Other Topics (Type 7)

Any topic in the Course and Exam Description may be the subject of a free-response question. The two topics listed here have been the subject of full free-response questions or major parts of them. Implicitly defined relations and implicit differentiation These questions may ask students to find the first or second derivative of an implicitly…

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Table & Riemann Sum Questions (Type 5)

Tables may be used to test a variety of ideas in calculus including analysis of functions, accumulation, position-velocity-acceleration, theory and theorems among others. Numbers and working with numbers is part of the Rule of Four and table problems are one way this is tested.  What students should be able to do: Find the average rate…

Graph Analysis (Type 3)

The long name is “Here’s the graph of the derivative, tell me things about the function.” Most often students are given the graph identified as the derivative of a function. There is no equation given and it is not expected that students will write the equation (although this may be possible); rather, students are expected…

Linear Motion (Type 2)

“A particle (or car, or bicycle) moves on a number line ….” These questions may give the position equation, the velocity equation or the acceleration equation of something that is moving, along with an initial condition. The questions ask for information about motion of the particle: its direction, when it changes direction, its maximum position…

Rate and Accumulation Questions (Type 1)

The Free-response Questions The free-response questions fall into 10 general categories or types. The multiple-choice questions fall largely into the same categories plus some straight-forward questions asking students to find limits, derivatives, and integrals. Often two or more type are combined into one question. The types are the following. Rate and Accumulation Linear motion Graph Analysis…