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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