Warm up involved finding area of a region that was under 2 different curves. Did another FTC algebraic problem involving an accumulation function, but this time both bounds were variables. Reviewed intervals of increase and concavity/inflection points. Started looking at the concept behind area between curves.
Notes from board
Homework
- watch and take notes on video below: direct link
- study for assessment: additional practice problems suggested below
I-A4a: p288 #35-44
I-U4: p.290 #81-92
I-U7: p 274 #41-44
I-U5: p. 313 #43-48
I-U9: p. 290 #73-74
- see Friday's post for practice assessment solutions and review videos for every skill
Discussed area between curves in DS, doing an example together including finding the points of intersection algebraically. Assessed in class and picked up area between curves handout and AP packet.
Notes from board
Homework
- due Friday: area between curves handout #1-6 (blank copy here)
- due Monday: 2003 AP test multiple choice section (NO CALCULATOR) (blank copy illegal to post sorry)
Resources
brand new vids for you! area between curves power rule
and trig functions
Warm up was an AP FRQ no calculator question dealing with the FTC graphically, including a question about finding the absolute minimum (which could occur at either a relative minimum OR an endpoint of the interval). Looked at finding area a different way, as the sum of rectangles oriented horizontally, with an x-value for a width (as opposed to y height) and a dy height (as opposed to dx width). These can also be accumulated to find exact area under a curve (or even between, using 'right minus left' as the paradigm, rather than top minus bottom).
Switched gears to study the net change theorem, which is just a rearranged version of the FTC Pt 2. It states that the future value of a function is equal to the initial value plus the accumulation of all the change (aka derivatives summed together) in between the initial moment and the time in question. Worked through a simple and then an AP-test style question involving net change, using the numerical integration capabilities of the calculator.
Notes from board
Homework
continue working on AP packet due Monday (no calculator)
Resources
forthcoming