<p>OTOH, many colleges will give you a math placement exam in addition to looking at your AP score. For example Carnegie Mellon says if you can’t remember enough calculus to ace their own test, they don’t think you should skip their course.</p>
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I’m just seconding the poster who said homeschoolers take AP tests without the official classes all the time. It’s no big deal. I’d recommend an AP study guide from the bookstore, and with your help, he’ll be fine.</p>
<p>If a student is declaring math as his/her major, many schools do a math placement test. For my son, who was only considering it as such, his school screened him despite the 5 on his AP test.</p>
<p>It is possible to start with some differential calculus concepts and then simultaneously take AB in class, and independently study integral calculus. It will be time-consuming, but it is not necessary, conceptually, to complete a course in derivatives to be prepared for integrals. I believe the College Board offers anoutline of topics to be covered in BC that is available to parents to peruse. </p>
<p>Stewart has some detractors, but it is widely used, and my kids used it for both home and college study, finding it easy to understand, with useful text/exercise correlations. Although it is a university/college textbook, a goodly number of private prep schools use it rather than “AP Calculus”-titled textbooks designed solely for high school use.</p>
<p>Don’t you get an AB subscore when you take the BC exam?</p>
<p>Is Stewart a non-theory based text, Ivyparent?</p>
<p>It has been claimed to lack some rigor, but it gives a good intuitive sense of things. This was actually true for calculus originally, a rigorous axiomatic basis justifying its concepts was not developed until modern mathematical era. It was after all invented as a means to quantitatively address real-world physical phenomena.</p>
<p>Thomas’s classic MIT text was criticized for being more suitable for engineers than mathematicians, yet widely beloved.</p>
<p>For a thorough analytical treatment that cuts no corners, many mathematicians recommend Tom Apostol or Michael Spivak. These are typically used in honors calc courses that are offered to students who have aced Calc BC in hs, and are encouraged to revisit the subject in a deep rigorous-foundational manner, rather than take pass-out credit for Calc I/II and proceed directly to regular Calc III. </p>
<p>For a student who has only studied conventional Alg I/II and pre-calc, who is taking hs Calc AB, the latter books would probably be overwhelming. Even Caltech freshman struggle studying Apostol.</p>
<p>We used Leithold. I wonder how that compares. Boy that book was heavy.</p>