Took the big honkin' assessment. Turned out to be a little too big and too honkin' because no one got finished...so we finished it in Wednesday DS.
Wednesday
Finished assessment in DS. Then applied the average value formula (see here for an example link) and found the average y-value for a rational function. Then extended it farther by noticing that continuous functions must equal their average (in contrast to discrete sets, like a person's test grades) so setting f(x) equal to the average value allows one to find the x-value within the interval that the function takes on its average.
This led to a review of the Mean Value Theorem which states that for a differentiable function on an interval [a,b], there must be some c in that window where the slope at exactly c (instant slope) is equal to the slope over the whole interval (average slope). See here for a review of the MVT from last semester: link
Combining the result of the MVT with the result from the FTC (the method you use to get evaluate a definite integral) yields the new idea, the MVT for Integrals, which states that a continuous function MUST actually include its average value. Geometrically this means that the area under a weird curve (blobby shape) can be "rectified" into a rectangle with the exact same area covering the same base from a to b.
Then finished group work problems dealing FTC, Riemann sums, and accumulated change.
Notes from board
If today's class made no sense, see here for a GREAT summary: link
Homework:
FTC worksheet #1-14 [I-U4 and I-U8] (see here for blank copy)
p. 288 #45-55 odd [I-A7a]
Resources
Finding the average value of a function: link
Finding the c guaranteed by the MVT for integrals example by me (PDF not a video) link
Finding the c guaranteed by the MVT for integrals video: link
Went over homework, worked out a few examples. Looked at more perspectives of the Mean Value Theorem for integrals and net change: see link here for board notes.
Gave groups time to finish posters and then did gallery walk of AP-style problems on chart paper. Then passed out 2003 AP multiple choice no-calculator section and scantrons. These are due on Wednesday. See below for the PDF of the test.
Homework:
Due Wednesday: AP multiple choice on scantron (copy here)