New Paltz High School

Here are many free response questions and videos. 

Note: Occasionally I make reference to the 2020 exam (which didn't include topics like area, volume, average value of a funtion)... so ignore any of those references. 

Data with two functions and derivatives problem 2016 6, Rubric and watch this video on this data problem

Particle calculator problem 2016 2 , Rubric

extrema tangent line problem with graph of deriv, ANSWERS (RUBRIC) and watch the video: Extrema tangent line problem with graph of f' video 

Differential Equation with slope field problem 2016 4, Rubric 

Water pumped into tank problem 2016 1 , Rubric and watch this video on this water tank problem

 Piecewise graph problem 2016 3, Rubric

Data graph composite functions, Data graph Rubric 

Graph of deriv 2017 3, Graph of deriv Rubric

Tank with data given on horiz cross section, Tank Rubric

Particle Motion Problem, Particle Rubric and here's a video going over this particle problem!

Potato differential equation problem, Potato Rubric  and here's a video going over the potato problem

Banana rate problem , Banana Rubric

Height of tree, Height of Tree Rubric.  Watch this  video that goes over the tree problem

e^x cos(x) free response, e^x cos(x) Rubric

Grass Clipping Free response, Grass clipping Rubric

Cylindrical barrel free response , cylindrical barrel Rubric

Graph of derivative with integrals inflection points, ANSWERS (RUBRIC)

slope field problem, RUBRIC for slope field problem

rate problem with trains.  Try this problem and then check out the video that goes over this train problem.

data with f, f', g, g', ANSWERS (RUBRIC)

graph of f with definite integrals absolute max limit, After you do the problem, check out the rubric

Free response question with Squeeze theorem, ANSWERS (RUBRIC)

extrema tangent line problem with graph of deriv, ANSWERS (RUBRIC) and watch the video: Extrema tanglent line problem with graph of f' video 

Here's a concept that came up for this first time on a recent AP Calculus exam...It's called the Squeeze Theorem....it's intuitive and makes sense, so check it out.

video from Khan academy: video on Squeeze Theorem

practice from Khan academy: practice on Squeeze Theorem from Khan Academy

Try this problem: separable diff equation with linear approx  , ANSWERS (RUBRIC)

Piecewise continuity free response question, ANSWERS (RUBRIC).  

Every year, I notice that the College Board is emphasizing some topics that they may have not emphasized before.  One topic is re-writing a definite integral as a limit of a Riemann sum and then going the other direction, re-writing a limit of a Riemann Sum as a definite integral.  We talked about this quickly in class (and I think some of you may have even been on a field trip!) so it's worth spending more time on it now.

Sal Khan does a great job with this, so rather than creating a video myself, I'll link you to the two videos below.  If you need to, you can backtrack in his sequence to remind yourself of summation notation, Riemann Sums, etc.  After you watch the two videos below, then work on the practice.

video: Re-write definite integral as a limit of a Riemann Sum

video: Re-write limit of a Riemann Sum as a definite integral