F1nite

How to Accelerate (School Math)

Hey!
This is your guide to accelerating to AP Calculus BC (Calc BC) from whatever/level grade you are!

I'm going to aim this at people like me -- freshman who want to jump ahead because they're too good in their math class and/or just want to be in Calc BC. So, here's your guide, or at least, here's how I did it.

Please also keep in mind that skipping classes does not guarantee a placement (at least in our district). Things worked out for me because I got lucky1 (see the last section).

Step 1: To jump or not to jump

If you're struggling in your math class, it's probably best not to skip to the math class that's harder than that one. With that being said, you know your own skill level much better than I ever do, and judge accordingly. For some bits of advice on judging your own math skill:

  1. Do you like math? If so, you already get a boost -- you'll want to learn, you'll want to do well, and accordingly, you'll probably do well.
  2. Are you good enough? Do you know the fundamentals of algebra, and precalculus? For me, I did math competitions (AMC, AIME), so that's how I kept my skills sharp. If you don't do math competitions, just make sure you just kinda know math. For some specific concepts, take a look at trigonometric functions, exponential/log functions, polynomials, and play around with everything.2
  3. Calculus is not as hard as it seems. You can take a look at 3b1b's essence of calculus to get a grasp3, but in the end, calculus is just fancy algebra taught in the same classroom. You'll have a teacher that teaches, and (if you're interested in math) most likely ample time to soak up all the matériel.

Also, this isn't really your own skill, but factor in your resources. Perhaps you do really like math, but don't really know that much about some pre-calc concepts, and calculus is hard at your school, yet you have a lot of friends that can help you. Or perhaps you're really good at studying on your own, and can grasp some concepts quickly. In that case, the lack of math knowledge might not be detrimental.

---- (Editor's note: I don't really like making back edits, but I think this next part is also sorta necessary -- this part was written 02/11/2025.)

Playing Leapfrog

So let's say you meet some of the bullet points above yet you know you aren't skilled enough to jump -- for example, perhaps you're a student who really likes math yet can't do much trigonometry (and thus can't pass pre-calculus).
In this case, assuming that you still want to accelerate to Calculus and beyond, I would advise you to learn on your own then take the courses when you have a grasp of your knowledge, as overall, those online courses (or at least SVHS) is at best just a collection of resources bundled up together still for you to look at. There's nothing new, nothing innovative, just a bare bones structure that almost seems like you're supposed to know the content before taking the class.

So then, go learn on your own. Start with websites like Khan Academy and/or just random .pdf files on the internet4. Go to your friends and maybe mentors that can help you figure out various math concepts and will take the time with you to go through something. Go to perhaps teachers, and ask them questions that you have no clue about. Just don't be afraid to reach out and take a look around you.

Afterwards, assuming you've leapfrogged the competition in terms of math ability and understand the class you need to skip, proceed on to the steps below.

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Step 2: Jumping

If you've stayed along, I'm assuming that you have your mind set on skipping a few classes.

Step 2.1: The plan

The plan to Calculus is simple. Not easy, but simple. The idea is to basically take those courses that you're missing before Calculus then tell the school you took those equivalent courses and then skip straight into Calculus. As such, I somehow managed to take Comp 1 (Geometry + half of Algebra 2) to Calculus BC by doing Algebra 2 part 2 and the whole of precalculus over the summer.5

Step 2.2: Execution

Execution is also simple. Essentially, you tell the counselor that you plan to take some courses, fill out a form to do so6, take the courses, provide proof that you actually took the courses (to the district), and then ask to be moved into the higher math class.

A big question I haven't touched on is where you take those courses. For me, it was SVHS (Silicon Valley High School). For others, uhhh i'm not sure. go ask around.
As a review of SVHS, it lowkey functions as just a credential pumper. As mentioned above, I took Algebra 2 Part 2, Precalculus Part 1, and Precalculus Part 2 there, and overall it is only worth taking courses there if you already know the material (and are looking for a certificate proving you know that material). The UI is not great, the resources are not great, and some tests are scuffed. With that all being said though, the one big upside (besides low-ish cost) that SVHS has over its competitors is fast grading -- for example, the Precalculus Part 1 course had 5 modules, and besides a final project that needed manual review (~3 day grading), everything else was graded almost instantaneously. As such, I ended up finishing a semester-long class in like a few hours.

Anyways, assuming you've decided on where you want to take these online courses (make sure they're accredited aka they have a stamp saying they're legit), it's also good to plan timing. For example, if you do all your courses the week before school starts, that might not cut it as perhaps the course you're taking needs some things to be graded manually, and maybe verifying your credentials takes a moment, and then sending things to the school/district takes a bit, etc etc. Essentially, these small delays stack up and might derail your otherwise awesome achievement, so make sure to end early and save room for bureaucratic shenanigans.
Other than that, a good time to take these courses is over some sort of break, but if you're good at math (and motivated), it's not inconceivable that you could take these online classes simultaneously with school during the school year.

Anyways, assuming you've decided where and when you want to take your class, just walk into your counselor's office, state your intentions, and start filling out some forms. The counselor may advise you against accelerating and might even try to dissuade you (and will probably remind you that a spot is not guaranteed even if you accelerate), but basically, kindly accept these concerns yet continue to push towards taking these classes. At the end of the day, they really can't stop you from taking the classes if that's what you so desire to do.

And then, go take those classes, send your certificates off to the school, and when course selection/schedule reveals come out or will soon come out, make sure to remind/pester your counselor to put you into that advanced class!

3. Me

As I mentioned above, I accelerated from Compressed Math 1 (basically Algebra 2) in freshman year to Calculus BC sophomore year, and turned out completely fine (Calc was not a very hard class for me). Here's how I did it, and my story.

I decide to take courses at SVHS from my friend's recommendation and also since, well, I know how to do the math that I supposedly need to take a year-long class for. Anyways, starting in spring (March/April), I go to the counselor's office and basically say "I want to take these classes over the summer and accelerate." After some back and forth7, my counselor eventually relents, and over the summer, I successfully pass those online classes.
Afterwards, like I've told you to do, I sent those scores/diploma things to our district's "Student Data Analyst" who signed me off on completing these courses.

(Now for the luck.) Now, everything on my part is done, and really, I can only hope and pray that I get put in. Well, because I was busy racking up accolades/positions/titles (which is not something you should do, unless you find it fun), I was in my school's freshman orientation program, and I was at school early, preparing to orient these freshman and show them around the school and guide them. Anyways, one of the perks of being the guides/docents is that I get my schedule early!

After getting my schedule that Saturday afternoon, the school is also gracious enough to get all our counselors out and help clear out some schedule requests for these Link Crew (this was the name of the freshman orientation program) kids, me included. Bear in mind that no one else had really recieved their schedule, so the only complaints the counselors were getting were from us.

So I look at my schedule, and I don't see AP Calculus BC. Instead, I see Precalculus listed on my schedule. :(. Being me, I go up to the counselors and ask to be transferred into the Calculus class. Lo and behold, based on some scheduling miracle, there was 1 singular spot open in 2nd Period Calculus BC, and I had 2nd Period Precalculus on my schedule. As such, I got that final spot and thus ended up in Calc BC my sophomore year.

And where did that lead me? That's right. To blogging. Sure, I accelerated to get ahead in math, but I ended up blogging in my free time. Back to English.

:P

  1. Part of it was also me making my own luck but still, luck is luck.↩

  2. If I keep on talking, this will get too long, but basically, know how the graph of the functions look like (or at least be able to figure out by guessing and plugging in values), know the properties of the function (e.g. exponential looks like a rotated parabola, one side has limit 0 and the other side just grows super duper fast), and be able to do math well -- basically boiling down to not making calculation mistakes.↩

  3. Although I didn't use it. I tried watching a few of those in the series, and while everything was cool and the animation worked, I think I just didn't have the bigger picture in mind. Whatever. Those videos may or may not work for you.↩

  4. fun fact: if you search with the pdf tag at the end of your search, most of your results should be a pdf file. In the context of math, this is really cool as most of the "real math" (e.g. not crappy websites) is contained within random pdf files on various topics -- for example, try searching up harmonic series pdf or some other query, and you'll be delighted by what comes up. With that being said however, the pdf files you'll find are most likely aimed at college students (or above), which means that they can be a little dense to read.↩

  5. Lowkey pretty easy for me. For some reason, the precalculus class I was in dealt with conics (never doing that again) and matrices, but I managed to just get it done. Not sure I understand either topic currently.↩

  6. At least in my school district you had to.↩

  7. When you're negotiating, be kind and respectful but also firm. Don't be rude and be like "Yeah but you don't know how good I am at math" or demean, but basically just keep on saying something along the lines of "I understand you're concerns, but I believe that I can overcome them / I understand that there may not be a spot for me if I accelerate." Niceness helps a lot, and considering that your counselor may need to write some letters of recommendation for you, it's best not to burn that bridge early only to find out that you need to cross it later.↩