The Writing Questions
on the AP Calculus
Exams
P R E SE NT ED B Y
LIN MCMULLIN
‘ I O L A NI SCHO O L
Why worry about writing on the exam?
• Students should be able to communicate
mathematics and explain solutions to problems
both verbally and in written sentences.
– from the GOALS of the AP Calculus Program
Why worry about writing on the exam?
“Writing” points on
the operational
exams freeresponse questions
Year
2007
2008
2009
2010
2011
2012
2013
AB
9
7
7
7
7
9
9
BC
9
8
3
7
6
7
7
NUMBER EACH RESPONSE
Writing Prompts 1. Summarize this slide
• Justify your answer
• Explain your reasoning
• Why?
• Give a reason for your answer
• Explain the meaning of a definite integral in the context of the
problem 2. (explain general meaning of an integral)
• Explain the meaning of a derivative in the context of the problem
3. (explain general meaning of an derivative)
What to do?
. . . the short answer
• Determine which theorem or definition applies
4. (list what you feel are 5 main theorems we have
covered…no wrong answer
• State (show) that your problem meets the hypotheses
of the theorem or definition – BE SPECIFIC!
• 5. (what is the hypothesis? May give an example from a
covered theorem to explain)
Continuity 6. List the 3 conditions that must
be met for a function to be continuous
2007 AB 6
Justify your answer 7. When is a particle’s
speed increasing and when is it decreasing?
2013 AB 2 – Increasing/decreasing and Speed
Justify your answer.
8. Look up this question in your
packet and explain what units your are given and what units
your are asked for in part d and explain how you get from the
given to the answer.
2013 AB 1 / BC 1 – The Candidates’ Test
Justify your answer 9. Notice the first statement says that the
graph is f’. So, what does the slope represent?, what does the
area under the curve represent? What do the horizontal tangents
represent on the graph of f’? What part of the graph represents a
local max or min?
2013 AB4 / BC4 – The First Derivative Test
Justify your answer 10. What role does f(8)=4 play
in this question? Why is an absolute minimum
guaranteed?
2013 AB4 / BC 4 – The Candidates’ Test
Justify your answer 11. Explain the first and
second derivative test and how it is used.
2002 BC 5 – The Second Derivative Test
Justify your answer 12. Explain the Mean
Value theorem and how it is used.
2013 AB3 / BC 3 – The Mean Value Theorem
Explain your reasoning 13. When looking at the
graph of f’ how is concavity of f(x) represented on
that graph?
2013 AB4 / BC 4 – Concavity & Increasing/decreasing
Show the work … SKIP BC question
2013 BC 5 – L’Hôpital’s Rule
Explain the meaning of
. . . a definite integral
14. Summarize these three by giving a specific example
and explain each part below in the example.
Include three things in the context of the problem:
1. What the integral gives (amount, average value,
change in position, etc.)
2. Units
3. What the limits of integration mean.
Explain the meaning of a definite integral
15.Explain where each of the numbers came from
in the top line of part c after the ≈ ( you will need
to refer to the problem in your packet)
2013 AB3 / BC 3
Explain the meaning of
. . . a derivative
16. Summarize these three by giving a specific example
and explain each part below in the example.
Include three things in the context of the problem:
1. What the derivative gives (rate of change,
velocity, slope, etc.)
2. Units
3. Discussion of the argument .
Explain the meaning of a derivative 17.Explain why
the points from the table were chosen to estimate
W’(12), what does this represent and why?
2012 AB1 / BC 1
Explain the meaning of a derivative 18. For any function
in which the derivative is calculated…what does the
derivative of f(x) mean?
2007 Form B AB3
Other Theorems 19. Explain the intermediate Value
theorem and how it applies to this problem
2007 AB 3 – IVT, MVT
Theorem Questions 20. Explain the MVT and what
conditions guarantee an value c
2007 AB 6 – F0rm B
Theorem Questions Question on previous slide
2007 AB 6 – F0rm B
Theorem Questions 21. When does an inflection point
occur? Explain the conditions that must be present.
2007 AB 6 – F0rm B
Theorem Questions no question
2007 AB 6 – F0rm B
Quiz
x
f
x

e
• Let  
 x  3 for all x  0,5 . Find the location of
the minimum value of f  x  . Justify your answer three
different ways.
Quiz already asked-(first derivative test)
x
f
x

e
• Let  
 x  3 for all x  0,5 . Find the location of
the minimum value of f  x  . Justify your answer three
different ways.
Quiz already asked-(second derivative test)
x
f
x

e
• Let  
 x  3 for all x  0,5 . Find the location of
the minimum value of f  x  . Justify your answer three
different ways.
Quiz 22. What is this test?
x
f
x

e
• Let  
 x  3 for all x  0,5 . Find the location of
the minimum value of f  x  . Justify your answer three
different ways.
The Writing Questions
on the AP Calculus
Exams
P R E SE NT ED B Y
LIN MCMULLIN
‘ I O L A NI SCHO O L
L NMCMULL IN@ AOL .COM
HT T P:/ / WWW.LI NMCMULLIN.NE T
HT T P:/ / TEACHINGCALCULUS .WOR DP RE SS. CO M