It was a pitiful week for me on KA. I didn’t pass the Integration and Accumulation of Change unit test and only spent around 4 hours trying. Just like the past few weeks, I’d usually get around 15 questions into it and then would make a careless mistake or come up against some Sigma notation question that I’d get wrong and have to start over. Just like last week, when that happened I’d usually just give up for the day. It’s frustrating because most of the questions are simple and straightforward, but then I’ll get a question that completely befuddles and discombobulates me. I know I can pass this stupid test but am struggling. 😓
This is going to be a short post since I’m basically just rehashing everything I’ve talked about over the past few weeks. I took screenshots of six questions, so here they are:
Calculus AB – Unit 6 – Integration and Accumulation of Change – Unit Test
Question 1
I got this question correct but only because I used Symbolab (which is annoying because it’s not even that hard). I initially didn’t realize that (16 – x2) should be u and that the outer function would just be (x)–1/2. Based on the integrand, I assumed it would be some integral of the derivative of arcsin(x) or ln(x). Turns out I was wrong. When I realized how to do it properly, it was very easy to understand.
Question 2
This question wasn’t too difficult but I was still happy that I figured it out quickly and on my first try without cheating. I’d made a few careless mistakes leading up to this question so my faith in myself was somewhat restored after getting this one correct.
Question 3
You can see that I clearly did not solve this question the same way the KA did. I did my own funky math and then obviously used Symbolab to check my answer and, to my surprise<, I’d gotten the correct solution.
Also, a few weeks ago I did a question just like this one and KA’s answered recommended watching the same video then as they did in their answer this time. I watched that video and did not understand what Sal was saying. 🙁
Question 4
I was devastated after getting this question wrong since, as you can see, I was 20 questions into the test. The comment I wrote in my notes after getting this question wrong was, “I do not fu#%ing understand Sigma notation.” I think I understand the gist of what the notation is saying — that there’s an infinite number of infinitesimally thin lines within the bounds of a given area, and that the sum of those lines equals the area between the bounds, curve, and x-axis — but I definitely don’t intuitively understand the notation in the actual expression or what it represents. ☹️
Question 5
My notes above are clearly wrong but I thought I’d add them just to fill out this post and also to show my rough work and my thinking even though it was wrong. I actually worked through this same type of question last week writing out the integral of d/dx [(1/k) * arctan((x + h) / k)] but I forgot the formula when answering this question. I’m guessing that WHEN I pass this unit test (😤) it will be because I have formulas for questions like this memorized, not because I intuitively understand the math. 😒
Question 6
I got this question wrong so figured I’d add it here to talk about it. I didn’t take enough time to think it through and thought the solution was option b, “f in increasing”. The good news is that I can visualize the concept that f(t) represents the slope of g(x) and since f(t) is positive, g(x) has a positive slope (a.k.a. it’s increasing). Even though I got this question wrong, I’m happy that I intuitively understand what’s going on — so I’ve got that going for me which is nice.
And that’s all I have for this week. I feel like I could literally copy the ending of my last few posts and paste them here and they’d make sense. I’m getting pretty tired of saying that I need to get through this unit test, so hopefully this will be the last time. **ahem** I NEED TO GET THROUGH THIS UNIT TEST!! 😭 I’m praying to all the Math gods that will listen that this will be the week. 🙏🏼 🙏🏼 🙏🏼
As always… fingers crossed. 🤞🏼