Download Calculus BC Study Guide Name

Flashcard Review
Point Value
Accuracy and completeness
Neatness and Organization
Turned in on time - April 23
Turned in on time – May 1
Turned in on time – May 9
TOTAL
Total
72
16
4
4
4
100
You must PRINT(or type and paste). You must give credit where credit is due.
Use note cards held together with a ring or a note card book (not random pieces of paper).
This is meant to be a study guide for the AP exam and the final exam.
It will also be useful in reviewing next year if you go on in calculus. For these reasons, please do not copy
something out of a book or your notes that is meaningless to you.
Note cards or sections must follow the order and number as listed below.
To help you budget your time, the cards will be checked for completion on the following dates.
 Cards #1- 24 will be due on or before April 23
 Cards #25-48 will be due on or before May 1.
 Cards #49-72 will be due on or before May 9.
Name:____________________________
I. FUNCTIONS
___________
___________
___________
___________
___________
___________
___________
1.
2.
3.
4.
5.
6.
7.
How to find x & y intercepts of a graph
Tests for symmetry over the x & y axes and the origin
Slope of a Line formula
(5) Linear equation forms (include horizontal and vertical)
Analytic & geometric methods of determining odd or even functions
Intermediate Value Theorem
Graphs and properties of y = ln x and y = ex
II. LIMITS & CONTINUITY
___________ 8. (8) Basic properties of limits and the Limit of a Composite Function
___________ 9. Forms of simplifying
___________ 10.
___________ 11.
___________ 12.
___________ 13.
___________ 14.
0
0
(factoring, multiplying by conjugate, common denominator)
Two special trig limits
Definition of continuity (List the 3 steps.)
Diagrams/descriptions of removable and non-removable discontinuities
One-sided limits and piecewise functions (use a graph to illustrate)
Definition of a Vertical Asymptote (Include Limits associated with vertical asymptotes.)
___________ 15. Guidelines for Finding Limits at Infinity (Include
(AKA “end behavior”), and slant asymptotes)


, those producing horizontal asymptotes
III. DERIVATIVES
___________ 16.
___________ 17.
___________ 18.
___________ 19.
___________ 20.
your book.)
___________ 21.
Concept of derivative (geometrically, numerically, and analytically)
The definition of the Derivative of a Function
Alternate Limit Form of the Derivative
Relationship between differentiability and continuity
Basic differentiation rules (See the rules page in your notes and/or look in the front of
Guidelines for Implicit differentiation
Derivatives at a Point
___________ 22. Slope of a curve at a point, examples of points where there are vertical tangents or no tangents
___________ 23. Equation of a tangent line to a curve at a point
___________ 24. Instantaneous Rate of Change versus Average Rate of Change (Include instantaneous rate of
change as the limit of average rate of change.)
___________ 25. Normal Lines and how they relate to derivatives
Derivatives as a Function
___________ 26. Extreme Value Theorem
___________ 27. Definition of a critical number
___________ 28. Rolle’s Theorem
___________ 29. Mean Value Theorem for Differentiation and geometric consequences
___________ 30. Relationship between the increasing and decreasing behavior of f and the sign of f '
___________ 31. Monotonic Function
___________ 32. Corresponding graphs of f and f '
Second Derivatives
___________ 33. Relationship between concavity of f and the sign of f "
___________ 34. Points of inflection as places where concavity changes
___________ 35. Corresponding characteristics of the graph of f, f ', f "
Applications of derivatives
___________ 36. Meanings of positive velocity, negative velocity, and zero velocity
___________ 37. Interpretation of derivative as rate of change including velocity, speed and acceleration
___________ 38. If velocity and acceleration have the same sign, then the speed is ___?___.
If velocity and acceleration have different signs, then the speed is ___?___.
___________ 39. Guidelines for Solving Rate of Change and Related Rates problems
___________ 40. Absolute Extrema on an interval
___________ 41. First and 2nd derivative tests
___________ 42. When does a function have a horizontal tangent line? What is the equation of this line?
___________ 43. When does a function have a vertical tangent line? What is the equation of this line?
___________ 44. Guidelines for Solving Optimization problems
___________ 45. Local Linearization/Linear Approximation/Tangent Line Approximation
___________ 46. Definition of a Differential & Use of Differentiation to Approximate Function Values
___________ 47. Derivative of an Inverse Function
___________ 48. Geometric interpretation of differential equations using slope fields & relationship between
slope fields & derivatives of implicitly defined functions.
IV. INTEGRALS/ANTIDERIVATIVES
___________ 49. Computation of Riemann sums using left, right, and midpoint evaluation points
___________ 50. Definite integral as a limit of Riemann sums over equal subdivisions
___________ 51. Five Basic properties of definite integrals
___________ 52. Use of the Fundamental Theorem of Calculus to evaluate a definite integral
___________ 53. Mean Value Theorem for Integrals
___________ 54. Second Fundamental Theorem of Calculus
___________ 55. Integration by substitution (include change of limits for definite integrals)
___________ 56. Trapezoidal Rule to approximate definite integrals
___________ 57. Basic Integration Formulas (See your notes and the front of your textbook)
Applications of Integrals
___________ 58. Finding area of a region (Include the area of a region bounded by a function and the x-axis and the area
of a region between two curves.)
___________ 59. Solving Initial Value Problems (use initial value to find “c”)
___________ 60. Finding displacement traveled by a particle along a curve (in terms of velocity)
___________ 61. Finding total distance traveled by a particle along a curve (in terms of velocity)
___________ 62. Finding the average value of a function on an interval
___________ 63. Solving differential equations, including separable differential equation, particular,
and those involving exponential growth y '  ky
___________ 64. Finding volumes by Disc and Washer method
___________ 65. Finding volumes by known cross section
V. POTPOURRI TOPICS
___________ 66. Area Formulas: square, any triangle, an equilateral triangle, trapezoid, & circle
___________ 67. Volume Formulas: rectangular solid, cube, cylinder, cone, & sphere
___________ 68. Calculator keystrokes for locating zeros of a function
___________ 69. Calculator keystrokes for locating points of intersection of two graphs
___________ 70. Calculator keystrokes for storing values from the graph screen and home screen
___________ 71. Calculator keystrokes for differentiation on the home screen and graph screen
___________ 72. Calculator keystrokes for integration on the home screen and graph screen