AP Calculus AB/BC
Note Cards Project
Name______________________
For this project you are to create a set of note cards to review the AP Calculus AB and BC
topics. Topics that must be included are printed on the back of this sheet. The due date is
Thursday, April 11, 2013.
You may use 3” by 5” or larger index cards. “Spiral” index cards may also be used. “Homemade” cards are not allowed. The following information must be clearly hand written or
printed directly on the cards; do not “cut-and-paste.”
 The front side of the card must contain the theorem, definition, or property. An
example is Pythagorean Theorem: a2 + b2 = c2 where a, b, and c are the lengths of
the sides of a right triangle, with c being the hypotenuse.
 On the back of the card must be an example statement and work. For example, if a
= 4 and c = 8, find the length of b. 42 + b2 = 82, 16 + b2 = 64, b2 = 48, b = 48 =
4 3 . When possible, the example must come from your notes. If you cannot
find the example in your notes, find an example in the book and note the page
number it came from. Examples from previous years’ notes that were not
provided this year are not acceptable and will result in a 10 point deduction.
 Each card must be numbered (according to the list on the reverse side) in the upper
left-hand corner on the front of the card, using a pen in any color except black or
blue. If you need to borrow a colored pen, see me. Your initials must be written in
the upper right-hand corner on the front of each card, using the same colored pen.
 Each card should have the name of the topic (from the list) written at the top, also in
colored pen. The rest of the card can be completed in any color or type of writing
utensil you prefer.
 Every item on the list must be included. Up to four additional cards may be made for
topics that are of special need to you, such as trig exact values and logarithm
properties. Two possibly helpful extra topics for many of you are trig exact values
and properties of logarithms. These extra cards should be added at the end, do not
need to include examples, and should not be numbered.
 Up to four additional cards may be added if you need to elaborate on a particular
topic. If an additional card or cards is included for a topic, it should have the same
label and number as the topic, but with a letter (a, b, c, etc. after the number.
 The first card is not to be numbered and must have your name, date due, and words
“INOTE CARDS – AP CALCULUS AB and BC.”
This grade will be worth 80 points as a homework grade and cannot be dropped. Three
points will be deducted for every missing card or any card not completed as specified in the
above directions. Up to five points will be deducted if the cards are not easily legible. One
to three points will be deducted for every incomplete card. Late projects will be deducted 10
% for every day late.
Please follow these directions! This may take time, but it will help you summarize the past
year, organize the required notes in one place, and perhaps tie-up some “loose-ends” on
some of the more confusing topics.
Study Card Topics
1. Limits – definition, existence, and graphical
interpretation
2. Limits – methods to evaluate analytically
3. Special trig limits to memorize
4. HA and limits as x  
5. VA
6. One-sided limits, using VA, piece-wise
functions, and/or step functions
7. Continuity (definition in terms of limits)
8. IVT
9. Types of discontinuities
10. Limit Definition of the derivative as a
function and at a point, x = c.
11. Differentiability and continuity
12. Constant rule, Power rule for derivatives
13. Trig and inverse trig derivative rules
14. Product and quotient rules for derivatives
15. Chain Rule for derivatives
16. Exponential and log rules for derivatives for
base e and other bases
17. Implicit differentiation
18. Related rates
19. Tangent line and normal line problem
20. Average rate of change vs, instantaneous
rate of change
21. MVT and its graphical interpretation
22. Rolle’s Theorem
23. EVT
24. Absolute (global) extrema
25. Critical numbers
26. First derivative test and local (relative)
extrema
27. Inflection points and concavity
28. Second derivative test
29. Graphical relationships of f, f’, and f”
30. Optimization and modeling
31. Linearization and linear (or tangent line)
approximation of a function at a point
32. Derivative of a function and its inverse
33. Integration rules – constant, power, and 1/x
34. Integration rules – exponential with base e
and other bases
35. Integration rules – trig and inverse trig
36. U-substitution method for integration
37. Definition of the definite integral
38. FTC Parts 1 and 2
39. Riemann Sums for approximating areas (no
summation as i → ∞)
40. Trapezoidal Rule
41. Area under a curve, including interpretation
42. Area between curves
43. Volume of solid of revolution – disk method
– horizontal or vertical axes
44. Volume of solid of revolution – washer
method – horizontal or vertical axes
45. Volumes with known cross-sections
46. Average value of a function
47. Separable differential equations and initialvalue problems
48. Exponential growth/decay
49. Slope fields
50. Derivative and integral relationship of
position, velocity, and acceleration
functions; speed of a particle
51. Average velocity vs. instantaneous velocity
52. Distance versus displacement
53. Graphical interpretation of velocity,
acceleration, and speed
(ex: v(t) = 0 when particle is changing
direction)
54. L’Hopital’s Rule
55. Integration by parts
56. Integration with partial fractions
57. Improper integrals
58. Logistic growth
59. Euler’s Method
60. Arc length rule for functions, parametric,
curves, and polar curves
61. Parametric equations and their first and
second derivatives
62. Vector quantities and speed
63. Vector derivatives and integrals
64. Polar equations and their derivatives
65. Polar equations and area
66. Infinite geometric series and their sum
67. Power series, p-series, harmonic series, and
alternating harmonic series
68. Rules for convergence and divergence
(PARTINGRC) –two per card; 5 cards
69. Absolute vs. conditional convergence
70. Alternating series remainder (error)
71. Power series – general formula
72. Radius and interval of convergence
73. Taylor (and MacLaurin) polynomial
approximations
74. Operations with power series, including
differentiation and integration
75. Taylor (MacLaurin) series to memorize: sin
x, cos x, ex,1/(1-x)
76. Taylor Inequalities (Lagrange error
approximation)