integrated math 1 module 1 honors matrix madness ready ...teachers.sduhsd.net/dpillsbury/im1...

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Integrated Math 1 Module 1 Honors Matrix Madness

Ready, Set, Go! Homework

Adapted from:

The Mathematics Vision Project: Scott Hendrickson, Joleigh Honey, Barbara Kuehl,

Travis Lemon, Janet Sutorius

© 2012 Mathematics Vision Project | MVP In partnership with the Utah State Office of Education

Licensed under the Creative Commons Attribution‐NonCommercial‐ShareAlike 3.0 Unported license

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SDUHSD Math 1 Honors

Name: Matrix Madness 1.1H

Ready, Set, Go!

Ready Topic: Solve literal equations Solve each of the following equations for x.

1.

2.

( )

3.

( )

4. ( )

Solve for the indicated variable.

5. Solve the following equation to isolate F:

( )

6. For

, rewrite the formula to isolate the variable h.

Rearrange the following equations to solve for y (slope-intercept form). 7.

8.

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Topic: Create and solve equations. Create and solve the equations for the following problems. 9. Virginia’s Painting Service charges $10 per job and $0.20 per square foot. If Virginia earns $50 for

painting one job, how many square feet did she paint at the job? 10. Renting the ice skating rink for Dayne’s birthday party costs $200 plus $4 per person. If the cost was

$324, how many people were at Dayne’s birthday party?

Set Topic: Solve inequalities Solve each inequality. Write the answer in both inequality and interval notation. Then graph the solution on a number line.

11.

12.

13. ( )

Solve each multi-step inequality. Write the answer in both inequality and interval notation.

14. 15. ( )

16. ( )

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Go Topic: Solve the systems of linear equations by graphing Solve linear equations and pairs of simultaneous linear equations (simple, with a graph only) by graphing both lines and finding where they intersect. Justify the solution numerically by checking your solutions in both equations. 17. and 18. and 19. 2 and

Topic: Justify steps in solving equations Solve each equation, justify each step you use. 20. 21.

Justification

( )

Justification

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Ready, Set, Go!

Ready Topic: Working with inequalities and absolute value Find at least two numbers that fit the given clues (each clue goes to a new set of possible numbers). 1. On a number line, these numbers are 7 units away from zero. What are my numbers? 2. On a number line, these numbers are at least 5 units away from zero. What are my numbers? 3. On a number line, these numbers are less than 10 units away from zero. What are my numbers? 4. On a number line, these numbers are 4 units away from . What are my numbers? 5. On a number line, these numbers are more than 8 units away from 12. What are my numbers? 6. For each of the above questions, try to express a general solution using a variable.

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Topic: Solutions to an equation Graph the following equations using the coordinate graph, then say if the given point is a solution to the equation. 7.

Point: ( ) Yes/No

8.

Point ( ) Yes/No

9.

Point ( ) Yes/No

Set 10. The solution to an equation is . The equation has parentheses on at least one side of the equation

and has variables on both sides of the equation. What could the equation be? 11. Create a two-step equation that is true by expanding the given solution using properties of equality.

Draw a model to represent your expanded equations. a. b. c. 12. Determine if the two expressions are equivalent. Explain your reasoning. a. ( ) b. ( ) 13. Without completely solving, determine if these two equations have the same solution. ( ) and 14. Which of the following expressions are equivalent?

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Go Topic: Determining if a given value is a solution to an equation Check whether the given number is a solution to the corresponding equation.

15. ;

16.

;

17. ;

18. ; ( ) ( )

Topic: Solve systems of equations Solve linear equations and pairs of simultaneous linear equations (simple, with a graph only). Justify the solution numerically.

19. {

20. {

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Ready, Set, Go!

Ready Topic: Ratios, Proportions and making predictions The table below shows how Marco spends his time on a typical day. Use the table to answer the questions below.

Activity Hours Spent per

Day Hours Spent per

Week Hours Spent per

Month Exercise 1

Watch TV 2 Reading 0.75

Math 1.5 Household Chores 1.75 Other Schoolwork 3

Video games 0.5 Talk with Friends 2

Eating 1.5 Sleeping 10

1. What fraction of a day does Marco spend sleeping? 2. What percent of the day does Marco spend doing “Other Schoolwork”? 3. What amount of time would you predict Marco would spend on video games for an entire week? 4. Complete the table with predictions for Marco’s activities for an entire week. What other activities might

Marco engage in that are not on the table? Why is it possible that not every activity is listed? 5. Complete the table with predictions for Marco’s activities for an entire 30-day month. How do you use

the given data to make predictions for an entire week or month? Explain your reasoning.

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Set Topic: Organizing information in matrices Elvira has been running a private catering business to make extra money. She needs some help organizing the information in problems 6 through 8 below so that she can better predict amounts to purchase and improve her profits. Assist her by organizing the information in a meaningful way so that she can average the years and do better for the coming year. 6. The last three years Elvira has catered family gatherings and city events. Last year she provided the

following at family gatherings she catered: 5 bags of chips, 6 dozen cookies and 4 gallons of drink. Last year at city events she provided the following: 16 bags of chips, 19 gallons or drink and 24 dozen cookies. Organize this information.

7. Two year ago Elvira provided the following at family events: 5 gallons of drink, 4 bags of chips and 5

dozen cookies. While she provided the following at city events: 20 dozen cookies, 18 gallons of drink and 12 bags of chips.

8. Three years ago Elvira provided the following at city events: 14 bags of chips, 20 gallons of drink and 19

dozen cookies. She also provided the following at family gatherings: 6 bags of chips, 7 dozen cookies and 9 gallons or drink.

9. If you provide Elvira with an average amount to be ordered for the gatherings and events she caters in

the coming year, how much of each item would she need? Present the average in an organized way.

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Topic: Solving absolute value equations and inequalities Solve each equation or inequality. Graph your solution on the number line. For the inequality, write your answer in both inequality and interval notations. 10. | |

11. | |

12. | |

13. |

|

Topic: Scalar multiplication of matrices

14. Find the following, given matrices: [

], [

] [ ]

a. b. c.

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Go Topic: Creating expressions and equations 15. If cookies cost $2.50 a dozen, drink is $1.75 a gallon and chips are $2 a bag what would be the total cost

for a catered event according to your recommendation above (problem 9)? Show your calculations here. 16. Write an equation based on the information above that will calculate the total cost, T, for any amounts of

cookies c, drink d and chips h. 17. Write an expression that will calculate the cost for any amounts of cookies c, drink d and chips h, if prices

rise to the following: $2.75 for a dozen cookies, $2.25 for a bag of chips and $2 for a gallon of drink. Using this new expression calculate the costs for Elvira in the coming year.

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Ready, Set, Go!

Ready Topic: Equivalent Equations The pairs of equations below are equivalent. Determine what was done to the first equation in order to obtain the second equation. (For example, everything multiplied by 5 or Multiplicative Property of Equality) If more than one operation was performed please indicate the operations and the order they were performed. 1.

2.

3.

Determine whether or not the pairs of equations below are equivalent. If equivalent state the operations used to create the second from the first. If not equivalent show why not. 4.

5.

6.

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Set Topic: Matrix Multiplication The equipment manager for the school athletics department is attempting to restock some of the needed uniform and equipment items for the upcoming seasons of baseball and football. It has been determined based on current levels of inventory and the number of players that will be returning that more socks, pants and helmets will be needed. The equipment manager has organized the information in the matrix below.

Socks Pants Helmets

[

]

The school has contracted with two supply stores in the past for equipment needs. The matrix below shows how much each store charges for the needed items.

Big Sky Sportingoods

Play It Forever

Cost per pair of socks Cost per pair of pants

Cost per helmet

[

]

7. Calculate the values of a, b, c, and d in the “Total Costs Matrix” below.

Total Cost Matrix Big Sky

Sportingoods Play It

Forever

Baseball Football

[

]

8. Explain, in detail, how you would use the numbers in the first two matrices above to obtain the values for

the “Total Costs Matrix”.

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9. Alexandra, Megan, and Brittney want to calculate their final grades in math class. They know what their averages are for tests, projects, homework, and quizzes. They also know that tests are 40% of the grade, projects are 15%, homework 25%, and quizzes 20%. Use the following matrices to calculate their final grades:

Tests Projects Homework Quizzes

Alexandra Megan

Brittney

[

]

Weight

Tests Projects

Homework Quizzes

[

]

Given the following matrices, perform the indicated operation when possible.

A [

] [

] C [

]

10.

11. 12.

13.

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Go Topic: Representing visual patterns of change with equations, finding patterns Create tables and equations for each attribute of the visual pattern below. If you are unable to create an equation then state the pattern you notice. (All triangles are equilateral and the side length of the triangle in step 1 is one unit in length.)

Step 1 Step 2 Step 3 14. The width of the large triangle with respect to the Step number. 15. The number of small triangles with side length of one in the large triangle with respect to the Step

number. 16. The perimeter of the large triangle with respect to the Step number. 17. The number of 60° angles in the figure with respect to the Step number.

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Ready, Set, Go!

Ready Topic: Solve systems of equations Solve the following systems by graphing. Check the solution by evaluating both equations at the point of intersection. 1. and

2. and

Topic: Graph linear inequalities Graph the following inequalities on the coordinate plane. Name one point that is a solution to the inequality and one point that is not a solution. Show algebraically and graphically that your points are correct. 3.

Solution: Not a solution:

4.

Solution: Not a solution:

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Set Topic: Matrix arithmetic Perform each of the operations indicated on the matrices below.

5. [

] [

]

6. [

] [

]

7. [

]

8. [

] [

]

9. An ice-cream stall sells both green tea and mocha ice cream. A small portion of either costs $0.75 and a

large portion costs $1.25. During a short period of time, the number of ice creams sold is shown in the table below.

small large Green Tea 3 4 Mocha 6 3

a. Write down a column matrix N, representing the cost of each portion of ice cream.

b. Given that [

], evaluate .

c. Explain what the numbers given in your answer in (b.) signify.

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Go Topic: Evaluating expressions Evaluate each expression below given: , , and

10.

11. ( )

12. ( )

13. ( )

14. ( )

15. ( ) ( )

Topic: Solving absolute value equation and inequalities Solve each equation or inequality. Graph the solution on the number line. For the inequality, write the answer in both inequality and interval notations. 16. | |

17. | |

18. | |

19. | |

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Name: Matrix Madness 1.6H Solve the following equations for the unknown variable. 1. ( ) ( ) 2. ( ) ( ) ( ) Decide which of the two expressions is greater, if the expressions are equal, or if the relationship cannot be determined from the statement. Write an equation or inequality that shows your answer. Explain why your answer is correct. 3. Statement:

Which is greater? x or 2 4. Statement: n is an integer

Which is greater? n or −n 5. Statement: Given the number line at right

Which is greater? 1 or yz State the slope and y-slope intercept. Then graph each line. 6. 7. slope: slope: y-intercept: y-intercept:

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Solve linear equations and pairs of simultaneous linear equations (simple, with a graph only). Justify the solution numerically.

8. {

Write the equation that describes the situation. Then answer any additional questions. 9. A machine salesperson earns a base salary of $40,000 plus a commission of $300 for every machine he

sells. Write an equation that shows the total amount of income the salesperson earns, if he sells x machines in a year.

10. At a school play, children’s tickets cost $3 each and adult tickets cost $7 each. The total amount of money

earned from ticket sales equals $210.

a. Write a linear model that relates the number of children’s tickets sold to the number of adult tickets sold.

b. How many children’s tickets were sold if 24 adult tickets were sold? 11. Conner has $25,000 in his bank account. Every month he spends $1,500. He does not add money to the

account. a. Write a linear model that shows how much money will be in the account after x months.

b. How much money will Conner have in his account after 8 months?

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12. Solve the following equation to isolate B: Solve each inequality and write your answers in both inequality and interval notations.. Graph the solutions on the number line AND state 3 numbers in the solution set for each inequality. 13. 4( ) 3 numbers in the solution set: 14. 3 numbers in the solution set: 15. | |

16. | |

Answer the following questions on matrices. 17. If matrix A has dimensions and matrix B has dimensions what would be the dimensions of the

product matrix?

18. Are the matrices [

] and [

] equal? If not, what is one way to make them equal?

19. What has to be true about two matrices in order to add them?

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20. Given [

] and [

] answer the following:

a. b.

c. d.

e. What does this show about the commutative properties of matrices?

21. Use the following matrices:

[

] [

] [

] [ ]

a. Which product exists, AB or BA? b. Which product exists, AD or DA? c. Find BC d. Find

e. Calculate f. Calculate DA

22. A florist creates three special floral arrangements. One uses three lilies. The second uses three lilies and

four carnations. The third uses four daises and three carnations. Lilies cost $2.15 each, carnations cost 90 cents each and daisies cost $1.30 each. Write a matrix to represent the number of each type of flower in each arrangement. Write a matrix to represent the cost of each type of flower. Find the matrix representing the cost of each floral arrangement.

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Dear Integrated Math 1 Honors Student, Carlos and I are about to start a business in order to make money for our summer vacation. Our aunt has been complaining recently about how hard it is to find quality and affordable care for her pets. This will be the perfect opportunity to help our aunt out and to support ourselves. Our parents have given us permission to start our own pet sitting business in our backyard, which we’ll call “Carlos and Clarita’s Quality Creature Care.” We have a large, unused storage shed and a spacious fenced backyard where the pets can play. Before we can dive into this business, we need your help in brainstorming things that we need to take into consideration when starting and running “Carlos and Clarita’s Quality Creature Care” in order to maximize our profits. Two of the constraints for our new business are:

Space: Cat pens will require 6 ft2 of space, while dog runs require 24 ft2. Carlos and Clarita have up to 360 ft2 available in the storage shed for pens and runs, while still leaving enough room to move around the cages.

Startup Costs: Carlos and Clarita have at most $1280 to purchase cat

pens and dog runs. It will cost $32 for each cat pen and $80 for each dog run.

Thanks for your help! Sincerely, Carlos and Clarita Martinez

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End of Module 1H Challenge Problems The following problems are intended for students to work on after Module 1H Test. The problems focus on solving systems of equations and are meant to be done on their own –the next module covers systems of equations. The following page is blank for the teacher to copy and give to each student after the test. Below are the solutions. 1. For the following system of equations, what is the value of c?

{

2. Summer Fun Camp enrollment costs 85 dollars each week per camper. Each camper may register for up

to three of the optional workshops offered for an additional charge of $5.50 each week per workshop, or 15 dollars each week for three workshops. The total charge for Chloe’s enrollment to attend Summer Fun Camp for n weeks this summer is $768.00. If Chloe has registered to participate in two workshops each week, what is the value of n?

3. Watson is participating in the school fundraiser by selling cases of fruit. He sold 4 cases of oranges and 2

cases of apples and collected a total of $128. If the price of each case of oranges is half the price of each case of apples, what is the cost of each case of apples?

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