AP CALCULUS NOTEBOOK (AB)
Tape the table of contents in the inside cover of at least a 70 page spiral notebook. For each topic use
the following procedure.
1. On a page numbered the same as the entry, write the topic as a title.
2. State any relevant definitions, procedures, or theorems.
3. State and solve a specific problem that uses this procedure. Show clearly each step of
problem-solving needed.
TABLE OF CONTENTS
1. Graphs of the basic parent functions.
2. Graph basic transformations of functions.
3. Determination of Even or Odd Functions.
4. Determination of Symmetry of a curve – x-axis, y-axis, origin.
5. Comparisons of the graphs of
y  f ( x), y  f ( x) , y  f ( x ).
6. Formation of a Composite Function and finding its domain.
7. Graphs of three functions for which
lim f ( x) does not exist.
8. Graph of a function in which lim f ( x) exists but lim f ( x ) does not exist.
x a
xa 
x a
9. Three algebra techniques used to calculate limits.
10. Two limit theorems involving trigonometric functions.
11. Find
lim f ( x) and lim f ( x)
x 
for rational functions.
x 
12. Find vertical and horizontal asymptote equations.
13. Proving a function is continuous at a point.
14. Graph of a function where
lim f ( x) exists but does not equal f(a).
x a
15. Example of a function which is continuous on ( a ,b ) but discontinuous on [ a ,b ].
16. Application of the Intermediate Value Theorem.
17. Application of Average Rate of Change of a function on (a,b).
18. Two definitions of derivative involving limits of difference quotients.
19. Finding Tangent and Normal line equations to graph of a function at a point.
20. Using Tangent line equations for Local Linear Approximations of a function.
21. Give Verbal Descriptions of equations involving derivatives.
22. Estimating a Derivative of a Function from a table of values and from a graph of a function.
23. Four Different Graphs of Functions who Fail to have a Derivative at a point.
24. Relationship between Continuity and Differentiability. Give an example which satisfies this test
and one that fails this test.
25. Implicit Differentiation – How and When do you use it ?
26. Relationships Between Position, Velocity, Speed, and Acceleration of a particle moving on x-axis.
27. Related Rate Problems – How do you recognize them and what are the steps needed in solving?
28. Application of Extreme Value Theorem.
29. Application of The Mean Value Theorem (for Derivatives).
30. Finding Critical Points of a Function.
31. Application of First Derivative Test to Graphing a function. Perform and Verbalize this test.
32. Finding Absolute (Global) Extrema for a Function on a Closed Interval.
33. Inflection Points and Concavity of a function.
34. Give first and second derivatives for four possible arcs of a non-constant function.
35. Use Second Derivative Test for Max/Mins of a function.
36. Steps to solve Optimization Problems.
37. Estimate area under
y  x2  4
on [0,8] with four equal subintervals using Trapezoidal Rule and
Riemann Sums of Left Endpoint, Right Endpoint, and Midpoint Methods.
b
38. State and use The Fundamental Theorem of Calculus to evaluate
 f ( x)dx .
a
x
39. State and use The Fundamental Theorem of Calculus to evaluate
d
f (t )dt.
dx a
x
40. For a Function Defined as an Integral,
g ( x)   f (t )dt
with only the graph of f(t) given , give
a
three questions that could be asked about y=g(x).
41. Find and apply The Average Value of a Function f(x) on [a,b].
42. Use the Method of Substitution to evaluate an Indefinite Integral.
43. Change the Limits of Integration on a Definite Integral.
44. Logarithmic Differentiation – How and When do you use it?
45. Find Area Between Two Curves.
46. Compute the Volume of a Solid of Revolution using Disc and Washer Methods.
47. Compute the Volume of a Solid with Known Cross-Sections.
48. Compute Total Distance Traveled by an object given its velocity on [a,b]. Compare to Net
Displacement.
49. Use L’Hopital’s Rule for evaluation of limits.
50. Solve First Order, Variables Separable Differential Equations with given initial condition.
51. Construct a Slope Field and give hints on matching slope fields with their Differential Equations.
52. Given a Differential Equation that you cannot solve, what is the purpose of constructing its slope
field?
y   ky and y   k (a  y ) .
53. Solve for y these differential equations:
54. Growth – Decay Problems – How to Recognize and Solve Calculus problems involving Half-Life and
other forms of growth and decay.
55. Make a list of all Derivative Formulas that you have memorized this year.
56. Make a list of all Integral Formulas that you have memorized this year.