After 2,437 days of working through KA, I finally achieved my goal. 😭

I officially finished the Math: High School and College section of Khan Academy this past week by passing the Calculus BC Course Challenge. I ended up getting 100% on the Course Challenge which I was thrilled about, but I did use SymboLab and Desmos to double check a few of my solutions before submitting them. (But to be fair, every solution I had before checking SL and Desmos was correct except for one.) For some reason, the questions on this test were WAY easier than the questions from the Calc. AB Course Challenge. 🤔 What made it even better was that I finished it off on Tuesday, which happened to be my birthday! Something odd that happened that I didn’t expect was that I felt a small version of grief in the few days after being done. Waking up every morning for the past 6 years, 8 months, and 3 days and studying math has become such an ingrained part of my routine that not doing so for the past 5 days felt oddly unsettling. BUT, I’m not done with Khan Academy yet and am planning to start studying Computer Science, which I’ll talk more about at the end of this post. Suffice it to say, I’m THRILLED that I FIN-A-LLY finished this goal that I set out to achieve almost 7 years ago. And it only took me 5 years, 8 months, and 3 days longer than I thought it would. 

As I said, for some reason the questions on the Calc. BC Course Challenge were super easy compared to the Calc. AB CC questions. Nonetheless, here are 7 questions I worked through:

AP Calculus BC – Course Challenge

Question 1

This was the 11^th question on the Course Challenge. I’d already gotten through six questions by this point, all of which just asked me to solve pretty basic derivatives, integrals, and/or limits. After reading this question, I spent about 5–10 minutes thinking about x’(t), θ’(t), etc. and trying to basically solve for sin(θ’(t)). Eventually I looked at the given solutions and realized that the question was way simpler than I thought, only asking me to state the equation needed to solve the problem. I wasn’t 100% confident, but it seemed pretty obvious to me that a) sin(θ(t)) = y(t)/15 was the correct solution, which turned out to be correct.

Question 2

This was the 12^th question on the test. The only reason why I took screenshots of it was to show how easy so many of the questions were… Except for the first question I talked about, every question up to this point was this simple. I’ve already said this a few times, but it was very confusing to me that the Calc. BC questions were so much easier than the Calc. AB questions. 🤔

Question 3

This was the first sort of hard question on the test. As you can see from my notes, I did it in about 4 steps, although granted I didn’t write out the general equation of _a∫^b (base)² dy, but still. So, at this point I was halfway through the test and hadn’t really been “tested“. 🫤

Question 4

This was the 19^th question on the test and the first hard one I came up against. I was struggling thinking through that the radii would be (4 – x²/3) and (4 – x) given that 4 was the value of ‘y’ but the radii were in terms of ‘x’. I didn’t know what to do so just went with (4 – x²/3) and (4 – x) and it turned out that that was the correct way to solve it. (Also, the hand written notes above were my terrible rough notes, but I didn’t/don’t feel like rewriting them to make them more legible. 🙃)

Question 5

I got this question correct assuming that the answer had to be x = –8 given that it would be the only place where dy/dx = 0. 🤷🏻‍♂️ (To be honest, I didn’t even see that the question said, “ON the x-axis”. I thought it just said horizontal to the curve across the x-axis.)

Question 6

This was the 28^th question on the test. I wasn’t 100% sure if I had it correct, but I knew at p > 6, the sum would go to infinity, so therefore b) and c) were incorrect. I thought about a) and d) for a while and assumed that p would need to be less-than 6 (not p ≤ 6) in order for the fraction to get smaller and smaller (a.k.a “converge”). I wasn’t completely sure if my thinking was correct but decided to guess that the solution was a) which turned out to be correct. 😮‍💨

Question 7

The was the 30^th and final question of the test. To be completely honest, I actually would have gotten it wrong because for some reason I took the derivative of x² and got 2x instead of taking the integral of x² which is obviously x³/3. Before submitting my answer, I double checked Desmos and saw the mistake I made and then adjusted my answer accordingly. As always, I didn’t feel great about using Desmos to double check my answers, but it’s not like I didn’t know what I was doing… I just made a careless mistake. Also, on a different note, you can see in my notes above that I went ∫ f(x) – g(x) dx which lead to –4/3 but I should have gone ∫ g(x) – f(x) dx to get 4/3. I knew that the solution would need to be positive so when I got –4/3 it was obvious to me that I subtracted the functions in the wrong order.

As I said, I finished the Course Challenge on Tuesday. The entire time I was working through the test, I kept waiting for the questions to get harder but they never did… There were literally questions like, “solve d/dx[x¹³]” and “what’s the limit of lim_x->3[–4/(2(x) – 5)]?” So, I didn’t take notes or screenshots of the vast majority of the questions because it didn’t seem like it was worth it. I started the morning on question six and got through the remaining 25 questions in about 2 hours. I could have gone much faster than that but I went slow because I was nervous, and also because the questions were TOO easy and I kept thinking that I must have been misunderstanding what they were asking. But as it turned out, that wasn’t the case. (Not that I’m complaining. 😬)

A few stats worth mentioning are that, in the end, it took me 2,437 days to finish this off, I filled out 32 notebooks, all of which had 250 pages, i.e. 8,000 pages of rough notes, and I wrote 1,338 pages of notes in Microsoft Word for these blog posts, totalling ~445,000 words. Also worth mentioning is that there are a few “learning-to-learn” strategies that I figured out throughout this process — which I’m planning to write a separate article about and put in the About Me section of the website — which are:

1. The difference between learning WHAT a concept is, HOW it works, and WHY it works,
2. How helpful it is to watch three videos (give or take) from other creators when getting stuck on a concept, and
3. I never felt like I truly understood a subject until I needed to use it in the FOLLOWING subject.

I’m really hoping that these three learning-to-learn concepts will come in handy as I now move forward into learning Computer Science!

When I finished the Course Challenge on Tuesday, I decided to wait until this coming week to get started on CS — which KA simply calls “Computing” — mainly because I’m officially moving into my 350^th week of KA and it felt fitting to wait until precisely Week 350 to start a new subject. I’m excited about starting an entirely new subject, but am also genuinely sad that I won’t be studying math anymore. 😔 But as I mentioned in my previous few posts, I’ve been watching a lecture series about CS and started reading a book about it to get started, and I’ve been pleasantly surprised that the math I’ve come across so far has been super easy for me to understand thanks to everything I’ve learned! I’m excited to apply what I’ve been working on in Math to CS, so I’ve at least got that going for me which is nice.

And that’s… it. 🥺 It’s honestly crazy that I finished this thing off… When I think back to when I first started KA in September of 2019, I couldn’t have imagined how studying math would become such an important and integral part of my life. For close to seven years, waking up every morning knowing that I had something to work on has been incredibly valuable for me. (Especially during the pandemic!) Every week it felt like I was making progress towards not only learning math, but also towards becoming a better version of myself. When I first started in 2019, I was in a particularly dark place in my life. Working towards achieving this goal provided me with what felt like a path towards a brighter future. In my mind, finishing it off is proof that I can accomplish difficult things as long as I put my mind to it and commit. More importantly than the math I’ve learned, that has been the biggest and most valuable takeaway I’ve gained from this experience. 

So, with that said, this is officially my FINAL post about math. I’m sad but also excited to begin the next chapter of learning CS. So, as always, fingers crossed that I can have a solid, productive upcoming week week so that I can hit the ground running on CS and so that it doesn’t take me another 6.5 years before I finish this one off! 🤞🏼