AP Calculus AB
AP EXAM 2012
Section I: Multiple-Choice : 105 minutes = 1 hour 45 minutes
The multiple-choice section of the exam has two parts.
Part A, you'll have 55 minutes to complete 28 questions without a calculator.
Part B, you'll have 50 minutes to answer 17 questions using a graphing calculator.
Total scores on the multiple-choice section are now based on the number of
questions answered correctly. Points are no longer deducted for incorrect answers
and, as always, no points will be awarded for unanswered questions.
Section II: Free-Response : 90 minutes = 1 hour 30 minutes
The free-response section tests your ability to solve problems using an extended chain of
reasoning.
Part A: 2 Problems in 30 minutes requires the use of a graphing calculator.
Part B: 4 problems in 60 minutes does not allow the use of a calculator.
During the second timed portion of the free-response section (Part B), you are permitted to
continue work on problems in Part A, but you are not permitted to use a calculator during
this time.
AP Calculus AB
2012 Exam Format
50 % of Grade
Multiple Choice: 45 questions – 105 minutes (1hr 45 minutes)
Multiple Choice
Number of Questions
Time Allowed
Graphing Calculator
Part A
28
55
No Calculator
Part B
17
50
Graphing Calculator
Required
50 % of Grade
Free Response: 6 questions – 90 minutes (1hr 30 minutes)
Free Response
Number of Questions
Time Allowed
Part A
2
30
Part B
4
60
Graphing Calculator
Graphing Calculator
Required
No Calculator
If need be, you may work on Part A during Part B portion of the exam without the use of a
calculator.
AP Calculus AB
2010 Free Response Results
245,867 students
Question #
Average Score
out of 9 pts
1
3.67
2
2.60
3
2.19
4
3.67
5
1.75
6
3.14
Average
2.84
AP Calculus AB
2011 Free Response Results
255,357 students
Question #
Average Score
out of 9 points
1
2.79
2
3.31
3
4.64
4
2.44
5
1.63
6
3.03
Average
2.97
Calculators and the Exam
What you need to be able to do:
 plot the graph of a function within an arbitrary viewing window
 find the zeros of functions (solve equations numerically)
 numerically calculate the derivative of a function
 numerically calculate the value of a definite integral
Global Tips:
Show all work.
Remember that the grader is not really interested in finding out the answer to the problem.
The grader is interested in seeing if you know how to solve the problem.
Do not round partial answers.
Store them in your calculator so that you can use them unrounded in further calculations.
Do not let the points at the beginning keep you from getting the points at the end.
If you can do part (c) without doing (a) and (b), do it.
If you need to use an answer from part (a), make a credible attempt at part (a) so that you
can import the (possibly wrong) answer and get your part (c) points.
If you use your calculator to solve an equation, write the equation first.
An answer without an equation might not get full credit, even if it is correct.
If you use your calculator to find a definite integral, write the integral first.
An answer without an integral will not get full credit, even if it is correct.
Do not waste time erasing bad solutions.
If you change your mind, simply cross out the bad solution after you have written the good
one. Crossed-out work will not be graded. If you have no better solution, leave the old one
there. It might be worth a point or two.
Do not use your calculator for anything except:
(a) graph functions, (b) compute numerical derivatives, (c) compute definite integrals, and
(d) solve equations. In particular, do not use it to determine max/min points, concavity,
inflection points, increasing/decreasing, domain, and range. (You can explore all these with
your calculator, but your solution must stand alone.)
Be sure you have answered the problem.
For example, if it asks for the maximum value of a function, do not stop after finding the x
at which the maximum value occurs. Be sure to express your answer in correct units if units
are given.
If you can eliminate some incorrect answers in the multiple-choice section, it is
advantageous to guess.
Otherwise it is not. Wrong answers can often be eliminated by estimation, or by thinking
graphically.
If they ask you to justify your answer, think about what needs justification.
They are asking you to say more. If you can figure out why, your chances are better of
telling them what they want to hear. For example, if they ask you to justify a point of
inflection, they are looking to see if you realize that a sign change of the second derivative
must occur.
Common Student Errors
1.
is a point of inflection.
NO, you MUST check for a change in concavity!
2.
is a absolute maximum (minimum) if and only if
No, you MUST use the Closed Interval Method.
3. Average rate of change of
on [a, b] is
.
No,
4. Volume by washers is ∫
No,
.
∫
5. Separable differential equations can be solved without separating the variables.
6. Graders will assume things.
If the correct answer came from your calculator, the grader will assume your setup
was correct.
7. Universal logarithmic antidifferentiation:
∫
|
|
Generally, more complicated integrals require u-substitution.
8.
and other Chain Rule errors.
Always use the Chain Rule!
.