# 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

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?