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Foerster's Calculus question

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My son (14, 9th grade) is planning to prepare for the BC calculus exam on his own this year. He's quite capable -- took Advanced Precal last year at one of the top public high schools in the country and did very well. For several years before last year he'd mainly done AoPS online courses but can't schedule the AoPS Calc class this year on account of a standing time conflict. He plans to use David Patrick's AoPS text as his main resource, but he will need practice problems specifically to prepare for the AP exam as well.


I'm looking for a book with good problems and an available solutions manual -- one I can use to quiz him on the basics, to keep him on track, and to make sure he gets plenty of experience working the kinds of problems that show up on the test. I've had three semesters college-level calculus and four of physics with calc -- but that was decades ago. I expect to be able to give him guidance if he gets stuck on a concept, but not really to be able to teach him from the ground up.


I'm looking at Forester's -- I know it's pretty basic, but also that it's designed to prepare kids for the test, and that's what I need. I know that other texts such as Larson's probably do better presenting the theory -- but he'll get that from the Patrick book. Key Curriculum press sells teacher materials for both the old and new editions, the old one being much less expensive, of course. I think that part of the difference between old and new may be that the new includes more graphing calculator applications. Does anyone have experience with the different editions? In my mind real-world and graphing calculator experience are good (this kid has a bit of an anti-tech "purist" streak, and he's won three lovely programmable graphing calculators in math competitions) but I'm wondering what the real difference between these books is. Does the new one do a much better job of preparing students for the portions of the test where graphing calculators are allowed? Or is the main difference that it has even more easy problems to lead students into the harder material (we don't need that)?


I'd appreciate comments from anyone who's seen the two editions -- as well as anyone who has successfully coached a child through the BC Calculus exam without an external class.


Thank you.

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Hi BlueMorpho,


While I don't have experience using Foerster's calculus texts, we are a fellow AoPS and math competition loving family. I've also successfully coached my two kids (self-studying) through the Calc BC exam with great results. Dave Patrick's calculus text wasn't available back then, but we used a similar tough-but-slim calculus text approach, as opposed to the standard current texts.


What's worked for us to prepare for the AP examination is to use these resources:


1. Barron's AP prep book for a supply of practice multiple-choice questions. This book also has a succinct summary of the specific graphing calculator procedures required for the examination.


2. This excellent out-of-print book , Solutions AP* Calculus Problems Part II AB and BC 1987 - 2001 , for FRQ practice. It includes both calculator and non-calculator based problems, with solutions that show exactly what the examiners want. The problems are keyed by topic, which is convenient if you just want him to practice a FRQ on the topic he's studying this week. The topics haven't really changed over the years, so I was very comfortable using this book. If you wish, though, you could also use the FRQs from recent years and solutions available on the college board web site.


3. A released BC calculus exam purchased from the College board bookstore.


I'd be completely comfortable using these resources with Dave Patrick's calculus text. Your son would be more-than-well-prepared for the test.



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Hi Grace,


I used an old copy of Thomas & Finney (my own from the 70's) with my son. Back then, the calculus texts were slimmer and taught at a deeper level (epsilon-delta proofs, for example). The homework sets didn't have 100's of problems to choose from, just a few well-thought out exercises.


My daughter thought even that was too much text for her! She spotted a copy of Calculus for the Forgetful (by Kosek) at the MIT bookstore and begged to use that instead. Hmmm...a thin paperback of 150 pages?? But, knowing how she learns, (she's a big-picture girl with extreme visual spatial skills) I decided to give it a try. It worked for great for her. I was available and willing to help her, but she honestly didn't have many questions. For my peace of mind, I assigned plenty of practice from Barron's to make sure that she was also getting the details (her weakness).


Both of them had top scores on the actual BC exam. If your son has done lots of AoPS and math competitions, he'll most likely find calculus to be a breeze conceptually.



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