  # Study Guide For Math CSET III

The third and final CSET exam is all calculus all the time.  A good study tool would be any Calculus textbook as the topics are pretty traditional and apart of every Calculus curriculum.

## Trigonometry

• Pythagorean identities
• Sum and difference identities
• Unit Circle
• Special Right Triangles
• Reference Angles
• Equivalent Graphs
• Inverse Trig Functions
• Solve trig equations
• Polar Coordinates
• Demoivre’s Theorem
• Applications of Trig
• Double and Half angle identities
• Periodic behavior of trig graphs

## Limits

• Definitions
• Rules
• Squeeze Theorem
• Right and left hand limits
• When does the limit exist?
• Continuity
• Is something differentiable
• Intermediate Value Theorem
• How to find limits
• Chain Rule
• L’Hopital’s Rule
• How to find limits of
• Polynomials
• Logs
• Trig functions

## Derivatives

• Notation
• Slope of a curve
• Derivatives of polynomials
• Power Rule
• Instantaneous Rate of Change
• Newton’s Method
• Limit of difference quotients
• Rolle’s Theorem
• Mean Value Theorem
• Finding Max and Mins of Parabolas
• Finding velocity and acceleration
• Second derivatives
• Related Rates
• Finding average velocity and average speed
• Instantaneous velocity
• Finding concavity, inflection points, optima and extrema of graphs
• Exponential Growth

## Integration

• Riemann sums
• Even and odd shortcuts
• Power Rule
• Common Integration
• How to integrate
• polynomials
• logs
• by substitution
• by parts
• Numerical approximations
• Fundamental Theorem of Calculus
• Definition
• Proof
• Using integration to find
• area
• volume
• curve length

## Sequences and Series

• Arithmetic sequence
• Geometric sequence
• Limits of sequences
• How to use recursion
• Triangular numbers
• Convergence tests
• integral
• comparison
• limit comparison
• ratio

In following posts I’ll go into detail about the best ways to study each of these topics.  I promise we will have fun along the way and it will be anything but traditional.

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