1. Honors Algebra 2 1.1 Real Numbers and Real Operations Objectives: 1.Know the categories of numbers 2.Know where to find real numbers on the number line 3.Know the properties and operations of real numbers

2. …., -4, -3, -2, -1, 0, 1, 2, 3, 4,… counting numbers

3. …., -4, -3, -2, -1, 0, 1, 2, 3, 4,… counting numbers whole numbers

4. …., -4, -3, -2, -1, 0, 1, 2, 3, 4,… counting numbers whole numbers integers

5. rational numbers - numbers that can be written as a fraction or a decimal that repeats or terminates. Examples? irrational numbers - numbers that can’t be written as a fraction or a decimal that repeats or terminates. Examples?

6. Locate these numbers on a number line: 1.Approximate to decimal 2.Determine range and mark line 3.Plot original values

8. propertyadditionmultiplication closurea + b = real numberab = real number

9. propertyadditionmultiplication closurea + b = real numberab = real number commutative

10. propertyadditionmultiplication closurea + b = real numberab = real number commutativea + b = b + a

11. propertyadditionmultiplication closurea + b = real numberab = real number commutativea + b = b + aab = ba

12. propertyadditionmultiplication closurea + b = real numberab = real number commutativea + b = b + aab = ba associative

13. propertyadditionmultiplication closurea + b = real numberab = real number commutativea + b = b + aab = ba associative(a + b) + c = a + (b + c)

14. propertyadditionmultiplication closurea + b = real numberab = real number commutativea + b = b + aab = ba associative(a + b) + c = a + (b + c)(ab)c = a(bc)

15. propertyadditionmultiplication closurea + b = real numberab = real number commutativea + b = b + aab = ba associative(a + b) + c = a + (b + c)(ab)c = a(bc) identity

16. propertyadditionmultiplication closurea + b = real numberab = real number commutativea + b = b + aab = ba associative(a + b) + c = a + (b + c)(ab)c = a(bc) identitya + 0 = a

17. propertyadditionmultiplication closurea + b = real numberab = real number commutativea + b = b + aab = ba associative(a + b) + c = a + (b + c)(ab)c = a(bc) identitya + 0 = aa x 1 = a

18. propertyadditionmultiplication closurea + b = real numberab = real number commutativea + b = b + aab = ba associative(a + b) + c = a + (b + c)(ab)c = a(bc) identitya + 0 = aa x 1 = a inverse

19. propertyadditionmultiplication closurea + b = real numberab = real number commutativea + b = b + aab = ba associative(a + b) + c = a + (b + c)(ab)c = a(bc) identitya + 0 = aa x 1 = a inversea + -a = 0

20. propertyadditionmultiplication closurea + b = real numberab = real number commutativea + b = b + aab = ba associative(a + b) + c = a + (b + c)(ab)c = a(bc) identitya + 0 = aa x 1 = a inversea + -a = 0a x 1/a = 1

21. propertyadditionmultiplication closurea + b = real numberab = real number commutativea + b = b + aab = ba associative(a + b) + c = a + (b + c)(ab)c = a(bc) identitya + 0 = aa x 1 = a inversea + -a = 0a x 1/a = 1 distributive

22. propertyadditionmultiplication closurea + b = real numberab = real number commutativea + b = b + aab = ba associative(a + b) + c = a + (b + c)(ab)c = a(bc) identitya + 0 = aa x 1 = a inversea + -a = 0a x 1/a = 1 distributivea(b + c) = ab + ac opposite of a = -a Inverse of a = 1/a

23. propertyadditionmultiplication closurea + b = real numberab = real number commutativea + b = b + aab = ba associative(a + b) + c = a + (b + c)(ab)c = a(bc) identitya + 0 = aa x 1 = a inversea + -a = 0a x 1/a = 1 distributivea(b + c) = ab + ac Identify the property: 1. 5 + -5 = 0 2. 2(3 ● 5) = (2 ● 3)5 3. 4(3 + 7) = 4 ● 3 + 4 ● 7 4. 5 + 3 = 3 + 5 5. (x + 5) + 4 = x + (5 + 4) 6. 1x = x 7. 3 ● 1/3 = 1 8. 2 ● 3 ● 4 = 3 ● 2 ● 4

24. Honors Algebra 2 1.2 Algebraic Expressions and Models Objectives: 1.Evaluate algebraic expressions 2.Simplify expressions 3.Apply expressions to real world examples

25. Vocabulary: power – a number and it’s exponent Vocabulary: power base exponent 5252

26. Vocabulary: power – a number and it’s exponent Vocabulary: power 5252 =5∙5 5 to the second power 5 squared

27. Vocabulary: power – a number and it’s exponent Vocabulary: power 5353 =5∙5∙5 5 to the third power 5 cubed

28. 3434 2525 9393 1616 3∙3∙3∙3 2∙2∙2∙2∙2 9∙9∙9 1∙1∙1∙1∙1∙1 3 to the fourth power 2 to the fifth power 9 cubed (to the 3 rd power) 1 to the sixth power to the 4 th power 4 7

29. Please Excuse My Dear Aunt Sally P – parenthesis E – exponents M – multiplication D – division A – addition S – subtraction Left to Right

30. P – parentheses and other grouping symbols from left to right E – exponents from L to R M – multiplication/division from L to R A – addition/subtraction from L to R Please Excuse My Aunt

31. Evaluate these expressions:

32. Evaluate when x = 2 when x = 2/3 11 -7/3 **Calculator Tip : Decimal  Fraction Math, >Frac

33. Like terms – terms that have the same variables with the same powers

34. Simplify these expressions:

35. Real World Applications See Note Sheet…

36. You have 122 dollars from bagging at Dominick’s and you want to buy some DVD’s. If each DVD cost $13, write an expression to represent the amount of money you have left buying in DVD’s.

37. You want to buy either scented lotion or bath soap for 8 people. The lotions are $6 for each and the soaps are $5 each. Write and expression for the total amount you must spend. Evaluate the expression when 5 people get the lotion.

38. Write an expression for the total amount of juice in 15 cans if some hold 8 oz and some hold 12 oz. What is the total if 9 of the cans hold 8 oz?

39. Practice…Try These on the Back

40. HMWK! Worksheet 1.1-1.3: #s 7-15, 13-24

41. Today’s Agenda! Collect Signed Syllabus Return Syllabus Scavenger Hunt HW Questions/Concerns Section 1.3 Notes –1.3 Domino Worksheet Word Problems HA2 Pretest Tomorrow! (Bring #2 Pencil)

42. Honors Algebra 2 1.3 Solving Linear Equations Objectives: 1.Solve simplified linear equations 2.Solve linear equations that need simplifying 3.Solve linear equation from real life Vocabulary: solution, equation, identity equation, inconsistent equation

43. PEMA – used to evaluate an expression

44. Rules for Solving an Equation 1.Distribute 2.Combine Like Terms 3.Move variable to one side 4.Isolate variable using inverse operations 5.Check

45. Solving an equation – working backwards

46. (4/5)(x – 2) = 16

47. 2x + 5 = 7x – 16 3(x – 7) + 2x = -5(2x – 4) 2x + 8 = 5x – 2(x – 8)

48. Infinite Solutions/No Solutions 4x – 3 = 2(2x – 9) + 4 7x + 5 – 3x = -8x + 5 + 12x

49. Domino WKST!

50. Real World Applicaiton See Note Sheet…

51. Katie works at a restaurant. She earns $3 per hour base plus tips. She averages $12 in tip per hour. How many hours until she has earned $333? 22.2 hours

52. A car salesman base salary is $21,000 plus 5% commission on sales. How much must he sell to earn $65,000. $880,000 of cars

53. The bill from your plumber is $134. The cost for labor was $32 per hour. The cost for material was $46. How many hours did the plumber work? 2.75 hours

54. Honors Alg 2 The perimeter of a triangle is 35 feet. If the sides are 3x – 5, 2x – 3, and 15-x, what are its dimensions? x = 7 sides of 16, 13, and 8 units

55. Assignment: WS 1.1-3, #11-23 on backside Honors Alg 2