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
2014
2015
AB
9
7
7
7
7
9
9
6
8
BC
9
8
3
7
6
7
7
3
6
Writing Prompts
• 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
• Explain the meaning of a derivative in the context of the problem
What to do?
. . . the short answer
• Determine which theorem or definition applies
• State (show) that your problem meets the
hypotheses of the theorem or definition – BE
SPECIFIC!
Continuity
2007 AB 6
Justify your answer
2013 AB 2 – Increasing/decreasing and Speed
Justify your answer.
2013 AB 1 / BC 1 – The Candidates’ Test
Extreme Values
Justify your answer
2013 AB4 / BC4 – The First Derivative Test
Justify your answer
2013 AB4 / BC 4 – The Candidates’ Test
Justify your answer
2002 BC 5 – The Second Derivative Test
Justify your answer
2013 AB3 / BC 3 – The Mean Value Theorem
Explain your reasoning
2013 AB4 / BC 4 – Concavity & Increasing/decreasing
Show the work …
2013 BC 5 – L’Hôpital’s Rule
Explain the meaning of
. . . a definite integral
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
2013 AB3 / BC 3
Explain the meaning of
. . . a definite integral
Hint: Use the Fundamental Theorem of Calculus

b
a
f   x  dx  f  b   f  a 
Explain the meaning of a definite integral
2009 AB 3 Might Cable Company
Explain the meaning of
. . . a derivative
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
2012 AB1 / BC 1
Explain the meaning of a derivative
2007 Form B AB3
Other Theorems
2007 AB 3 – IVT, MVT
Theorem Questions
2007 AB 6 – F0rm B
Theorem Questions
2007 AB 6 – F0rm B
Theorem Questions
2007 AB 6 – F0rm B
Theorem Questions
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
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
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
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 .COM