Quiz Topics 8.78.12
Unit 8  Day 15
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 multiple choice and free response items

Write questions that reflect learning targets and success criteria

Determine scoring rubrics for FRQs before administering the assessment
Questions to Include

Calculate volumes of revolution using disk cross sections and definite integrals

Calculate volumes of revolution using washer cross sections and definite integrals

Calculate volumes of revolution using known cross sections and definite integrals

Set up and/or evaluate expressions for the volume of a region revolved around axes other than the
xaxis or yaxis 
Bounding functions requiring calculator assistance to define points of intersection
Grading Tips
Complex integrals are required to accurately represent the volumes generated in Topics 8.7 through 8.12. To best assess student understanding, consider awarding points for specific components in a student’s response.
Simply using the correct orientation of slices or washers (dx vs. dy) and the corresponding limits of integration may be the focus for a particular question on your quiz and may constitute all the points for that problem. For volumes incorporating washers or other cross section regions, emphasis should be placed on correct formatting of the integrand.
When asking students to evaluate their definite integrals, omitting constants (pi, incorrect denominators, etc.) typically results in a loss of point only for the final numeric answer. Students should not lose points for an incorrect intermediate expression AND the final value if their only mistake is a misplaced constant.
Encourage students to sketch a representative washer or slice when needed; just don’t assess the artwork!
Reflections
Students performed best when asked to find volumes by solid slices: especially when the axis of rotation was a major axis. These shapes are easy to visualize and the integrands are manageable.
As expected, washer problems presented more challenges than slices, especially when a region was revolved around a distant axis. Our students were successful horizontal slices and washers and also were able to find the correct limits of integration along the yaxis.
Thanks to consistent practice throughout the year, students were comfortable finding points of intersection and storing those values in their calculator for easy access later. The time saved during a test is well worth the time spent teaching this skill!