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