Algebra 2 BC



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|DAY |TOPIC |ASSIGNMENT |

|1 |SETS OF NUMBERS AND NOTATIONS |Skip Roster Notation |

| |(Emphasis on Set-Builder and Interval Notation) |1.1 p. 10-13 #15, 18, 20,27- 39 odd, 46, 47, 63-65 |

|2 |PROPERTIES OF REAL NUMBERS AND APPLICATIONS |1.2 p. 17-18 #15-26, 29, 30, 35-41 (you need to actually explain |

| | |#41) |

|3 |More on Notation and Properties |worksheets |

|4 |QUIZ |TO BE ANNOUNCED |

|5 |Solving Linear Equations and Inequalities |2.1 p. 94-95 #2, 3-19 odd, Choose 2 of the following: 21, 40, 48 |

|6 |Graphing Linear Equations |Graphs on graph paper; use a ruler |

| |p. 109 #21 together if time |2.3 p. 109-110 #1-8, 13, 14, 17-20; |

|7 |Finding slope, Writing Linear Equations |2.4 p.120-122 #1-11 (skip 9), 23-25, 42 |

|8 |same as above |2.4 p. 121-123 #13-18, 22a [use y-y1=m(x-x1)], 31, 35, 44-46 |

|9 |Solving and Graphing Linear Inequalities |2.5 p.128-130 #1-5, 10, 25, 26, 38-40, 44-46, 52, |

| |(#10 in class if time) | |

|10/11 |Loose Ends/REVIEW |Review: p.76 #1-12, p.166-168 #4-13, 19-40 |

|12 |TEST |PSSA/SAT Review TBA |

1. All numbers that you have dealt with up until this point are known as ___________ numbers.

a. ___________________ numbers are based on the idea that _________________. More on this to come in a later chapter!

2. Real numbers can be broken down into groups known as ____________________.

|Subsets of Real Numbers |

|Name |Explanation |Example |

|Natural Numbers | | |

|Whole Numbers | | |

|Integers | | |

|Rational Numbers | | |

|Irrational Numbers | | |

3. State which set(s) each number is in, choosing from N (natural), W (whole), Z (Integer), Q(rational), Irrational, and R (real). Then order from least to greatest.

a) [pic] b) [pic]

4. True or False?

a) Every natural number is an integer: ________________

b) Every integer is a whole number: ________________

c) Some rational numbers are integers: ________________

d) Every whole number is an integer: ________________

|Methods of Notation |

|Words |Set Notation |Interval Notation |Number Line |

| | | | |

| | | | |

| | | | |

|All numbers greater than or equal to 4 | | | |

| | |[pic] | |

| |[pic] | | |

|Properties of Real Numbers |

|If a, b, and c are all real numbers, then… |

|Property |Addition |Multiplication |

|Commutative | | |

| | |[pic] |

|Associative | | |

|Distributive | | |

| |[pic] | |

|Inverse | | |

| | | |

| |*opposite or additive inverse |*reciprocal or multiplicative inverse |

|Identity | | |

| |[pic], [pic] | |

1. Find the additive and multiplicative inverse of each number

Note: We are trying to find a number so that our “pair” will add to _____ and multiply to _____.

a) [pic] b) [pic] c) [pic] d) [pic]

add: add: add: add:

mult: mult: mult: mult:

2. Determine which property is being used and be sure to include which operation (add or multiply)

Property Operation

a. [pic] _______________________ ___________________

b. [pic] _______________________ ___________________

c. [pic] _______________________ ___________________

d. [pic] _______________________ ___________________

e. [pic] _______________________ ___________________

f. [pic] _______________________ ___________________

3. Fill in each of the blanks below, and then state the property (and operation) that was used.

Property Operation

a. [pic] _______________________ ___________________

b. [pic] _______________________ ___________________

c. [pic] _______________________ ___________________

d. [pic] _______________________ ___________________

e. [pic] _______________________ ___________________

f. [pic] _______________________ ___________________

4. Applications of the properties: Use the table at the right to answer each of the following questions.

a. Cost of 2 pens and 3 notebooks

b. Cost of 1 binder and 5 notebooks

c. Cost of 3 notebooks at 20% discount,

a binder at 25% discount, and 2 pens

1. Rewrite using set-builder notation: {-1, 0, 1, 2, 3, 4}

2. Rewrite using set-builder notation: {5, 6, 7, 8}

3. Represent the numbers between -7 and 11 using set-builder notation. Note: the word "between" suggests t

hat the endpoints are not included. Also note that I did not say the integers between -7 and 11, I said the numbers between -7 and 11.

4. Rewrite using interval: [pic]

5. Rewrite using interval: [pic]

6. Draw on a number line: [pic]

7. [pic]

8. [pic]

9. [pic]

10. [pic]

11. the numbers between 4 and 10

12. the numbers less than -2 or greater than 7

[pic]

13. Given the numbers above, determine which could be classified as the following:

a. Which numbers are Natural Numbers?_____________________________

b. Which numbers are Rational Numbers?____________________________

c. Which numbers are Integers?__________________________________

d. Which numbers are Real Numbers?_______________________________

e. Which numbers are Irrational Numbers?_________________________

14. List the numbers above in order from least to greatest…

15. Fill in the blank, where appropriate, and state the appropriate property.

[pic] [pic] [pic]

Property: Property: Property:

1. Solving inequalities is (almost) like solving equations….

1. When solving equations, one of three outcomes can occur…

a. [pic] b. [pic] c. [pic]

2. To summarize…

a. When the variable does not drop out, there is ________ solution.

b. When the variable drops out and the equation is true, then there are ____________ solutions (

c. When the variable drops out and the equation is false, then there are ________ solutions (

3. Examples to try:

a. [pic] b. [pic] c. [pic]

d. [pic] e. [pic] f. [pic]

4. Solving and Graphing Inequalities

a. All rules that apply for solving equations are ____________________, except for one…

When you multiply or divide by a ____________ number, you must…

|< or > | |[pic] or [pic] | |

|< or [pic] | |> or [pic] | |

5. Examples:

a. [pic]

b. [pic]

c. [pic]

d. [pic]

6. Word Problems

a. Blair wants to spend less than $50 at the grocery store. He already has $37 worth of groceries in his shopping cart and is going to buy some fresh vegetables for $0.75 each. How many vegetables v can he buy and stay under his limit?

b. The average of 4 numbers is 42. Three of the numbers are 35, 53, and 60. What must the missing number be?

c. You create a fenced in rectangle from 510ft of fencing. If the length of the rectangle is fifteen greater than three times the width, determine the area of the fenced in yard. Draw a diagram to help.

d. Find two consecutive even integers such that two times the first plus three times the second is 76.

7. Closure

a. What are the 3 possible scenarios when solving an equation? What makes them occur?

b. What dictates open and closed circles for graphing inequalities? How do you know which direction to shade?

c. What is the main difference between solving equations and solving inequalities?

1. There will be a mini quiz at the end of class today (starting @ the 8 minute bell).

2. For the quiz, you must know the following vocabulary words:

slope, x-intercept, rate of change, y-intercept, slope-intercept, linear function, horizontal, and vertical

3. In addition, you must be able to perform the following operations:

a. Determine if a set of data represents a linear function

b. Convert an equation into slope-intercept form

c. Graph lines (including horizontal and vertical ones)

4. Use the rest of this notes sheet as your guide to answer the questions on the next few pages. You may work in small groups. Use this time wisely to practice problems similar to those on the mini quiz.

A linear function can be written in the form [pic] (this is known as slope intercept form).

Note: Sometimes instead of y, we use the “fancy” function notation [pic].

To determine if data is a linear function, check to see if the ratios are the same.

This is linear function because the rate of change

is always the same.

x always adds 2, and f(x) always adds 3

This means the slope is 3/2!

This is NOT a linear function because the rate of

change is NOT always the same.

x always adds 2, but f(x) always different

numbers!!!

To convert an equation to slope-intercept form, solve for y! Example:

[pic]

With your partner, use the examples on the previous two pages to help you answer the following question. You, of course, may always ask your teacher for help as well.

Graph the following equations. Be sure to identify any information you used to graph the equations.

[pic] [pic] [pic]

[pic]

The first goal for today is to review how to find slope in the following situations:

a) From an equation in slope-intercept form

b) From an equation in a different form

c) From a graph

d) From a table

e) From a line parallel

f) From a line perpendicular

Next, we will review how to write the equation of a line – you must know two forms:

SLOPE-INTERCEPT FORM: POINT-SLOPE FORM:

Be able to write the equation of a line…

a) From a table

b) From two points

c) From a point and the slope

d) From a graph

e) Through a point and a parallel line

f) Through a point and a perpendicular line

[pic]

[pic]

Once you finish your mini quiz, you can start on tonight’s homework. The pages are copied here for you…

. [pic]

First we need to be able to solve for ____ in linear inequalities. Then we can ______________ them!

Example: [pic]

|< or > | |[pic] or [pic] | |

|< or [pic] | |> or [pic] | |

#2) [pic] #3) [pic]

Solid / Dashed Above / Below Solid / Dashed Above / Below

Word Problem:

For a football game, student tickets cost $3 and adult tickets cost $5. The school is hoping to raise at least $400 in ticket sales. If x represents the number of student tickets and y represents the number of adult tickets, write an inequality to model this situation.

a) If 40 student tickets are sold and 20 adult tickets are sold, will the school raise enough money?

For each graph below, write an inequality that represents it. Use the clues below to help you.

[pic]

m = ______ m = ______ m = ______

b = ______ b = ______ b = ______

Above or Below Above or Below Above or Below

Solid or Dashed Solid or Dashed Solid or Dashed

Inequality: ______________ Inequality: ______________ Inequality: ______________

1) [pic] 2) [pic]

3) [pic] 4) [pic]

5)

The review problems in class as well as the homework problems listed on day 10 of the syllabus will be the best way to prepare you for tomorrow’s tests.

The following topics will be covered:

1. Sets of Numbers: Make sure you know what Natural Numbers, Whole Numbers, Integers, Rational Numbers and Irrational numbers are.

2. Notation: Please know how to write answers in interval notation and set notation.

3. Properties of Numbers: Be familiar with Commutative, Associative, Distributive, Identity, and Inverse properties.

4. Solving Equations: Be able to solve (somewhat) complex equations.

5. Solving Inequalities: Be able to solve inequalities. Remember, when you multiply or divide by a negative number, you must flip the sign!

6. Slope: Know the definition of slope, and be able to find slope using the slope formula (you must memorize this!)

7. Writing Linear Equations: Be able to write an equation of a line when you know a) two points, b) a point and the slope, c) a point and a line parallel, d) a point and a line perpendicular

8. Graphing Lines: Be able to graph a line when given an equation (even if it is not given in slope-intercept form!)

9. Graphing Inequalities: Be able to graph inequalities – remember solid/dashed and above/below.

10. Word Problems: Be able to solve problems about the topics listed above!

Use the graphs when needed during the review game.

-----------------------

Mr. Werley

Name_______________________________

Unit 1: Equations, Inequalities & Linear Graphing

Date _________ Period_________

U1 D1: Sets of Numbers & Set, Roster, Interval Notations

Fill in the Diagram.

Word Bank:

➢ Whole Numbers

➢ Rational Numbers

➢ Real Numbers

➢ Whole Numbers

➢ Irrational Numbers

➢ Integers

Date _________ Period_________

U1 D2: Properties of Real Numbers & Consumer Applications

Conestoga Supply Store

Item

Price $

Notebook

$1.79

Pen

$2.89

Binder

$3.19

Date _________ Period_________

U1 D3: More on Notation and Properties

Date _________ Period_________

U1 D3: More on Notation and Properties

OVER

Date _________ Period_________

U1 D5: Solving Linear Equations and Inequalities

Date _________ Period_________

U1 D6: Graphing Linear Equations

y-intercept: the point where the line crosses the y-axis. (0, 3)

x-intercept: the point where the line crosses the x-axis. (5, 0)

OVER 2

UP 3

x = #

y = #

[pic]

[pic]

Undefined

Zero or

No Slope

Negative

Type of Line:

Vertical

Horizontal

Diagonal

Diagonal

Graph of Line

Equation of Line?

Positive

Slope of Line?

x

0

2

4

6

f(x)

-1

2

5

8

+3

+3

+3

+2

+2

+2

x

-1

2

5

8

f(x)

0

1

3

6

+1

+2

+3

+2

+2

+2

[pic]

Date _________ Period_________

U1 D7: Finding Slope & Writing Linear Equations

Date _________ Period_________

U1 D8: More on Slopes & Writing Equations of Lines

Date _________ Period_________

U1 D9: Solving and Graphing Linear Inequalities

Date _________ Period_________

U1 D10: Unit 1 Review

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