Homework Answers

1. Homework Answers Standardized Test Prep & Mixed Review P. 192 #s 58-68 all 58) 62) 59) 63) 60) 64) 61) 65)

2. Homework Answers Standardized Test Prep & Mixed Review P. 192 #s 58-68 all 66) Whole numbers 67) Natural numbers 68) Integers

3. Homework Answers Standardized Test Prep & Mixed Review P. 199 #s 53-66 all

4. Homework Answers Standardized Test Prep & Mixed Review P. 199 #s 53-66 all

5. Section 3 – 5 Working With Sets Objectives: To write sets and identify subsets To find the complement of a set

6. Warm-Up

7. Set: Subset: • A collection of distinct elements • Contains elements from a set

8. Writing Sets Roster Form • Lists the elements of a set within braces { } Example: Set-Builder Notation • Describes the properties of the elements in the set Example:

9. Problem # 1 Using Roster Form & Set-Builder Notation How do you write “T is the set of natural numbers that are less than 6” in roster form? In set-builder notation?

10. Problem # 1 Got it? N is the set of even natural numbers that are less than or equal to 12. How do you write N in roster form? How do you write N in set-builder notation?

11. Problem # 2 Inequalities and Set-Builder Notation a) How do you write the solutions of -5x+7 ≤ 17 in set-builder notation?

12. Problem # 2 Inequalities and Set-Builder Notation b) How do you write the solutions of 9 – 4n > 21 in set-builder notation?

13. Problem # 2 Got it? In set-builder notation, how do you write the solutions of -4x + 3 < 15?

14. You know that a set A is a subset of a set B if each element of A is also an element of B. Example: If B = {-2, -1, 0, 1, 2, 3} and A = {-1, 0, 2}, then A is a subset of B. Written as A B

15. Empty Set: The set that contains no elements. **The empty set is a subset of every set. *Use or { }

16. Problem # 3 Finding Subsets a) What are the subsets of the set {3, 4, 5}?

17. Problem # 3 Finding Subsets b) What are the subsets of the set {1, 2}?

18. Problem # 3 Finding Subsets c) Let A = and B = . Is A a subset of B? Explain.

19. Problem # 3 Got It? What are the subsets of the set P = {a, b, c}?

20. Classwork & Homework Assignment • 3 – 5 Worksheet #s 1-23 all

21. Homework Answers3-5 Practice Form G #s 1-23 all • M = {-4, -3, -2, -1, 0, . . .} M = • N = {2, 0, -2, -4, -6. . .} N = • P ={1, 5, 25} P = • R = R = 5) B = 6) M = 7) S = 8) G = 9) 10) 11)

22. Homework Answers3-5 Practice Form G #s 1-23 all 12) 13) 14) 15) 16) 17) 18) { }, {a}, {b}, {c}, {d}, {a,b}, {a,c}, {a,d}, {b,c}, {b,d}, {c,d}, {a,b,c}, {a,b,d} , {a,c,d} , {b,c,d} {a, b, c, d} 19) { }, {0}, {3}, {6}, {9}, {0, 3}, {0, 6}, {0, 9}, {3, 6}, {3, 9}, {6, 9}, {0, 3, 6}, {0, 3, 9}, {0, 6, 9}, {3, 6, 9}, {0, 3, 6, 9} 20) { }, {car}, {bus}, {truck}, {car, bus}, {car, truck}, {bus, truck}, {car, bus, truck} 21) { }, {-5}, {5}, {-5, 5} 22) { }, {0} 23) { }, {red}, {blue}, {yellow}, {red, blue}, {red, yellow}, {blue, yellow}, {red, blue, yellow}

23. Homework Answers3-5 Reteaching #s 1-13 all

24. Homework Answers3-5 Reteaching #s 1-13 all

25. Homework Answers3-5 Practice Form K #s 1-23 all • M = {-4, -3, -2, -1, 0, . . .} M = • N = {2, 0, -2, -4, -6. . .} N = • P ={1, 5, 25} P = 4) R = = • 6) 7) 8) 9) 10) 11) { }, {x}, {y}, {z}, {x,y}, {x,z}, {y,z}, {x,y,z} 12) { }, {0} • { }, {car}, {boat}, {airplane}, {car, boat}, {car, airplane}, {boat, airplane}, {car, boat, airplane} 14) { }, {-2}, {2}, {-2, 2} 15) A’={0, 5, 9} 16) R’ ={-4, -2, 0} 17) yes, each element of A is in U 18) no, 11 is not in B 19) no, 15 is not in A 20) A’ = {Mon., Tues., Wed., Thurs., Fri.} A’ =

26. 3 – 5 Working With SetsContinued Objectives: To write sets and identify subsets To find the complement of a set

27. Warm-Up

28. Universal Set: Complement of a Set: • The largest set you are using. • The set of all elements in the universal set that are not in the set. *The complement of A is A’

29. Problem # 4 Finding the Complement of a Set a) Universal Set U = {months of the year} and set A = {months with exactly 31 days}. What is the complement of set A? Write your answers in roster form.

30. Problem # 4 Finding the Complement of a Set b) Given that the universal set U = {car, truck, van, school bus, bicycle} and the set A is the set of all vehicles that have 4 wheels, what is the complement of set A?

31. Problem # 4 Finding the Complement of a Set c) Universal Set U = {1, 2, 3, 4, 5} and set A = {2, 3}. What is A’?

32. Problem # 4 Got It? Universal Set U = {…-3, -2, -1, 0, 1, 2, 3, …} and set A = {…-3, -1, 1, 3, …}. What is A’?

33. Classwork Assignment • 3–5 Practice Form G #s 24-32 all

34. Homework Assignment • 3–5 Practice Form G #s 24-32 all

35. Homework Answers 3-5 Practice Form G #s 24-32 all 24) 30) 25) 31) 26) 27) 28) 32) 29)

36. 3 – 6 Objectives: To write sets and identify subsets To find the complement of a set

37. Warm-Up

38. Interval Notation: • Used to describe an interval on the number line, using three special symbols: • Parenthesis: • Brackets: • Infinity:

39. Problem # 5 Using Interval Notation • What is the graph of [-4, 6)? How do you write [-4, 6) as an inequality? • What is the graph of (-∞, 2]? How do you write (-∞, 2] as an inequality?

40. Problem # 5 Using Interval Notation • What is the graph of x ≤ -1 or x > 2? How do you write x ≤ -1 or x > 2 in interval notation? • What is the graph of x < -2 or x ≥ 1? How do you write x < -2 or x ≥ 1 in interval notation?

41. Problem # 5 Got It? a) What is the graph of (-2, 7]? How do you write (-2, 7] as an inequality? b) What is the graph of y > 7? How do you write y > 7 in interval notation?

42. Classwork Assignment • 3-6 Pp. 204 – 205 #s 23-34 all

43. Homework Assignment • 3-6 Pp. 204 – 205 #s 23-34 all

44. Homework Answers3-6 Pp. 204 – 205 #s 23-34 all 23) 24) 25)

45. Homework Answers 26) 27) 28)

46. Homework Answers 29) 30) 31) 32)

47. Homework Answers 33) 34)

49. 3 – 6CompoundInequalities Objectives: To solve and graph inequalities containing the word and To solve and graph inequalities containing the word or

50. Warm-Up Inequality ______________________