AP Calculus / HL 1
AP Calculus/Math HL1
Google Classroom Code for S1: skeoy3c
Hello all! Join our Google Classroom using one of the codes above.
Head down to the "What's Been Happening" section on this page to see (often with links) what is going on each day or the "Announcements & Resources" section to find links to helpful websites/documents/videos.
Email me (sarsfields@sau25.net) with any questions at any time!
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Announcements & Resources
8/25/23 - Here is a link to the AP Syllabus (this course prepares you for the AP exam in May)
8/25/23 - AP Calculus/Math HL 1 Syllabus
What's Been Happening
6/6/24 - (1) Today is our last class! We will...
6/4/24 - (1) Integration assessment today
5/29/24 - (1) We'll tackle an integration problem set (solutions). (2) Partial Fractions Check-In. (3) integration assessment (4) We'll play with polar coordinates.
5/24/24 - (1) We'll begin with one or two integration problems that utilize partial fractions. (2) We'll discuss this partial fractions practice (SOLUTIONS) in groups. (3) We'll work on this integration sampler (solutions) in pairs. (4) We'll pair up for a partial fractions problem (solution).
5/22/24 - (1) We'll battle through some partial fractions examples. (2) Here is a sum up of the partial fraction rules. Here is a video introducing partial fractions. Here is a video about partial fraction rules. Here is a video example of applying partial fractions. Here are some wordy notes (with examples) on using partial fractions. (3) We'll check in on the HW...Further IBP practice (solutions), (4) HW: Complete this partial fractions practice (SOLUTIONS).
5/20/24 - (1) We will work on two integration problems (one that begs for IBP "in circles" and another that begs for "completing the square"). (2) We'll field a couple of questions from this assignment (solutions). (3) We will introduce rewriting expressions using partial fractions...using this assignment. (4) We'll battle through some partial fractions examples. (5) Here is a sum up of the partial fraction rules. Here is a video introducing partial fractions. Here is a video about partial fraction rules. Here is a video example of applying partial fractions. Here are some wordy notes (with examples) on using partial fractions. (6) We might begin on Further IBP practice (solutions), but should work on it for HW. (7) We'll end with One IBP problem (solution) .
5/16/24 - (1) We will explore the technique called "integration by parts" using this assignment (solutions). (2) Here are some integration by part resources: Video #1 on IBP. Video #2 on IBP. (3) We'll work on one of two IBP problems together (xlnx). (4) HW: Attempt all remaining problems from this assignment (solutions).
5/14/24 - (1) The exam is over! We'll be fairly low-key today. We'll talk about the exam a bit. We'll bond a little. (2) HW: complete the Google form that was share via Classroom
5/10/24 - (1) We'll start by sharing solutions to the HW in groups. (2) We'll work on (and take home if needed) a calculator-friendly multiple-choice set (solutions). (3) The AP exam is Monday!!! Good luck!!!! When I see you Tuesday, we'll process a little and have an easy-going sort of day.
5/8/24 - (1) We'll run through the problems assigned for HW. (solutions for packet) (2) We'll finish up some FRQ's from 2023 [we paired up for #3 and #5 and chatted about the scoring guidelines. (3) We'll take home, for HW, a non-calculator multiple-choice set (solutions) and should complete #4 from 2023 FRQ's. (5). Some AP exam tips! (we ran through these in class today)
5/6/24 - (1) We'll meet in expert groups for 12' to chat about a specific FRQ from 2014. We'll then divide up into new groups to finish our discussion about the 2014 FRQ's. (2) We'll chat about the upcoming two days and what's to come. (3) We'll run through the 2014 set with the "what do they want" mindset. (4) We'll tackle a non-calculator multiple-choice section individually. (5) We'll begin work on #2 from the 2023 FRQ's. (6) HW: Complete #2 from the 2023 FRQ's and also complete at least #'s 4 and 7.25 from this free-response set. (solutions)
5/2/24 - (1) We'll begin with one free response question (individually). (2) We'll chat about the scoring for that FRQ. (3) We'll collect questions from the HW (2012 M-C questions) and groups will share solutions/steps. (4) We'll work on a few more FRQ's at whiteboards (possibly for some points). (5) HW: Complete the FRQ's from 2014.
4/30/24 - (1) We'll work on #'s 18, 16, and 23 from the 2012 multiple-choice set and discuss results. (2) We'll work in pairs on #'s 7-11 from the 2012 multiple-choice questions. (3) We'll chat about the exam format and our remaining schedule. (4) Pairs will work on #1 from the 2023 FRQ's. (5) HW: Finish the remaining problems from the non-calculator section of the 2012 multiple-choice questions and also complete the calculator section from 2012. (6) I invite anyone who's interested to come in after school to sit and work on AP review problems to get ready for the exam.
**April Break**
4/17/24 - (1) We'll discuss the 2022 FRQ's. (2) Individuals will work on these FRQ's.. (3) If anyone would like any extra problems sets, I suggest looking at the AP website and checking out some FRQ's from the past, along with the scoring guidelines.
4/15/24 - (1) We'll begin with one FRQ (#1 from 2010b). (2) Trios will discuss multiple-choice questions from 2003. Here are some solutions. (2) Trios will continue their work on the FRQ's from 2022 and should complete these for HW .
4/11/24 - (1) We'll start by going over the 2008 Calculator Multiple-Choice solutions. These were the questions. (2) We'll chat about 2021 FRQ #4. (3) We'll complete some multiple choice questions alone and with a partner. (4) We'll individually complete #1 from the 2010 FRQ's. (5) We'll start on and take home for HW the remaining multiple-choice questions from 2003.
4/9/24 - (1) We'll discuss #4 from the 2019 FRQ's. (scoring guidelines). (2) Groups will chat about the FRQ's from the 2021. (scoring guidelines) . (3) Individuals will work on one FRQ question. (4) We'll begin work on these calculator-friendly MC questions and will finish these for HW.
2008 Multiple-Choice Calculator Section Solutions
4/5/24 - (1) We'll start with two multiple-choice questions. (2) We'll chat about one or two of the FRQ's from 2019. (3) Groups will chat about the rest of the 2019 set. (4) We'll work in pairs on one FRQ from the 2021. (scoring guidelines) (5) HW: Finish #'s 1,3,4,5,6 from the FRQ's from the 2021. (scoring guidelines) .
4/4/24 - Snow Day
4/3/24 - (1) Individuals will complete 3 DE Questions. (2) We'll discuss some of the questions that folks emailed about from the 1993 and 1997 multiple-choice questions. Here is a link to the 1997 MC solutions. (3) We'll start work on the 2019 FRQ's. (scoring guidelines). (4) HW: Finish #'s 3-6 from 2019 FRQ's.
4/1/24 - (1) Individuals will complete 3 DE Questions. (2) We'll work through some of the 1993 multiple-choice set. This link as solutions if you scroll down a bit. (3) We'll work through some of the 1997 AP Multiple-Choice problems Part A(skip #25). Some problems were graded individually...some were graded in pairs. (4) HW: Finish the rest of the 1993 multiple-choice set(after #30) and the rest of the 1997 AP Multiple-Choice problems Part A(skip #25). Recall that we've already finished #'s 1-4 and 8-10 from 1997.
3/28/24 - (1) We'll have some group time to chat about the 2018 AP FRQ's (scoring guidelines). (2) We'll complete a random set of multiple-choice questions. (3) We'll begin work on the 1993 multiple-choice set. (4) HW: Complete #'s 1-30 from the 1993 multiple-choice set. (for later: skip #'s 43 and 45)
3/26/24 - Juniors will be out to take the SAT today! All non-juniors will just have a "work day" instead.
3/22/24 - (1) Individuals will complete 3 DE Questions. (2) We'll check over the scoring for the remaining 2017 AP Free Response Questions. Here are the scoring guidelines. (3) We'll complete a random set of multiple-choice questions. (4) We'll take home #'s 1, 3,4, and 5 from the 2018 AP FRQ's (scoring guidelines).
3/20/24 - (1) We will chat about integrals of velocity functions. and we will work on some position-velocity-acceleration multiple-choice questions. (2) We'll go over #'s 3 and 6 from the 2017 AP Free Response Questions. (3) HW: Finish the rest of the 2017 AP Free Response Questions.
Details that came up today: ****The integral of the absolute value of velocity gives us the total distance travelled. **** *****When the signs of velocity and acceleration are the same, the related object would be speeding up.*****
3/18/24 - (1) Pairs will start work on a DE/Separation Quiz (solutions). (2) We'll chat about a few questions from "Some DE/IVP Questions from Ostebee ". (3) We'll begin work on the 2017 AP Free Response Questions (3,6,5,1,2,4). Here are the scoring guidelines. (4) HW: Finish #'s 3 and 6 only (the first two in the copied packet) from the 2017 AP Free Response Questions.
3/14/24 - (0) We'll begin with a very quick slope field question. (1) We'll tackle a graded task on area/volume. (2) We'll share solutions to the HW. (3) HW: Complete #'s 2,9,10,&12 from Some DE/IVP Questions from Ostebee
3/11/24 - (1) We'll be graded on something. (2) We'll check on this slope field packet (solutions) and share solutions together. Here is a resource that discusses how to tackle problems where you're trying to match slope fields to equations. (3) We'll have further discussion about some specific DE's and will do some guessing/checking....perhaps look at related slope fields....then try using separation of variables (see videos from last class). (4) We'll bring up the term IVP. (5) We'll generalize solutions to y' = ky with y(0) = A. (6) We'll work on some separation of variables problems (solutions: page 1 / page 2 / video on #6)....and will finish these for HW.
3/7/24 - (1) Spiral Task 6 (2) We'll discuss HW solution.s (3) Any 7.2 questions? (4) We'll discuss what a differential equation is and will guess and check at solutions to a couple of them. Here is a video introducing differential equations. (5) We'll discuss looking at DE's and IVP's graphically. Here is a video discussing “slope fields”. Here is a video discussing “separation of variables”. Here is another video example. (4) HW: work on this slope field packet (solutions).
3/5/24 - (1) Starter problem on average rate of change/average value. (2) We'll review a couple of volume problems (maybe these two examples). (3) We may try one of the multiple choice questions from 1988 (tin can) together. (4) Do we need to discuss any problems from section 7.2 #'s 11-18,37,38? Here are textbook solutions for 7.2. Here are my written solutions to #'s 17,18, and 37. (5) We'll work on these four volume problems . (6) Pairs will work on (and submit) these two problems . Here’s a video solution. (7) HW: Finish classwork and work on these problems on area/volume as well. (Here are solutions to the 2nd set) . (8) Expect random graded tasks every day from here on out. (9) Spiral task #6
2/23/24 - (1) We'll check in on some volume problems from the HW (section 7.2 #'s 11-18,37,38). Here are textbook solutions for 7.2. Here are my written solutions to #'s 17,18, and 37. (2) We'll tackle this AP review set (solutions). this AP review set (solutions). (3) Enjoy your break!
2/21/24 - (1) Groups will meet up to discuss HW from Section 7.1 and will share needed solutions. (2) We'll tackle a definite integral task. (3) We will discuss finding volume of solids with known cross sections(and practice a bit), work on one board problem (find the volume of the solid generated when the area between x^2 and sqrt(x) is revolved about the x-axis/y=-3/y-axis). (2) Here are two videos on finding volume: (Video #1 & Video #2) including ones where we integrate "in y" . (3) We'll also look at volume problems with known bases and cross sections. Here is a video discussion with two examples. Here is a third example.(4) We will get a copy of section 7.2 (#'s 11-18,37,38) and will attempt some of these problems. (5) Website to visualize solids here. This link can also help create solidsd. (6) This website has a few good examples of finding volumes of solids of revolution. (7) HW: Finish section 7.2 (#'s 11-18,37,38)
2/19/24 - (1) We'll work on/start these four u-substitution problems. (2) We'll discuss questions from "Just a Bit More Area" (solutions). (3) We'll work on a couple of other "area between curves" problems. (4) We'll tackle a graded task on integration. (5) HW: Complete circled problems (#'s 13,15,16,18,19,22,23,37) from Section 7.1 on "area between curves". (some solutions to 7.1 here)
2/15/24 - (1) We'll begin with one definite integral needing u-substitution. (2) We'll find some areas between curves. This video discusses some of the ideas that will come up. (3) We will work on "Just a Bit More Area" (solutions). (4) HW: Finish "Just a Bit More Area".
2/13/24 - We worked on work on this set of old AP problems. Unfinished problems went home as HW.
2/9/24 - (1) We'll discuss HW questions ( section 5.4; #'s 24-31, 34, 36 AND these five other u-subs. probs.). (2) We'll work on area function task for individuals. (3) We may work on couple of multiple-choice questions on integrals. (4) HW: section 5.4; #'s 32,33,35,37-41,48-53
2/7/24 - (1) We'll have a graded task on integral basics. (2) We'll complete one quick assessment question on Riemann sums. (3) We'll share solutions to (and discuss) this initial set of u-substitution problems). (4) We'll complete some board problems (one relating average rate of change with average value, one definite integral, one indefinite integral). (5) HW: section 5.4; #'s 24-31, 34, 36 AND these five other u-subs. probs.
2/5/24 - (1) We'll start with a problem on average rate of change and will also be introduced to the idea of "average value". (2) We will start a conversation about indefinite integrals. Here are a few more u-substitution examples. (3) We'll have a graded task on integral basics. (4) We'll gather any questions from 5 MC questions and "Def. Integrals and Area Functions". (5) We'll check in on what the 'dx" means for integrals. (6) We'll complete one quick assessment question on Riemann sums. (7) We'll be assigned this initial set of u-substitution problems). (8) HW:
2/1/24 - (1) We'll begin by collecting questions from 5.3 and uploading our efforts. (2) We'll grapple with an assessment on related rates. (3) We'll have a graded task on integral basics. (4) Some groups will work on 5 MC questions. (5) "Optional" HW: "Def. Integrals and Area Functions"
1/30/24 - (1) We'll begin with a couple of FTC questions. (2) We'll work on "irregular Riemann". (3) We'll work with one integral that will have us going around in circles. (some may have started this...but most haven't) (4) We'll discuss Some Area Function Questions (solutions---but the first problem should be 3-7-8-4-6-2-5-1). (5) Pairs will tackle "Some Area Function and FTC Stuff" (6) HW: Complete 5.3; #'s 9-13,15,26-29,31,33,59-63
1/26/24 - (1) We'll have some starter problems applying the FTC...including these (solutions) (2) We'll discuss solutions to section 5.2 (HW). (3) We'll have a graded task on integral basics. (4) We'll work on "irregular Riemann". (5) We'll work with one integral that will have us going around in circles. (6) We'll work on Some Area Function Questions (solutions) and should finish for HW.
assessment on related rates. This other Riemann sum task Complete 5.3; #'s 9-13,15,26-29,31,33,59-63 "Some Area Function and FTC Stuff". three derivative application problems .
1/24/24 - (1) We'll start right out in groups to discuss HW from 5.1. Here are some video solutions for a select set of problems from 5.1: #21, #24, #46, #54, #70. [also some solutions to a few problems from 5.1 (#'s 3,21,46,52,55)] (2) We'll discuss Area Function Task #1 and sum up our findings (video discussion here). This brings up the "FTC ". (3) HW: Complete "part 2" which is: section 5.2; #'s 3-8,21-27,51-56
1/22/24 - (1) We'll start with some Riemann sum problems. (2) We'll collect HW (last page from this packet). (3) We'll have one related rates problem to work on individually. (4) We'll verify these rules with integrals. (5) Spiral Task #5. (6) We'll start on Area Function Task #1. (7). HW is to complete Section 5.1 (text); #'s 3,7-9,16,18-21,23-26,33-35,46,50,52,54,55
1/18/24 - (0) Hey Juniors/Seniors! Know what the M3 challenge is? (1) We'll start with a couple of integral problems and will discuss estimation (including Riemann sums and the trapezoidal rule). We'll also discuss when limits of integration are switched. (2) We'll pair up and then work independently on a couple of related rates problems from our earlier HW set. (3) HW: finish the last page from this packet on integrals.
1/16/24 - SNOW DAY!
1/10/24 - (0) We'll start with the second problem from this set. (1) We'll work on this Helicopter Problem. (2) We'll discuss problems from #'s 26-28 from 4.5. (3) We'll pair up for this related rates task. (solution) (4) We'll begin work in groups on "integrals" using this packet
1/8/24 - (1) We'll begin with one very quick related rates problem (individually). (2) Groups will present two problems from section 4.5; #’s 7-13,16-19,21-23. (and we will discuss a few of these problems as a class) (3) Groups will work on 4.5; #'s 26-28. (4) HW: If you didn't complete #'s 26-28 from 4.5, you should finish them.
1/4/24 - (1) We'll clean up a couple of other related rates problems (last two from the slides). (2) Groups will check in on HW due today and present solutions. (3) Groups will work on section 4.5; #’s 7-13,16-19,21-23, 26-28. Here are the solutions (be sure to battle hard before peeking at these). (4) HW: Complete any unfinished problems from section 4.5 started in class (stop after trying #23).
Some video (mostly) solutions to 4.5:
Section 4.5; #10; (video); Section 4.5; #’s 11 & 13 (not a video); Section 4.5; #18 (video); Section 4.5; #19(video); Section 4.5; #21; Section 4.5; #22; Section 4.5; #23; Section 4.5; #26; Section 4.5; #27 & Section 4.5; #28
1/2/24 - (1) We'll tackle a Kahoot quiz. (2) We'll jump back into a discussion of "related rates problems" using these example problems. Here is a video discussion of the first problem. Here is a discussion of the remaining problems. And here are written solutions to the same problems. (3) Here are some tips on related rates problems. (4) HW: Work on these problems. (solutions)
12/21/23 - (1) We'll tackle a check-in on the IVT/EVT/MVT. (4) We'll begin a discussion of "related rates problems" using these example problems. Here is a video discussion of the first problem. Here is a discussion of the remaining problems. And here are written solutions to the same problems.
12/19/23 - (1) We'll tackle a problem-solving NRT. (2) We'll collect this IVT/EVT/MVT task. (3) We'll start a discussion on "related rates" breifly. (4) We'll check out one "related rates" problem. (5) No HW.
12/15/23 - (1) We'll have an assessment on limits. (2) Groups will meet up to complete this task (solutions here). (3) We'll look at a few sample review problems (optimization, finding inflection points, a limit from a graph, an antiderivative). (4) We'll continue work on this IVT/EVT/MVT task...and should finish it all for HW.
12/13/23 - (1) Pairs will work on this pair of questions on inverses & derivatives. (2) We'll look at any connections between continuity and differentiability. (3) We'll chat about the MVT (and the related HW exploration) and add in a discussion of the IVT and EVT. Here are some "slides" we'll look at. Here is a video discussion of those theorems. (4) We'll begin work on this IVT/EVT/MVT task (solutions here). (5) HW: Finish this IVT/EVT/MVT task AND problems A through F from this task (solutions).
12/11/23 - (1) We'll turn in these Limit problems. (2) We'll tackle the "skills" section of an NRT. (3) We'll wrap up A Set of Problems With a Dash of Limits". (4) HW: Work on this exploration of something called the Mean Value Theorem (MVT).
12/7/23 - (0) We'll complete "spiral task #4". (1) We'll work with these limit evaluation problems. (2) We'll discuss solutions to problems 26, 66, 67 from section 2.3. (3) We'll chat about the formal definition of continuity. (4) We'll go over HW problems from section 4.2 (5) We'll chat about this topic list for the NRT next class. (10) HW: These Limit problems
12/5/23 - (1) We'll start in trios working on "Take it to the Limit" (Here are the solutions). (2) We'll chat about #34 from section 2.8. (3) Groups will check in on HW from Section 2.3; #'s 13-26,39-45,50,51,66,67 (solutions) (4) We'll complete "spiral task #4". (5) We will start work on "A Set of Problems With a Dash of Limits". (held onto this) (6) HW: section 4.2 (see circled problems) (7) We'll be having an NRT on symbolic differentiation (product, quotient, chain rules, implicit differentiation, antidifferentiation, etc.) on 12/11/23 (and another on general problem solving later on 12/19/23).
12/1/23 - (1) We'll begin with some starter problems involving inverses, (2) We'll chat about basic rules for limits. (3) :We will complete another graded task on applying the product/quotient/chain rules....and perhaps implicit differentiation as well. (4) Here are some "Tips for Evaluating Limits" if interested. (5) We'll chat about Section 2.8; #'s 14-20,31,33,34,42. and these optimization problems (solutions). (6) HW: Section 2.3; #'s 13-26,39-45,50,51,66,67 (solutions)
11/29/23 - (0) We'll work on one differentiation problem. (1) We'll clean up our ideas related to derivatives of inverses. (2) We will complete another graded task on applying the product/quotient/chain rules....and perhaps implicit differentiation as well. (3) We'll upload and chat about Section 2.8; #'s 14-20,31,33,34,42. (4) We'll continue our discussion of limits using these examples. Here is a video discussing slides 22-28 only, which includes a discussion of L'Hopital's Rule. (5) HW: work on these optimization problems (solutions).
11/27/23 - (1) We'll start with an implicit differentiation review problem. (2) We'll check on (and upload) HW from 3.4. (3) We'll begin a conversation about limits that extend beyond our previous limit conversations (including limits to infinity---and we'll use these examples to get at things(we got up through slide 17). (4) HW: Section 2.8; #'s 14-20,31,33,34,42
11/20/23 - (1) We'll begin with a brief, timed, graded check-in on basic derivatives. (2) We'll chat about solutions to section 3.3. Here is a write-up of #24. Here is a video discussion of #24. Here (3) We'll complete a graded task on product/quotient/chain rules. (4) We'll start a task on how derivatives connect to inverse functions and sum up the findings. (5) HW: Section 3.4; #'s 4-6,22-24,37-39. (6) This practice set on implicit differentiation is just being shared as some extra for those interested. (solutions here)
11/16/23 - (1) We'll begin with one logarithmic differentiation problem and another basic implicit differentiation problem. (2) We'll chat about HW in random groups. (3) We'll problem solve with some antidifferentiation problems, mainly involving inverse trig. functions. (4) We'll work on another implicit differentiation problem involving vertical/horizontal tangent lines. (5) Pairs will tackle this graded task on product/quotient/chain rules. (6) HW: Section 3.3; #'s 9,10, 15 - 22, 24, 25 (solutions) Note: You do not need to plot any of the curves!
11/14/23 - (1) We'll start off with one implicit differentiation problem and one differentitation problem with a base and exponent with variables in each. (2) We'll chat about the Derivative of Arcsine and the Derivative of Arccosine. and the derivative of y=arctan(x). (3) We'll start work. on "1st Try at Implicit Differentiation" (solutions). (4) We'll complete a spiraling graded task (#3). (5) (6) We'll check out an example of "logarithmic differentiation". .(Video here) (7) HW: Complete "1st Try at Implicit Differentiation" (solutions).
11/9/23 - (1) We'll differentiate an expression. (2) We'll take questions from 3.5. (3) We'll briefly check in on the optimization problems from last class done in groups. (4) We will look at an example of implicit differentiation along with a "logarithmic differentiation" example. .(Video here) (5) We'll begin work on "1st Try at Implicit Differentiation" (solutions). (6) HW: Complete #'s 67-76 from section 3.5; #'s 1 - 61.
11/7/23 - (1) We'll chat about problems from Section 2.8; #'s 14-20,30-33,37,41,42,59,60,66.
We'll start with another implicit differentiation problem involving vertical/horizontal tangent lines. (2) We'll run through some requested 3.5 problems. Here are written solutions to #'s 4,7,36,46,50,60,61. (3) Groups will check in on "1st Try at Implicit Differentiation" (solutions). (4) We found the Derivative of Arcsine and the Derivative of Arccosine. (6) HW due next time: "More Early Derivative Problems" We'll have a graded task on symbolic differentiation using the product/quotient/chain rules. (2) We'll look at another implicit differentiation problem (involving an ellipse). (3) We will take questions folks had about section 3.5; #'s 1 - 61. Here are written solutions to #'s 4,7,36,46,50,60,61. (4) Groups will battle through two graded optimization problems (not finished).
11/3/23 - (1) We'll have our NRT today. (2) When finished, folks will work on Section 2.8; #'s 14-20,30-33,37,41,42,59,60,66 and finish it at home.
11/1/23 - (0) Spiralling task #3 (1) We'll begin with some chain/product/quotient rule practice....with an antiderivative problem thrown in there. (2) Folks will share questions they had from section 3.5 (HW was to complete 15 problems). (3) We may clean up questions from the 2nd side of this practice set. (4) We may discuss one problem from an earlier practice set (2.4; #'s 3-11,22,25,29,40,44,47,50,53,56,57,60,62,65). Here are some select detailed solutions: (5) We'll work on "More Early Derivative Problems". (6) HW: Differentiate 10 MORE problems (of your choice) from section 3.5; #'s 1 - 61....and remember there's an NRT next class. Topics include basic differentiation(no product/quotient/chain), tangent lines, limit definitions, finding antiderivatives, graphs of derivatives, relationships between f, f', and f'', finding maxima/minima (and also inflection points).
10/30/23 - (1) We'll work on a "shortest distance" optimization problem. (2) We'll check on the 2nd side of this practice set. (3) We'll have a cleaned-up discussion of the chain rule and work through some examples. (4) We'll take on a multiple-choice task on symbolic differentiation. (5) HW: Differentiate 15 problems (of your choice) from section 3.5; #'s 1 - 59. It's OK to choose problems that seem manageable this time around. (6) NRT on 11/3.
10/26/23 - (1) We may start with one differentiation problem requiring both the product & quotient rule. (2) We'll complete "spiraling task #2". (3) We'll check in on this practice and maybe even those problems from section 2.4; #'s 3-11,22,25,29,40,44,47,50,53,56,57,60,62,65. Here are some select detailed solutions. (4) We'll be having an "NRT" (a unit assessment) on 11/3. Topics include basic differentiation(no product/quotient/chain), tangent lines, limit definitions, finding antiderivatives, graphs of derivatives, relationships between f, f', and f'', finding maxima/minima (and also inflection points). (5) Soda can problem. (not all finished) (6) We'll sum up the derivatives of the basic trig functions (memorize those!). (7). HW: Complete the 2nd side of this practice set.
We'll create "table/graph" problems that apply the product/quotient/chain rules. We'll tackle this task on optimization.
10/24/23 - (0) We'll begin by finding an absolute minimum of a particular polynomial. (1) We'll chat about problems D,E, and F from "Let's Use Some Derivs" (solutions here) with more depth. (2) We'll discuss the Product Rule and Quotient Rule and chain rule for differentiation. (3) We will tackle this graded task on the "limit definition". (4) Soda can problem. (5) HW will be uploaded....and some of it may be discussed if time allows. (6) HW: this practice (but only the first side)
10/19/23 - (0) We'll group up to share solutions to C through F from "Let's Use Some Derivs" (solutions here). (2) Individuals will complete "Tangent Line Task 1" (solutions). (3) We will work on this task on two curves "meeting smoothly" (4) HW is to complete section 2.4; #'s 3-11,22,25,29,40,44,47,50,53,56,57,60,62,65
10/17/23 - (0) We'll create limit definition examples to share and evaluate with others. (1) We'll evaluate a few limits. (2) We'll chat about the "fencing problem"....and what's the best way to justify things within an optimization problem. (3) Individuals will complete "Tangent Line Task 1" (solutions). (4) We'll start on "Let's Use Some Derivs" (solutions here). (5) We may work on this task on two curves "meeting smoothly" (6) HW: Complete problems C through F from "Let's Use Some Derivs"
10/13/23 - (1) We'll turn in HW. (2) We'll check out a new version of the limit definition using this task. (3) Pairs will work on "Some Problems from 1.8". (4) We'll check out this "fencing problem" and finish this for HW .
10/11/23 - (1) We'll find the derivative of an absolute value function. (2) We'll check on solutions to "13ish" Problems on Differentiation together. (3) Groups will continue to fight through these limits questions after hearing about notation for limits "from the left" and "from the right". (4) We'll discuss some of the limits from today's work. (5) Spiral Task #1 (6) HW: "Further Practice on Differentiation and the Limit Definition"(solutions).
10/6/23 - (1) One "recognition" problem to start. (2) Groups will discuss section 1.8; #'s 13,14,25,27ab,29,38,41,42,63-67,69,70 and perhaps share some solutions with others. (3) Solo check-in on symbolic differentiation. (4) Groups will look into these limits questions...for a short time....to be continued. (5) "13ish" Problems on Differentiation
10/4/23 - (0) Two quick power rule problems to start.... (1) We'll work through a couple of "limit definition" problems (one with radicals...one with fractions) ...and may have to "recognize" one. The term "conjugate" popped up in our work. (2) We'll discuss how to graphically check out resulting values for a couple limit definition set-ups. (3) HW will be collected. (4) HW: section 1.8; #'s 13,14,25,27ab,29,38,41,42,63-67,69,70.
10/2/23 - (1) We'll start with a brief check-in on symbolic differentiation/antidifferentiation with transformations (and may come up with challenges for others. (2) We'll chat about the definition of the derivative as the limit of a difference quotient. Here are videos with more examples of using the limit definition. Video 1 / Video 2 / Video 3 / Video 4 (3) We'll sum up the "power rule". (4) HW: this task that reviews the limit definition of the derivative. (5) What's an NRT? (6) We'll check in on "Basics You Should Know" (and complete the ones we didn't have to do using the power rule).
9/28/23 - (1) We'll start by trying to find some antiderivatives and also checking in on solutions to the HW (we'll also check on "More Calc Things to Solidify".) (2) Pairs will work on "Texty Task" (collected). (3) Individuals completed or at least started "Testing & More with Derivatives". (4) What's an NRT? (5) HW: "Basics You Should Know" (you do not need to find the derivatives for 2,9,10,14,15).
Brief solo task on connections between functions and their derivatives. (4) Here are some possible topics. "Testing 1,2,3".
9/26/23 - (1) We'll begin with a couple of differentiation problems involving exponentials/logarithms. (2) Groups will discuss the HW from section 1.8; #'s 3,6,8,10,15-24,35-37,47-51...and may present a problem or two. #'s 8 and 49 seemed to get a lot of attention... (3) We'll work in class on "More Calc Things to Solidify". (4) HW: "Finding Derivative Equations with Transformations" (solutions).
9/22/23 - (1) Starter problems on writing derivative AND antiderivative equations (and maybe one speed limit law problem). (2) We'll check in on this problem set . (3) We will sum up derivatives of exponential and logarithmic functions. (4) We'll complete a graded task on numerous recent topics. (5) HW: section 1.8; #'s 3,6,8,10,15-24,35-37,47-51
9/20/23 - (1) Starter problems on equations of derivatives involving transformations ...and then we'll continue with one of the last problems from this set of slides (2) We'll tackle a graded task. (3) These problems will be collected. Here are some solutions. (4) (4) We'll meet up to complete this task on summing up derivative relationships (SOLUTIONS). (5) HW: Work on this problem set ...but will skip the section on ln(x) that you see on the digital copy only.
9/18/23 - (1) We'll start with a review problem on finding estimates for derivative values...and how we could use shortcuts in our GDC's to find slopes and graph derivatives. (2) We'll run through "Just a Task" together. (3) We'll discuss how transformations affect derivatives of known functions. (4) We'll begin to tackle one of the last problems from this set of slides....we only started to graph the derivative. (6) HW: these problems.
9/14/23 - (1) We'll begin by looking at the connections between f and f''. (2) Groups will work on some problems from 1.6 & 1.7. (and we'll hear about some of those from an old person). (3) We'll work on a follow-up to questions folks had about 1.6/1.7 and will share solutions. (4) We'll address questions from "Basics of Derivatives" and finish it (Here are some solutions). (5) HW: "Just a Task".
9/12/23 - (0) We'll work on a quick, individual derivatvie-graphing task. (1) We'll work on a board problem on tangents...and another where we graph the derivative of y=ln(x) with precision with the help of the technology. (2) We'll discuss more of this set of slides. n (3) We will solidify the derivatives of the functions: sin(x), cos(x), mx+b, ln(x), e^x. (4) We will discuss a few ideas from section 1.4 & 1.5. (5) We'll start on "Basics of Derivatives" (Here are some solutions) (7) HW: "Basics of Derivatives" Complete #'s 1-12, 15 only.
Here are some video solutions to some of the textbook problems from 1.4-1.7:
9/8/23 - (1) We will look at some derivatives numerically using these graphs. (2) We'll tackle a board problem on tangent lines. (3) We will collaborate for a graphing task. (4) We'll collect HW questions from 1.4 and 1.5. (5) We'll discuss more of this set of slides. (6) HW is to complete the 2nd set of textbook exercises handed out last class (this set ). Here is a link to the exercises.
9/6/23 - (1) We'll work on graphing a derivative and an antiderivative in groups. (2) Groups will discuss this problem-solving task and may work on remaining problems. Here is a video discussion of B&F. (3) We'll work through more from this set of slides. (4) HW is to complete the first stage of this set of textbook exercises .
9/1/23 - (0) We'll begin at boards with groups battling through a couple of problems from this set.....and should touch on at least a couple of HW problems (HW solutions). (1) We'll join Classroom (code above) if we didn't already and check out this Google site. (2) We'll work on this task on a "trip to school". (3) We'll start discussing some basic ideas related to derivatives using this set of slides (only got up to "average rate of change") (4) We'll work on graphing a derivative and an antiderivative in groups. (5) We'll be asked to work on some of this problem-solving task at home (up to problem F). (6) Do we all have graphing calculators?
8/30/23 - (0) We'll begin working in groups on some specific problems. (1) We'll check in, take initial questions, and then work on this graphing task. (2) We'll join Google Classroom and will later get a link to the HW due next time.