Last week, I received an email from a mother whose concern really ticked me off. The mother of a student entering eleventh grade this fall wrote because her son wanted to take AP Calculus next fall. He will not be allowed to take the course because he missed the cut-off grade in his precalculus course…
As exam time nears, teachers become concerned about exactly what to give credit for and what not to give credit for when grading their students’ work on past AP free-response questions. Former Chief Reader Stephen Davis recently posted a note on the grading of a fictitious exam question showing how 2 points might have been…
AP Questions Type 10: Sequences and Series (BC Only) The last BC question on the exams usually concerns sequences and series. The question may ask students to write a Taylor or Maclaurin series and to answer questions about it and its interval of convergence, or about a related series found by differentiating or integrating. The…
AP Questions Type 9: Polar Equations (BC Only) Ideally, as with parametric and vector functions, polar curves should be introduced and covered thoroughly in a pre-calculus course. Questions on the BC exams have been concerned only with calculus ideas related to polar curves. Students have not been asked to know the names of the various…
AP Questions Type 8: Parametric and Vector Equations (BC Only) The parametric/vector equation questions only concern motion in a plane. Other topics, such as dot product and cross product, are not tested. In the plane, the position of a moving object as a function of time, t, can be specified by a pair of parametric equations or the…
AP Questions Type 7: Other topics Any topic in the Course and Exam Description may be the subject of a free-response or multiple-choice question. The topics discussed here are not asked often enough to be classified as a type of their own. The topics listed here have been the subject of full free-response questions or…
AP Questions Type 6: Differential Equations Differential equations are tested in the free-response section of the AP exams almost every year. The actual solving of the differential equation is usually the main part of the problem accompanied by a related question such as a slope field or a tangent line approximation. BC students may also…
AP Questions Type 5: Riemann Sum & Table Problems Information given in tables may be used to test a variety of ideas in calculus including analysis of functions, accumulation, theory and theorems, and position-velocity-acceleration, among others. Numbers and working with numbers are part of the Rule of Four and table problems are one way they are tested.…
AP Type Questions 4: Area and Volume Given equations that define a region in the plane students are asked to find its area, the volume of the solid formed when the region is revolved around a line, and/or the region is used as a base of a solid with regular cross-sections. This standard application of…
AP Questions Type 3: Graph Analysis The long name is “Here’s the graph of the derivative, tell me things about the function.” Students are given either the equation of the derivative of a function or a graph identified as the derivative of a function with no equation is given. It is not expected that students…
AP Questions Type 2: Linear Motion We continue the discussion of the various type questions on the AP Calculus Exams with linear motion questions. “A particle (or car, person, or bicycle) moves on a number line ….” These questions may give the position equation, the velocity equation (most often), or the acceleration equation of something…
The Free-response Questions There are ten general types of AP Calculus free-response questions. This and the next nine posts will discuss each of them. NOTE: The numbers I’ve assigned to each type DO NOT correspond to the CED Unit numbers. Many AP Exam questions intentionally have parts from different Units. The CED Unit numbers will be…
Teaching Calculus 