Ok, so I’m not progressing as quickly as I had hoped BUT, even still, I’m surprisingly happy with the progress that I’ve been making. This week I did the course test of Algebra 2 twice and ended off with a 90% (27/30 questions correct). When I do the unit tests, I always make sure to get 100% before moving on but when it comes to the course tests I’ve always been a bit more lenient. (I’ve never moved ahead with less than a 90%, however!)  Though I didn’t get started on the next course, Trigonometry, I’m quite pleased that I’ve not only made it through Algebra 2 but that for the most part I truly understand the material. I feel like I’ve accomplished a lot since I first started and come quite a long way which I must say is a nice feeling.

No new news to report on the Corona virus. Social isolation is getting more boring by the day. It sounds like businesses may be allowed to open up soon but, in my view, it all seems like a complete experiment which we don’t know how things will turn out. I feel like opening things up early could lead to a huge second wave of the virus. week by week I continue to feel less stressed and anxious about the entire situation which has certainly been relieving.

I started this week off by finishing the unit Rational Functions. I was happy that it only took me one try this week to get all 9 questions correct. Though I felt more confident this week, I was nervous on all 9 questions entering my answer. Even though it was difficult, I’m happy that this unit helped to give me a much better feel for how to factor polynomials, work with different degree terms, cancel common factors, expand polynomials, etc.

I scored 26/30 on my first attempt at the course test which I thought was a decent score. I realized afterward that the questions I got wrong bumped down my score of the units they pertained to to indicate what parts of the course I needed more practice with. I went back and redid those sections ( which included redoing the three unit tests), scored 100% on everything, and then retook the course test. Redoing these sections is what took up the majority of my time this week, but in doing so I felt much more confident with those questions I got wrong. Often when I revisit a subject the concepts seem easier to understand the second time around which is something that’s happened on other occasions. Somehow, taking time off from a subject and then coming back to it later seems to allow the concepts to settle in my mind and become easier to wrap my head around the next time.

In a way, I kind of cheated on both attempts at the course test. I used Desmos (the graphing-calculator website) to double check my answers before entering them. Often what would happen was I’d be given a question that would ask me to come up with an equation, I’d come up with the equation, and then enter it into Desmos to see if the graph it produced looked right and made sense. I’m fairly certain, however, that after inputting any of the equations I came up with into Desmos I didn’t have to make any alterations to any of them, meaning I had the right answer before double checking. On the glass-half-full side, using Desmos actually helped me to more intuitively understand how certain equations work and how eliminating/changing the variables alters the graph. 10/10 would recommend using Desmos. (*Thumbs up emoji*)

I only managed to get through some of the questions using what I consider in my mind as ‘brute force’, not by fully understanding the formulas. For example, one question asked me to find the sum of the terms in a geometric series using the formula S(n) = a(1-r^2)/(1-r). I could recall the formula but didn’t have any idea how or why it worked. I managed to get the correct answer through trial and error by inputting the data into the formula and, through the process of elimination, coming to what I realized had to be the right answer. I was disappointed that I didn’t fully understand the formula but, nonetheless, I was happy that I understood it well enough to figure out the right answer even if I didn’t go through it the way it was intended.

Of the 3 questions I got wrong in my second attempt at the course test, in my opinion I “should” have only got one of them wrong.

1. The first question I got wrong asked me to come up with an equation for an inequality from the information given to me in a word problem. I essentially came up with the right equation except I used the wrong sign. I used less-than and should have used greater-or-equal-than which, I admit, is a fairly important mistake to have made but, really, I got the harder part of the question correct which was figuring out the equation itself. If I had taken 30 more seconds to think it through properly I’m sure I would have used the correct sign.
2. The second question I got wrong I can admit that I didn’t do it properly or, at the least, I didn’t think through it thoroughly enough. I was asked to find the solutions to a semi-difficult polynomial equation. It took me about 8-10 steps which I correctly did and which gave me the right solutions, however I forgot to input both solutions into the original equation to check if either solution was extraneous. One of the solutions was in fact extraneous so I got the question wrong by marking that value as a valid solution to the equation.
3. The third question I got wrong was B.S. in my opinion. The question asked me to change the expression 4Log(3) into the form Log(c). I knew that in order to do change it I had to turn the 4 of the original expression into an exponent on the 3 of the second expression which I did and left as Log(3^4) but didn’t realize I was supposed to expand the exponent and turn it into Log(81). I suppose I should have realized that based on it saying to change it into Log(c) and not Log(a^b), but considering that 3^4 = 81 I think that should have counted.

Although I had a bit of a hard time remembering a few of the concepts throughout the course test, the biggest thing stood out to me this week was how happy I was that I remembered the majority of the material. I would say ~70% of what came up on the test I knew the answer to, or knew how to get the answer, off the top of my head. When I said at the beginning of this post that I am happy with my progress so far, this is exactly what I was talking about. Of the ~70% of the material that I knew without having to think about, I’m sure I knew none of it before I started KA. I know and understand so much more about math now than I did when I first started which makes me incredibly happy to think about.

I’m FINALLY going to be starting the unit Trigonometry (2100/2800 M.P.) next week which I’m surprisingly 75% of the way through already. Being that trigonometric functions gave me so much trouble in the last unit, I still plan on going through the sections that I’ve already completed to review and make sure I fully understand them. Like I said earlier, when I come back to certain subjects after taking time off from them they often seem easier to understand and I have my fingers crossed that that’s the case with trigonometry. I was hoping to get through this unit by the end of May but, considering how long the last unit took me, I think aiming to get through it by the end of June is more realistic so I’ve decided to make that my goal.

I’m just now realizing the importance of setting your expectations; if you set the bar to high, you set yourself up to be frustrated and disappointed but if you set the bar to low, you reduce your motivation and urgency to push forward. Turns out I’m out here learning more than just math.