Unit 8 Test (Topics 8.1-8.12)

Unit 8 - Day 18

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)

Questions to Include
  • Differentiation between displacement and total distance and then interpretation of the meaning of their solution in the context of the problem

  • Analytic calculations and interpretations of particle motion when given equation(s) for position, velocity, or acceleration with appropriate initial conditions, including: speeding up/slowing down, moving toward/away from the origin, displacement/total distance, etc.

  • Analytic calculations and interpretations of particle motion when given a graph of s’(t) = v(t), including: speeding up/slowing down, moving toward/away from the origin, displacement/total distance, etc.

  • Finding the area within a bounded region using dx or dy integrals

  • Finding the volume created when a bounded region is revolved around a major axis or another horizontal or vertical line using either disks or washers

  • Finding the volume created when cross sections (perpendicular to either the x- or y-axis) are placed on a region

  • Using calculus in context to find and describe the meaning of the average value of a function, rates of change in rectilinear motion, integrals as accumulation functions, and integrals as representations of net change

  • Problems that require students to find, store and recall points of intersection

  • Applications of integrals to novel contexts which demonstrate a command of the content beyond previous classroom work (see previous AP FRQs for possible material)

Grading Tips

Remember, we recommend preparing a scoring rubric for all free response items before you begin grading assessments. Know what information is necessary for a complete and correct response and award points when a student presents that information. Grade for what they know, not what they don’t.
 

Consider awarding multiple points for complex integrands: correct limits of integration, using the format R2 - r2, correct orientation (dx vs. dy integrals), and appropriate constants (pi, denominators, etc.).
 

We expect students to reference the functions defined in the question. If the stem names a function H(t), we certainly don’t want them writing about f(x)!  So, tell your students before the test if you will accept that f(x) --- or a(t) instead of v’(t) --- if a student has not made the connection explicitly.

Reflections

Students performed better when given functions within the stem of a multi-part question and asked to manipulate those functions in different ways: finding the area of a region defined by the functions, revolving the region around a major axis, revolving the region about an axis such as y = +k or x = +k, or using the region as a base for cross sections. This also saves time for most students as the need for new graphs and calculator manipulation is eliminated.  
 

Knowing how and when to interpret total distance (as opposed to displacement or net change) remained a challenge as did the language of justification. The practice of writing complete responses to FRQs should remain a top priority for teachers right up to the date of the AP Test. 

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