The AP Exam Review Type Questions

Below are the notes on the ten type questions I’ve been updating and posting every year. The first post contains suggestions and resources for reviewing and for using the ten type questions as a guide for reviewing.

These ten types cover the concepts tested on the AP Calculus AB and BC exams. They are not the same as the ten units that make up the AP Calculus courses. The type questions almost always contain concepts from more than one of the units. Sometimes more than one type is included in one exam question. The types are based on the free-response questions, but the multiple-choice questions fall into the same types. Using the ten types to review is explained in the first post, AP Exam Review.

Also, be aware that each type may be based on an equation, graph, and/or table given in the stem.

Additional posts with exam review suggestions and ideas appear after the ten types.

AP Exam Review – notes on reviewing and how to use the ten types.

Rate & Accumulation (Type 1) – using rates of change to determine amounts, in-out questions.

Linear Motion (Type 2) – analysis of motion on a line, position, velocity, acceleration, and speed.

Graph Analysis Questions (Type 3) – increasing, decreasing, extreme values, concavity, asymptotes.

Area and Volume Problems (Type 4) – area between curves, volumes of solid figures with regular cross -sections, volumes of rotation.

Riemann Sum & Table Problems (Type 5) – questions with a table in the stem, Riemann sums, approximate rates of change.

Differential Equations (Type 6) – initial value problems, slope fields, Euler’s method, the logistic equation.

Other Problems (Type 7) – related rate questions, implicit differentiation, and others.

Parametric and Vector Equations (Type 8) – a BC topic about motion in a plane, position, velocity and acceleration vectors.

Polar Equation Questions (Type 9) – area and rate of change questions based on polar curves.

Sequences and Series (Type 10) – sequences, convergence, convergence tests, Taylor and Maclaurin polynomials and series, error bounds.

I will try to update these each year.

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Calculator Use on the AP Exams – What students should be able to do and what they cannot do on the exam with their graphing calculator.

Writing on the AP Calculus Exams – Why and how to teach writing on the exams.

A Modest Proposal – The answers are online. What to do about it.

Common Mistakes that Make Readers Pull Their Hair Out – Exam mistakes to avoid.  To dx or not dx – Don’t worry about the fine points of grading the AP Exams.

An index of all free-response questions from 1971 – 2018 – listed by major topics. These were researched by Kalpana Kanwar a teacher at Wisconsin Heights High School. Thank you, Kalpana! They include precalculus topics that were tested on the exams before 1998. These may be good for your precalculus classes. (Remember that the course description underwent major changes in 1998 and some topics were dropped at that time. These include the “A” topics (precalculus), Newton’s Method, work, volume by cylindrical shells, among others. Be careful when assigning old questions; they’re good, but they may no longer be tested.)