Unit 5 Test (Topics 5.1-5.12)

Unit 5 - Day 14

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
  • Finding a value of c that satisfies the MVT

  • Analysis of f’ graph to determine relative extrema, points of inflection, intervals of increasing/decreasing, and intervals of concave up/down on f(x)

  • Justifying an absolute extrema with the Candidates Test

  • Justifying a relative extrema with the second derivative test (tabular data works great for this!)

  • Given info about the sign of the first and second derivative of f, choose a possible graph of f(x)

  • Optimization problem (we kept it pretty basic with a fencing question)

  • Finding the critical points of an implicit function

  • Determining if the EVT, IVT, and MVT can be applied for a given function (represented analytically or graphically)

Grading Tips

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. 


We used two old FRQ questions from previous AP tests (with slight modifications) for our free response questions (2018 AB5 and 2017 AB3 parts b and d). The parts that students struggled with most were those requiring L’hospital’s rule and evaluating the given function in the Candidates Test (unit circle knowledge required!)

Students have improved a lot throughout this unit in their justifications. Even when arithmetic errors were made, many correct justifications were given for absolute extrema, relative extrema, points of inflection, etc.