I’m happy to say that I finished the Parametric Equations, Polar Coordinates, and Vector-Valued Functions unit test this week AND made it through the sixth unit’s unit test in the Statistics and Probability course, Study Design! 🥳 After that, I got my butt kicked on the first few questions in the next unit test (the ninth unit in Statistics and Probability, Random Variables), so that was a bummer, but overall it was pretty good week. I’m pumped that I’m now finished Calculus AB and BC, and I’m really starting to feel like I’m on the homestretch! I’m guessing it will be at least a few months before I completely finish it all off, but I’m definitely feeling a bit of a motivation boost having gotten through two unit tests this week—something I don’t think I’ve done for months. To be fair, a lot of the questions this week were pretty easy, and there were a handful where I didn’t know what was going on but I was able to guess correctly, BUT it was still a pretty solid week, nonetheless, so I’m chalking it up as a win. 💪🏼😤

Here are four questions from the Parametric Equations, Polar Coordinates, and Vector-Valued Functions unit test:

Calculus BC – Unit 9 – Parametric Equations, Polar Coordinates, and Vector-Valued Functions – Unit Test

Question 1

I ended up getting this question wrong, screwing it up multiple ways. First of all, I didn’t work through my d²y/dx² = d/dt[y’/x’]/x’ equation properly. I was having a hard time with the exponent rules and algebra and was so caught up in the y’/x’ that I only solved that part of the equation first and submitted my answer as y’/x’ = 3(t)^1/2/2. 🤦🏻‍♂️ After I got it wrong, it took me two more times to work through it to get to the proper solution as I kept screwing up the exponent rules and derivatives. I was annoyed that I got it wrong, but it was good review.

Question 2

I’ve worked through this type of question a dozen or so times over the past few weeks so at this point I’ve memorized how to solve these questions, but I don’t know what’s going on with the implicit differentiation. ☹️ That is, I don’t know why d/dt[xy³] = (x * 3y² * y’) + (y³ * x’). I really don’t understand why the y’ and x’ show up in the derivative… 😒 But, nonetheless, solving this question was since I’d done it a million times in the past few weeks, and the calculus is pretty straightforward.

Question 3

I got this question wrong but think I could have gotten it correct. I initially thought I needed to expand (sin(6θ) + θ)(sin(θ)) and thought that doing so would give me sin²(6θ) + θsin(θ). I should probably know this by now, but it turns out that since there’s a 6 in sin(6θ), you can’t combine sin(θ) and sin(6θ) to get sin²(6θ) and just have to leave it as sin(θ)sin(6θ). Also, in my written notes above solving this question, I solved it was d/dθ[(sin(θ)sin(6θ) + θsin(θ)] but KA’s solution solved it simply as d/dθ[(sin(6θ) + θ)sin(θ)].

Question 4

I should have redone my notes for this question for this post but I’m too lazy. The good news is that I understand what’s going on with this question having to find the antiderivative of the velocity vector’s x- and y-functions which give you the functions for the particle’s displacement in the x- and y-directions. This is the type of question I got wrong at the end of last week, so I was definitely happy to know what I was doing working through it this week.

I ended up getting through the unit test on Thursday afternoon. I started it in the morning and spent around 1.5 hours working on it — I screwed up some questions a handful of times and had to keep restarting — and then restarted in the afternoon and got through all 14 questions in about 30 mins. The next day I moved onto the Study Design unit test in Statistics and probability:

Statistics and Probability – Unit 6 – Study Design – Unit Test

Question 5

This was the first question I worked on in the test. It was a very easy question, but I was glad that I was able to remember the terminology. 

Question 6

Again, this was another very easy question but. even still, I was happy that I remembered how it worked. As you can see, you go from left to right choosing each set of two digit numbers and skip the numbers outside of the given range.

Question 7

This was another easy question that just required a bit of algebra. You can see from KA’s solution that you just need to figure out how many people were in the sample, find out the proportion that preferred bowling, and then multiply the proportion by the number of students.

I pretty quickly got all three of those questions correct, but then ended up coming up against some much harder ones. I stupidly didn’t screenshot any of the harder questions I got wrong, so I don’t have much else to say other than it took me about an hour to pass the test and I had to review a few statistical terms. I got through it on Friday night and then began the Random Variables unit test on Saturday morning:

Statistics and Probability – Unit 9 – Random Variables – Unit Test

Question 8

This question took me about 5 minutes to think through but I managed to figure it out eventually. I wasn’t confident in my answer, but it seemed to me that I needed to multiply (0.9)(0.9)(0.9) since that would mean the player would NOT get the bonus three times in a row, and then multiply that product by (0.1) since that would be would be the odds of the player GETTING the bonus on the fourth attempt. Like I said, I wasn’t confident that I had it figured out, but it turned out I was right. (Probably because I’m a gangster.)

Question 9

I guessed on this question based on the phrasing of the possible answers. I got it correct but don’t know what a binomial variable is or what’s required for something to be considered a binomial variable.

Question 10

This was the final question I worked on before calling it a week, and I got it wrong. 👎🏼 I was annoyed that I got it wrong because I actually knew how to do the math — it’s the same math used in the first question from this test above — but I misunderstood the phrasing of the question. Where it says “more than 4 vehicles before she registers and SUV”, that in my mind sounded like I needed to find the odds that she registered five vehicles (which is more than 4) and then registered an SUV, i.e. the sixth vehicle. So, I multiplied (0.88)⁵(0.12) which would be the odds that she registered the SUV on sixth vehicle, and it turned out I was wrong since they wanted the odds of it being registered on the fifth vehicle. 😡

And that’s where my week ended. I’m a bit worried that it’s going to take me a long time to get through this Random Variables unit test as it’s 21 questions long, not to mention that I struggled with statistics when I did it five years ago. That said, I did okay on the first few questions I worked through this week, but I didn’t get too far into the test, so there could be some much more difficult questions coming up. In any case, I’m hoping it won’t take me more than a few weeks to get through the test, and then I’ll REALLY be on the home stretch of KA. I just checked and there’s only one exercise and one unit test I need to get through in AP College Statistics, three unit tests I need to get through in Multivariable Calculus, and then the Multivariable Calculus Course Challenge and then I’ll be done… 😳 It literally is hitting me as I’m typing this just how close I am to finishing this all off. I’m pumped to be so close to the finish line so (as always) my fingers are crossed I can have a good week and get there sooner rather than later! 🤞🏼