Took first assessment on Riemann sums and definite integrals.
Homework
Watch and take notes on this video. Ignore bit at very end about bookwork hw: link
Passed back assessments in DS, went over them in small groups. Practiced with properties of definite integrals in DS and for our warm up. Looked at motion (position-velocity-acceleration) in the context of "finding C" when given an initial value of some kind (does not have to be 'initial,' although the work is easier if it is). Compared the method of taking an indefinite integral and using algebra to find C with a method that utilizes the FTC Part 2 and rewrites the problem as one of net change--that is, to find the position at a future time, add an accumulation of change to some starting value. Also worked backwards from a single acceleration function and specific velocity and position data to find the position at some other time. Gave out some information regarding the AP test format and passage rates. Started an AP FRQ related to integration in jigsaw groups at end of class, will pick up with this on Friday.
Notes from board
Homework
watch and take notes on this video: link
Did 2 no-calculator AP multiple choice questions for warm up. Examined the relationship among area, antiderivatives, and derivatives through some geometric examples, and illustrated the FTC pt 2 as yielding the function under which we were finding area. Then used a geometric/algebraic approach to accumulation functions and investigated how area changes with small incremental changes in x to arrive at the Fundamental Theorem of Calculus, which shows that derivatives are the inverse operation of accumulation/definite integrals.
Notes from board
Homework
#924-932 and #940-952 (evens) on this handout
Resources
summary of what we did in class: link
examples similar to first part of hw: first half of this video