So yes - Khan Academy has what appears to be an excellent AP Calculus AB course, with numerous videos by Sal himself (Grant Sanderson of 3b1b fame recorded some additional videos for their multivar calc course), as well as with numerous mastery assessments. They even provide "college board math" assumptions, like assuming that the maximum of a sin/cos function is always 1 when estimating the Lagrange error bound (regardless of actual interval). And they break it down by AB and BC. They also have testimonials by some private school teachers who have adopted that course at their schools. It's really well done and if you try it yourself, you soon get addicted to their little success jingles and confetti. Now it doesn't have a human in the loop, and there are no writing assignments, which is of course a drawback. |
Many schools with yearlong schedules can accommodate two DE courses in different semesters. |
The base school can (and do) refuse to allow self-study students to sit for the exam. This is a question for your school’s AP coordinator. |
There is no value to taking AP Pre-Calc, OP, if your kid is moving on to better things in math. College admissions officers know it's just an exam for those who max out at that level. One less thing to do off your list.
Your kid needs a tutor for AP Calc BC, and a center who can allow them to test. So get going on those two things. After AP Calc BC, does your kid have a plan? He needs to show he can take post-AP math courses every year after that, otherwise all this acceleration comes to naught. |
^ I said he, but maybe it's a she, of course. I have a DD taking AP Calc BC in 10th. ![]() |
What will they take senior year? |
if they take BC in 10th, what can they take junior and senior year? |
11th is Multivariable Calculus / Differential Equations 12th is either a course at UMD (we're in MD), or community college, or AP Stats at her own school. |
If she wants to be a math major, check out math 340/341 at UMD |
AP/DE Precalc is not a choice, it's the prescribed course (and the only offered course) on the track. There's no more Precalculus Honor or similar. She has to take it or else she wouldn't be on the "most rigorous track" of what's offered at her school. She also doesn't need a tutor for Calc BC. With where she's currently at, and if she gets to sit through a school year full of practice in 10th grade, she'll be (more than) fine. I did both the AB and BC material on Khan myself, along with some example FRQs and multi-choice tests, and the material (like all school math we've encountered in the US school system so far) is rather shallow. Put differently, I didn't see a single question that rose to the level of what I would consider problem solving. It's nearly all plug-and-chug, and the rest are maybe one or rarely two-step problems. So we're going to have to supplement in any event like we've been doing all along since kindergarten. After Calc BC we'll see. Governor's school is maybe an option, or else external courses at local colleges. It's not ideal. But right now the question is how to properly plan to avoid having to sit for 2 years in a Calc AB/BC course sequence that appears to unnecessarily stretch material over that time frame. We'll cross that bridge when we get to it, and I don't think it'll be for naught. There's a world of math and science calculus opens up. |
The AoPS calc book has some good problems, and you only need the very basic notions of what a derivative is and what an integral is to be able to benefit from calc based physics |
Halliday Resnick Krane is a good calc based physics book |
So you know your daughter will be (more than) fine in AP Calculus AB and BC because you’ve done the relevant Khan Academy course yourself? I don’t follow but I’ll take your word for it. You can sign up for AP exams at her high school even if she doesn’t take the class, you’ll have to talk to the AP coordinator. Other high schools might also agree to let her take it, but you have to talk to them directly. |
The math curriculum at most schools in the US is easy for a certain percentage of kids, just like the English, Social Studies, and Science curriculum is easy. It is challenging for some segment, the right pace for others, but easy for kids who are naturally inclined in math. We supplement with math competition classes because the problems require thought and have different solutions that the kids int he class discuss. Many are multi-step and nearly all have a degree of challenge to them. I would not able to handle the math competition material my child does but I was a kid who found regular math, not honors, hard because of LDs. I was a book worm and had read every book that was on the syllabus for Freshman and Sophomore year before 9th grade. There was a larger variety of English classes offered my Junior and Senior year so I was able to pick AP prep classes that covered books and authors I had not read before, which was awesome. It really isn't different then a kid who naturally grasp math concepts, enjoys math, and plays with it. They find the regular pace of a math class, even honors or AP classes, to be slow. DS has never been challenged in math at school. We have told him that math at school will help him firmly set the foundational knowledge he needs and give him extra practice with those skills that will serve him well when he does move into more challenging math. He does all the work and is happy to have more time to focus on classes that are more demanding, like his foreign language, while earning his A. It is possible that he will run into a math class in HS that will be more challenging for him, I hope that happens, but I suspect that would occur at a place like TJ where math is taught in greater depth and more quickly than in the regular MS/HS. |