To kick off my SEVENTH YEAR of KA (…😳…), I had a pretty mid week. I got through two unit tests and an exercise which sounds pretty good, but none of the questions I worked through were really all that difficult, and I also used Desmos a bunch of times to check my answers before submitting them (i.e. I sort of cheated). Nonetheless, I’m pretty happy with how the week went overall. I’m pretty sure I studied for at least five hours, which is more than what I’ve done for the past few weeks, so I’ve got that going for me which is nice. I started and finished the Trigonometry unit this week which I’m happy about, although I only had to do one exercise before doing the unit test so it really wasn’t that difficult. Even still, I’m glad to have gotten through it and am now only one unit away from finishing off Alg. 2! The finish line is finally in sight. 😮‍💨 (Seven years later…)

Here are a bunch of questions from the unit tests and the exercise I got through this week:

Unit 10 – Equations – Unit Test

Question 1

This is what I mean when I said that the questions were all pretty easy. It took me about a minute to realize that when it said log₃(x) = 1.5, what the question was asking was, at y = 1.5, what was x equal to? Looking at where y = 1.5, it was clear that the function was pretty much right at x = 5. Even though this question was easy, it had been a while since I’d done log questions, in general, and I find them pretty easy/satisfying, so it was nice to get back to them.

Question 2

I put the given equation from this question into Desmos to solve it, so I essentially cheated to figure out the correct solution. For some reason, when I was going the algebra I got the equation down to 0 = x² + 3x + 2 but then couldn’t factor it to 0 = (x + 1)(x + 2) and only realized that would be the factorization after seeing KA’s answer. I also likely would have forgot to check to see if at x = -2 the OG equation would be undefined (which it would be), so I probably would have also gotten this question wrong for that reason if I hadn’t used Desmos. 😒 

(That said, I know I’m just rusty with this stuff and after seeing KA’s solution, I understand how it all works.)

Question 3

This was a question I didn’t cheat on and was a tiny bit proud of myself for solving properly from my own memory. I was happy I remembered the quadratic equation and knew how/when to use it. Honestly, this math isn’t too difficult—I’m guessing this is like grade 8 or 9—but still, it’s nice that I can do it without much difficulty.

Question 4

I did cheat with Desmos to solve this question. 😔 I entered the equation into Desmos which stated that z = 3/2 but I still didn’t understand. I did the algebra myself and got to z = 3/2 but still didn’t understand if that was the answer. I wasn’t sure what to do, so I just entered z = 3/2 and got it correct even though I didn’t know what was going on. Looking at KA’s answer, I understand now why if you enter z = 3/2 into the equation you’re left with an inequality, meaning z = 3/2 is what’s called an extraneous solution. Again, I feel like I’m just rusty with this type of math and that it shouldn’t take me too long to remember how to do it if it comes up again in the next few exercises/unit tests.

Question 5

I ended up getting this question correct but had no idea what I was doing. I remembered that to find the inverse of this type of function you replace the x’s with y’s and then use algebra to rearrange the equation to solve for y. As you can see in my notes, I did exactly that but wasn’t confident that I had done it properly. I entered both the OG function and my solution to what I thought the inverse function would be into Desmos to see what the functions looked like and still wasn’t sure if I had done it correctly. I entered my solution anyways and it turned out that I had it correct. (Which was a relief since this was the final question I needed to get correct to get through the test! 😮‍💨)

Unit 11 – Trigonometry

Exercise 1 – Interpret Trigonometric Graphs in Context

I think I got through this exercise in about 10 minutes. The questions were all very easy and didn’t require me to write out any math of my own, I just needed to interpret what the function was saying/remember the different parts of a sinusoidal function. (Side note – In case you were wondering, I hate that word “sinusoidal”.) Anyways, here are two questions which I’m not going to comment on since they’re pretty simple:

Question 6

Question 7

Unit 11 – Trigonometry – Unit Test

I started this unit test on Friday and finished it on Saturday. Although it took me two days, I got through it on my first attempt. 🧨

Question 8

This question was easy since I have the ratio of the side lengths of a 30-60-90 triangle memorized. Nonetheless, it’s SUPER satisfying for me to know how to solve these problems (and trig problems, in general) since I vividly remember struggling with trig for so long back in the day. 😤

Question 9

There was some more algebra I did on a page not shown in my notes above to find the solution to the equation here. I also did a little trial-and-error entering the equation into Desmos to figure out and confirm my solution before submitting it. But I pretty much had 90% of it figured out before entering it into Desmos, it was just the period of the function that I was a bit confused on.

Question 10

This question took me longer than it should have to solve. I was struggling to make sense of how to solve it but then realized that (1 rad)/2π = x°/360°. After that I just did some algebra to set x° = ((1 rad) * 360°/ 2π) * (257π/360) leaving me with x = 128.5°.

Question 11

This looks like a pretty straight forward pythag’s theorem question, and it is, but I hadn’t seen a question like this where the sides in question (adj = -13 and hyp = 30) were such large values that I didn’t trust myself that I was doing it correctly. After looking at my answer for a few minutes, it seemed like I had it correct even though it was a large fraction so I went with it and it turned out my answer was correct because I’m a gangster.

Question 12

This question was hard for me because I couldn’t figure out how to stretch the period of the function. I used Desmos and did a bunch of trial and error and eventually figured it out. I eventually thought about it as:

• Period = 2π = x
  • (If I was to stretch the period, x, to 3π/2 then I can say:)
• x = 2π = 3π/2
  • x = 2π * 2/3π
  • x = 4/3

I’m not sure if that makes sense, but it made enough sense to me that I was able to figure it out and get the question correct. (After about 10 minutes of trial and error…)

Question 13

As you can see, I used Desmos to confirm my solution before submitting it. I’m not sure if using Desmos in this question (or any of the questions for that matter) is actually cheating. I had to understand the question and trig well enough to at least enter what I thought the solution was into Desmos in the first place, PLUS maybe if I was given this test by an evaluator, they might have let me use a graphing calculator in the first place (!), but I still feel like I sort of cheated. But also, like I said earlier, I’m just rusty and I was at least able to understand all of KA’s solutions when I looked at them afterwards. 🤷🏻‍♂️

And that was it for this week. For the first time in a while, I’d say it wasn’t such a terrible week and was actually fairly productive. AND, I forgot to mention, that my week didn’t even get started until Thursday as I was away from Monday to Wednesday. So considering that as well, I’d say it was a pretty solid start to Year 7. I only have one more unit left to get through in Algebra 2, but there are three exercises I need to in it before I can redo the unit test. I think I’ll have a lot of free time this week—and potentially a LOT more free time, going forward, which I alluded to in my last two posts, but I still don’t know the final details of what’s going on yet so I’m not going to bother sharing what’s happening right now—so I think I should be able to start making some serious progress soon. If that’s the case, I think I’m probably only two or three months away from finishing this all off. As always fingers crossed I can make it happen sooner rather than later! 🤞🏼