Talk:Calculus pre-test

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I am currently a first year mathematics student at Wollongong University Australia.
Whilst I am fully aware that courses do differ in content, I thought I would give another prespective on how we approach calculus in its various levels.

Pre-Calculus[edit]

Algebra

  1. Algebra comes first
  2. What is a logarithm?
  3. What is a slope-intercept equation?

Trig

  1. What is a radian?
  2. What is a trigonometric function?
  3. Name a trigonometric identity.

Functions

  1. What is a function?
  2. What is an inverse function?
  3. What is a parametric equation?

I have not even covered these things

  1. What does it mean for something to be proportional?
  2. What does injective, surjective, and bijective mean?

Calculus I[edit]

Limits

  1. I will accept an intuitive or formal answer for this, although a formal answer is obviously preferred, what is a limit?
  2. What is a one-sided limit?
  3. What does it mean for a function to be continuous? Is it possible for a function to be discontinuous everywhere?

Differentiation

  1. What is a derivative?
  2. What is the product rule?
  3. What is the relation between differentiability and continuity?
  4. What is the chain rule?

I have not even covered these things

  1. What is the relation between a local extrema and a derivative of a function?
  2. What is the mean value theorem?
  3. What is L'Hôpital's rule?

Calculus II[edit]

Integration

  1. What is the Fundamental Theorem of Calculus?
  2. What is an integral?
  3. What is the substitution method?
  4. What is the difference between a definite and indefinite integral?

I have not even covered these things

  1. What is a Riemann Sum?

My Outline[edit]

It seems clear below that
Pre Calculus covers

  1. Algebra
  2. Trigonometry
  3. Functions

Calculus I or Differentiation covers

  1. Limits
  2. Differentiation rules

Calculus II or Integration covers

  1. Integration rules

there should be
Calculus III or Advanced Calculus covers

  1. What is the relation between a local extrema and a derivative of a function?
  2. What is the mean value theorem?
  3. What is L'Hôpital's rule?
  4. What is a Riemann Sum?