Pre Calc—Chapter 1

1. Pre Calc—Chapter 1 Fundamentals

2. Real Numbers • Whole (Natural) Numbers • Counting (kindergarten) numbers • Integers • Natural numbers along with their negatives and 0 • Rational Numbers • Ratios of integers • Irrational Numbers • Numbers that cannot be expressed as ratios of integers

3. Properties of Real Numbers • Closure: For all real numbers a,b, the sum a + b and the product a . b are real numbers.

4. Properties of Real Numbers • Associative laws: For all real numbers a,b,c, a + (b + c) = (a + b) + c and a . (b . c) = (a . b) . c.

5. Properties of Real Numbers • Commutative laws: For all real numbers a,b,a + b = b + a and a . b = b . a.

6. Properties of Real Numbers • Distributive laws: For all real numbers a,b,c, a . (b + c) = a . b + a . c and (a + b) . c = a . c + b . c.

7. Properties of Real Numbers • Identity elements: There are real numbers 0 and 1 such that for all real numbers a,a + 0 = a and 0 + a = a (addition) a . 1 = a and 1 . a = a (multiplication)

8. Properties of Real Numbers • Inverse elements: For each real number a, the equations a + x = 0 and x + a = 0 have a solution x in the set of real numbers, called the additive inverseof a, denoted by -a. • For each nonzero real number a, the equations a . x = 1 and x . a = 1 have a solution x in the set of real numbers, called the multiplicative inverse of a, denoted by a-1.

9. Set Notation • Set • Collection of objects or elements • Elements • Objects in a set • Set Builder Notation

10. Set Notation • Let S and T be sets: • Union • Intersection • Empty

11. Intervals • Open Intervals • Closed Intervals • Can Infinity be a closed interval?

12. Absolute Value

13. Properties of Absolute Value

14. p.12 #1, 5, 9, 13, 17, 21, 25, 29, 33, 37, 41, 45, 49

15. Exponents and Radicals—1.2

16. Exponential Notation

17. Properties of Exponents

18. Properties of Exponents

19. Properties of Exponents

20. Properties of Exponents

21. Radicals

22. Properties of Radicals

23. Properties of Radicals

24. Rational Exponents =????

25. Rational Exponents • Examples:

26. Examples

27. p.23 #13, 16, 19-22, 37-40, 48,49

28. Simplifying radicals by rewriting as rational expressions

29. Simplifying radicals by rewriting as rational expressions

30. Rationalizing the Denominator • Multiply the entire fraction (top and bottom) by the denominator…or by 1

31. Rationalizing the Denominator • Examples:

32. p.24 #53-67, 70, 71, 86

33. Algebraic Expressions—1.3

34. Scientific Notation

35. Definitions • Variable • Letter or symbol representing a number • Constant • Fixed or specific number • Domain • The set of numbers a variable is permitted to have • Input

36. Definitions • Degree • Highest power of the variable • Monomials • Binomial • Trinomial • Polynomials

37. Polynomials A polynomial of degree n, where n is a non-negative integer, and

38. Adding/Subtracting Polynomials

39. Product of Polynomials • FOIL

40. Product of Polynomials • Examples:

41. Special Product Formulas

42. Special Factoring Formulas

43. Factoring

44. Factoring

45. Factoring

46. Factoring

47. p.33 #6-16, 30-33

48. Factoring Completely

49. Factoring

50. Factoring