I’m getting pretty sick of saying this, but I didn’t make very much progress working through KA this week. I worked through the unit test for Applications of Integrals two times but still didn’t pass it. I just realized, however, that I ended up writing 61 pages of notes this week (😳) so, even though I didn’t make progress towards moving on to the next unit, I got a TON of practice in working on solving integral questions, which also gave me a lot of practice with algebra and arithmetic. I’m annoyed that I haven’t gotten as far as I feel like I should have by this point but am still happy that I genuinely feel like I’m getting better at math. 🤷🏻♂️
A few little notes before I get going on this blog post – Since mid June I’ve been on my ‘summer-schedule’, as in I start work at 9am and finish at 3:00pm instead of starting around 3:30pm and finishing at 8:00pm. In order to have enough time to study math, throughout the summer I’d wake up between 2:00-3:00am, but now that we’ve finished our summer camps, I’ll be back to my normal schedule which means I’ll have much more time in the mornings to study math. I’m REALLY looking forward to have my mornings/early afternoons back and think it will make a big difference in me making progress though KA.
There are two not so positive things that slowed me down this week. I’ve been having pretty terrible allergies the last 2 weeks which are SO annoying and make it a lot harder to focus on KA when I’m constantly blowing my nose and have low energy from taking antihistamines in the morning. 🤬 My allergies typically get better midway through September so I’m hoping that by the end of next week they should be much less noticeable. The other bad thing is that I tore the tendon in the top my right, ring finger. I have a splint on it now which I’ll need to keep on for ~6-8 weeks and hopefully (🤞🏼) the tendon will reattach itself by then. It doesn’t effect me too much but it’s a bit hard to write and type. I’m sure as the days go on I’ll get better both at writing and typing the more I get used to having the splint on. I feel fine about it now but I spent Thursday to Sunday pretty stressed out about how it will effect my work which is partly why I didn’t get as much done on KA as I otherwise would have.
Back to KA – I was 8 questions through the unit test when I began the week on Tuesday. I’d already gotten 2 questions wrong at that point so I knew I was going to have to redo the test. I ended up getting through the remaining 12 questions on Tuesday but I think I got a few more wrong. (I can’t actually remember.) Here’s a question I worked through from the test on Tuesday:
Question 1
Before this week I thought I had a pretty good handle on how to use vol = B * W * H in these types of questions and, for example, would think of them as vol = a∫b πr2 dx or dy. I always thought of the Base as being a∫b either being measured along the x-axis, using dx, or along the y-axis, using dy. For some reason, I was having a hard time with this concept especially when I worked through the following exercise which dealt with the washer-method. I kept getting confused as to whether the integral should be calculated in terms of x or in terms of y. By the end of the week I was able to get it sorted out in my mind and remembered that the area of each ‘disc’, ‘rectangle’ or ‘square’ would always be perpendicular to which ever axis I should be using as the Base.
Once I got through the unit test on Tuesday, I had to go back and work through an exercise titled Volume: Washer Method (Revolving Around Other Axes). Here’s a question I worked through:
Question 2
As you can see from this question, there are a number of steps to go through before you reach the solution. That’s why I find these questions so difficult, because I have to make sure I take my time and not make any mistakes by rushing through any step. For the past few weeks, I rarely used my calculator or Desmos for these questions and would do all the arithmetic and algebra in my notes, but recently I’ve been double checking all my work with both.
I took me Wednesday and Thursday to get through that exercise so I didn’t restart the unit test until Friday. I got through all 20 questions on the unit test by the end of Saturday which I was happy about but got 2 questions wrong so I’m going to need to redo the test once again for the millionth time… Here’s one question I worked through on my second attempt at the test this week:
Question 3
One random side note from this question is that I’ve begun to cross out terms inside of the brackets in the same way that Sal does which you can see in the 2nd last step of my notes. It’s a weirdly satisfying way of working through the arithmetic and I think, after I continue to use this technique, it’ll make things easier for me and will lead to me making less mistakes.
As I’ve said for the past few weeks, I REALLY hope I can get through the Applications of Integrals (1,960/2,000 M.P.) unit test this coming week. I luckily don’t need to redo any exercises before getting started on it this week so I think if I go slowly through each question, I might be able to pass it by Tuesday. I’m happy and confident that I’m getting a much stronger grasp on integrals and calculating them, but I’m SOOO ready to move on. I’m praying to the math gods that this will be the last week working through this test! 🙏🏼