“Deriving” into Pre Calculus, Course S68–S.I.G., University of Texas, Austin

Day 1 – Pre-Assessment

  • Areas of interest, individualized personal objectives
  • Five hardest questions in different areas of calculus
  • Informal class discussion

Day 2 – Graphing

  • General equation of a line, Physical meaning of slope and y-intercept
  • Parallel and Perpendicular lines
  • Applications of lines and slopes (water usage, F to Celsius conversion…)

Days 3 – 9 – Functional Relationships – between 2 variable quantities

Functions

  • linear
    • Examples from daily life – water usage bill, gas mileage
  • quadratic and polynomial
    • throwing stones, parabolas, polynomial division
  • exponential
    • Compounded interest versus Simple interest
    • Continuous compounding versus daily compounding
    • Present Value
  • logarithmic
    • Calculating ‘how long’ instead of ‘how much’
    • Real world examples
  • trigonometric
    • Quadrants, terminal points, sine, cosine
    • Law of Sines, Law of Cosines, Half-angle identities
    • Unit circle, rotating radius
  • rational functions
    • asymptotes, roots
  • Irrational Numbers, Square root of 2

Day 10 – Mathematical Induction

  • 2^2^n + 1 = prime – failure. counter example found
  • All horses are the same color – Logical reasoning fallacy
  • Useful proofs – infinity of primes, more examples

Days 11 – 14

Mathematical Models

  • Material decay, half-life
    • radioactive decay
  • Population Growth
    • Algae growth
  • Sound Waves and Trigonometry
  • Physics Equations – Waves, Newton’s laws…
  • Contest – Derivatives, Optimization – Soda can , Area of Material vs. Cost

Day 15

Evaluation, Future direction/interests for each student

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