Talk:Calculus pre-test

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

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

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

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

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?

Course Outline

Precalculus should probably follow an outline similar to OpneStax: Precalculus. -- Dave Braunschweig (discuss • contribs) 00:33, 2 May 2020 (UTC)