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…
Next in line are differential equations. Here are links to some past posts on differential equations Differential Equations Outline of basic ideas for AB and BC calculus Slope Fields Euler’s Method – a BC only topic Domain of a Differential Equation mentioned on the new Course and Exam Description Good Question 6 2000 AB 4…
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:…
A reader recently asked me to do a post answering some questions about differential equations: The 2016 AP Calculus course description now includes a new statement about domain restrictions for the solutions of differential equations. Specifically, EK 3.5A3 states “Solutions to differential equations may be subject to domain restrictions.” Could you write a blog…
Differential equations are tested every year. The actual solving of the differential equation is usually the main part of the problem, but it is accompanied by a related question such as a slope field or a tangent line approximation. BC students may also be asked to approximate using Euler’s Method. Large parts of the BC…
After my last post, I realized I have never written about the logistic growth model. This is a topic tested on the AP Calculus BC exam (and not on AB). Here is a brief outline of this topic. Logistic growth occurs in situations where the rate of change of a population, y, is proportional to…
The logistic growth model describes situation where the growth of some population is proportional to the number present at any time and the difference between that amount and some limiting value called the “carrying capacity.” The standard example is this: a small group of rabbits is placed on an island. The population will grow rapidly…
