Unit 8 Test (Topics 8.18.12)
Unit 8  Day 18
Unit 8
Day 1
Day 2
Day 3
Day 4
Day 5
Day 6
Day 7
Day 8
Day 9
Day 10
Day 11
Day 12
Day 13
Day 14
Day 15
Day 16
Day 17
Day 18
All Units
Writing an AP Calc Assessment

Include calculator and noncalculator 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 yaxis) 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 multipart 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.