I’m currently a freshman taking geometry, although I would like to make it to calculus 3 (multivariate). The furthest I could get is calculus 2 (BC) by taking a class which combines algebra 2 and Precalculus my sophomore year. I plan on majoring in something science-related, therefore taking calculus 3, instead of calculus 2 my senior year would look much better. I only have two ways of getting to calculus 3, which are:
-Taking algebra 2 and Precalculus the summer after my freshman year.
Or
-Taking AP calculus AB the summer after my sophomore year and taking BC my junior year, thus achieving multivariate calculus. In this situation, I would have to take the math combo class.
What should I do? Should I be content with just getting to calculus BC? Or… Should try to get to multivariate?
I wouldn’t make such a huge effort to reach Calc 3 in high school. It is great that you would have the equivalent of Calc 2. Some people think the high school versions of these classes are not as rigorous as the real university versions, and perhaps you would benefit from having some calculus instruction at a U.
Either option is doable, but will be undoubtedly fast. However, since HS algebra covers a lot of topics that are useful in higher math, it is not a good idea to rush through the curriculum unless you can learn quickly.
You don’t necessarily have to take the equivalent of calculus BC at a university - you can achieve a good understanding of the topics in a BC class or on your own. Granted, AP Calculus isn’t all that rigorous compared to, for example, a real analysis course.
If you’re planning to major in science, I would take particular care to get a solid background is Algebra II & Trig in high school. Worry less about what looks better for admission, and concentrate on getting a good introduction to the basics.
If you’re going to go with summer school, definitely take AP Calc AB after sophomore year. It would be easier to learn a semester of calculus over the summer than two years of math.
Rushing through Algebra II and Precalc is probably the worst thing you can do. You need a strong base to learn and understand calculus properly.
I’m hearing more and more math professor lament that they have to un-teach high school calculus in order to teach college calculus because students tend to be weak in their algebra and precalc. They would prefer strong students with less calculus but a strong base than students with a superficial formulaic understanding Calc 1-3.
I’m not sure why the rush in high school. Having MVC may look impressive to the admissions office (maybe) but having a weak understanding of calculus will frustrate you and your professors in college. Focus on making yourself the strongest student for college by getting a solid base.
Well, if I do NOTHING over the summer, I would only make it to calculus BC by my senior year. Is that good enough for a science related major and a selective school?
With no disrespect intended to any previous posters, I personally find the emphasis placed on algebra 2 and precalc to be a bit more than what I’ve felt in calculus (and MVC / diff eq) classes. Just for a bit of background, I’m homeschooled and skipped from algebra 1 -> algebra 2 / trig -> dual enrollment calc (BC equivalent). I’ve found my largest problem is with trig, since I sort of crammed that into a couple of weeks.
I haven’t had any real problems with any precalc or algebra 2 stuff I skipped, but it could be because I’m taking it at a community college that sort of assumes students forget some stuff…
But to focus on your issue, BC calc is far enough for even selective universities, unless most students take MVC at your school. If you do want to skip farther, and think you could do well in them, I think it’s doable. I do have two questions:
Is trig with algebra 2 or precalc for you?
Can you take BC without having taken AB first?
If trig is with algebra 2 and you can skip AB:
Sophomore: Algebra 2 + trig
Summer: Precalc
Junior: BC calc
Senior: MVC
If trig is with precalc and you can or cannot skip AB:
Summer: Algebra 2
Sophomore: Trig + precalc
Junior: BC calc
Senior: MVC
If trig is with algebra 2 and you cannot skip AB, it will be harder (unless you’re totally unlike me and find trig really easy…):
Summer: Algebra 2 + trig <–not recommended because like I said…trig…
Sophomore: Precalc
Summer: AB calc
Junior: BC calc
Senior: MVC
But it’s really all up to you. Please don’t feel like you have to take anything higher–you don’t. BC is far enough for even top colleges, but if you want to go higher for the challenge, and are a strong math student, I think any of the above paths are doable. Good luck!
Algebra 2 and precalc sounds pretty ambitious, I’d only try to skip both if you’re a strong math student AND willing to put in lots of time and effort. Also, if you are planning on doing that, why wait for the summer? You have the algebra one background, I’m assuming, for algebra 2. If you want to skip and not wind up struggling in math later, you need to be really devoted to learning and not just remembering steps. If you only skip alg2/trig, then you have the benefit that much of precalc is a review of alg2/trig, so anything you miss should be covered in class. It’s really too much information to squeeze into a few months. I’m self studying algebra 2/trig right now, here’s what I’m doing.
Method-wise:
-Trying to average a few hours per week on extra math (although sometimes I’ll do a lot more or less)
-Taking care to understand everything, and if I’m too lazy to make myself understand then I’ll force myself to at least write down the notes and come back to it later (cough conics cough).
-Doing lots of example problems
-Seeking out other resources if my main sources aren’t sufficient for me to understand
Source-wise:
-Khan Academy, the Algebra two and trigonometry sections
-I’m doing portions of the KA precalc but I’m planning on finishing the KA precalc course over summer, so I’d suggest doing something like that if you’re only skipping algebra 2
-A textbook, the same one my school uses, it was pretty cheap since I bought it used. Although it isn’t much help to me in terms of learning, I use it as a content guide and for practice problems
-Life of Fred Trigonometry: I just got this book, and so far I’m very pleased with it. I was really intimidated by trigonometry but it’s making a lot more sense now, and it correlates nicely with my geometry class. I would definitely recommend it, and the other LoF books are probably good as well.
-As additional resources to supplement those, I’m using Paul Lamar notes, Purplemath, and MathIsFun.
Feel free to PM me for more details, if you’d like.