Name: ______________________ Class: _________________ Date: _________ ID: A

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Algebra 2 Honors Chapter 3 Test

Multiple ChoiceIdentify the choice that best completes the statement or answers the question.

Solve the following system of equations by any method

____ 1. Solve the system of equations - Use any method y = 11x - 6y = - 6x + 11a. (–1, 5) c. (5, 1)b. (1, 7) d. (1, 5)

____ 2. Solve the system of equations - Use any method 2y + 8x = 58y - 5x = 11a. (2, 21) c. (4, 20)b. (21, 2) d. (1, 21)

Graph each system of equations and describe it as consistent and independent, consistent and dependent, inconsistent, or none of these.

____ 3. 9x - 8y = 1527x - 24y = 3a. consistent and independent c. consistent and dependentb. inconsistent d. none of these

____ 4. 5x - 8y = 66x - 6y = 6a. inconsistent c. consistent and dependentb. consistent and independent d. none of these

Solve each system of equations by using substitution.

____ 5. Solve the system of equations - Use any method 8x + 7y = 183x – 5y = 22a. (–2, 4) c. (4, –2)b. (3, –2) d. (4, 0)

____ 6. Solve the system of equations - Use any method 3r + 3s = 93r- 6s = 18a. (4, –0.5) c. (4, –1)b. (5.5, 3) d. (2, –1)

Name: ______________________ ID: A

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Solve the system of inequalities by graphing.

____ 7. x > 2y > 8a. c.

b. d.

Name: ______________________ ID: A

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____ 8. y > x – 6y|| || £ 6

a. c.

b. d.

Find the coordinates of the vertices of the figure formed by each system of inequalities.

____ 9. y + x ≥ -9y ≥ x - 72y + x £ 16a. (–1, –8), (–30, 23), (–34, 25)b. (–1, 8), (10, 3), (34, 25)c. (–1, 25), (–34, 3), (10, –8)d. (–1, –8), (10, 3), (–34, 25)

Name: ______________________ ID: A

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____ 10. y ≥ -22x + y £ 2y £ 2x + 6a. (2, –2), (–4, –2), (–1, 4)b. (2, 4), (–1, –2), (–4, –2)c. (2, –2), (4, 2), (1, –4)d. (2, –2), (4, –2), (0, –8)

Name: ______________________ ID: A

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Given below are some inequalities. Plot the feasible region graphically.

____ 11. x ≥ 2.8y £ 4.82.8x + 4.8y £ 9f x,yÊËÁÁ

ˆ¯̃̃ = x - y

a.

vertices: (–5.01, 4.8), (2.8, 0.24)max: f(2.8, 0.24) = 2.56min: f(–5.01, 4.8) = –9.81

c.

vertex: (4.8, –0.93)max: f(4.8, –0.93) = 5.73min: none

b.

vertices: (2.8, 4.8)max: f(2.8, 4.8) = –2min: f(2.8, 4.8) = –2

d.

vertex: (2.8, 0.24)max: nonemin: f(2.8, 0.24) = 2.56

Name: ______________________ ID: A

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____ 12. y ≥ -5x £ 4y £ x - 4f x,yÊËÁÁ

ˆ¯̃̃ = x + y

a.

vertices: (4, –5)max: f(4, –5) = –1min: f(4, –5) = –1

c.

vertices: (4, –5), (4, 0), (–1, –5)max: f(4, 0) = 4min: f(–1, –5) = –6

b.

vertices: (4, –5), (4, 0), (–1, –5)max: f(4, 0) = 4min: f(–1, –5) = –6

d.

vertices: (4, –5), (4, 0), (–1, –5)max: f(4, 0) = 4min: f(–1, –5) = –6

Solve the given system of equations.

____ 13. –3a = 3610a + 3c = 92b + 5c = 23a. a = –12, b = –96, c = 43 c. a = 12, b = –96, c = 43b. a = –12, b = 43, c = –96 d. a = 43, b = –12, c = –96

Name: ______________________ ID: A

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____ 14. 11a + 2c = 10–2a = 328b + 10c = 18a. a = –16, b = –114, c = 93 c. a = –16, b = 93, c = –114b. a = 16, b = –114, c = 93 d. a = 93, b = –16, c = –114

Chocos is a dish made from wheat, sugar, and cocoa. Bertha is making a large pot of chocos for a party. Wheat (w) costs $5 per pound, sugar (s) costs $3 per pound, and cocoa (c) costs $4 per pound. She spends $48 on 12 pounds of food. She buys twice as much cocoa as sugar.

____ 15. Write a system of three equations that represents how much food Bertha purchased.a. 5w + 3s + 4c = 48

w + s + c = 12c = 2s

b. 5w + 3s + 2c = 48w + s + c = 12c = 2s

c. 5w + 3s + 4c = 12w + s + c = 48c = 2s

d. 5w + 3s + 4c = 48w + s + c = 12s = 2c

Short Answer

Choco pies are cookies made from chocolate (c), sugar (s), and flour (f). Chocolate costs $5 per pound, sugar costs $3 per pound, and flour costs $2 per pound. You spend $50 on 18 pounds of food and buy twice as much flour as sugar.

16. Write a system of three equations that represents how much food you should purchase.hint: the variables represent the value in pounds of each item.

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ID: A

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Algebra 2 Honors Chapter 3 TestAnswer Section

MULTIPLE CHOICE

1. ANS: DGraph the equations and find their point of intersection.

FeedbackA What is the x-coordinate of the intersection?B Did you graph both equations correctly?C Write the coordinates of the intersection carefully.D Correct!

PTS: 1 DIF: Average REF: Lesson 3-1 OBJ: 3-1.1 Solve systems of linear equations by graphing. STA: MA.912.A.3.14 | MA.912.A.3.15TOP: Solve systems of linear equations by graphing. KEY: System of Linear Equations | Graphs

2. ANS: AGraph the equations and find their point of intersection.

FeedbackA Correct!B Did you plot the graphs correctly?C Did you read the intersection of the graphs correctly?D What is the x-coordinate of the intersection?

PTS: 1 DIF: Average REF: Lesson 3-1 OBJ: 3-1.1 Solve systems of linear equations by graphing. STA: MA.912.A.3.14 | MA.912.A.3.15TOP: Solve systems of linear equations by graphing. KEY: System of Linear Equations | Graphs

3. ANS: BGraph the equations and check the number of solutions.

FeedbackA Did you check the number of solutions?B Correct!C Are the y-intercepts equal?D Did you find the slope of each line?

PTS: 1 DIF: Average REF: Lesson 3-1 OBJ: 3-1.2 Determine whether a system of linear equations is consistent and independent, consistent and dependent, or inconsistent. STA: MA.912.A.3.14 | MA.912.A.3.15TOP: Determine whether a system of linear equations is consistent and independent, consistent and dependent, or inconsistent. KEY: System of Linear Equations | Consistent System | Inconsistent System

ID: A

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4. ANS: BGraph the equations and check the number of solutions.

FeedbackA Are the slopes equal?B Correct!C Are the y-intercepts equal?D Did you plot the graphs correctly?

PTS: 1 DIF: Average REF: Lesson 3-1 OBJ: 3-1.2 Determine whether a system of linear equations is consistent and independent, consistent and dependent, or inconsistent. STA: MA.912.A.3.14 | MA.912.A.3.15TOP: Determine whether a system of linear equations is consistent and independent, consistent and dependent, or inconsistent. KEY: System of Linear Equations | Consistent System | Inconsistent System

5. ANS: CBy using the method of substitution, solve one equation for one variable in terms of the other variable. Then, substitute this expression for the variable in the other equation.

FeedbackA Did you calculate the values correctly?B Recalculate the value of x.C Correct!D Recalculate the value of y.

PTS: 1 DIF: Average REF: Lesson 3-2 OBJ: 3-2.1 Solve systems of linear equations by using substitution. STA: MA.912.A.3.14 | MA.912.A.3.15 TOP: Solve systems of linear equations by using substitution. KEY: System of Linear Equations | Substitution

6. ANS: CBy using the method of substitution, solve one equation for one variable in terms of the other variable. Then, substitute this expression for the variable in the other equation.

FeedbackA Recalculate the value of s.B Did you calculate correctly?C Correct!D Recalculate the value of r.

PTS: 1 DIF: Average REF: Lesson 3-2 OBJ: 3-2.1 Solve systems of linear equations by using substitution. STA: MA.912.A.3.14 | MA.912.A.3.15 TOP: Solve systems of linear equations by using substitution. KEY: System of Linear Equations | Substitution

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7. ANS: CBoth the inequalities should be plotted and the region common to both should be shaded.

FeedbackA You have plotted the first inequality incorrectly.B You have plotted the second inequality incorrectly.C Correct!D You have plotted the inequalities incorrectly.

PTS: 1 DIF: Average REF: Lesson 3-3 OBJ: 3-3.1 Solve systems of inequalities by graphing. STA: MA.912.A.3.14 | MA.912.A.3.15TOP: Solve systems of inequalities by graphing. KEY: System of Inequalities | Graphs

8. ANS: DPlot the first inequality. Then, plot the positive and negative values of y and shade the common region.

FeedbackA What is the y-intercept of the first related equation?B Did you plot the second equation correctly?C Did you plot all the equations?D Correct!

PTS: 1 DIF: Average REF: Lesson 3-3 OBJ: 3-3.1 Solve systems of inequalities by graphing. STA: MA.912.A.3.14 | MA.912.A.3.15TOP: Solve systems of inequalities by graphing. KEY: System of Inequalities | Graphs

9. ANS: DSolve the system of inequalities by graphing the inequalities on the same coordinate plane. The solution set is represented by the intersection of the graphs.

FeedbackA Did you plot the inequalities correctly?B Did you check the sign of the coordinates?C You have interchanged the coordinates.D Correct!

PTS: 1 DIF: Advanced REF: Lesson 3-3 OBJ: 3-3.2 Determine the coordinates of the vertices of a region formed by the graph of a system of inequalities. STA: MA.912.A.3.14 | MA.912.A.3.15 TOP: Determine the coordinates of the vertices of a region formed by the graph of a system of inequalities. KEY: System of Inequalities | Graphs

ID: A

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10. ANS: ASolve the system of inequalities by graphing the inequalities on the same coordinate plane. The solution set is represented by the intersection of the graphs.

FeedbackA Correct!B You have interchanged the coordinates.C Did you check the sign of the coordinates?D Did you plot the inequalities correctly?

PTS: 1 DIF: Advanced REF: Lesson 3-3 OBJ: 3-3.2 Determine the coordinates of the vertices of a region formed by the graph of a system of inequalities. STA: MA.912.A.3.14 | MA.912.A.3.15 TOP: Determine the coordinates of the vertices of a region formed by the graph of a system of inequalities. KEY: System of Inequalities | Graphs

11. ANS: DPlot all the four graphs and shade the feasible region. Then find the coordinates of the feasible region, maximum value, and minimum value.

FeedbackA The first inequality is plotted incorrectly.B You have not plotted all the inequalities.C Did you use the correct sign for the coefficient of x?D Correct!

PTS: 1 DIF: Average REF: Lesson 3-4 OBJ: 3-4.1 Find the maximum and minimum values of a function over a region.STA: MA.912.A.3.14 | MA.912.A.3.15 TOP: Find the maximum and minimum values of a function over a region.KEY: Maximum Values | Minimum Values

12. ANS: CPlot all the four graphs and shade the feasible region. Then find the coordinates of the feasible region, maximum value, and minimum value.

FeedbackA You have not plotted all the inequalities.B Did you check the graph properly?C Correct!D You have plotted the first equation incorrectly.

PTS: 1 DIF: Average REF: Lesson 3-4 OBJ: 3-4.1 Find the maximum and minimum values of a function over a region.STA: MA.912.A.3.14 | MA.912.A.3.15 TOP: Find the maximum and minimum values of a function over a region.KEY: Maximum Values | Minimum Values

ID: A

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13. ANS: ASolve three equations simultaneously.

FeedbackA Correct!B Check whether the values of the variables have been interchanged.C Only two of the values are correct.D The values of a, b, and c are interchanged.

PTS: 1 DIF: Average REF: Lesson 3-5 OBJ: 3-5.1 Solve systems of linear equations in three variables. STA: MA.912.A.3.14 | MA.912.A.3.15 TOP: Solve systems of linear equations in three variables. KEY: System of Equations | Three Variables

14. ANS: ASolve three equations simultaneously.

FeedbackA Correct!B Only two of the values are correct.C Check whether the values of the variables have been interchanged.D The values of a, b, and c are interchanged.

PTS: 1 DIF: Average REF: Lesson 3-5 OBJ: 3-5.1 Solve systems of linear equations in three variables. STA: MA.912.A.3.14 | MA.912.A.3.15 TOP: Solve systems of linear equations in three variables. KEY: System of Equations | Three Variables

15. ANS: ADefine variables for each of the ingredients and write a system of equations.

FeedbackA Correct!B What is the price of cocoa?C You have interchanged the price and quantity of the food.D Did you interchange the values of cocoa and sugar?

PTS: 1 DIF: Average REF: Lesson 3-5 OBJ: 3-5.2 Solve real-world problems using systems of linear equations in three variables.STA: MA.912.A.3.14 | MA.912.A.3.15 TOP: Solve real-world problems using systems of linear equations in three variables.KEY: System of Equations | Three Variables | Real-World Problems

ID: A

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SHORT ANSWER

16. ANS: 5c + 3s + 2f = 50c + s + f = 18f = 2sDefine variables for each ingredient and write a system of equations.

PTS: 1 DIF: Average REF: Lesson 3-5 OBJ: 3-5.2 Solve real-world problems using systems of linear equations in three variables.STA: MA.912.A.3.14 | MA.912.A.3.15 TOP: Solve real-world problems using systems of linear equations in three variables.KEY: System of Equations | Three Variables | Real-World Problems