Hello! I am a rising senior and am looking to take AP Calculus next year straight from Honors Trigonometry. I’ve heard our school’s AP Calculus class is very rigorous and that the grade average of the class is extremely low even though only the best and brightest attempt the class–The rest who want to take calculus but do not want to face the challenge either take Business Calculus, which is the normal equivalent, or Honors Calculus, which is slower and less intensive than AP. I love math, did very well in Algebra II and relatively well in Honors Trig, but I want to be prepared for the calculus course when it comes and want to begin studying for it over the summer. Can anyone help in recommending the best introductory course book in calculus I can study from and get a general background of calculus before attempting the class? Thanks!
Khan Academy Khan Academy Khan Academy. They have an amazing calc curriculum set up, with teaching videos and tutorials as well as online practice. Plus, its free!
Calculus Made Easy by Sylvanus Thompson. Published originally ca 1910, the more recent update via Martin Gardner rewords some of the problems. The original is available as a PDF, or at least it used to be.
Gilbert Strang’s MIT Open Courseware lectures are pretty good. Search OCW and get lecture notes and sample problems.
A friend recommended “math bff” on YouTube as well.
Over on physicsforums this question comes up from time to time, so that might be worth tracking down. I recall the Thompson book getting recommended there. It really is a nicely done treatment…
Why not take Pre-calculus?
Stewart Calculus is a tradition. One of the older editions should work fine.
All the other answers are excellent, too.
Also make sure to check out OpenStax. https://openstax.org/
I just finished AP Calculus BC at my high school and we used Early Transcendentals 6th edition. To study for the AP test I found Princeton Review to be very succinct. However, this is only good as review after you know the information, and I honestly rarely used the textbook to learn but it is good practice. I find that Khan Academy only does basic examples that don’t help much in the long run. I like PatrickJMT on YouTube for anything math related and especially calculus. He has playlists with both Calc semester one and two. I’m honestly skeptical about how one would go about passing a calculus class without taking precalc beforehand, but good luck regardless.