respect to be shown to myself as well as your fellow classmates.

2. Respect the room – Do not bring food, candy, gum, or drinks into the room. Bottled water is permitted as long as the bottle is clear and the top is securely tightened.

3. Be on time for class! If you are late you will miss valuable time to check your homework. You will be warned once each quarter. After your warning, disciplinary action will follow any subsequent tardiness. Tardiness is defined as not being in the room at the time the bell rings.

4. Have your materials with you everyday and be ready to learn.

5. Follow all rules as stated in the Greer High School handbook.

Course Topic Outline

Analysis of Graphs

Students will review graphical representations of various functions both manually and using the graphing calculator. They will note various behaviors in each graph. {Chapter 1 (1,2,3,4) }

* Relations, functions, and their graphs

* Identification of essential functions: constant, linear, quadratic, cubic, square root, cube root, absolute value, greatest integer, exponential, logarithmic, trigonometric, and piecewise

* Transformation of functions

* Using the graphing calculator to determine an appropriate viewing window

* Using the graphing calculator to find roots

* Domain, range, intercepts, and asymptotes

* Composition of functions

* Writing equations of lines

Limits and Rates of Change

Students will discover several methods of finding a limit of a function. They will investigate limits and their properties. {Chapter 2 (1,2,3,5); Chapter 4 (1,4)}

* Tangent to a curve and velocity of an object-understanding limits intuitively

* Evaluate the limit of a function numerically

* Evaluate one-sided limits

* Evaluate the limit of a function using limit laws

* Evaluate the limit of a function analytically

* Determining when a limit does not exist

* Continuity of a function

* Discontinuity of a function

* Limits involving infinity and the asymptotic relationship

* Asymptotic and unbounded behavior

* Understanding asymptotes in terms of graphical behavior

* Describing asymptotic behavior in terms of limits involving infinity

* Comparing relative magnitudes of functions and their rates of change

* Geometric understanding of graphs of continuous functions using the Intermediate Value Theorem and the Extreme Value Theorem

Derivatives

Students will discover the concept of the derivative graphically, numerically, and analytically. {Chapter 2 (6); Chapter 3 (1,2,3,4,5,6,7,8,9,10); Chapter 4 (1,2,3,5,6,7,8,9); Chapter 7 (2,3,4,5)}

-Concept of the derivative

* Presentation of the derivative graphically, numerically, and analytically

* Interpretation of the derivative as a Rate of Change

* Derivative defined as the limit of the difference quotient

* Slopes, tangent lines, and derivatives

* Relationship between differentiability and continuity

* Differentiation Formulas-Constant Rule, Power Rule, Product Rule, Quotient Rule, and Chain Rule-of polynomial, rational, trigonometric, inverse trigonometric, exponential, and logarithmic functions

* Implicit Differentiation

* Logarithmic Differentiation

-Derivative at a point

* Slope of a curve at a point- tangents, vertical tangents, and no tangents

* Tangent line to a curve at a point and local linear approximation- Slopes, tangent lines, and derivatives

* Instantaneous rate of change as the limit of the average rate of change

* Approximate rate of change from graphs and table values

-Derivative as a function

* Corresponding characteristics of the graphs of f and f’

* Critical Values

* Relationship between the increasing and decreasing behavior of f

and the sign of f’

* Rolle’s Theorem

* The Mean Value Theorem and its geometric consequences

* Translations of verbal descriptions into equations involving derivatives and vice versa

-Second derivatives

* Corresponding characteristics of the graphs of f, f’, and f’’

* Relationship between the concavity of f and the sign of f’’

* Inflection points as places where concavity changes

-Derivative applications

* Curve sketching involving derivatives and sign lines

* The Newton- Raphson Method

* The first and second derivative tests

* Analysis of curves, including notions of monotonicity and concavity

* Graphing Summary including roots, domain and range, asymptotes, intervals of increase and decrease, extrema, concavity, and inflection points

* Optimization, both absolute (global) and relative (local) extrema

* Modeling rates of change, including related rates problems

* Use of implicit differentiation to find the derivative of an inverse function

* Interpretation of the derivative as a rate of change in varied applied contexts, including velocity, speed, and acceleration

* Geometric interpretation of differential equations via slope fields and the relationship between slope fields and solution curves for differential equations

Integrals

Students will understand the concept of integration and the definite integral as area under the curve, the accumulated change of a rate of change, and representation of the limit of an approximating Riemann sum, as well as a method of finding the area of a region, the volume of a solid, the average value of a function, and the distance traveled by a particle along a line.

{Chapter 4 (10); Chapter 5 (1,2,3,4,5); Chapter6 (1,2,3,5); Chapter 7 (5); Chapter 8 (7); Chapter 10 (1,2,3,4)}

-Interpretations and properties of definite integrals

* Understand the concept of area under the curve using a Riemann sum over equal subintervals

* Calculate the definite integral as a limit of Riemann sums

* Definite integrals and antiderivatives

* Definite integral of the rate of change of a quantity over an interval interpreted as the change of quantity over the integral: a^b f’(x) dx = f(b) – f(a)

* Use of the graphing calculator to compute definite integrals numerically

* Basic properties of definite integrals including additivity and linearity

-Applications of integrals

* Use of definite integrals to find the area under a curve

* Use of definite integrals to find the area between two curves

* Volumes of Solids of Revolution using Disks and Washers

* Cylindrical Shells

* Average Value of a function

* Volumes of Solids with known cross sections

* Distance traveled by a particle along a line

-Fundamental Theorem of Calculus

* Use of the Fundamental Theorem of Calculus to evaluate definite integrals

* Use of the Fundamental Theorem of Calculus to represent a particular antiderivative, and the analytical and graphical analysis of such defined functions

-Techniques of antidifferentiation

* Antiderivatives following directly from derivatives of basic functions

* Antiderivatives by substitution of variables including changing limits

for definite integrals

-Applications of antidifferentiation

* Finding specific antiderivatives using initial conditions, including applications

to motion along a line

* Solving separable differential equations and using them in modeling such as

with the equation y’ = ky and exponential growth

-Numerical approximations to definite integrals

* Use of Riemann sums using left, right, upper, lower, and midpoint evaluation

points to approximate definite integrals of functions represented algebraically,

graphically, and by tables of values

* Use of trapezoidal sums to approximate definite integrals of functions

represented algebraically, graphically, and by tables of values

*** Remaining time prior to the administration of the AP examination is spent

reviewing past AP multiple choice and free response questions and taking practice

exams. These are assigned as homework as well as assessed through quizzes and

tests.