Applied net change theorem to financial math example. Board notes here.
Homework:
Complete AP 2003 multiple choice no calculator section for Wednesday.
No DS because of SLC. Upcoming assessment will include these topics:
I-U4: Applying FTC 1 (front of worksheet, #1-8)
I-U7: Definite integral properties (p. 274 hw)
I-A7a: Average Value (p 288 hw)
I-A4b: Area Between Curves (worksheet from a few weeks ago, tonight's wksht)
Worked privately and then collaborated on the 2000 FRQ #4 which involved integrating a rate to find accumulated change. Here is a video that explains the problem; link
Then introduced idea of finding area using horizontal rectangles for spaces that are not "under" the curve so to speak, but beside curves that are functions of y.
Then looked at how this is similar and how it is different to the concept of area between curves, and worked out a HW problem dealing with horizontal rectangles.
Board notes
Homework:
Worksheet linked here #1-8
[I-A4b]
Resources
area between curves that intersect, dx (turn volume down at first, horrendous audio quality) link
area between two curves: part 1 (good stuff starts at 6:50) part 2
area between two curves dy: link
Friday
Went over area between curves homework. Numerical solutions posted here; you should be able to set up an integral for these--using a calculator to evaluate the answer is okay for Monday's assessment.
Then did an AP free response problem dealing with applying the FTC: explained BEAUTIFULLY right here: link
Finally went over the most commonly missed problems on the AP multiple choice packet that was collected Wednesday. Here are the notes from the board.
Then passed out the 2003 AP Calculus multiple choice section that allows a calculator. This is due next week. Digital copy linked below.
Homework:
- Assessment on Monday covering stuff outlined above; see help videos below
- 2003 Multiple Choice packet due Wednesday (later if you are on the NY trip) [digital copy here]
Resources:
Applying FTC (including the chain rule) link
Properties of Definite Integrals: link
Average Value example: link
Area between curves: intersection, vertical rectangles: link
Area between curves: 2 intersections, vertical rectangles: link
for more on area between curves, just see Wed's post.