Writing an AP Calc Assessment
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
Items requiring the set up (not necessarily evaluating) of integrals to find areas using vertical rectangles (integrals with respect to x; dx integrals)
Items requiring the set up (not necessarily evaluating) of integrals to find areas using horizontal rectangles (integrals with respect to y; dy integrals)
Finding the areas of regions below the x-axis
Finding the areas of regions above or below a horizontal line that divides the initial region into two smaller regions
Finding the area of a region defined by functions that intersect more than once
Using a calculator to find the limits of integration
Using a calculator to evaluate definite integrals
Evaluating definite integrals by demonstrating techniques of integration without technology
Generally, calculator-assisted solutions earn points for the set up and another for the final numeric value and perhaps correct units. Non-calculator solutions can earn additional points for intermediate steps.
Consider how you will allocate points for an integral written in terms of x that contains a dy term; also, determine how you will assess an integral written in terms of x while the limits of integration are y-values.
This quiz is divided into two sections: calculator allowed and non-calculator. Using a calculator to find points of intersection and the values of definite integrals are important skills to master before the AP Exam. As we near the exam date, our students need to be allowed as much practice as possible to become familiar with the functions on their calculator.
Equally important, however, is the ability to communicate correct mathematical processes and notation. For example, students were required to write integrals with respect to x and integrals with respect to y. Homework questions that proved to be especially challenging (integral expressions to represent the area of a region divided into equal parts with the horizontal line, y = k) have been reworked for this quiz.
We were pleasantly surprised by students who chose to use formulas for geometric areas (triangles, rectangles) instead of working with integral expressions.
Finally, all our practice with calculator functions and shortcuts paid off: students made fewer copy errors and were much less likely to round off too early in their calculations.