“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