# HS calculus coursework/outline?

1. Jul 10, 2006

### dnt

hope this is the right forum to ask but can someone list a syllabus/outline for a typical AP calculus AB high school class?

i know schools are all different but in general, what would be the topics covered during a typical school year?

thanks

2. Jul 10, 2006

### buddyholly9999

If the class is for college credit at your local community college or something then they would be following the same syllabus as the institution that is giving you the credit. You can find links to course syllabi on most college websites. As for me..my opinion is that differentiation and integration would be the primary topics for first calculus classes.

3. Jul 10, 2006

### d_leet

I'll try and give you a general outline of what the AP calc class goes through, but this definitely won't be exact or in any great detail, but I hope it helps.

Review
-functions
--polynomials
--rational functions
--trig functions
-possibly some other review

Limits
-introduction to the limit concept
-infinite limits and limits at infinity
-Assymptotes (possibly)
-Continuity
- Epsilon-Delta proofs (Note: that my AP calculus class didn't cover these, but I'm pretty sure that almost all college calculus courses will)

Derivatives
-The derivative as a limit
-differentiablity rules
-applications of differentiation
--Related rates
-differentials
-approximating functions
-Chain rule

Integration
-The Riemann sum
- The definite integral as a limit of Riemann sums
-The fundamental theorem(s) of Calculus
-Indefinite integrals
-Applications of Integration
-- Finding area under curves
--Area between Curves
-- Volume obtained rotating a cure about an axis or line
-- Work problems
- Integration by parts

Note: Integration by parts is not covered on the AB test, but is on the BC test, I think this also goes for work problems but it's been a while since I took the AB test so I can't remember exactly.

Miscellaneous Topics
-Very simple seperable differential equations -- again this might be only in BC but I'm not totally sure
- Exponential functions
-- derivatives and integrals of exponential functions
- The natural log defined as an integral
-- derivatives and integrals of the natural log and other logarithms
-Inverse trig Functions
-- Derivatives (and integrals) of inverse trig functions

I'm sure that I've probably left some large or important topic out, and exponential and logarithmic functions as well as almost everything under my miscellaneous category is introduced after you have studied some integration.

4. Jul 10, 2006

### dnt

would that cover an entire year of high school calc?

5. Jul 10, 2006

### d_leet

Pretty much, excluding things that I may have possibly left out unintentionally, but that is the bulk of the material that is covered in AP Calculus AB.

6. Jul 12, 2006

### mathwonk

unfortunately it is not at all true that the AP syllabus is the same as that of the college course it receives credit for as a substitute. this would be only logical, but is in fact often not the case.

AP is a business entity and AP syllabuses are just what the AP corporation says it is, nothing more. however today, so many incoming students have only AP preparation, that many colleges have indeed rolled their standards back to accomodate the lower AP ones, so it is more true than before.

still, good college courses, especially for honors or math majors, are often much deeper than high school AP level.

in my freshman honors second semester calc course last time we did sup norm convergence of functions, and rigorous infinite series representation of functions.

the detailed syllabus above does look a lot like our non honors syllabus, except that we have almost completely stopped teaching epsilon and delta there.

when I taught epsilon and delta last time in my 1st semester honors course, including proof of existence of maxs and mins of continuous fucntions, one of my scholars wrote in evaluation that the course was the "most challenging one" he had ever had, "certainly in mathematics" in his life.'' And he was a survivor.

7. Jul 12, 2006

### dnt

so would a high school course basically follow what an AP review book covers?

8. Jul 12, 2006

### d_leet

In general, this would probably be true because unfortunately the ultimate goal of an AP course is to prepare students to take the AP test and most teachers tend to do only this and prepare you for the AP test as opposed to thoroughly teaching the material so that it is well understood. Note that not all teachers who teach AP classes are like this though it just seems to be the general trend since the AP program is all about taking the tests. So to answer your question a high school AP calculus class should cover, as a minimum, all of the material you will find in an AP review book and possibly some additional material as time allows.

9. Jul 13, 2006

### buddyholly9999

Notice I used the word "if"...when I took Calculus 1 and 2 in high school...we were dual-enrolled in college and high school. We got college credit for Calc 1 and 2..following the same syllabus as the one the college instructors gave..at the local community college. On my high school transcript it says Calc AP. So, if you want overly complicate things and go into all the details of what "AP" really means and all that then you have to know that different places do it differently......that or they are just not following the status quo..

but i think we can all agree...that differentiation..limits and all that are going to be the first things shown to a calculus student.

Last edited: Jul 13, 2006