**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 = n
^{2} - 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