"Calculus is where you finally learn algebra and trigonometry." Why do people say that? (I haven't taken calculus yet)

if you want to do well in a calculus class, the only thing that really matters is that you can do high school algebra well (including trigonometric functions, exponentials, logs, etc.) and you actually understand what you are doing (as opposed to just knowing what to do because you memorized the answer-getting procedures).


here's a test that I give to check whether your algebra is good enough for calculus or not:

let f(x) = (x+1)/(x2-x+1) and let g(x) = f(x)+f(-x).
a) write down the expression defining g(x) and add the fractions together and simplify it
b) use the result to solve the equation g(x) = 1
c) [hard] use the identity tan(x)2 = (1-cos(2x))/(1+cos(2x)) to show that g(tan(x)) = 8(cos(2x)+3)/(cos(4x)+7)-2. google any other trig identities that you need

this is a reasonably difficult problem so expect it to take some time even if your algebra is good (I have a math degree so this type of problem is easy for me, but it still took 10 minutes to do part c). can you do it:

  1. without needing to be reminded how to add fractions,
  2. without needing to be reminded how to multiply polynomials,
  3. without needing to be reminded what f(-x) means.
  4. without someone to tell you exactly which steps to take,
  5. without doing something completely nonsensical?

if you can get through...

  • the whole problem, then you will not have any trouble with calculus
  • parts a) and b), but c) is hard, then you'll probably still be fine as long as you know basic trigonometry
  • parts a) and b) with a small mistake like a sign error, or maybe it just took a while for you to do, that's fine too and you should still be ok with some practise
  • none of it without being guided step by step, then you are not ready for calculus
/r/learnmath Thread