Happy New Year ! A few more links to posts on accumulation. Painting a Point (2-4-2013) Paint often and the paint accumulates. Good Question 6: 2000 AB 4 (8-25-2015) Accumulation Good Question 8 – or not? (1-5-2016) Accumulation Density (1-10-2017) Accumulation and Differential Equations (2-1-2013) Solving differential equations without the “+C“ Review Notes: Type 1 Questions:…
The idea that the definite integral is an “accumulator” means that integrating a rate of change over an integral gives the net amount of change over the interval.Many of the application of integration are based on this idea. Here are some past posts on this idea. Accumulation An introductory activity to explore accumulation and the relationship…
In this post we look at another part of the AP Calculus BC exam. Good Question 15 discussed the unusual units in 2018 BC 2(a). In this post we look at 2018 BC 2(b) where units help us find the correct integral to answer the question. How do you answer a question of a type…
The Free-response Questions There are ten general categories of AP Calculus free-response questions. As I’ve done in part years, I will consider each individually over the next few weeks posting on Tuesdays and Fridays. These will be updates of last year’s posts. Here is the list of the types and the schedule: Tuesday March 6 –…
More posts on differential equations Good Question 2 (2002 BC 5) and A Family of Function (Good Question 2 continued) – one of my all-time favorite AP exam questions. Parts a, c, and d are suitable for AB students. Part b is a Euler’s method question. Part d is an example of a question where…
Integration, at its basic level, is addition. A definite integral is a sum (a Riemann sum). When you add things you get an amount of whatever you are adding: you accumulate. Here are some previous posts on this important idea that often shows up on the AP Calculus exams (usually the first free-response question!) Accumulation:…
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…
