The Writing Questions on the AP Calculus Exams PRESENTED BY LIN MCMULLIN ‘IOLANI SCHOOL.

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Presentation transcript:

The Writing Questions on the AP Calculus Exams PRESENTED 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 ABBC “Writing” points on the operational exams free- response questions

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. Extreme Values 2013 AB 1 / BC 1 – The Candidates’ Test

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

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 Let for all. Find the location of the minimum value of. Justify your answer three different ways.

Quiz Let for all. Find the location of the minimum value of. Justify your answer three different ways.

Quiz Let for all. Find the location of the minimum value of. Justify your answer three different ways.

Quiz Let for all. Find the location of the minimum value of. Justify your answer three different ways.

The Writing Questions on the AP Calculus Exams PRESENTED BY LIN MCMULLIN ‘IOLANI SCHOOL