Maths Algebra

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1.2.5.pdf

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1.2.5 Journal: Arithmetic Sequences Journal Algebra I Sem 2 (S2923741) Brady Odom Points possible: 20 Date: ____________

Scenario: Swim Training

Instructions:

View the video found on page 1 of this journal activity.

Using the information provided in the video, answer the questions below.

Show your work for all calculations

The Students' Conjectures: Two students, Ernest and Denise, are training for a swim halfmarathon in 10 weeks, and they disagree about their training schedule. If they follow Ernest's suggested training schedule, will they be ready to swim 5 km in time for the halfmarathon?

1. Complete the table to summarize each student’s suggested training schedule: (2 points: 1 point for each row of the chart)

Classmate Conjecture

Ernest

Denise

2. Do the distances they swim every week make an arithmetic sequence? Why? (1 point)

Analyzing the Data:

3. Fill out the schedules for the first four weeks of training: (2 points: 1 point for each person)

Ernest's Schedule Denise's Schedule

Week Kilometers to swim daily Week Kilometers to swim daily

1 1

2 2

3 3

4 4

4. Write the recursive formula for each sequence: an = an – 1 + d.

(2 points: 1 point for each formula)

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Student d Recursive formula

Ernest

Denise

5. Find the explicit formula for each arithmetic sequence: an = a1 + (n – 1) • d.

(4 points: 2 points for each formula)

Student Explicit formula

Ernest

Denise

6. Using the explicit formula, calculate how far the students will be swimming on week 10 using Ernest’s schedule: (2 points)

7. Using the explicit formula, calculate how far the students will be swimming on week 10 using Denise’s schedule: (2 points)

8. What is the domain for the functions describing Ernest’s and Denise’s training schedules? (1 point)

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Making a Decision

9. Which training schedule will get them ready to swim 5 km in time for the halfmarathon? (1 point)

10. Look at the two graphs below. Which one represents Ernest's training schedule? Explain your answer. (2 points)

11. Sketch a graph of Denise’s training schedule for the 10 weeks before the race. (1 point)

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1.3.5.pdf

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1.3.5 Practice: Modeling: Geometric Sequences Practice Assignment Algebra I Sem 2 (S2923741) Brady Odom Points possible: 20 Date: ____________

YOUR ASSIGNMENT: Ball Bounce You have chosen one ball; now you will predict how high it bounces on the 10th bounce.

1. Circle the ball you chose, and explain why you selected it. (1 point)

Basketball Tennis ball Tabletennis ball

I chose this ball because:

Writing an Equation

2. Assume that the ball rebounds the same percentage on each bounce. Using the initial drop height and the height after the first bounce, find the common ratio r. Note: Round r to three decimal places. (2 points: 1 point for showing your work, 1 point for the answer)

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r = _________

3. State the general version of the recursive formula. (1 point)

4. Find the recursive formula for the height of your ball. (1 point)

5. Fill out the following table for your ball's height after the first three bounces. Note: Let n = bounce number. On the initial drop, n = 0. (4 points: 1 point for each line)

Bounce n Height

Initial drop 0

First bounce 1

Second bounce 2

Third bounce 3

6. Write the explicit formula for the geometric sequence of the height of the ball on the nth bounce. Use the formula an = a1 • r

n – 1. (2 points)

Solving the Problem

7. Using the explicit formula, find the height of the ball on the 10th bounce. (2 points: 1 point for showing your work, 1 point for the answer)

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8. Using your previous calculations, draw a graph and plot the ball's maximum height (y) when the number of bounces (x) = 0, 1, 2, 3, and 10. Be sure to label your axes. (2 points)

Taking Time to Reflect

9. What are some factors that could affect the ball's bounce? Why might a ball bounce higher or lower than the regulated height? (1 point)

10. For the sport you chose, why would it matter if a player used a ball that bounced higher than the regulation? (1 point)

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1.5.4.pdf

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1.5.4 Test (TS): Sequences and Functions Test Algebra I Sem 2 (S2923741) Brady Odom Points possible: 50 Date: ____________

Answer the following questions using what you've learned from this unit. Write your answers in the space provided. Be sure to show all work.

FINDING PATTERNS

1. Draw the correct shapes in the empty boxes to complete the pattern. (4 points)

2. Write in the missing words to complete the pattern. (3 points)

Male Son Female Daughter Male ________ Female Aunt Male Brother Female _________ Male Father ____________ Mother

SEQUENCES

3. Describe and extend each sequence.

A. 5, 7, 19, 31, ...

Step 1: Describe the rule for the sequence. (2 points)

Step 2: Find the next two terms of the sequence. Show your work. (2 points)

THE EXPLICIT FORMULA

4. Use the following arithmetic sequence and the formula to answer the questions below.

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123, 116, 109, 102, 95, ...

5. State whether each sequence is arithmetic or geometric, and then find the explicit and recursive formulas for each sequence. (10 points; 5 points each)

6. You visit the Royal Gorge Bridge near Canon City, Colorado. When walking across the bridge you nudge a small stone off the bridge deck and watch it fall. The distance the stone drops is 16 feet the first second, 48 feet the next second, 80 feet the third second, and so on in an arithmetic sequence.

7. You want to use the hot tub at the hotel you're staying at, but it's not hot enough. The hotel manager tells you that they will turn the heat up and the temperature will increase by 10% each hour. The initial temperature of the hot tub is 68°.

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2.1.4.pdf

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2.1.4 Practice: Modeling: Numerical Data Practice Assignment Algebra I Sem 2 (S2923741) Brady Odom Points possible: 20 Date: ____________

Your Assignment: Furry Friends

Choosing a Group of Dogs

Josue and Sara both walk dogs during the week. They each walk 10 dogs in the morning and 10 other dogs in the afternoon. Select one of the groups to see how much the dogs in each group weigh. The heavier dogs usually have more energy and want to take longer walks than the smaller dogs.

1. Which dogwalker did you select? Circle one. (1 point)

Josue Sara

Comparing the Morning and Afternoon Groups

2. Create frequency tables to represent the data for the morning and afternoon dogs as two sets of data. Group the weights into classes that range 10 pounds. Add the intervals for each class in the weight column of the table. (6 points: 2 points for the correct number of charts, 2 points for appropriate intervals, 2 points for correctly portraying data)

3. Create a comparative stemandleaf plot for the morning and afternoon dogs. (6 points: 2 points for the correct form of plot, 2 points for appropriate intervals, 2 points for correctly portraying data)

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Walking the Dogs in One Group

4. The average weights of the dogs are the same for the morning and afternoon groups. Which group of dogs would be easiest to walk as one group? Why? (2 points: 1 point for answer, 1 point for justification)

5. Which group would you choose if you wanted to take a longer walk? Why? (2 points: 1 point for answer, 1 point for justification)

6. Which group do you think would be more difficult to walk? Why? (2 points: 1 point for answer, 1 point for justification)

7. How would you reorganize the dogs to make it easier to walk them together? (1 point)

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2.5.4.pdf

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2.5.4 Journal: Describing Distributions Journal Algebra I Sem 2 (S2923741) Brady Odom Points possible: 20 Date: ____________

Scenario: Relay Track Teams

Instructions:

View the video found on page 1 of this journal activity.

Using the information provided in the video, answer the questions below.

Show your work for all calculations.

Three teams are racing in the district meet. Below are the box plots representing the race times for each team. Analyze the data and decide who you think will win.

The Racer’s Conjectures

1. Complete the table below to describe why each team member thinks his team will win the district meet. (1 point)

Team Reason

Red

Yellow

Blue

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2. Looking at the box plots, do you agree or disagree with each team’s conjecture? Explain your reasoning. (3 points: 1 point for each row of the chart)

Team Yes or No Reason

Red

Yellow

Blue

Analyzing the Data

3. Use the box plots to complete the fivenumber summary chart. (3 points: 1 point for each row of the chart)

Minimum Lower quartile

Median Upper quartile

Maximum

Red

Yellow

Blue

4. Look at the box plots and decide if each team’s distribution is symmetrical or skewed. Circle your answers. (1 point)

Red Negatively skewed Symmetrical Positively skewed

Yellow Negatively skewed Symmetrical Positively skewed

Blue Negatively skewed Symmetrical Positively skewed

Below are the actual race times, in seconds, for each team. They are listed in numerical order, not in the chronological order of actual races.

Race 1

Race 2

Race 3

Race 4

Race 5

Race 6

Race 7

Race 8

Race 9

Red 47.5 42 48.5 44.5 47 41 48 43 49

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Yellow 47.5 45.5 48.5 46.5 47 45 48 46 49

Blue 48.1 46.8 52 47.9 48 46 50 47 53

5. Use the race times to calculate the mean time for each team. Show your work. (3 points: 1 point for each team)

Red

Yellow

Blue

6. How do the three teams rank based on mean times? List them in order from fastest to slowest, and explain your ranking. (1 point)

7. How do the three teams rank based on median times? Explain your ranking. (1 point)

8. The standard deviations for the blue and yellow teams are shown below. Complete the chart by calculating

the variance, , and the standard deviation, , for the red team. Show your work.

(2 points)

Red Yellow Blue

S 1.37 2.41

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9. What do the standard deviations tell you about how the teams race? Explain your thinking. (2 points)

Making a Decision

10. Now that you’ve analyzed the data, it’s time to make a decision. Who do you think will win the district meet?

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Describe how you think each team will do, and explain your reasoning. (3 points)

Red:

Yellow:

Blue:

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2.7.4.pdf

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2.7.4 Test (TS): Descriptive Statistics Test Algebra I Sem 2 (S2923741) Brady Odom Points possible: 50 Date: ____________

Answer the following questions using what you've learned from this unit. Write your answers in the space provided. Be sure to show all work.

DISPLAY DATA

1. The list below shows the ages of the first 20 customers at a new computer game store.

17, 20, 14, 38, 59, 26, 34, 67, 40, 26, 9, 15, 6, 7, 10, 51, 35, 29, 16, 31

Part A. Display the customer age data on this stemandleaf plot. (2 points)

Part B. Use your plot from Part A to display the data in this frequency table. (2 points)

Part C. Use your table from Part B to display the data on this histogram. (2 points)

Part D. Use your results from Parts A – C to answer these questions. (4 points)

a. What does it mean that the customer data are numerical and univariate?

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b. Are the data discrete or continuous? Explain.

c. Which age group had the most customers? Explain how to find the answer using each of the three data displays.

d. Write a question that can be answered using the stemandleaf plot but cannot be answered using the frequency table or histogram.

MEASURE AND DESCRIBE DATA

2. Mike bought a new computer game at the store. He went home and played the game all day! The list below shows the scores for Mike’s first 10 games.

15, 13, 8, 12, 15, 17, 14, 9, 11, 16

Part A. Find the range, mean, median, and mode of Mike's scores. Show your work. (4 points)

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Part B. Use your mean result from Part A to find the variance and standard deviation of Mike's scores. Show your work. Round your answers to the nearest hundredth. (4 points)

Part C. Are your results in Part B for a sample or a population? Explain. (1 point)

Part D. Use your results from Parts A – C to describe the shape of the distribution of Mike's scores. (1 point)

Part E. Use your results from Parts A – D to answer these questions. (3 points)

a. If Mike scored 30 on his next game, would it be an outlier for the set of his first 11 games? Explain. How would a score of 30 affect the range, mean, median, and mode of Mike's scores?

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b. If Mike could add 5 points to every game's score, how would it affect the mean, median, and standard deviation of his scores?

c. If Mike could double every game's score, how would it affect the mean, median, and standard deviation of his scores?

BOX PLOTS

3. The list below shows the number of computer games the store sold each day for the first 11 days it was open.

35, 46, 28, 27, 37, 79, 43, 35, 42, 29, 36

Part A. Find the fivenumber summary for the data. Show your work. (2.5 points)

Part B. Use your results from Part A to display the data on a box plot. (2 points)

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Part C. Use your plot from Part B to find the interquartile range (IQR) of the data. (1 point)

Part D. Use your result from Part C to identify any outliers for the data set. Show your work. (1.5 points)

Part E. The box plot below shows the number of computer games the store sold each day for the second 11 days it was open.

Use the plot above and the one you made in Part B to answer these questions. (2 points)

a. Which data set has the greater range: the first 11 days or the second 11 days? Explain how you used the plots to answer the question.

b. In which data set are the middle 50% of the data values closer to the median? Explain how you used the plots to answer the question.

SELECTING DATA DISPLAYS

4. When training for the state longdistance track championship, Levi charts race times. The results for seven races are in the chart below:

Date Distance run Time

April 3 5 km 35 minutes

April 10 5 km 35 minutes

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April 17 5 km 34 minutes

April 24 5 km 33 minutes

May 1 5 km 31 minutes

May 8 5 km 32 minutes

May 15 5 km 31 minutes

What is the best data display to use to chart Levi's progress? Create that display and describe what it shows. (3 points)

THE LINE OF BEST FIT

5. Kyle and Caitlyn are lab partners in physics class. They are hanging mass on a spring and measuring the resulting stretch. The table and scattergram below display the data they collected. Their goal is to find an equation that models the data.

m (mass in grams) 10 20 30 40 50

s (stretch in cm) 5.8 9.2 12.9 20.2 23.2

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Part I: Explain which variable is the independent variable and which variable is the dependent variable. (2 points)

Part II: Kyle drew an estimated line of best fit. Use the appropriate words from the list next to it to describe the correlation coefficient. (2 points)

positive

negative

perfect

strong

weak

none

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Part III: Assume Kyle and Caitlyn were extremely accurate and the correlation coefficient is r = 0.99. Find the line of best fit to model the data.

Step 1: Use the formula to find the slope of the line of best fit. Caitlyn already calculated the

standard deviation of the yvalues as s y = 7.32. (4 points)

Step 2: Find the yintercept using the formula a = y − bx. (2 points)

Step 3: Write the line of best fit, , to model the data. Replace y and x with the variables

used in the experiment and on the graph. (2 points)

Part IV: What do the slope and the yintercept tell you about the variables in the experiment? (2 points)

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Part V: Use the line of best fit from Part III, Step 3 to predict how far the spring will stretch with a mass of 67 grams. (1 point)

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3.3.6.pdf

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3.3.6 Practice: Modeling: Multiplying Binomials Practice Assignment Algebra I Sem 2 (S2923741) Brady Odom Points possible: 20 Date: ____________

YOUR ASSIGNMENT:

Choosing a Photo

Francesca wants to give one of her photographs to a friend as a gift. Help her choose the photograph and determine the style and size of the mat she can afford.

1. Describe the design and original dimensions of the photo you chose for Francesca to give as a gift.

(2 points: 1 point for describing the photo and 1 point for including the dimensions)

Photo description:

Dimensions (including units):

Finding the Total Area of the Photo and Mat

2. Francesca wants to glue her photo on top of a mat that will increase the length of each side. The mat border has a width of x, so the length of each side would increase by 2x inches.

Use the tile tool to model the total area of the mat. Draw your completed model below.

(1 point)

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When you're done, count the tiles in your diagram and find the polynomial expression that represents the total area covered by the mat and photograph.

(2 points: 1 point for the correct polynomial expression and 1 point for identifying the units)

Polynomial expression:

What units would you expect to use for this area? Why?

3. Using the distribution method, multiply the factors you used in the tile tool to verify your polynomial expression. Do the same using the FOIL method. Show your work below.

(2 points: 1 point for the distribution method and 1 point for the FOIL method) Polynomial factors displayed in the tile tool model:

Multiply factors using the distribution method:

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Multiply factors using the FOIL method:

4. Write your polynomial expression representing the total area of the mat in the top of the right table column below. Then evaluate the expression to find the total areas of various sizes of mats Francesca might use with her photo. Don't forget to add unit labels.

(4 points: 1 point for each mat area)

0.5 in

1.0 in

1.5 in

2.0 in

Determining the Cost of the Mat

5. If a white mat costs $0.03 per square inch and a black mat costs $0.05 per square inch, determine the cost of each size of black and white mat. To get started, copy your previous calculations for the total areas of the mats into the first column of the table below.

(4 points: 2 points for the costs of the white mats and 2 points for the costs of the black mats)

x Total area of mat Cost of white mat Cost of black mat

0.5 in

1.0 in

1.5 in

2.0 in

The Final Mat Design

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6. Francesca has $5.00. She wants to add a second mat that would extend uniformly beyond the edges of the first mat. Use the graph paper below to draw a diagram showing a twomat design that would fit within Francesca's budget. Identify the size and color of each mat, and include the total cost of the mats.

(5 points: 1 point for completely identifying each item in the checklist)

On your diagram, remember to identify the:

❑ Size of the original picture ❑ Size of each mat ❑ Color of each mat ❑ Cost of each mat ❑ Total cost of both mats

The scale of each square in the diagram equals (number of units): ___________

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3.4.5 Journal: Multiplying Polynomials Journal Algebra I Sem 2 (S2923741) Brady Odom Points possible: 20 Date: ____________

Scenario: Multiplying Polynomials

Instructions:

View the video found on page 1 of this Journal activity.

Using the information provided in the video, answer the questions below.

Show your work for all calculations.

The Students' Conjectures

Emily and Zach have two different polynomials to multiply:

Polynomial product A: Polynomial product B:

They are trying to determine if the products of the two polynomials are the same. But they disagree about how to solve this problem.

1. Complete the table to summarize each student's conjecture about how to solve the problem. (2 points: 1 point for each row of the chart)

Classmate Conjecture

Emily

Zach

Evaluating the Conjectures

Who do you think is correct? (1 point)

Analyzing the Data

Table Method:

2. Use the table to find the products of the two polynomials. Write your answer in descending order. (4 points: 2 points for each product)

4x 3 –4x

x 2

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–4

____ ____ ____

____

3. Are the two products the same when you multiply them with the table method? (1 point)

Multiplying Using the Distributive Property:

4. Multiply the two polynomials using the distributive property. (4 points: 2 points for each product)

5. Are the two products the same when you multiply them horizontally? (1 point)

Multiplying Vertically:

6. Find the product for both sets of polynomials below by multiplying vertically. (4 points: 2 points for each product)

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7. Are the two products the same when you multiply them vertically? (1 point)

Making a Decision:

8. Who was right, Emily or Zach? Are the products the same with the three different methods of multiplication? (1 point)

9. Which of these three methods is your preferred method for multiplying polynomials? Why? (1 point)

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3.7.2 Project: Your DogWalking Business Project Algebra I Sem 2 (S2923741) Brady Odom Points possible: 120 Date: ____________

The Scenario: Your cousin Caleb has a dogwalking business, and you'd like to start one in your own neighborhood. Caleb has had his business for more than a year and has experimented with different prices for his services. He is willing to share what he has learned with you as you begin to plan your business.

The Project: Use the information provided in the Performance Task to learn more about your customers, your competition, and the costs of your business. See what you can discover by looking at Caleb's sales records to help you decide how to set up and price your own dogwalking services.

Use the questions below to help you gather information and get your new business off to a profitable start.

Understanding Your Business Location

1. Knowing about the neighborhood where your business is located will help you understand your potential customer base. Complete the following table to better understand your business location. Show your work for any calculations.

(10 points: 2 points for each table cell)

Location Did you choose city, suburb, or small town?

Radius of service How far from your home will you travel to serve your customers?

Number of people in your service area

How many people live in the area your business will serve?

Number of dogowning households

How many households own dogs in the area your business will serve?

Number of dogs How many dogs are in your service area?

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Understanding the Competition

2. Explore the three competitors in your area to learn more about the services they offer and how they reach their customers. Fill in the table below to help you compare their businesses.

(24 points: 2 points for each table cell)

Outward Hound

A1Pet Services

Debbie's Daily Dog Walks

What services does the business offer?

What do you know about the type of business and its staff?

Who are the target customers?

How much does the business charge?

3. Based on the competitor research, what is the overall price range for dogwalking services in your area?

(1 point: 1 point for identifying the range)

4. Choose one of the three competitors. Briefly explain why you think that business charges the price it does for its services.

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(2 points: 1 point for identifying services, 1 point for rationale of pricing)

Dogs and Your Services

5. These are the top 10 most popular dog breeds in the United States. You should expect many of your potential customers to have these types of dogs. Notice the different sizes among breeds. Your customers’ dogs will also vary in personality and age.

Think about the differences — in breed, size, personality, and age — and write a few sentences about what they might mean for your dogwalking business.

(4 points: 2 points for describing services, 2 points for describing how differences among dogs may or may not influence your services or supplies needed)

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6. Now that you know a bit about the competition and have considered the needs of various dogs, it’s time to get more specific about your business offering.

(18 points: 8 points for describing services, 4 points for describing and explaining any special items required, 4 points for explaining customer type, 2 points for pricing)

List four services you would like to offer.

Do any of these services require you to buy special items? If so, what would you need to buy?

Describe the type of customer you believe your business will appeal to and explain why.

If you had to guess now, how much do you think you should charge for a 30minute dog walk?

Calculating Your Business Costs

7. Use the table below to summarize your monthly business costs. Record each option you choose in the “Options selected” column.

(9 points: 1 point for each completed table cell)

Cost type Total cost per month Options selected

Advertising

Goods

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Transportation

Licensing

TOTAL

8. Explain the choices you made that determined your business costs in each cost category.

(8 points: 1 point each for describing the choices in each category, 1 point each for explaining the reasons)

In your explanation, be sure to describe:

❑ Your advertising choices ❑ The goods you will purchase ❑ Your transportation needs ❑ Whether you chose bonding ❑ The reasons for your choices

Advertising:

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Goods:

Transportation:

Bonding:

Investigating Sales Records

9. Based on the sales data Caleb sent you, answer the questions below to find the relationship between the change in customers per month and a $1 change in price.

Price (per 30 min) Customers per month Revenue per month

$12 214 $5136

$14 202 $5656

$18 178 $6408

$22 154 $6776

$28 118 $6608

$34 82 $5576

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(24 points: 1 point per blank or circled word)

Using Caleb's data, give two examples of price increases and two examples of price decreases. Include the change in the number of customers with each example.

Price Increases

• If Caleb increased his price from ______ to _______, the price increased by _________ and the number of customers (increased/decreased) by _______________.

Price Decreases

• If Caleb decreased his price from ______ to __________, the price decreased by _________ and the number of customers (increased/decreased) by _______________.

• With every price increase of $1, Caleb (gained/lost) ___________ customers.

• With every price decrease of $1, Caleb (gained/lost) ___________ customers.

10. According to Caleb’s email, his business goal was to serve up to 160 customers per month. This is the maximum number of customers he could handle on his own.

(3 points: 1 point per question)

• At what price did Caleb make the most revenue per month?

• When Caleb was making the most revenue, was he still able to run the business on his own?

• At what price range would Caleb have to get extra help? You may need to use what you know about the relationship between change in price and change in the number of customers to extend the data in the table for some prices not currently listed.

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Maximizing Your Profits

You’ve done a lot of research. Now it’s time to try to maximize the profit of your new business. Remember:

Profit = Price • Number of customers – Cost

To write your profit expression, use the following assumptions:

❑ Express price and number of customers in terms of the same variable, x.

❑ Let x = the change in price from the price that gave Caleb the greatest revenue.

11. Write and simplify your personalized profit equation.

(Hint: If you’re stuck on how to formulate your profit equation, consider revisiting pages 3 and 4 of the radio problem study in this lesson.)

(6 points: 1 point for each element: price, number of customers, and cost; 3 points for writing and simplifying the profit equation)

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12. Use the graphing tool to graph your profit equation. Plot enough points to find the maximum and the breakeven points. Circle and label these points. Sketch a copy below.

(3 points: 1 point each for identifying the breakeven points and maximum)

13. Answer the following questions based on your graph.

(8 points: 2 points per question)

What price for a 30minute dog walk gives you the maximum profit? Round your answer to the nearest dollar, and explain how you found this value.

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At this price, how many customers would you need to have per month just to cover your monthly business costs?

How does this price compare with the price you thought you might charge for your business in question 6?

What breakeven price (to the nearest dollar) is so high that you start to lose money because you don't have enough customers? Where does this value appear on your graph of the profit equation?

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3.8.4 Test (TS): Polynomials Test Algebra I Sem 2 (S2923741) Brady Odom Points possible: 50 Date: ____________

Answer the following questions using what you've learned from this unit. Write your responses in the space provided.

1. Part I: The degree of a polynomial is the greatest/least value exponent among the terms of the polynomial. (Circle the term that correctly completes this definition.) (1 point)

Part II: In order to write a polynomial in standard form, you must write the terms in ascending/descending order with the exponents decreasing/increasing from left to right. (Circle the terms that correctly complete this rule.) (2 points; 1 point each)

Part III: For each polynomial, determine the degree and write the polynomial in standard form. (4 points; 2 points each)

A. B.

2. Use addition and subtraction to simplify the following polynomials.

Step 1: Rewrite the polynomials without the parentheses. (1 point)

Step 2: Write the polynomial in standard form and use parentheses around like terms. (1 point)

Step 3: Add the like terms identified in Step 2 to simplify the polynomial. (1 point)

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Step 1: A minus sign in front of an expression in parentheses works the same way as using the distributive property to multiply the expression by 1. Change the subtraction sign between the polynomials to an addition sign and multiply each term in the second polynomial by 1. Rewrite the polynomials without the parentheses. Show your work. (1 point)

Step 2: Write the polynomial in standard form and use parentheses around like terms. (1 point)

Step 3: Add the like terms identified in Step 2 to simplify the polynomial. (1 point)

3. Use the FOIL method to multiply binomials.

Part I: When multiplying binomials, the FOIL method helps you to organize the multiplication of each term of the first binomial by each term of the second. Fill in the blanks of the mnemonic device that describes the order in which you multiply the terms of the two binomials together. (2 points; 0.5 points each)

Part II: Using the FOIL method, multiply the terms in the binomials below. Show your work in the blanks provided. Then, add any like terms and write the polynomial in standard form in the space provided. Show your work. (8 points; 2 points each)

A. (3x + 7)(2x 5) B.

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______ + _______ + _______ + _______ ______ + _______ + _______ + _______

______________________ ______________________

C. (5y + 4)(5y 4) D.

______ + _______ + _______ + _______ ______ + _______ + _______ + _______

______________________ ______________________

4. Use the distributive property to multiply the trinomial by the binomial.

Circle the first term in the trinomial, multiply it by each term in the binomial, and place each result in the blank spaces provided. Repeat this process for the second and third term of the trinomial until all of the spaces are filled in. Finally, in the space provided beneath the blanks, simplify the expression by combining like terms and arranging the terms from highest to lowest order. Show your work. (4 points)

______ + _______ + _______ + _______ + ______ + _______

5. Use long division to divide the trinomial by the binomial.

Part I: In order to use long division, you must rewrite the division of the trinomial by the binomial as a long division problem. Then, divide the first term of the trinomial by the first term of the binomial and write the result above the second term of the trinomial. Continue the process of long division until you cannot divide any further. Write the answer above the long division bar. Show your work. (4 points)

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Part II: Check your answer by multiplying your answer by the divisor. You should produce the original trinomial. Show your work. (2 points)

6. Sabrina is making an open box from a piece of cardboard that is 12 inches by 18 inches. She’ll form the box by making cuts at the corners and folding up the sides so that the flaps are square. If she wants the box to have the greatest volume possible, how long should she make the cuts?

Part I: The formula for volume is . Given what you know about the box Sabrina is making, identify each variable and write an equation to find the volume of the box. Show your work. (2 points)

Width = Length = Height =

V =

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Part II: Explain what would be a reasonable range for the xvalues. (1 point)

Part III: Complete the table of values for the polynomial equation you found in Part I. Show your work. (7 points)

x v

Part IV: Graph the polynomial equation by plotting your table of values. Be sure to label your graph appropriately. (3 points)

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Part V: Based on your graph, what flap size appears to create a box with maximum volume? What is that maximum volume? (2 points)

Part VI: Where are the roots of the graph and what do they tell you? (2 points)

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4.2.4 Practice: Modeling: Factoring with Tiles Practice Assignment Algebra I Sem 2 (S2923741) Brady Odom Points possible: 20 Date: ____________

Your Assignment: Patio Project

You have a small patio and want to improve it with a project. Circle the project you picked:

Fish Pond Planter Box Fire Pit

Making Sense of the Problem

Make Sense of the Problem (3 points: 1 point for each answer)

What do you know?

What do you want to find out?

What kind of answer do you expect?

1. Draw a tile picture that represents what you know about the patio project. (2 points: one for each dimension)

2. Use the tile tool to find two different ways to factor this polynomial. Describe the tile tool box associated with each factoring. (4 points: 2 point for each polynomial)

Factor pair (a):

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Factor pair (b):

Writing an Equation

3. Set your polynomial equal to the total area of your patio to create the equation: (1 point)

4. Set the equation equal to zero: (1 point)

5. Can the polynomial in question 3 be factored using the tile tool? Why or why not? (1 point)

Solving the Problem

Suppose that the factoring of the polynomials breaks down as follows:

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Fish Pond: Planter Box: Fire Pit:

6. Complete this problem and solve for x. (2 points: 1 point for each value)

7. Check your work. Plug the two values of x into the equation to confirm that it equals zero. (2 points: 1 point for each value of x)

8. What are the dimensions of your project? (2 points: 1 points for each dimension)

Width = __________

Length = __________

9. Draw a new picture of your patio that shows the dimensions of your project and the walkway. (2 points) Check to confirm that the total area equals the area of your patio.

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(Equation 1)

(Equation 2)

(Equation 3)

4.6.5 Journal: Factoring ax2 + bx + c Journal Algebra I Sem 2 (S2923741) Brady Odom Points possible: 20 Date: ____________

Scenario: The Garden

Instructions:

View the video found on page 1 of this Journal activity.

Using the information provided in the video, answer the questions below.

Show your work for all calculations

Analyze Your Classmate's Conjecture (2 points, 1 point for each answer)

What conjecture is being made?

Is that the easiest way to factor the trinomial?

1. What is the trinomial expression that represents the area of the garden? (1 point)

2. Instead of dividing by 6, simplify the trinomial expression by separating the common factor. Show your work. (1 point)

3. After dividing by 6, what was the trinomial expression found at the end of the scenario? (1 point)

Comparing factoring steps for different leading coefficients

4. Complete the following table. (Some columns have more rows than you will need.) (8 points: 4 points for each equation)

Equation 2: Equation 3:

a = c = a = c =

Guess & Check b = p • s + r • q =

Guess & Check b = p + q =

r s p q r s p q

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Factored form: Factored form:

5. List the steps you used to factor these expressions. (2 points)

6. Explain any differences in the steps you used to factor equation 2, compared with equation 1. (3 points)

7. What is the length of a single garden plot? Show your work. (2 points)

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4.8.4 Test (TS): Factoring of Polynomials Test Algebra I Sem 2 (S2923741) Brady Odom Points possible: 50 Date: ____________

Answer the following questions using what you've learned from this unit. Write your responses in the space provided.

1. Factor a number, variable, or expression out of each polynomial.

Step 1: Underline each term in the following polynomials and write the number, variable or expression that each term has in common in the space provided. (4 points; 2 points each)

A. B.

Step 2: Using your answer from Step 1, factor out the number, variable, or expression that each term has in common from the polynomial and multiply it by the fully factored polynomial. Show your work. (4 points; 2 points each)

A. B.

2. The roots of a polynomial are where the graph crosses the xaxis. Find each of the following polynomials' roots and find the factorization of the polynomial graphed.

Step 1: Identify the roots for each polynomial. You may assume that each graph crosses the axes at a tick mark. (4 points; 2 points each)

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Step 2: Using the roots you identified in Step 1, write the factorization for each polynomial. (4 points; 2 points each)

A. B.

3. Factor the following trinomial.

x 2 – 15x + 56

Step 1: When factoring a trinomial in the form of , you need to find the values of p

and q in the factored form The product of p and q is the constant term of the

trinomial. The sum or difference of p and q is the coefficient of the xterm in the trinomial. (4 points)

Fill in the following table with all of the possible values of p and q, using the fact that their product is the constant term 56.

p q p+q

Step 2: Which factors for p and q add to equal a coefficient of 15 for the xterm in the trinomial? (1 point)

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Step 3: Using the factors from Step 2, write the trinomial in factored form. (2 points)

Step 4: Follow Steps 1 through 3 to factor the trinomial . Show your work. (5 points)

4. Factor completely.

Step 1: Look for the greatest common factor for each term in the polynomial and factor it out of the polynomial. Show your work. (2 points)

Step 2: Factor the trinomial from Step 1 into two binomials, leaving the greatest common factor in place. Show your work. (4 points)

5. Factor by grouping.

Step 1: In order to factor by grouping, put parentheses around the first two terms and the last two terms with an addition sign between the two sets of parentheses. (1 point)

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Step 2: Rewrite the polynomial from Step 1 below with parentheses in place. Factor out the greatest common factor out of each set of parentheses and write it outside of each set. Use the blanks provided. Show your work. (4 points)

Step 3: Rewrite the greatest common factors you identified in Step 2 as a sum inside parentheses, producing a binomial. (2 points)

( )

Step 4: When you factored out the common factor in Step 2, this produced the same binomial for each set of parentheses. Write the product of the binomial for Step 3 beside the identical binomial from Step 2. This completes the factoring of the polynomial. (2 points)

( ) ( )

6. Factor each polynomial completely. Look for common factors and special cases. Show your work. (3 points; 1 point each)

A. B. C.

7. Stuart had insulation blown into his rectangular attic. The length and width of the attic, and the depth of

the insulation, are factors of the polynomial x 3 – 30x 2 – 4x + 120. (You’ll use x to find the dimensions of the attic, but x itself doesn’t have a realworld meaning.)

Part I: Factor completely. Look for special cases. Show your work. (2 points)

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Part II: Suppose that these factors represent the dimensions of the attic and the depth of the insulation, as given in the table. If x = 32, complete the table to find the dimensions of the attic, the area of the attic, the depth of the insulation, and the volume of the insulation. (3 points)

x (ft) Attic length x + 2 ft

Attic width x – 2 ft

Area covered Insulation depth x – 30 ft

Insulation volume

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5.3.5 Journal: Completing the Square Journal Algebra I Sem 2 (S2923741) Brady Odom Points possible: 20 Date: ____________

Scenario: The Stage

Instructions:

View the video found on page 1 of this Journal activity.

Using the information provided in the video, answer the questions below.

Show your work for all calculations.

Analyze The Students' Conjectures

Malcolm wants to build an outdoor stage with a total area of 350 square feet. The length of the stage should be three feet shorter than the width. He calculated the equation to be w2 − 3w = 350

1. Complete the table to summarize each student's suggestion for figuring out the equation: (2 points, 1 point for each row of the chart)

Student Conjecture

Malcolm's bandmate

Malcolm

2. Malcolm and his bandmate have different ideas for figuring out the equation. Which one do you think will make it easiest to solve the equation? Why? (2 points)

3. To make a perfect square trinomial, Malcolm said the rule for figuring out the number to add is . Is he

correct? If not, what is the rule? (1 point)

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4. Calculate the number that you need to add to each side of the equation w2 − 3w = 350 to create a perfect square trinomial. Show your work. (3 points)

5. Factor the trinomial. (3 points)

6. Now that you've factored the equation, find the square root of each side and solve for w. Show your work. (2 points)

7. What are the maximum dimensions of the stage that Malcolm can build? (Round to the nearest foot.) (2 points)

w = _____

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l = _____

8. There's been a lastminute change of plans. The lumberyard has decided to donate 480 square feet of lumber, and Malcolm's band now wants the length of the stage to be four feet shorter than the width. Create an equation that reflects the new requirements. (2 points)

9. Using the new equation, complete the square and solve for w. (2 points)

10. What are the new dimensions of the stage? (1 point)

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Yellowstone x Year

y 1 Population 1, Grizzly Bears (per square mile)

y 2 Population 2, Pocket Gophers (per square mile)

y 3 Population 3, Osprey (per square mile)

x y1 y2 y3 0 4.0 4.0 4.0

1 4.5 4.5 5.8

2 5.0 5.3 7.2

3 5.5 6.4 8.2

4 6.0 8.1 8.8

5 6.5 10.6 9.0

8 8.0 28.6 7.2

10 9.0 60.7 4.0

Everglades x Year

y 1 Population 1, American Alligator (per square mile)

y 2 Population 2, Marsh Rabbit (per square mile)

y 3 Population 3, Florida Panther (per square mile)

x y1 y2 y3 0 6.0 6.0 6.0

1 6.5 6.5 7.8

2 7.0 7.3 9.0

3 7.5 8.4 9.8

4 8.0 10.1 10.0

5 8.5 12.6 9.8

8 10.0 30.6 6.0

10 11.0 62.7 1.0

5.7.4 Practice: Practice Assignment Algebra I Sem 2 (S2923741) Brady Odom Points possible: 20 Date: ____________

YOUR ASSIGNMENT: National Park Animal Populations

You are studying the populations of three animals in a national park. Below are the data sets for the animal populations. Circle the park that you chose:

Make Sense of the Problem

What do you want to find out?

Analyze the Data

Population 1 (y1): ______________________________ (Write the animal species' name.)

Answer the following questions about the growth function of population 1:

1. Is population 1 increasing or decreasing? (0.5 point)

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2. What is the rate of change for this population? (1 point)

3. Is this population growth function symmetric? (0.5 point)

4. What type of function best models the growth for population 1? (1 point)

Population 2 (y2): ______________________________ (Write the animal species' name.)

Answer the following questions about the growth function of population 2:

5. What is the maximum population per square mile during the first 10 years? (0.5 point)

6. What is the average rate of change for this population between years 5 and 10 (x = 5 to x = 10)? (1 point)

7. Is this population growth function symmetric? (0.5 point)

8. What type of function best models the growth for population 2? (1 point)

Population 3 (y3): ______________________________ (Write the animal species' name.)

Answer the following questions about the growth function of population 3:

9. For what years is population 3 decreasing? (0.5 point)

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10. What is the maximum population during the first 10 years? In what year did this occur? (1 point)

11. What is the average rate of change for this population between years 5 and 10 (x = 5 to x = 10)? (1 point)

12. Is this population growth function symmetric? (0.5 point)

13. What type of function best models the growth for population 3? (1 point)

Comparing the three populations:

14. Sketch a graph and plot the points for x = 0, 5, and 10 for each function. Using these points and what you know about the shape of each population, sketch each function. (3 points: 1 point for each population) Note: It's O.K. if population 2 goes off the grid.

15. When do all three populations contain the same number of animals? (2 points)

16. During approximately what years does population 3 (osprey/Florida panthers) have the most animals? (2 points)

17. Assuming that your growth models are accurate, estimate the population of each animal per square mile for year 12. (3 points: 1 point for each population)

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5.8.4 Test (TS): Quadratic Equations and Functions Test Algebra I Sem 2 (S2923741) Brady Odom Points possible: 50 Date: ____________

Answer the following questions using what you've learned from this unit. Write your answers in the space provided. Be sure to show all work.

1. The vertex form equation for a parabola that opens upward is where (h, v) is the vertex of the parabola. Write an equation of a parabola with a vertex at (2, 2), opening upward and going through the point (3, 1).

Part I: To find the value of a, subtract the ycoordinate of the vertex from the yvalue of the point on the parabola that is one unit to the right of the vertex. Find the value of a. Show your work. (5 points)

Part II: Write the equation of the parabola described. (5 points)

SOLVING QUADRATIC EQUATIONS

2. At the state fair, Erin and her cousin ride the Ultra Drop roller coaster. When the ride plummets down the first hill it dips below the loading platform. At the bottom, a camera snaps the rider’s picture before hurtling them back toward the sky.

The equation models the roller coaster's path over time. The variable y represents height (in feet) above or below the platform. At y=0 the roller coaster is even with the platform. The variable x represents the amount of time (in seconds) elapsed since the ride began.

Factor and solve the equation to better understand Erin’s ride. (8 points)

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Part I: Write the equation in standard form. (1 point)

Part II: Write the factored form of the equation you found in Part I. (1 point)

Part III: Use the zero product rule to solve the factored form of the equation you found in Part II. Show your work and check your solution(s). (2 points)

Part IV: What does your answer to Part III tell you about the roller coaster's height at certain points in time? (2 points)

Part V: The equation for the roller coaster's path can also be written as . What is the name for this form of the equation? What is the height and time at which Erin's picture is taken during the roller coaster ride? (2 points)

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COMPLETING THE SQUARE

3. Solve each equation by completing the square. Show your work.

x 2 – 30x = –125

Step 1:

Add to both sides of the equation. (2 points)

Step 2: Factor the left side of the equation. Show your work. (2 points)

Hint: It is a perfect square trinomial.

Step 3: Take the square root of both sides of the equation from Step 2. (1 point)

Step 4: Simplify the radical and solve for x. Show your work. (1 point)

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THE QUADRATIC FORMULA

4. Joe made a rectangular garden. The perimeter of the garden is 27 ft, and the area is 35 ft 2. Find the length and width of the garden.

Step 1: Let L = length of the garden, and let W = width of the garden. Write an equation for the perimeter of the garden. (1 point)

Hint: perimeter = 2(length + width) = 2(L + W)

Step 2: Solve the equation you wrote in Step 1 for W. Show your work. (1 point)

Step 3: Write an equation for the area of the garden. Use W from Step 2. (2 points) Hint: Area = LW

Step 4: Write the equation from Step 3 in the form ax 2 + bx + c = 0, with x = L. Show your work. (2 points)

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Step 5: Solve the equation from Step 4 for L. Show your work. (3 points)

Hint: Use the quadratic formula with x = L:

Step 6: Use the values for L you found in Step 5 to find the values of W. Show your work. (2 points)

Hint: Use your equation from Step 1 or Step 3.

Step 7: (1 point)

The garden is _____________ long and _____________ wide.

FINDING THE VERTEX

5. The equation below is for a quadratic function. Follow the steps to find the vertex of the function.

y = x 2 – 2x – 8

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Step 1: Write the equation in vertex form y = a(x – h)2 + v. Show your work. (4 points)

Hint: Complete the square.

Step 2: Find the vertex. (2 points)

Hint: The vertex is at the ordered pair (h, v).

SOLVING QUADRATIC EQUATIONS

6. To solve the system of equations below, Tina isolated a variable in the first equation and substituted it into the second equation. What was the resulting equation? Show your work. (8 points)

6y = 18x

x 2 + y 2 = 49

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6.4.6 Journal: Shifting Functions Journal Algebra I Sem 2 (S2923741) Brady Odom Points possible: 20 Date: ____________

Scenario: Model Rocket Path

Instructions:

View the video found on page 1 of this Journal activity.

Using the information provided in the video, answer the questions below.

Show your work for all calculations

The Students' Conjectures: Serena and Jack are launching three identical model rockets, each at a different time. Jack says that they need to recalculate the graph each time, but Serena thinks they can just shift the function of the first graph.

1. Complete the table to summarize what you know about each rocket: (3 points: 1 point for each row of the chart)

First rocket

Second rocket

Third rocket

Evaluate the Conjectures:

2. Do you agree with Serena that you can draw the graphs for the other two rockets by shifting the functions? Or do you think that Jack is correct that you need to recalculate the other two? (1 point)

Analyzing the Data:

Suppose that the path of the first model rocket follows the equation

D(t) = −6 • (t − 3.7)2 + 82.14,

where t is the time in seconds (after the first rocket is launched), and D(t) is the height of each rocket, in feet.

3. In the equation, what does the term −3.7 do to the rocket's graph? What does the value t = 3.7 represent in the science project? (What happens to the rocket?) (2 points)

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4. In the equation, what does the term 82.14 do to the rocket's graph? What does the value D(t) = 82.14 represent in the science project? (What is happening to the rocket?) (2 points)

5. In the equation, which term does not cause a horizontal or vertical shift? (1 point)

6. They launch the second rocket 3 seconds after the first one. How is the graph of the second rocket different from the graph of the first rocket? Describe in terms of the vertical and horizontal shift. (2 points)

7. What is the equation of the second rocket? (2 points)

8. They launch the third rocket 3 seconds after the second rocket and from a 20foottall platform. What will the graph of the third rocket look like? Describe in terms of the vertical and horizontal shift. (2 points)

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9. What is the equation of the third rocket? (2 points)

10. Answer the following questions about the three rockets. Refer to the graph of rocket heights and times shown above. (3 points: 1 point for each question)

a. Approximately when is the third rocket launched?

b. Approximately when does the first rocket land?

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c. What is the approximate interval during which all three rockets are in the air?

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6.5.4 Practice: Modeling: Stretching Functions Vertically

Practice Assignment

Algebra I Sem 2 (S2923741) Brady Odom Points possible: 20 Date: ____________

YOUR ASSIGNMENT: Desert Temperatures

In this assignment you will work in a small group or with another student to complete the questions. Once you and your classmates have completed the questions, you should discuss the results of your work and/or any lingering questions with your teacher.

Temperature in the desert can be modeled by the function C(t), where t represents hours after midnight (0 ≤ t ≤ 24), and is the temperature measured in degrees Celsius. Examine what happens to the graph when you transform the function to use different temperature scales: degrees Fahrenheit and units Kelvin.

Circle the desert you picked:

Sahara Desert Patagonian Desert Death Valley California

Exploring Degrees Celsius

1. Below is the graph of the parent function, G(x) = x 2. List the transformations you must perform on G(x) to get the graph of C(t). (2 points)

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2. Fill out the following chart to find the temperatures for t = 12 (noon) and t = 24 (midnight). (2 points: 1 point for each row)

t C(t)

3. Plot the three points from the chart onto the graph below. Use the plotted points to sketch the graph of C(t). (2 points: 1 point for correct coordinates, 1 point for correct shape)

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Shift the Function to Kelvins:

4. Suppose you want to describe the temperature in kelvins. How would you transform the function C(t) to make the new function, K(t)? (2 points: 1 point for the description, 1 point for the new function)

Note: The conversion rule for Celsius to Kelvin is K = °C + 273.15.

Write the new function K(t) that results from this transformation.

5. Which of the following graphs represents the graph for kelvins, K(t)? (1 point)

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(a) (b) (c)

Shift the Function to Degrees Fahrenheit:

6. Suppose you want to represent the desert temperature in degrees Fahrenheit instead. How would you transform the function C(t) to make the new function, F(t)? (1 point)

Note: The conversion rule for Celsius to Fahrenheit is .

7. Take your values from the previous chart (in question 2) and convert them from Celsius to Fahrenheit. Follow the example below, and use the conversion rule to fill out the chart for degrees Fahrenheit when t = 12 and t = 24. (2 points: 1 point for each row)

t F(t)

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8. Use the conversion formula (from question 6) to transform C(t) into a new function, F(t). (2 points: 1 point for setting up the equation, 1 for answer)

9. Plot the points from the Fahrenheit chart in question 7 onto the graph below. Use the plotted points to sketch out the graph of F(t). (2 points: 1 point for correct coordinates, 1 point for correct shape)

Take Time to Reflect

10. Which measurement would you use if you were presenting a paper on daily desert temperatures: Celsius, Kelvin, or Fahrenheit? Discuss with another student which measurement you would use and why. Record your answer here. (1 point)

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