Q1 Benchmark Review

A store records the number of shirts ordered in one week in a matrix labeled A. The second week the number of shirts ordered was 2A. What matrix represents 2A?

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CCSS.HSN.VM.C.7

CCSS.HSN.VM.C.8

A soccer group has a junior team and a senior team. Both teams keep track of the number of wins and losses during the season. Matrix M represents the 2022 season and matrix N represents the 2023 season. What matrix represents the total number of wins and losses over the 2022 and 2023 seasons?

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CCSS.HSN.VM.C.6

CCSS.HSN.VM.C.8

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CCSS.HSN.VM.C.6

CCSS.HSN.VM.C.8

• Change the order of the rows.

• Change all values to negative.

• Change the order of the values in the first column.

• Change the values of the second column to negative.

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CCSS.HSA.REI.C.9

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CCSS.HSA.REI.C.6

CCSS.HSA.REI.C.8

Given the system of equations: 3x + y - z = 4 2x - 3y + 5z - 1 = 0 -6y + 3x - x = -3 How would this system be rewritten using matrix representation?

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CCSS.HSA.REI.C.8

Juan bought 3 bags of apples and 4 bags of grapes for a total cost of $33. The cost of each bag of grapes is twice the cost of each bag of apples. Amber bought some strawberries and blueberries which had total cost of $33. The matrix representation of the system of linear equations that will determine the price of each bag of apples, x, and price of each bag of grapes, y, would be the exact same as the matrix representation of the system of linear equations that would determine the number of pounds of strawberries and blueberries Amber bought. In the matrix representation for Amber's situation x would represent the number of pounds of strawberries Amber bought and y would represent the number of pounds of blueberries Amber bought. Which TWO statements are TRUE?

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• Amber bought twice as many pounds of strawberries as blueberries.

• Amber bought 3 pounds of strawberries and 4 pounds of blueberries for $33.

• The cost of each pound of strawberries is $3 and the cost of each pound of blueberries is $4.

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CCSS.HSA.CED.A.2

CCSS.HSA.CED.A.3

CCSS.HSA.REI.C.6

CCSS.HSA.REI.C.8

Jean needs to buy at least 80 total light bulbs but needs to spend at most $500. There are two types of lightbulbs that she can buy. - Light bulb A costs $4 and on average lasts 10,000 hours. - Light bulb B costs $7 and on average lasts 20,000 hours. The graph shows the possible number of $4 lightbulbs, x, and $7 lightbulbs, y, that Jean can buy within her constraints. Jean wants to maximize the number of bulb hours for the light bulbs purchased represented by the objective function H = 10000x + 20000y. Which statement is TRUE?

• (5, 75) is a solution to the graphed system of constraints and maximizes the objective function.

• (125, 0) is a solution to the graphed system of constraints and maximizes the objective function.

• (80, 20) is a solution to the graphed system of constraints but does not maximize the objective function.

• (80, 125) is a solution to the graphed system of constraints but does not maximize the objective function.

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CCSS.HSA.CED.A.2

CCSS.HSA.CED.A.3

CCSS.HSA.REI.C.6

CCSS.HSA.REI.D.10

CCSS.HSA.REI.D.12

A farmer plants x acres of soybeans and y acres of corn. The equation x + y = 150 represents a constraint on the total number of acres the farmer planted. The equation 40x + 120y = 9000 represents a constraint on the cost of planting the soybeans and corn. Which data point represents a solution for the constraints?

• (100, 50)

• (50, 100)

• (112.5, 37.5)

• (37.5, 112.5)

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CCSS.HSA.CED.A.2

CCSS.HSA.CED.A.3

CCSS.HSA.REI.C.6

Wayne is getting ready for a craft fair where he will sell handmade toy planes and cars. He does not have any toys ready yet to sell. The table shows how many days it takes to make each toy, the cost of materials for each toy, and the profit made for each toy sold. Wayne uses the following constraints and graph to represent the possible number of toy planes, x, and toy cars, y, that he can make for the craft fair. Wayne determines the solution (6, 14) will help him best meet his goal. Which statement BEST represents the situation?

• Wayne wants to make at least 90 total planes and cars and at least 20 of each type. He has at least 6 days to make the toys before the craft fair. Wayne is trying to minimize his material costs which will occur when 6 planes and 14 cars are made.

• Wayne wants to make at least 90 total planes and cars and at least 20 of each type. He has at least 6 days to make the toys before the craft fair. Wayne is trying to maximize his possible profit which will occur when 6 planes and 14 cars are made.

• Wayne wants to make at least 6 each of the planes and cars and at least 20 total toys. He has at most 90 days to make the toys before the craft fair. Wayne is trying to minimize his material costs which will occur when 6 planes and 14 cars are made.

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CCSS.HSA.CED.A.2

CCSS.HSA.CED.A.3

CCSS.HSA.REI.C.6

CCSS.HSA.REI.D.10

CCSS.HSA.REI.D.12