This may have been one of the top 10 best weeks I’ve had on KA in the last 6.5 years. The bad news is I didn’t remember as much calculus as I thought I would coming back to Calculus AB which I was very disappointed about, but the silver lining is that as I reviewed a lot of the questions, not only did most of it come back quickly, but I actually started to understand some of the concepts better than I did when I initially worked through them 100 years ago. I’m guessing I spent 12–15 hours working on KA this week which is the most amount of time I’ve spent studying in months. I ended up writing 70 pages of rough notes which I think might literally be the most I’ve ever written in a single week. Even though there were moments this week where I was super demoralized not remembering how to solve some of the calc questions, overall I was happy with what I was able to remember and, more importantly, really happy with the effort I put in. 😊
I started the week by getting rocked by the AB Calculus Course Challenge only getting 19/30 questions correct… 😒 After that, I had five unit tests I needed to redo. By the end of the week, I managed to make it through two of them and was SO close to making it through a third but fell just short. I ended up getting through the Course Challenge on Tuesday afternoon. Although I got 11 questions wrong, I only took screenshots of three of them because I didn’t want this post to end up being too long. Plus, I knew I’d get a chance to highlight/talk about the other questions I got wrong since I’d have to redo the unit tests they were from. But nonetheless, here are the three questions I took screenshots of from the Course Challenge:
AP College Calculus AB – Course Challenge
Question 1
This was the very first question I attempted on the Course Challenge this week, but I’d actually seen it at the end of last week but just didn’t get to it. When I saw it last Sunday, I used Symbolab to find out that the solution was (y2 – x2)/y3 but I didn’t understand how to get there myself. I watched a video on implicit differentiation on Monday and remembered the technique, but I couldn’t figure out how to get past at (y – x*dy/dx)/y2. I couldn’t figure out that I needed to substitute x/y in for dy/dx. After I looked at KA’s solution and saw that’s what I was supposed to do, I was able to solve it on my own, but clearly I cheated to solve this. (And the worst part is that I really have a clue as to what’s going on with implicit differentiation and can’t visualize how it works. 😞)
Question 2
I wasn’t really sure what to do on this question so I tried to solve it with a double integral and got it wrong. I wasn’t sure what to put in the integrand so that was the main reason I tried to use a double integral, but in my mind it “should” have worked. Looking at KA’s answer, the process was much simpler. You just use πr2 as the integrand but go π(r2 – r1)2 and convert y = 2(x – 3)1/2 to x = (y)2/4 + 3 as r2.
Question 3
I’ll let my written speak for themselves here, but one thing I will say is that I got this question wrong because, although I did everything correct, I forgot to divide my solution by 2 because it’s a semi-circle and not a full circle. 😡
After finishing off the Course Challenge, on Wednesday I got started on the first unit test I needed to redo which was from Unit 3, Composite, Implicit, and Inverse Functions. I actually managed to finish it off that day in around 2 hours. It wasn’t too hard but I did have to look up a derivatives of some trig functions like arctan(x), arcsin(x), etc. The test was really good practice reviewing trig, derivatives, and even some tricky algebra that I was rusty on, but I only ended up taking screenshots of one question:
AP College Calculus AB – Unit 3 – Unit Test – Composite, Implicit, and Inverse Functions
Question 4
I was able to do all the calculus and algebra on this on my first attempt without cheating which I was pretty happy about. I didn’t think this question was that hard, but it was a relief working through this question and reminding myself that even though I got rocked by the Course Challenge, I’ve at least managed to learn some math over the last 6.5 years. 😮💨
The next unit test I had to do was from Unit 4, Contextual Applications of Differentiation. It took me two days to get through, starting it on Thursday and finishing it off on Friday afternoon. It took me about 10 attempts to get through mainly because the phrasing in SO many of the questions was hard to understand. (As a side note, this is always the worst part of KA — when I can do the alg/trig/calc but I have no clue what the question is asking me to do. 🤬) I only took screenshots of a few questions, but here they are:
AP College Calculus AB – Unit 4 – Unit Test – Contextual Applications of Differentiation
Question 5
I got this question correct but only because I’d attempted the exact same type of question five minutes before this one and got it wrong. 😒 It’s not really “hard” (as in the calc/alg isn’t too hard) but I find it hard work through the process of these questions step by step, and also find it hard to understand what the question is even asking me to do.
Question 6
Most of the questions on this unit test looked like this where you had to put the measurements in terms of ‘t’ (like b = b(t)), then take the derivative of the object’s formula and input the given values at t0. I got a bunch of questions like this wrong on the Course Challenge but they’re not actually that hard, I just didn’t remember how to solve them at the time.
I got started on the third unit test from Unit 5, Applying Derivatives to Analyze Functions, on Saturday. Overall my attempts at the test went well, usually getting me close to 50% of the way through the 18 questions before getting one wrong, and by Sunday I made it to the 14th question but then made a careless mistake and decided to call it there for the week. Most of the questions were fairly easy, but a few of them I found quite difficult. Here are two questions from the test:
AP College Calculus AB – Unit 5 – Unit Test – Applying Derivatives to Analyze Functions
Question 7
This was the very first question I attempted on the unit test and had no clue what to do to solve it. I couldn’t even figure out how to setup the equation for R(x). 😔 When I looked at KA’s solution, the equation for R(x) made sense, but I didn’t understand what “critical points” were so I watched three of the recommended videos which helped me remember. Critical points are where the derivative equals 0 and they indicate a minimum or maximum value of the OG function, R(x) (i.e. they tell you the minimum/maximum area of R(x) based on the length * width of the rectangle within f(x)). Also, the vids I watched helped by making it clear that these types of equations, if in ‘x’ and ‘y’, need to be rewritten in terms of only one variable (which most often would likely be ‘x’).
Question 8
I’ll admit that I used Desmos to double check my answer for this question but only after I’d already got to the correct solution. I figured out that the only critical point was x = 0, but since g’’(x) was concave down at x = –1, then the function would have one of those weird plateau things at x = 0 and that g(–2) would be the lowest value. Actually, just to be extra clear, here’s a screenshot of the function from Desmos that shows what I’m talking about when I say “one those weird plateau things”:
And that was “it” for this week, although IMO “it” was actually quite a lot. Like I said, I’m really happy with how much work I was able to get done this week and am hoping to keep that momentum going forward heading into this coming week. Part of why I worked so hard this past week was because I decided that instead of starting the English section of KA after I’m done Math, I’m going to start the “Computing” section and work through all those courses. I decided to do this because 1) it will teach me a skill that I think I might be able to practically apply to a new job/career if need be, and 2) (the main reason) I could potentially learn how to code a program for CodaKaizen. I watched a handful videos on YT on how to start learning how to program and how long it takes to become half decent at it, and those vids made me pretty optimistic and interested about going for it. I also started watching a lecture series from Harvard called CS50 which has been really interesting, so I’m that much more excited to get through the Math section of KA so I can attempt to teach myself how to program! So, as always, fingers crossed I have a productive week so I can FINALLY get through it! 🤞🏼