Aops Calculus Book
Vickiana Sconyers
A comprehensive textbook covering single-variable calculus. Specific topics covered include limits, continuity, derivatives, integrals, power series, plane curves, and differential equations.
Related course: Calculus
Calculus is part of the acclaimed Art of Problem Solving curriculum designed to challengehigh-performing middle and high school students. Calculus covers all topics from a typical high school or first-year college calculus course, including: limits, continuity, differentiation, integration, power series, plane curves, and elementary differential equations. The text is written to challenge students at a much deeperlevel than a traditional high school or first-year college calculus course.
The book includes hundreds of problems, ranging from routine exercisesto extremely challenging problems drawn from major mathematics competitions such as thePutnam Competition and the Harvard-MIT Math Tournament. Manyof the problems have full, detailed solutions in the text, and the rest have full solutions in theaccompanying Solutions Manual. This book is used in our Calculus course.
We're not there yet. But in the process of looking for online classes for DS for 9th grade, I saw that the online Calculus course offered by AoPS is not an AP course. But they do say that after completion of the course, the student would be ready to sit for the AP Calculus BC test.
DS has used AoPS Intro Algebra, and just finished online AoPS Intro Geometry. And he really enjoyed the online class. Would it be better for him to take Caluculs online with AoPS or AP Calc with PA Homeschooler? What would the differences be? He can sit for the AP Calc test even without taking an "AP" class, right? Would colleges look at the courses differently?
We struggled with the same decision. I originally signed my ds for PAH's cal class. He detested it. From his perspective it was a lot of replicate plug and chug busy work type problems. He dropped that class and signed up for AoPS. He loved it. He did have to prep for the BC exam (the exam is changing for next yr.) He needed to learn how to write the form for free response answers and he needed calculator practice. Kathy in Richmond helped him with the prep, so I am not 100% sure exactly what the prep was I all, but those 2 things stick out in my memory. He prepped for just a few weeks before the exam.
Sure he can sit for the AP test without taking an official AP class. I'd list it as Calculus with AP test and let the test score speak for itself. I don't think most colleges would treat the two as any different.
My son did AoPS all the way through precalc and since has done much of the AoPS calculus book on his own. He also took PA homeschoolers AP Calculus BC so I can tell you some differences. Private message me if you want my opinions.
I also don't think most colleges would treat AoPS Calculus with AP test differently than a standard AP Calculus BC course, but a few probably will and they should. AoPS would provide a much, much better preparation for college math, IMO, at least for a math major. I don't know about PA HS, so my comments are not about that class in particular, but rather about typical AP calc classes. In many cases, AP classes as well as the test provides a modest floor on the course as well as preparing for the AP test, but AoPS is at a much deeper level than the minimum AP calc course.
PA Homeschoolers will use a traditional textbook, assign readings & lots of practice problems on a regular basis, and will do focused test review. We've used PA Homeschoolers (not for Calc, though) and have been pleased. As a general rule, they'll over-prepare you for the test & make it possible to earn a top score, with lots of support. It's more school-like; they usually have x number of points for each component of the course, & will notify you & nudge/dock your student if he gets behind, etc.
AoPS uses their own text, will go much deeper conceptually and will require many proof-based problems. They'll assign fewer, but tougher, problems, and there won't be a lot of rote practice. They'll cover all of the AP topics, but you'll be on your own for AP specific test review. AoPS expects that their students are mature and will do their work without constant reminders. Grades are not emphasized at all, though you can request one through their school if needed.
(2) Used this book for targeted FRQ practice. It has very detailed solutions, cross-referenced by topic, from past exams showing exactly what the AP graders are looking for; it's an older book that's still relevant today. There are lots of FRQs & grading rubrics on the CB website, too, for additional practice.
(3) After completing the above review, I administered a full released exam (purchased from CB) under testing conditions. We did this about one week before the real exam just to catch whether or not we missed any topics & to give us a few days to fix those gaps.
On the AP exams, one section of the multiple choice and one section of the free response questions will allow calculator usage. Not all of the questions in those sections will require a calculator, but there WILL be some questions that cannot be solved any other way. They won't be easy examples that can be done by hand, but instead will be messy integrals, functions that cannot be quickly graphed by hand, etc.
Be aware that the AP Calc exams are changing next year. The changes are classified as minor, but I'd keep my ears open anyway. There is supposed to be a greater emphasis on conceptual understanding. Calculus is still calculus, though, and the above review methods should still be helpful! (just checked quickly and the calculator procedures, for ex., have not changed at all.)
Kathy's post is so great. I just wanted to comment on the calculator part. Perhaps my kid isn't "most kids", but it's taken him a fair amount of practice on the graphing calculator. He started using it about a month ago (so four weeks before the exam) and spent an hour or two learning the functions. It's true it's not too hard to learn. But getting speedy at it has taken longer. And the hardest thing for him has been learning to *recognize* problems that he should use the calculator on. His inclination is to pound away at a problem trying every possible integration technique rather than to turn to the calculator. The number of problems you really, truly need a graphing calculator for is pretty small from what I can tell, but when you come to one, you'd better know how to recognize it and not waste precious minutes.
There's time getting comfortable with the calculator in general (we'd been using them for a few years before AP calc), a bit of time to learn the 4 procedures, and then the practice exams to gain intuition on when to use those procedures. And the last IS the tricky part!
Wow, Kathy, thanks so much for sharing with me your plan for prepping for the Calc AP exam. I really appreciate it. Will be sure to use it when the time comes. Yeah, calculator practice is not something that I would have thought important on my own. Thanks for letting me know, so that I give DS plenty of time to use it efficiently.
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1 - Introduce a problem, or a goal, basically give something that the section of the book is working towards (for example, when talking about limits towards/involving infinity, presenting the need to more generally be able to rigorously take the limits of quotients of functions)
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