AP Calculus BC
Note Cards Project
Name______________________
For this project you are to create a set of note cards to review the AP Calculus BC topics.
Topics that must be included are printed on the back of this sheet. The due date is Friday,
April 12, 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 blue pen.
 Your initials must be written in the upper right-hand corner on the front of each card,
using a blue pen.
 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 AP Calculus AB cards you created last year should also be included.
 The first card is not to be numbered and must have your name, date due, and words
“INDEX CARDS – AP CALCULUS BC.”
This grade will be worth 40 points as a homework grade. Three points will be deducted for
every missing card or any card not completed as specified in the above directions. Five
points will be deducted if the cards are not easily legible. Fifteen points will be deducted if
the AB cards are not included. One to three points will be deducted for incomplete cards.
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, produce a good and quick study guide, and
perhaps tie-up “loose-ends” on some of the more confusing topics.
Index Card Topics
AB Topics
1. Limits – definition, existence, and graphical
interpretation
2. Limits – methods to evaluate analytically
3. Special limits to memorize
4. HA and limit as x  
5. VA
6. Continuity
7. Types of discontinuities
8. Definition of the derivative as a limit as f(x)
and as f(c)
9. Differentiability and continuity
10. Product and quotient rules for derivatives
11. Chain Rule
12. Tangent line and normal line equations
13. MVT and its graphical interpretation
14. Rolle’s Theorem
15. IVT
16. EVT
17. Absolute (global) and relative (local)
extrema
18. Critical numbers of the first derivative
19. First derivative test
20. Second derivative test
21. Inflection points
22. Graphical relationships of f, f’, and f”
23. Implicit differentiation
24. Related rates
25. Optimization and modeling
26. Linearization and linear (or tangent line)
approximation of a function at a point
27. Newton’s Method
28. Relationship of position, velocity, and
acceleration functions; speed of a particle
29. Graphical interpretation of the derivative to
include velocity, acceleration, and speed
(ex: v(t) = 0 when particle is changing
direction)
30. Distance versus displacement
31. Average rate of change, instantaneous rate
of change, average velocity, instantaneous
velocity
32. Definite integral rules and definition of a
definite integral
33. Area under a curve
34. FTC 1 and 2
35. Riemann Sums for approximating areas (no
summation as i → ∞)
36. Trapezoidal Rule
37. U-substitution method for antiderivatives
38. Average value of a function (not average
rate of change)
39. Natural logarithm function – change of base
theorem, rules, derivatives, antiderivatives
40. Derivative of a function and its inverse
41. Exponential function – rules, derivatives,
antiderivatives
42. Inverse trig functions and their derivatives
43. Integrals involving inverse trig functions
44. Separable differential equations and initialvalue problems
45. Exponential growth/decay
46. Slope fields
47. Area between curves
48. Volume of revolution – disk method –
horizontal or vertical axes
49. Volume of revolution – washer method –
horizontal or vertical axes
50. Volume of solid of revolution – shell
method
51. Volumes with known cross-sectionals
BC Topics
52. L’Hopital’s Rule
53. Integration by parts
54. Integration with partial fractions
55. Improper integrals
56. Logistic growth
57. Euler’s Method
58. Arc length rule for functions, parametric,
curves, and polar curves
59. Parametric equations and their first and
second derivatives
60. Vector quantities and speed
61. Vector derivatives and integrals
62. Polar equations and their derivatives
63. Polar equations and area
64. Infinite geometric series and their sum
65. Power series, p-series, harmonic series, and
alternating harmonic series
66. Rules for convergence and divergence
(PARTINGRC) –two per card; 5 cards
67. Absolute vs. conditional convergence
68. Alternating series remainder (error)
69. Power series – general formula
70. Radius and interval of convergence
71. Taylor (and MacLaurin) polynomial
approximations
72. Operations with power series, including
differentiation and integration
73. Taylor (MacLaurin) series to memorize: sin
x, cos x, ex,1/(1-x)
74. Taylor Inequalities (Lagrange error
approximation)