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## Unit 6 - Day 12

##### All Units
###### Writing an AP Calc Assessment
• Include calculator and non-calculator items

• Include multiple choice and free response items

• Write questions that reflect learning targets and success criteria

• Determine scoring rubric for FRQs before administering the assessment (see below)

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###### Questions to Include
• Items to reflect all representations: numerical, graphical, verbal, analytical

• Defining functions as integrals that represent area between a ROC graph and an axis

• Defining functions as integrals whose values are determined from a tabular presentation

• Context questions requiring students to write and evaluate original integrals

• Tasks requiring implementation of both parts of the FTC

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We recommend that you prepare a rubric for the free response items before you begin grading your quizzes or tests. Know what information is necessary for a complete and correct response and award points when a student presents that information. Many of the “Why did I get marked down?” questions are eliminated when you share the components that earn points.

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###### Reflections

Following the style and format of the AP Test for quizzes and tests give students practice with AP-style questions all year, instead of just during an intense review period in April. So, this quiz followed our usual format of combining multiple-choice and open response questions.

The notation and conclusions of the FTC were a primary focus of Quiz 6.4 – 6.8: students were required to evaluate definite integrals using both graphical and tabular analysis, substitute limits of integration into an antiderivative expression, and combine an initial value with an integral expression.

Almost all quizzes communicated to us an understanding of the integral as a net area calculation. We were also gratified to see that most students recognized the need to use values of the function h(x) when evaluating integrals of h’(x).

A number of students felt compelled to add a constant of integration to a definite integral and then incorporate the initial condition when solving for the constant. While their final values were often correct, their work did not reflect the notation and structure of the FTC.  This topic will need to be revisited tomorrow.

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