This unit seems to fit more logically after the opening unit on integration (Unit 6). The Course and Exam Description (CED) places Unit 7 Differential Equations before Unit 8 probably because the previous unit ended with techniques of antidifferentiation. My guess is that many teachers will teach Unit 8: Applications of Integration immediately after Unit…
Applications (Unit 8) seems to fit more logically after the opening unit on integration (Unit 6). The Course and Exam Description (CED) present differential equations first probably because the previous unit ended with techniques of antidifferentiation. My guess is that many teachers will teach Unit 8: Applications of Integration before Unit 7: Differential Equations. Therefore,…
Unit 6 develops the ideas behind integration, the Fundamental Theorem of Calculus, and Accumulation. (CED – 2019 p. 109 – 128 ). These topics account for about 17 – 20% of questions on the AB exam and 17 – 20% of the BC questions. Topics 6.1 – 6.4 Working up to the FTC Topic 6.1…
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…
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 the integral has appeared every year since…
This is an exploration based on the AP Calculus question 2018 AB 6. I originally posed it for teachers last summer. This will make, I hope, a good review of many of the concepts and techniques students have learned during the year. The exploration, which will take an hour or more, includes these topics: Finding…
More posts on differential equations Good Question 2: 2002 BC 5 (2-17-2015) A differential equation that cannot be solved by separating the variables is investigated anyway. Most of this question is AB material. A Family of Functions (2-21-2015) Further investigation of the general solution of the equation discussed above in Good Question 2. Most of…
