AP+Calculus+AB



AP CALCULUS

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**Course Description: ** The main focus of this class is to prepare students to perform well on the advanced placement calculus exam. In doing so, the students will enforce concepts taught in previous mathematics classes as well as develop an understanding of the basic concepts of introductory calculus, such as limits, continuity, derivatives and their applications, and integrals.


 * Course Outline: **

I. Limits · Informal definition of a limit, including one- sided limits · Graphical interpretation of a limit · Numerical interpretation of a limit · Algebraic interpretation of a limit
 * PART ONE **

II. Continuity · Informal and formal definition of continuity · Removable discontinuity · Determining continuity of a function graphically, numerically, and algebraically (relative to limits)

III. Derivatives · Relationship between continuity and differentiation · Definition of the derivative as the limit of the difference quotient · Rules for finding the derivatives of polynomials, products, quotients, trigonometric functions, inverse trigonometric functions, logarithmic and exponential functions · <span style="font-family: 'Arial','sans-serif';">The chain rule and implicit differentiation · <span style="font-family: 'Arial','sans-serif';">Higher order derivatives

__<span style="font-family: 'Arial','sans-serif';">Applications of the Derivative __

<span style="font-family: 'Arial','sans-serif';">IV. Tangents and Normals · <span style="font-family: 'Arial','sans-serif';">The derivative as the slope of the tangent to a curve at a point · <span style="font-family: 'Arial','sans-serif';">Tangent line to the curve at a point and local linearity · <span style="font-family: 'Arial','sans-serif';">Normal line as normal to the tangent line at a point · <span style="font-family: 'Arial','sans-serif';">Relation of derivative to horizontal and vertical tangents and no tangents

V. Curve Sketching · <span style="font-family: 'Arial','sans-serif';">Relationship between increasing and decreasing behavior f and the sign of f’ (the first derivative test) · <span style="font-family: 'Arial','sans-serif';">Relationship between the concavity and points of inflection of f and the sign of f’’ (the second derivative test) · <span style="font-family: 'Arial','sans-serif';">Relationship between the graphs of f. f’, and f’’ · <span style="font-family: 'Arial','sans-serif';">The Mean Value theorem

VI. Optimization

VII. Related Rates

VIII. Particle Motion · <span style="font-family: 'Arial','sans-serif';">Velocity as the first derivative of position (change in position over the change in time) · <span style="font-family: 'Arial','sans-serif';">Acceleration as the second derivative of position or the first derivative of velocity ( the change in velocity over the change in time)

IX. Miscellaneous Topics · <span style="font-family: 'Arial','sans-serif';">Infinite limits · <span style="font-family: 'Arial','sans-serif';">Indeterminate forms and L’Hopital’s rule · <span style="font-family: 'Arial','sans-serif';">Newton’s Method · <span style="font-family: 'Arial','sans-serif';">Slope Fields


 * <span style="font-family: 'Arial','sans-serif';">PART TWO **

<span style="font-family: 'Arial','sans-serif';">I. Integration Theory · <span style="font-family: 'Arial','sans-serif';">Integration as Reimann sums · <span style="font-family: 'Arial','sans-serif';">Areas using left and right hand sums, upper and lower sums, midpoint, and trapezoidal sums · <span style="font-family: 'Arial','sans-serif';">Area · <span style="font-family: 'Arial','sans-serif';">Integration theorems (including the fundamental theorem of integration) · <span style="font-family: 'Arial','sans-serif';">Antiderivatives

II. Integration forms · <span style="font-family: 'Arial','sans-serif';">The “basic four” · <span style="font-family: 'Arial','sans-serif';">Adjusting the differential (ie. Integration by substitution) · <span style="font-family: 'Arial','sans-serif';">The basic trigonometric integrals · <span style="font-family: 'Arial','sans-serif';">Special trigonometric integrals · <span style="font-family: 'Arial','sans-serif';">Integration by parts

III. Applications of Integration o <span style="font-family: 'Arial','sans-serif';">Area of region Between two curves o <span style="font-family: 'Arial','sans-serif';">Volume: the disk/washer method o <span style="font-family: 'Arial','sans-serif';">Volume: the shell method o <span style="font-family: 'Arial','sans-serif';">Volume: cross sections o <span style="font-family: 'Arial','sans-serif';">Particle motion (Finding the velocity and position given acceleration and initial conditions)

IV. Miscellaneous Topics o <span style="font-family: 'Arial','sans-serif';">Integration of inverse trigonometric functions o <span style="font-family: 'Arial','sans-serif';">Integration of absolute value functions o <span style="font-family: 'Arial','sans-serif';">Average value o <span style="font-family: 'Arial','sans-serif';">Separation of variables

A graphing calculator is necessary for this class. The TI Nspire CAS is highly recommended.

Grades will be given in each of the three following categories: tests, quizzes, and homework. You will be made aware not only of the grade you earned but also into which category this grade falls. It is important for you to keep track of your grades. In doing so, you will know at all times your standing in this class and will not need to ask me for your grades. Your grade should be as important to you on the first day of class as it is on the last day of class.

TEST AVERAGE (arithmetic mean) 50% QUIZ AVERAGE (arithmetic mean) 25% HOMEWORK AVERAGE 25%

Example: Test: 90%, 79%, 100%, 89%, Quizzes: 100%, 95%, 98%, Homework: 100%

Tests: (90+79+100+89)/4=89.5 89.5(.50)=44.75 Quizzes: (100+95+98)/3=97.67 97.67(.25)=24.52 Homework: 100(.25)=25.00

Grade: 44.75+24.52+25=**94%**


 * __**
 * Expectations**:
 * 1) All work must be done in **PENCIL!**
 * 2) All cell phones (and other electronic devices not required for classroom instruction) are to be placed in the cell phone caddy.
 * 3) Bring your book, paper, **pencil**, (and calculator where appropriate) to class regularly, unless otherwise instructed.
 * 4) Homework will be assigned and checked on a regular basis. Failure to **__complete__** the assignment will result in five points being deducted from your homework average.
 * 5) Missed homework assignments should be completed in a timely manner. It is the student’s responsibility to check the homework folder and turn in the missed assignment.
 * 6) Notes, assignments, handouts, etc. should be kept in a notebook of some sort and not crammed in the textbook.
 * 7) I dismiss the class. Students need to be seated and quiet before dismissal.
 * 8) Pencils are to be sharpened before the class begins. (Mechanical pencils work well.)
 * 9) Having your books, etc. on your desk is not the same thing as you being in class. You need to be in your seat at the start of class!
 * 10) School rules are to be followed at all times.