Honors Precalculus
Mt Lebanon HS 2004-5
David Kosbie

• Deriving the Quadratic Formula by Completing the Square
• Matrix Quick Study Guide (or as a Word document)
• Linear Regression with Vertical Least Squares Example
• Chapter 7 Proofs
• Some proofs/derivations you should know:
  • The Pythagorean Theorem (Euclid's Proof and the Siamese Proof)
  • The Distance Formula (using the Pythagorean Theorem)
  • The square root of 2 (or any prime) is irrational
  • The Binomial Theorem
  • There is no greatest prime number (the infinitude of primes)
  • Euclid's GCD Method
  • Using GCD to find LCM
  • 1 + ... + n = n(n+1)/2
  • sum of first n odds = n²
  • sum of first n squares / cubes / etc (using Gaussian Elimination)
  • divisibility criteria (by 2,3,4,5,7,9,11)
    see http://mathforum.org/k12/mathtips/division.tips.html
  • Countability
    • Countability of integers, rationals, algebraics
    • Uncountability of reals (hence transcendentals), power sets
  • e^(iπ) = -1
• Some proofs/hypotheses you should have heard of:
  • Fermat's Last Theorem (proven by Andrew Wiles!)
  • Goldbach's Conjecture
  • The Riemann Hypothesis
  • The Halting Problem
  • Goedel's Incompleteness Theorem
  • Heisenberg's Uncertainty Principle