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What qualifies someone as being calculus ready? Anyway to test myself? (I cannot seem to find anything free.) I recently took a university exam which was suppose to find my mathematics placement, but it placed me in beginner algebra. I am mostly self taught (my actual teachers were horrible); however, I forgot a lot of stuff. Surprisingly a lot of programming stuff I have down, combinatorics, truth tables, etc. I think my knowledge has gaps that are making me screw up hard on the placement exam. My apologies for the slight rant /sci/.


you should be extremely comfortable with algebra, i've heard that khan academy is a good recommendation for those who prefer the self-taught approach.

then you'll want to know trigonometry, which is sometimes called pre-calculus. it's possible to do calculus without trig functions but you're missing out on a lot of the more intuitive and "beautiful" concepts. if you know the 23 fundamental trigonometric identities by heart you'll be fine.

combinatorics and logic will help you with discrete math


i can't speak for anything past calc one, but in my experience in that class the calculus itself isn't the hard part. if you aren't confident with trig and algebra you're probably in for a rough time, since that's where a majority of the hard stuff is


i would say you're calculus ready when you're good with dealing with abstractions, also proofing is a major part of calculus.
sources: am super cool scientist


Most of what you learn in Algebra is factoring.

(x^2 + 3x -10) = (x + 5) * (x - 2)
(x^2 - 4) = (x + 2) * (x - 2)
(x^2 + 4) = (x - 2i) * (x + 2i)

Calculus doesn't use very much of that. You'll spend most of your time shunting variables around an equation with Algebra.


>know the 23 fundamental trigonometric identities by heart
Ya no.


>if you know the 23 fundamental trigonometric identities by heart you'll be fine.
i'm a cal III student and i only know nine. knowing them by heart is fine and dandy, but being very good at cramming works as well.



Math major here. I know like five, plus the definitions of all the different functions.


>Calculus doesn't use very much of that.
Maybe not Calc 1, but my diff. eq. class does a LOT of factoring, and I remember doing a little bit of factoring for the AP Calc BC exam.
Mainly the particular method of e.g.
Solve integral[dx / (x^2 - 1)]
x^2 - 1 = (x+1)(x-1)
1/(x^2 - 1) = A/(x+1) + B/(x-1)
1 = A(x-1) + B(x+1) = (A+B)x + (-A + B)
and so on...


I'd say that if you can:
>do basic algebraic manipulations
>solve quadratic equations
>draw parabolas and basic trig functions

then you're ready to learn about calculus, if it interests you. You will naturally pick up anything you're missing as you go. Just don't be afraid to look things up and ask questions.


I am soon starting calculus I and the highest math I have completed is algebra II. I am hoping that what >>530 is true.

Interestingly enough, my calculus textbook lists 12 fundamental trig identities to know.



you should just learn euler's identity and index notation for 3d calc and you can prove whatever identity when you need it.


Have any resources for that? I would quite enjoy looking at them!



https://en.wikipedia.org/wiki/Euler's_identity (lets you prove all those annoying trig identities)


Index notation is p. common in physics but it's also the easiest way to prove vector calc identities.


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I really just wanna comment on how great that index notation primer is, it got me thru em, mech and GR. Everyone thats familiar with calculus should read it, it's a more intuitive problem setup IMO for a lot of lin. alg you encounter.

Only thing I can say I learned well besides pic related from physics.



Oh read a physics books to get good at 3d calc. Pick up a stat mech book as well. And then jump into modern algebra which ties into differential geometry, and then you're a math god gratz.


In my experience the amount of algebra you need to know for calculus largely depends on the instructor.

I took Calc I twice, ten years apart. The first time, each problem we were assigned would fill at least half a sheet of notebook paper - mostly with algebra. The algebra was mostly transforming the problem into calculus-friendly forms and the combining the results after the calculus.

The second time, the assignments were a lot easier and didn't pound the algebra nearly as much. The problems were already calculus-friendly. Honestly, I learned more the first time around.

I think a lot of it has to do with paperless grading. The first time around, we turned in assignments on paper; the second time, we used WebAssign.

I've completed Calc II but I'm a bit concerned that given how easy Calc I and II were this last time around, I'll have trouble with higher level math courses.


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Think of pre-calculus as a course designed to review *all* mathematics necessary for calculus. It literally starts with basic arithmetic. I would highly suggest checking out this textbook to help you evaluate your skill level and catch you up with whatever you're lacking.