The Writing Questions on the AP Calculus ExamsPRESENTED BY

LIN MCMULLIN‘ IOLANI SCHOOL

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?

Year AB BC2007 9 92008 7 82009 7 32010 7 72011 7 62012 9 72013 9 7

“Writing” points on the operational exams free-response questions

NUMBER EACH RESPONSEWriting 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 question2013 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 derivative16. 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 question2007 AB 6 – F0rm B

Quiz

• Let for all .

Find the location of the minimum value of

. Justify your answer three different ways.

3xf x e x 0,5x

f x

Quiz already asked-(first derivative test)• Let for all .

Find the location of the minimum value of

. Justify your answer three different ways.

3xf x e x 0,5x

f x

Quiz already asked-(second derivative test)

• Let for all .

Find the location of the minimum value of

. Justify your answer three different ways.

3xf x e x 0,5x

f x

Quiz 22. What is this test?

• Let for all .

Find the location of the minimum value of

. Justify your answer three different ways.

3xf x e x 0,5x

f x

The Writing Questions on the AP Calculus ExamsPRESENTED BY

LIN MCMULLIN‘ IOLANI SCHOOL

LNMCMULLIN@AOL.COM

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