# 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

- Algebra comes first
- What is a logarithm?
- What is a slope-intercept equation?

Trig

- What is a radian?
- What is a trigonometric function?
- Name a trigonometric identity.

Functions

- What is a function?
- What is an inverse function?
- What is a parametric equation?

I have not even covered these things

- What does it mean for something to be proportional?
- What does injective, surjective, and bijective mean?

# Calculus I[edit]

Limits

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

Differentiation

- What is a derivative?
- What is the product rule?
- What is the relation between differentiability and continuity?
- What is the chain rule?

I have not even covered these things

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

# Calculus II[edit]

Integration

- What is the Fundamental Theorem of Calculus?
- What is an integral?
- What is the substitution method?
- What is the difference between a definite and indefinite integral?

I have not even covered these things

- What is a Riemann Sum?

## My Outline[edit]

It seems clear below that

**Pre Calculus covers**

- Algebra
- Trigonometry
- Functions

**Calculus I or Differentiation covers**

- Limits
- Differentiation rules

**Calculus II or Integration covers**

- Integration rules

there should be

**Calculus III or Advanced Calculus covers**

- What is the relation between a local extrema and a derivative of a function?
- What is the mean value theorem?
- What is L'Hôpital's rule?
- What is a Riemann Sum?