Name:____________________________________________________________ Date: _______________ Algebra 2011-2012

Name:______________________________

Teacher:____________________________

Pd: _______

DAY 1: (Ch. 3-1 to 3-3) SWBAT: Identify solutions to inequalities; write and graph inequalities with one variable

Table of Contents

Pgs: 1-5 HW: Page 6 & 7 DAY 2: (Ch. 3-4 to 3-5) SWBAT: Identify solutions to inequalities; Solve two-step Inequalities

Pgs: 8-11 HW: Page 12 & 13 DAY 3: (Ch. 3-5) SWBAT: Identify solutions to inequalities; Solve multi-step Inequalities

Pgs: 14-17 HW: Pages 18 DAY 4: (Ch. 3-6) SWBAT: Solve compound inequalities with one variable.

Graph solution sets of compound inequalities with one variable.

Pgs: 19-25 HW: Page 26 & 27

• DAY 5: Quiz: Day 1 to DAY 4

DAY 6: SWBAT: Determine Unions and Intersections of Sets Pgs: 28-31 HW: Page 32 Day 7: SWBAT: Determine the Complement of a Subset Pgs: 33-36 HW: Page 37 Day 8: SWBAT: Create Venn diagrams to solve problems with subsets Pgs: 38-40 HW: Page 41 & 42

• DAY 9: Chapter 3 - Practice Test: Review using E-Clickers

• DAY 10: Chapter 3 Test

1

Writing & Graphing Inequalities - (Day1)

Directions: Compare. Write < , > , or = in the box.

Warm – Up

1) – 3 □ 2 2) 6.5 □ 6.3 3)21 □

43 4) 0.25 □

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Graphing Inequalities

Interval Notation

Non-ending Interval: is interpreted as x > a where a is not included and infinity is always expressed as being "open" (not included).

Non-ending Interval: is interpreted as x < b where b is included and again, infinity is always expressed as being "open" (not included).

2

Example 1: Identifying Solutions to Inequalities and Graphing Inequalities

A) 1

Practice: Identifying Solutions to Inequalities and Graphing Inequalities

1) 1−<x

2) p≤9

3) x<− 4

4) 16≤x

3

Example 2: Writing Inequalities from a Graph

Write the inequality and the interval notation shown by the graph.

C)

Practice: Writing Inequalities from a Graph

Write the inequality and the interval notation shown by the graph.

5)

6)

7)

8)

4

Example 3: Solving One Step Inequalities Solve the inequalities and graph the solutions. Write your solution using interval notation.

9.

10.

11.

Practice Solve the inequalities and graph the solutions. Write your solution using interval notation.

12. 13. 14. -9r

5

SUMMARY

Exit Ticket

1. Does the inequality sign change for any of the following? Answer YES or NO

a) 102 >x

b) 123 ≤− x

c) x105 −>

d) x416 <−

2.

6

Day 1 - Homework

Directions: Graph each inequality and express in interval notation.

1) x<7 3) 5.0−≤t

2) 12−>d 4) 5≥k

Directions: Write the inequality shown by each graph and express in interval notation.

5)

8)

6)

9)

7)

10)

7

Solve each inequality and graph the solutions.

11)

15)

12)

16)

13)

17)

14)

18)

8

Day 2 – Solving Multi-Step Linear Inequalities Warm – Up

From each graph, write as an inequality and write in interval notation.

Example 1: Solve each inequality and graph the solutions.

a.

b. 4(x + 3) 24

9

c. d.

Practice!

1. 2. 3.

10

Example 2: Interpreting Solutions e.

f.

g. fdfd Practice!

4.

11

5.

6.

Summary

Exit Ticket

12

Day 2 - Homework:

4.

5. Which value of x is in the solution set of the inequality -2x + 5 > 17 ?

(1) -8 (3) -4 (2) -6 (4) 12

13

Solve each inequality, graph the solutions, and write your answers in interval notation.

6.

7.

8.

9.

14

Day 3 – Solving Multi-Step Linear Inequalities Warm - Up:

Example 1: Combining like terms.

Set-Builder Notation

Example: { }: 2x x > (We read this as “the set of all x such that x is greater than 2.”)

There are 3 parts to Set-Builder Notation

1. Curly Braces: { } 2. Variable: x| 3. Inequality: x ≤ 5

The solution to in set builder notation is ___________________

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Practice

a.

Example 2: Variable on both sides of the equal sign.

b. Practice

16

Example 3: Complex Multi-Step Inequalities

Practice

c.

17

Challenge Write an inequality to solve the problem below.

SUMMARY Exit Ticket Which choice represents the solution to the inequality below?

18

Day 3 –HW Solve each inequality. Graph the solutions and write your answer in interval and set-builder notation.

1.

5.

2.

6.

3.

7.

4.

8.

19

Day 4 - Solving Compound Inequalities Warm – Up

Directions: Solve each inequality and graph the solution.

1) xx 38 >+ 2)

You can graph the solutions of a compound inequality involving AND by using the idea of an overlapping region.

How do you think we can write this solution using interval notation? __________________

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Compound Inequalities The inequalities you have seen so far are simple inequalities. When two simple inequalities are combined into one statement by the words AND or OR, the result is called a compound inequality.

NOTE the following symbols:

Λ means AND V means OR

Ex 1

Practice:

21

Interval Notation: (description) (diagram)

Open Interval: (a, b) is interpreted as a < x < b where the endpoints are NOT included. (While this notation resembles an ordered pair, in this context it refers to the interval upon which you are working.)

(1, 5)

Closed Interval: [a, b] is interpreted as a < x < b where the endpoints are included.

[1, 5]

Half-Open Interval: (a, b] is interpreted as a < x < b where a is not included, but b is included.

(1, 5]

Half-Open Interval: [a, b) is interpreted as a < x < b where a is included, but b is not included.

[1, 5)

____________________________________________________________________________________________

Example 2: Writing Compound Inequalities from a Graph

as an inequality.

in interval notation.

22

Practice: Writing Compound Inequalities from a Graph

Example 3: Solve the following compound inequality and graph the solution.

5 ≤ 4x + 1 ≤ 13

23

Practice

Example 4: Solve the following compound inequality and graph the solution.

24

Practice: Solve the following compound inequality and graph the solution.

Challenge

25

Summary

Exit Ticket

26

Day 4 - Compound Inequalities HW

Directions: Circle your answer.

1)

Directions: Solve the inequality, graph the solution, express in interval notation and set builder notation.

2)

4)

3)

5)

27

Directions: Write a compound inequality from the graph provided and express solution in interval notation.

6)

7)

8)

9)

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SET THEORY – Day 6

SWBAT: Determine Unions and Intersections of Sets

Warm – Up

Use interval notation to represent the set of numbers. Rewrite each in set – builder notation.

A. – 1 < x ≤ 2 C. ( -∞, 4]

B. 3 ≤ x ≤ 10 D. (-2, ∞)

A set is a collection of objects called elements.

The elements included in {…} are in roster form.

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The union of sets A and B is the set of all elements that are in both A and B. To indicate the union of sets A and B, write A ∪ Β. The union of two sets can be thought of as the “joining” of the sets (any element in either set must appear in their union).

Example 2: Finding the Union of Two Sets Find the union of the sets.

1) A = {0, 2, 4, 8, 16} and B = {2, 4, 6, 8}

2) M = {x : x < 10} and P = {x : x > 5}

Practice: Finding the Union of Two Sets Find the union of the sets.

1) J = {-3, -2, -1} and K = {0, 1, 2, 3}

2) A = {3, 6, 9} and B = {2, 4, 6, 8}

3) R = {x│ x > 3} and S = {x│ x > 7}

4) C = {x│ x ≤ -1} and D = {x│-1 < x ≤ 0}

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The intersection of sets A and B is the set of all elements that are in both A and B. To indicate the intersection of sets A and B, write A ∩ B.

A set with no elements is called the empty set, or the null set. The symbol for the null set is Ø.

Example 3: Finding the Intersection of Two Sets Find the intersection of the sets.

1) X = {5, 6, 7, 8, 9} and Y = {1, 3, 5}

2) S = [0, 3) and T = [-1, ∞)

Practice: Finding the Intersection of Two Sets Find the intersection of the sets.

1) F = {1, 3, 5, 7} and G = {2, 4, 6, 8}

2) M = {7, 8, 9, 10} and N = {5, 6, 7, 8, 9}

3) P = (-3, -1] and V = (-2, −1)

4) X = [-4, 5) and Y = (2, 10]

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Challenge Problem:

Summary:

Exit Ticket:

32

Homework

Find the union and intersection of each pair of sets.

1) A = {red, blue, yellow} and B{green, red} Union Intersection

2) X = {-10, -8, -6, -4, -2} and Y{-4, -2, 0, 2, 4} Union Intersection

3) L = {x│0 ≤ x ≤ 10} and M = {x│5 ≤ x ≤ 15} Union Intersection

4) A = (0, 2) and B = [2, 5) Union Intersection

5) F = {x│ x > 3} and G = {x│ x ≤ 5} Union Intersection

6) K = (-∞, -1) and L = (-6, 2) Union Intersection

33

SET THEORY – Day 7 SWBAT: Determine the Complement of a Subset

Warm – Up

Write the union and intersections of each pair of sets.

1) A = {a, e} B = {a, b, c}

C = {a, x, y, z}

2) A = {1, 2, 3} B = {-5, -3, -2, 0}

C = {-2, 0, 2, 3}

Let B = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10} A = {3, 6, 9}

Set A is a subset of set B, since every element in set A is also an element of set B. The notation is: A ⊂ B

Set B on the other hand would not be a subset of A, since every element in set B is not an element of set A. The notation is: B ⊄ A

The empty set is denoted with the symbol: ∅ or { }

The complement of a set can be represented with several differing notations. The complement of set A can be written as: Ac or A1

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Example 1: Let U (the universal set) = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10} (a subset of the positive integers) A = {2, 4, 6, 8} B = {1, 2, 3, 4, 5}

1) A ∩ B =

2) A ∪ B =

3) Ac =

4) Bc =

5) A ⊂ B = YES or NO

Practice

1) U = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10} A = {2, 4, 6, 8, 10} B = {1,2,3,4,5,6}

35

Example 2: Suppose that the universe in each of the following is the set of real numbers. State the complement of each set using set-builder notation.

{x : x ≥ 4}

Practice: Suppose that the universe in each of the following is the set of real numbers. State the complement of each set using set-builder notation.

• {x : x < −3}

• {x : x ≥ -2}

Example 3: Suppose that the universe in each of the following is the set of real numbers. State the complement of each set using interval notation.

(−∞, 3]

Practice: Suppose that the universe in each of the following is the set of real numbers. State the complement of each set using interval notation.

• (−2, ∞)

• [−4, 9)

Determine if A is a subset of B. If so, find the complement of A in B.

A = (0, ∞)

B = (-∞, ∞)

36

Challenge Problem: 1. (A ∩ B) c = 2. (A ∪ B) c =

Summary:

Exit Ticket:

37

Homework

1) U = {2,4,6,8,10,12,14,16,18,20} 5) In the set of real number, the complement of the set A = {2, 4, 8, 16} [5, ∞) would be which of the following? B = {6, 8, 10, 12, 14, 16}

• A ∪ B =

• A ∩ B =

• Is A ⊂ B? = Yes or No

• Bc =

• Ac =

• 2) U = {10, 20, 30, 40, 50, 60}

A = {10} B = {10, 40, 60}

• A ∪ B =

• A ∩ B =

• Is A ⊂ B? = Yes or No

• Ac =

• B c =

3) Given: Set A = {(-2,-1), (-1,0), (1,8)} Set B = {(-3,-4), (-2,-1), (-1,2), (1,8)}. What is the intersection of sets A and B?

4) Suppose that the universe in each of the following is the set of real numbers. State the complement

of each set. Use set-builder notation.

• {x : x < −12}

• {x : x > 8}

• {x : x < −3or x ≥ 6}

38

Venn Diagrams with Set Theory (Day 8)

SWBAT: Create Venn diagrams to solve problems with subsets

Warm – Up

A Venn diagram is a visual aid used to assist us in sorting through the logic of certain types of questions. Venn diagrams show the relationships between different sets.

EXAMPLE 1: Use the Venn diagram below to answer each of the following.

(a) How many elements are contained in A ∩ B? ______

(b) How many elements are contained in A ∪ C ? ______

(c) How many elements are contained in Ac? ______

(d) How many elements are contained in Bc? ______

(e) How many elements are contained in A ∩ B ∩ C ? ______

(f) How many elements are contained in A ∪ B ∪ C ? ______

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Practice: Use the Venn diagram below to answer each of the following.

(a) How many elements are contained in A ∩ B ∩ C? ______

(b) How many elements are contained in A ∪ B ∪ C? ______

(c) How many elements are contained in C ∩ B? ______

(d) How many elements are contained in B ∪ C? ______

(e) How many elements are contained in Ac? ______

(f) How many elements are contained in Bc? ______

EXAMPLE 2: Create a Venn diagram below to answer the following question.

In a class of 50 students, 18 take Chorus, 26 take Band, and 2 take both Chorus and Band. How many students in the class are not enrolled in either Chorus or Band?

Practice: Create a Venn diagram below to answer each of the following questions.

1. In a school of 320 students, 85 students are in the band, 200 students are on sports teams, and 60 students participate in both activities. How many students are not involved in either band or sports?

2.

40

Challenge: Create a Venn diagram below to answer the following question.

A veterinarian surveys 26 of his patrons. He discovers that 14 have dogs, 10 have cats, and 5 have fish. Four have dogs and cats, 3 have dogs and fish, and one has a cat and fish. If no one has all three kinds of pets, how many patrons have none of these pets?

Summary:

Exit Ticket

41

HOMEWORK:

1. Use the Venn diagram below to answer each of the following.

(a) How many elements are contained in T ∩ B? ______

(b) How many elements are contained in T ∪ F? ______

(c) How many elements are contained in Tc? ______

(d) How many elements are contained in Bc? ______

(e) How many elements are contained in Fc? ______

(f) How many elements are contained in T ∩ B ∩ F? ______

(g) How many elements are contained in T ∪ B ∪ F ? ______

(h) (Challenge) How many elements are contained in (T ∪ B) ∩ F? ______

2. In a survey of 400 teenage shoppers at a large mall, 240 said they shopped at Abernathy's, 210 said they shopped at Bongo Republic, and 90 said they shopped at both stores. How many of the teenage shoppers surveyed did not shop at either store?

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3. There are 1200 people working in an office building. 750 people get to work by using an automobile, 900 people get to work using public transportation, and 650 people get to work by using both an automobile and public transportation. How many people get to work without using an automobile or public transportation?

4. A store selling major appliances has 550 sales this week. 300 sales are for appliances only, 10 sales are for extended service agreements only, and 100 sales are for appliances and extended services agreements. How many sales are not for appliances nor extended service agreements?

5.