Download AP Calculus AB Notebook

AP Calculus AB Notebook
Due Date: Thursday, November 17
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Your calculus notebook will serve as a summary of most of the topics that we will
encounter during this semester of AP Calculus AB and will be a ready reference when
studying for the final exam and the AP test next May.
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You should include an example and the completely worked solution for each topic
within each bullet from the attached outline. Add explanations where appropriate. Any
examples selected from sources other than class notes, worksheets, or the
Rogawski textbook must be documented by a footnote that completely identifies
the source of the example.
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The notebook must be legibly hand written in either a spiral or a composition notebook.
A typed document will NOT be accepted. Loose pages will NOT be accepted. All
diagrams or graphs must be clearly labeled and identified.

Set aside the first few pages of your notebook for a Table of Contents. Number each of
the rest of the pages so that you can refer to specific topics easily. (You may want to
leave 3-4 pages blank for the Table of Contents.)
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Write only on the front side of each page.
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Write neatly and only in ink. You may use different colors of ink.
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Write in enough detail to help yourself later when you may have forgotten the material.

The notebook grade will be based on completeness, accuracy of mathematics, and
neatness and will be worth 75 points. Five of those points will be awarded based on
following directions and the neatness and organization of the notebook.

Late notebooks will not be accepted and will receive a grade of zero. The notebook
is due at the beginning of your class period on Thursday, November 17. If you are
absent, it is your responsibility to get the notebook to your teacher by 3:30 on
Thursday, November 17.

The notebook should include the signed Statement of Integrity on the first page:

I certify the work I am submitting is my original work. I have not shared nor
exchanged information or materials with anyone, nor will I do so in the
future.
Rev. 9-10-11
Rev. 9-10-11
AP Calculus AB Notebook
1. Limits of functions
 Identify and use the Limit Laws
 Calculate limits with algebraic manipulations (at least two different examples)
 State two important trigonometric limits and use them to evaluate limits
 Estimate limits graphically and numerically from tables of data
 Determine limits involving infinity and other indeterminate forms
 State and use the Intermediate Value Theorem
 State and use the Squeeze Theorem
 Relate the instantaneous rate of change and the average rate of change with the slope of a
tangent line and the slope of a secant line
2. Continuity
 Define when a function is continuous at a point x  a and when a function is left-continuous
or right-continuous.
 Identify continuity in terms of limits and graphs of continuous functions
 Describe different types of non-continuous behavior
 Identify the Laws of Continuity and list types of functions that are continuous
3. Introduction to Derivatives
 State and use the difference quotient definition for the derivative of a function
 Explain the relationship between continuous and differentiable functions
 Identify all notations related to derivatives and higher order derivatives
 Identify four types of points at which a function may not be differentiable
 Determine equations of tangent lines and normal lines at x  a
 Solve a particle motion problem that involves distance, displacement, instantaneous velocity,
average velocity, speeding up and slowing down, moving forward and backward,
acceleration, maxiumum height, etc.
 Sketch the graph of f '  x  from f  x  .
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State the general rule (where appropriate) and determine the derivative of functions using:
(do an example of each one of these)
power, product, quotient, and chain rules; implicit differentiation for polynomials; list all
derivatives of trigonometric and inverse trigonometric functions; derivatives of inverse
functions, exponential, e, logarithmic and natural log functions; and logarithmic
differentiation.
4. Applications of Derivatives
 Use the first derivative to determine whether a function is increasing and/or decreasing and to
identify critical points
 State and use the First Derivative Test to determine local extrema
 State and use the Second Derivative Test
 Use the second derivative to determine concavity and points of inflection
 Analyze the relationships between the graphs of f  x  , f '  x  , and f "  x  .
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State and use the Mean Value Theorem and Rolle’s Theorem
Explain vertical and horizontal asymptotic behavior in terms of limits
State and use the Extreme Value Theorem to find the absolute extrema of a function
State and use Linear Approximation to approximate a change in f  x 
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Solve rate of change, related rate, minimal path, and optimization problems.
State and use L’Hopital’s Rule to evaluate limits
Rev. 9-10-11
5. Introduction to Integrals
 Compute Riemann sums using left, right and midpoint evaluation
 State the definition of the integral as a limit of Riemann sums over equal subdivisions.
 State the basic properties of definite integrals
 State and use the Fundamental Theorem of Calculus Parts I and II
 Apply integration techniques for determining antiderivatives:(do an example for each).
Include power rule and “u” substitution including “u” substitution with a definite integral
 Determine antiderivatives of exponential functions and list the antiderivatives of the six basic
trigonometric functions and the functions whose antiderivative is an inverse trigonometric
function
 State the trapezoidal rule and approximate an area using the rule
6. Applications of Integrals
 Find the area of a region between two curves
 Find the volume of a solid of revolution around each of these: x = 0, y = 0, x = a, and
y = b, using the disk or washer method, a volume using the shell method, and the volume of a
solid with known cross-sections
 Find the average value of a function and determine the point(s) at which the average value is
achieved
 Find the distance traveled and displacement by a particle along a line using an integral
 Use the integral to give an accumulated change
 Find specific antiderivatives using initial conditions
 Solve separable differential equations and use them in modeling physical, biological, and
other real-world situations ( y '  ky and exponential growth)
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Interpret differential equations through slope fields
Analyze the relationship between slope fields and solution curves for differential equations
Rev. 9-10-11