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    Calculus
     
    Course Overview
    Calculus is a mathematical subject that focuses on the study of functions, limits, derivaties, and integrals. Both Isaac Newton and Gottfried Leibniz are credited with the invention of Calculus. Some interesting topics covered in the course include maxima and minima, related rates, numerical integration, areas under curves, and solids of revolutions.
     
     
    Course Syllabus
     
    Upcoming Assignments/Assessments
    Hey guys, hope you're all doing well! In order to keep it easier and more organized for you I've decided to just use this website instead of reedcalc. Please continue to check here for all future updates! Listed directly below you can find our game plan for each week leading up to the AP test. Under that you'll be able to find all of the stuff I've uploaded to reedcalc over the last few weeks. At the very bottom you can also find a section with updated information regarding the test and practice problems and videos provided by College Board. I highly recommend checking these out - they are an excellent resource to help prepare for the AP test! I sincerely miss seeing all of you. Please feel free to contact me by email if you have any questions or concerns whatsoever. Stay safe and healthy, and may the force be with you!

     
    Game Plan for This Week
    5/25-5/29 – Hi guys, welcome to your last week of calc! Congratulations on making it to the end! Thank you so much for all of the awesome work you’ve put in – it’s been a fun time getting to experience this unique method of learning with all of you. As I mentioned before, for our final lesson we’re going to check out an integration technique called partial fractions! My YouTube lesson is here (link) and you can grab a copy of the notes here (link). When you finish you can find your final assignment of the year here (link). You can also find a copy of the solutions for it here (link), as well the answers to last week’s assignment here (link). You do not need to email me a copy of your own solutions this week unless you want me to provide you with feedback. I also put together a table of contents for your binder so you can reference it easily when you go off to college - you can find that here (link). And finally, check out my small congratulations letter here (link)! It’s been an absolute blast getting to know you these last two years and I am very proud of all of you! I wish you all the absolute best and hope you keep in touch! May the force be with you!
     
    Update: Don't forget to return your graphing calculators when you come up to return your books! Please physically give them to Mr. Bressi, Mr. Motuk, or Mr. Spotts. Thanks!
     
    5/18-5/22 – Hey ladies and gents, welcome to your second to last week of school! Good times! Thank you so much for all of your continued work and effort in the class – only two weeks to go! This week we’re going to continue our exploration of integration by parts and look at a few more intriguing examples of the technique. You can find my YouTube lesson here (link) and a copy of the notes in pdf form here (link). When you finish going through the lesson do Integration by Parts Assignment 2 (link) and send me a picture of your work before Sunday midnight. Also, if you had any trouble with last week’s assignment you can find a copy of my answer key here (link). If you have any questions, you know where to find me! Stay safe and healthy!
     
    5/11-5/15 – Update: Hi guys, welcome to the last tiny bit of the course! Over these remaining few weeks I’m going to touch on the last couple topics of the course, which are integration by parts and partial fractions. Should be a nice way to finish the year! Anyway, I’ve recorded a YouTube lesson going over this week’s topic: you can find the video here (link) and a copy of the notes here (link). You don’t need to recopy the notes if you don’t want to, but it would probably be beneficial to work through the problems yourself as you go through the video. Once you go through the lesson complete Integration by Parts Assignment 1 (link). You can find the solutions at the bottom. Once you finish, send me a picture of your answers and supporting work before midnight Sunday and I’ll mark down that you’re engaged. If you have any questions or concerns, my email is always open. Hope you have a great week - only a couple more left in the school year! Stay safe and healthy!
     
    5/4-5/8 – Hey guys, happy May! If you’re reading this on Monday, May the 4th be with you (haha)! Before I give you our game plan for this week, I wanted to take a moment to thank you for the excellent work you guys have been putting in. I know it’s definitely different working on an online platform like this, but it’s really awesome to see all the effort you’re putting in. Thank you! Anyway, for this week’s game plan we are going to continue on with our prep for the AP test. It’s hard to believe that it’s only a week away! If you haven’t checked your email recently, please do, I sent around some really important information for you to read over and a link to a video you should definitely watch if you’re taking the exam. I’ll be sending around some tips and pointers later this week so be on the lookout for that! For our actual assigned work for the week, once again I’ve gone through AP Classroom and picked out 5 practice free response questions. You can find them at the bottom of this post. Same procedures as last week: if you want them scored as an AP reader, I need them by midnight of the day assigned, otherwise they will all be due no later than 11:45 Sunday. Please make sure you continue to put in the time and effort so I can mark down your level of engagement for the week. Also, don’t forget to check out the AP Live practice videos linked at the bottom of this page. This week they are holding two mock exams on Monday and Wednesday and are going over the solutions on Tuesday and Thursday. I’m sure these will be an invaluable resource for prepping for this year’s test, so be sure to check them out! As always, feel free to email me with any questions or concerns! Stay safe and healthy!
     
    As an added bonus, I also put together a small study guide going over the major topics for this year’s test. It should be a nice little resource you can use in addition to your own preparations. You can find the link to it here (link). Please note that topics pertaining to volumes of revolutions or volumes of cross-sections unfortunately are not being assessed on this year’s AP exam, so you can ignore those sections!
    • Monday's Problem (just #1, not #2): (link) (solution) Note: Unfortunately I didn't get to cover the information in part d before we left. Check out this video for a quick overview (link). Write down the formula and keep it handy - it will show up again in Wednesday's problem!
    • Tuesday's Problem (just #1, not #2): (link) (solution)
    • Wednesday's Problem: (link) (solution) Note: The final part in this problem is seeing if you can work backwards from the formula used in Monday's!
    • Thursday's Problem (just #1, not #2): (link) (solution)
    • Friday's Problem (just #2, you already did #1): (link) (solution)

    UPDATE: Please check your email for important info about the exam and some additional tips/tricks! If you didn't get the email for whatever reason, you can find a pdf doc of it here (link).

    Note: If you would like to try #2 in Monday's, Tuesday's, and Thursday's problems you are more than welcome but it is not required. However, if you are interested in seeing how you would have scored on those I need them submitted along with that day's problem (AP Classroom requires me to score both parts at the same time). Even if you don't want them scored, I would still check them out at some point - there's some really fun topics in there!

    4/27-5/1 - Hi guys, May is almost here! This week we’ll be kicking off our routine of daily free response review. I’ve assigned five different free response questions for this week on AP Classroom. You can find a link to each individual problem directly below this post. If you want to have these scored as an actual AP reader would I need them submitted by midnight of that day. I’ll score the questions the next morning and upload a video of me going through the problem as well. So, for example, Monday’s free response question would have to be submitted Monday night, and I’ll score your results Tuesday morning and upload the video Tuesday as well. Tuesday’s question would be submitted Tuesday night, and your scores and solution video will be available Wednesday. If you’re not taking the AP test or don’t want a practice AP score, then the five questions can be submitted at any time throughout the week and are due no later than 11:45 pm Sunday. Please make sure you are putting in the time and effort so I can mark down your level of engagement for the week. Remember each of these questions is designed to ideally be completed in about 15 minutes, so it might be helpful to try and time yourself as well. Also remember I am not scoring these as graded assignments – I am simply providing these to you for feedback purposes and will only be recording whether or not you are trying. Don’t forget it is of the utmost importance to keep watching those practice AP videos College Board is uploading to YouTube as well if you are taking the AP test. This week they are specifically covering free response style prompts, so that will be great additional practice! As always, feel free to email me with any questions or concerns! Stay safe and healthy!

    If you would like to try #2 in Thursday and Friday's problems you may but it is not required. Also, as a little bonus you can also find a short video detailing last week's solutions here: (link).

    Update: If you're submitting your problems early and are having trouble accessing your scores and feedback on AP Classroom, check your school email. I've sent around some directions on how to navigate the website. Should help!

    4/20-4/24 - Welcome to a brand new week and the start of our AP review! It's around this time in the year where we shift gears and focus on specifically preparing for the AP exam. You should definitely get in the daily routine of watching the College Board practice videos that are uploaded Monday through Friday. Last week they started reviewing key topics such as limits, derivative rules, and differentiation applications such as related rates. If you haven't watched any yet you should start with April 13th's video and continue from there (links are at the very bottom of this page). In the description of each video you can find additional practice problems - spend some time working through these and please email me with any questions. They usually upload an answer key to these problems a day or so later. While some of them may seem a little more challenging than what you're used to seeing, these are the style you can expect to encounter on the real AP test! Remember this year's test is open notebook and calculator allowed (but not necessary!), and that it only consists of two free response questions - one 25 minutes and the other 15 minutes. I'm also planning to work through free response questions with you but for now I want to wait until after our math department meeting this Tuesday morning. Once I get more information I'll update you and start my own review as well. Stay tuned...
     
    Update: Happy Tuesday! Exciting news - according to our math department meeting we have officially gotten the go-ahead to continue with new curriculum. We will be doing free response questions for the next few weeks to help prepare for the AP test. For this week we'll be doing 2 free response questions on AP Classroom (apclassroom.collegeboard.com), specifically Unit 1 Progress Check: FRQ Part A. I believe they will show up right when you log in, otherwise you can follow this link directly to the assignment: https://apclassroom.collegeboard.org/25/assessments/assignments/4818641. You can practice viewing these problems either on your computer or your phone. However, you will need to show your work on paper and upload them to the site probably as a picture file (you'll see what I mean when you go to the website). Since this is your first time working through problems like this, these two problems will be due Sunday night, but you can turn them in earlier if you'd like to. I will score these using the AP guidelines and provide you feedback as to how you would have done. Next Monday I will be uploading a video going over these in case you had any questions. My game plan for next week is to start working through and assigning free response questions daily to prep you for the test. I'll update you on any new information. Look forward to it, and don't forget to send me an email if you have any questions!
     
    4/13-4/17 - Hi guys, hope you had a pleasant spring break! This week we're going to focus on reviewing limits. Check out this website (link) for a quick brushup on the basic types of limits. It's also worth checking out this page on limits approaching infinity (link), as well as this page on one-sided limits (link). Try working out the practice problems on each of these pages as well as the extra problems located at the bottom of the pages. If you're feeling especially ambitious, I would encourage you to check out this site on L'Hopital's Rule (link), which deals with how to find limits when you get back indeterminate forms! L'Hopital's Rule is a topic you should know for the AP test! On that note, don't forget to check your school email as well as reedcalc and the videos linked at the bottom of the page for important info about the AP test! Next week we begin our free response review!
     
    4/6-4/10 - Hope you're all doing well! For this week's general review, check out the following articles reviewing the Intermediate Value Theorem (link), the Mean Value Theorem (link), and Rolle's Theorem (link). Then try some of the practice problems at the bottom of each page. Additional practice problems on the IVT and MVT can be found at this page (link) and this page (link). Don't forget to check your school email as well as the videos linked at the bottom of the page for important updates on the AP test!
     
    3/30-4/3 - Check out this article (link) reviewing Riemann sums and complete this worksheet (link). Remember to be careful choosing the y-values for the heights of your rectangles, and take note that we are not finding areas - we are approximating the integral with a Riemann sum! Other good topics to review are Riemann sums using the midpoint method (link) or trapezoidal method (link). Additional review for these two methods can be found at this website (link).
     
    Reed Calc Lessons
    Listed below are some of the additional topics we would have been covering over the past month had we been in school. These are simply migrating over from reedcalc just so you can access everything in one place. Remember, this is information that you should know for the AP test so take the time to watch the videos, look over the notes, and work through the enrichment problems. Answers are provided at the bottom of each assignment but please feel free to email me with any questions you may have!
     
    • Natural Log Derivatives & Integrals
      • Notes in pdf form: (link)
      • Youtube lesson on Natural Log Derivatives: (link)
      • Enrichment 1 for April 3: (link)
      • Youtube lesson on Natural Log Integrals: (link)
      • Enrichment 2 for April 5: (link)
    • Exponential Functions
      • Notes in pdf form: (link)
      • Youtube lesson on Exponential Function Derivatives: (link)
      • Enrichment 3 for April 7: (link)
      • Youtube lesson on Exponential Function Integrals: (link)
      • Enrichment 4 for April 9: (link)
    • L'Hopital's Rule
      • Notes in pdf form: (link)
      • Youtube lesson on L'Hopital's Rule: (link)
      • Enrichment 5 for April 13: (link)
    • Slope Fields
      • Notes in pdf form: (link)
      • Youtube lesson on Slope Fields: (link)
      • Enrichment 6 for April 15: (link)
    • Derivatives of Inverse Functions
      • Notes in pdf form: (link)
      • Youtube lesson on Derivatives of Inverse Functions: (link)
      • Enrichment 7 for April 17: (link)
    • Extra: Exponential Growth/Decay
      • Notes in pdf form: (link)
    • Extra: Inverse Trig Derivatives
      • Youtube video on Inverse Trig Derivatives: (link)
     
    Additional AP Practice 
    This year the AP test will be given as a 45-minute online test with just two free response questions (no multiple choice). The videos listed at the bottom of this page are provided by the College Board to help prepare students for the upcoming AP tests. These are topics that you should be familiar with if you are planning to take the AP test. I haven't gotten to some of these in class because of school being closed, but we definitely would have covered them by the time of the test on a normal schedule! In each video's description you can usually find a copy of the notes as well as additional review documents with excellent practice problems. As always, please feel free to email me with any questions that you may have while working through these lessons!
      
    College Board Practice Videos:
     
     
     

    Image retrieved from http://berto-meister.blogspot.com/