Name: Systems 2.1H Ready, Set, Go! Ready - Ms....

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SDUHSD Math 1 Honors

Name: Systems 2.1H

Ready, Set, Go!

Ready Topic: Writing linear equations from context 1. Mrs. Samaniego gave a quiz to 25 of her Algebra students. She brought the papers to correct on the

airline flight she took with her volleyball team to Reno, Nevado. She had to wait until the plane had taken off and gained some altitude before the “fasten seat belt” light went out so she could fold down the little table in front of her and begin grading. Twenty minutes after she had started, she stopped to count how many she had left and counted 19. One hour (60 min) after she started grading, she counted again and had only 7 left.

a. What is the starting point (vertical axis or y-intercept)? The starting point is a because at time 0, there were 25 tests left to be graded. b. What is the rate of change (slope)?

The rate of change is

, or 3 tests graded in 10 minutes

c. Write an equation that tells how many papers (p) Mrs. Samaniego has left when she had been grading

for (m) minutes, assuming she graded the papers at the same rate for the entire time.

or

d. Use your equation to predict how many papers Mrs. Samaniego had left after grading for a total of one hour and 20 minutes.

test left to grade after grading for one hour and 20 minutes

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Topic: Creating equations, solving real world problems, solve systems of equations 2. A phone company offers a choice of three text-messaging plans. Plan A gives you unlimited text messages

for $10 a month; Plan B charges you $5 a month and plus $0.05 for each text message you send; and Plan C has no monthly fee but charges you $0.10 per message.

a. Write an equation for the monthly cost of each of the three plans.

Plan A: Plan B: Plan C:

b. If you send 30 messages per month, which plan is cheapest?

Plan C

c. What is the cost of each of the three plans if you send 50 messages per month?

Plan A: $10 Plan B: $7.50 Plan C: $5

d. Determine the values for which each plan is the cheapest?

Plan A when more than 100 texts are sent Plan C when less than 100 texts are sent

Topic: Solving equations Solve the following equations. Check your solutions. 3.

4.

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Set 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.

5.

Solution: Not a solution:

6.


7.


8.


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Topic: Writing two variable inequalities Given the graph with the regions that are shaded write the inequality. 9.

10.

11.

12.

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Topic: Graphing systems of inequalities. Graph each system of inequalities. Be sure to darken in the solution set. 13. 14.

15. Shade the solution to the following system on the graph below:

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Go Topic: Solve literal equations Re-write each of the following equations for the indicated variable.

16.

for d 17. for y

Topic: Operations with matrices Complete the following matrix operations.

18. *

+ *

+ 19. [

]

*

+ [

]

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Name: Systems 2.2H

Ready, Set, Go!

Ready Topic: Exponents Write the following in exponential notation. 1. 2.

Find each value.

3. 4. 5. 6. 7. (

)

8 0.25

Write the following expression three different ways (one way can include the simplified value). 8. 9.

216

Set Topic: Solve system of equations from a context

10. Nadia and Peter visit the candy store. Nadia buys three candy bars and four fruit roll-ups for $2.84. Peter

also buys three candy bars, but can only afford one additional fruit roll-up. His purchase costs $1.79. What is the cost of a candy bar and a fruit roll-up individually?

Candy bar costs $.48 each and a fruit roll-up costs $.35 each

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11. A farmer noticed that his chickens were loose and were running around with the cows in the cow pen. He quickly counted 100 heads and 270 legs. How many chickens did he have and how many cows?

x = chickens, y = cows There were 35 cows and 65 chickens. 12. Tickets to a show cost $10 in advance and $15 at the door. If 120 tickets are sold for a total of $1390, how

many of the tickets were bought in advance? Assign variables and create a system of equations that models this situation. Solve the system algebraically using you preferred method. Graph the system to verify your solution.

Advance tickets bought (A) = 82 Tickets bought at the door (D) =38

Solve the following systems of equations using elimination of variables, then justify graphically.

13. {

(

)

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Go Topic: Solve one variable inequalities. Solve the following inequalities. Graph the solution set on a number line.

14. (

)

15.

16.

Infinitely many solutions

Topic: Solving systems of inequalities. 17. Peggy is buying a balloon bouquet. Her favorite colors are silver and purple. The silver balloons are $1

and the purple balloons are $0.80. Graph a system of inequalities that shows how many of each color balloon she can put in her bouquet if she doesn’t spend more than $20 and she would like to have at least 3 times more silver then purple. Let s represent the number of silver balloons and let p represent the number of purple balloons.

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Topic: Proportional relationships For each proportional relationship below, one representation is provided. Show the remaining representations and explain any connections you notice between representations.

18. Equation: Graph

Table

Days Cost 1 8 2 16 3 24 4 32

Create a Context answers vary

19. Equation: Graph

Table

week allowance 1 9 2 18 3 27 4 36 5 45 6 54 7 63

Create a Context Claire earns $9 per week allowance

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Topic: Graphing systems of inequalities Graph each system of inequalities. Be sure to darken in the solution set. 20. 21.

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Name: Systems 2.3H

Ready, Set, Go!

Ready Topic: Solve exponential equations Find the value of x for each situation. 1. 2. 3. 4.

Set Topic: Writing equations of two variable inequalities 5. Write the system of inequalities that is represented in the graph to the

right.

Topic: Graph two variable inequalities Graph each set of inequalities and determine the solution region.

6. {

7. {

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8. Jane is buying fruit salad and potato salad for a picnic. Fruit salad costs $2.00 per pound and potato salad costs $4.00 per pound. Jane needs to buy at least 6 pounds of salads and she doesn’t want to spend more than $20. Write and graph a system of linear inequalities. Also, list 2 possible combinations of salad Jane could buy.

Let: f = pounds of fruit salad and

p = pounds of potato salad.

2 possible combinations: and

9. Food and clothing are shipped to victims of a natural disaster in an airplane that can hold 7200 pounds

and has space for 1000 cubic feet. Each box of food will feed 12 people, while each box of clothing will help 5 people. Each 50-cubic-foot box of food weighs 200 pounds and each 10-cubic-foot box of clothing weighs 360 pounds. In addition, the relief team wants a minimum of 5 boxes of food shipped. How many boxes of food and clothing should be shipped to maximize the number of people that can be helped?

a. Write the constraints, let x represent the number of boxes of clothing and y represent the number of

boxes of food. Include a brief description of each. In addition, write an expression using your variables to show how many people will be helped by shipping food and clothing.

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b. Graph the constraints and clearly label the solution region.

c. Find the coordinates of the corners of the solution region. Show your work algebraically.

(

)

d. Use the help expression to determine which of the corners gives an optimal number of boxes of food and clothing in order to help the most people. Write your solution in context of the problem and state the number of people helped.

(

)

Therefore, 10 boxes of clothing and18 boxes of food should be shipped.

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Topic: Determine the number of solutions in a system of equations Express each equation in slope-intercept form. Without solving, state whether the system of equations has zero, one, or infinite solutions. Justify your response.

10. {

11. {

One solution because their slopes are No solution because their slopes are different and the lines are not parallel. the same and the lines are parallel.

Topic: Solve a system of equations with three variables.

12. {

13. {

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Go Graph each set of inequalities below.

14. {

15. {

16. On the same set of axes, graph and . What values do these two have in common?

No values in common

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Name: Systems 2.4H

Ready, Set, Go!

Ready Topic: Determine patterns Find the next two values in the pattern. Describe how you determined these values. 1. 3, 6, 9, 12, __15____, __18____ Description: Add 3 for the next number in the pattern 2. 3, 6, 12, 24, __48____, ___96___ Description: Multiply by 2 to get the next number in the pattern 3. 24, 20, 16, 12, ___8___, ___4___ Description: Subtract 4 for the next number in the pattern 4. 24, 12, 6, 3, ___ ___, ___ ___ Description: Divide by 2 for the next number in the pattern Topic: Solving systems by substitution and elimination Solve each system of equations using any algebraic method.

5. {

6. {


7. {

No solution

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Set Topic: Row reductions in matrices 8. Create a matrix to match each step in the solving of the system of equations given. Also, write a

description of what happened to the equation and the matrix between steps.

System of Equations Description Matrix

Given System {

*

|

+

Step 1 {

[

|

]

Step 2 {

[

| ]

Step 3 {

[

|

]

Step 4 {

[

|

]

Step 5 {

[

|

]

Solve the system by finding a sequence of matrices that will create a matrix in Reduced Row Form. Be sure to show all your steps. 9.

*

|

+

10.

*

|

+

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Create a system of equations and solve by using a matrix. 11. In one week, math club sold 14 calculators for a total of $1140. Blue calculators cost $75 each and silver

calculators cost $85 each. How many of each type of calculator were sold? 5 blue calculators and 9 silver calculators 12. You are making gift baskets. Each basket will contain three different types of candles: tapers, pillars ad

jar candles. Tapers cost $1 each, pillars cost $4 each, and jar candles cost $6 each. You put 8 candles costing a total of $24 in each basket, and you include as many tapers as pillars and jar candles combined. How many of each type of candle will be in a basket?

4 tapers, 2 pillars, and 2 jar candles.

Go Topic: Solving systems of equations by graphing Solve each system of equations by graphing.

13. {

14. {

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Topic: Solving system of equations with three variables Solve each system of equations using any method.

15. {

16. {

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Name: Systems 2.5H

Ready, Set, Go!

Ready Topic: Solving systems of equations using matrices. 1. In an earlier assignment you worked the following problem:

“A theater wants to take in $2000 for a certain matinee. Children’s tickets cost $5 each and adult tickets cost $10 each. If the theater has a maximum of 350 seats, write a system of equations that can be solved to determine the number of both children and adult tickets the theater can sell.”

Set up a matrix that goes with the situation described above.

*

|

+

Set Topic: Solving systems using row reduced form Assume that the matrices below represent linear systems of equations. Solve the system by Row Reduction.

2. *

|

+

*

|

+

3. *

|

+

*

|

+

4. *

|

+

[

|

]

5. *

|

+


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6. [

|

]

[

|

]

7. The school the Martinez twins go to is selling tickets to the annual talent show. On the first day of ticket

sales the school sold 6 senior citizen tickets and 7 student tickets for a total of $116. The school took in $26 on the second day by selling 4 senior citizen tickets and 1 student ticket. What is the price of one senior citizen ticket and one student ticket? Create a system of equations and solve using matrices.

$3 for each senior citizen ticket and $14 for each student ticket

Go Topic: Solving systems of equations Solve the following systems of equations with a method of your choice.

8. {

9. {

10. {

11. {

(

)

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Name: Systems 2.6H

Go! Topic: Solving systems by graphing For #1-3, solve each system of equation by graphing. Verify your solution using substitution or elimination. 1.

2. No Solution

3.


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Topic: Solving systems using a matrix For #4-5, solve each system using a matrix 4.

5.


6. –

7. –

–

No Solution

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Topic: Systems of equations word problems 8. Carlos and Clarita have found two different cat foods that seem to appeal to even the most finicky of cats:

Tabitha Tidbits and Figaro Flakes. Each ounce of Tabitha Tidbits contains 2 grams of protein, 4 grams of carbohydrates and 4 grams of fat. Each ounce of Figaro Flakes contains 3 grams of protein, 4 grams of carbohydrates and 2 grams of fat. Since Tabitha Tidbits is fairly expensive, while Figaro Flakes is very cheap, the twins have decided to create a new cat food by mixing the two. After studying some nutritional guidelines for cats, Carlos and Clarita have decided to create a mixture based on the following constraints.

Amount of Protein: Each meal should contain at least 12 grams of protein. Amount of Carbohydrates: Each meal should contain more than 16 grams of carbohydrates. Amount of Fats: Each meal should contain no more than 18 grams of fat. Size of a Feeding: Each meal should consist of less than 10 ounces of food.

a. Write an inequality for each of the constraints. Let T represent the number of ounces of Tabitha Tidbits in a meal and let F represent the number of ounces of Figaro Flakes.

Amount of Protein: Amount of Carbohydrates: Amount of Fats: Size of a Feeding:

b. Graph the solution set for each of the inequalities

c. Find the corner points of the feasible region algebraically. ,

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9. Brutus Bites is a brand of dog food that contains 4 grams of protein and 6 grams of fat per ounce. Lucky Licks is another brand of dog food that contains 12 grams of protein and 4 grams of fat per ounce. Carlos wants to make a meal for dogs that contains at least 8 grams of protein and no more than 6 grams of fat.

a. Write an inequality for each of the constraints. Let B represent the number of ounces of Brutus Bites

in a meal and let L represent the number of ounces of Lucky Licks

Amount of Protein: Amount of Fats:

b. Graph the solution set for each of the inequalities

c. Find the corner points of the feasible region algebraically.

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Topic: Solving systems of inequalities For #10-12, solve each system of inequalities. 10.

11.

12. Jason is buying wings and hot dogs for a party. One package of wings costs $7. Hot dogs cost $4 per

pound. He must spend less than $40.

a. Write an inequality to represent the cost of Jason’s food for the party.

b. Jason knows that he will be buying at least 5 pounds of hot dogs. Write an inequality to represent this

situation.

c. Graph both inequalities and shade the intersection.

d. Identify two solutions and justify your answers. 1 package of wings and 6 pounds of hot dogs

1 package of wings and 7 pounds of hot dogs

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Topic: Solving 3 variables systems For 13-14, solve each system of equations using any method. Verify your solution using a graphing

utility.

13. {

14. {

Topic: Solving systems using reduced row matrices 15. Use a matrix to solve the system of equations. Verify your solution using a graphing utility.

{

[

| ]

Name: Systems 2.1H Ready, Set, Go! Ready - Ms....

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