Name: lass: ate: I: lgebra 2 Honors hapter 3 Test Multiple hoice Identify 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 - 6 y = - 6x + 11 a. ( 1, 5) c. (5, 1) b. (1, 7) d. (1, 5) 2. Solve the system of equations - Use any method 2y + 8x = 58 y - 5x = 11 a. (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 = 15 27x - 24y = 3 a. consistent and independent c. consistent and dependent b. inconsistent d. none of these 4. 5x - 8y = 6 6x - 6y = 6 a. inconsistent c. consistent and dependent b. 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 = 18 3x 5y = 22 a. ( 2, 4) c. (4, 2) b. (3, 2) d. (4, 0) 6. Solve the system of equations - Use any method 3r + 3s = 9 3r - 6s = 18 a. (4, 0.5) c. (4, 1) b. (5.5, 3) d. (2, 1) 1
Name: I: Solve the system of inequalities by graphing. 7. x > 2 y > 8 a. c. b. d. 2
Name: I: 8. y > x 6 y 6 a. c. b. d. Find the coordinates of the vertices of the figure formed by each system of inequalities. 9. y + x -9 y x - 7 2y + x 16 a. ( 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) 3
Name: I: 10. y -2 2x + y 2 y 2x + 6 a. (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) 4
Name: I: Given below are some inequalities. Plot the feasible region graphically. 11. x 2.8 y 4.8 2.8x + 4.8y 9 fê ËÁ x,yˆ = x - y a. c. b. vertices: ( 5.01, 4.8), (2.8, 0.24) max: f(2.8, 0.24) = 2.56 min: f( 5.01, 4.8) = 9.81 d. vertex: (4.8, 0.93) max: f(4.8, 0.93) = 5.73 min: none vertices: (2.8, 4.8) max: f(2.8, 4.8) = 2 min: f(2.8, 4.8) = 2 vertex: (2.8, 0.24) max: none min: f(2.8, 0.24) = 2.56 5
Name: I: 12. y -5 x 4 y x - 4 fê ËÁ x,yˆ = x + y a. c. vertices: (4, 5) max: f(4, 5) = 1 min: f(4, 5) = 1 vertices: (4, 5), (4, 0), ( 1, 5) max: f(4, 0) = 4 min: f( 1, 5) = 6 b. d. vertices: (4, 5), (4, 0), ( 1, 5) max: f(4, 0) = 4 min: f( 1, 5) = 6 vertices: (4, 5), (4, 0), ( 1, 5) max: f(4, 0) = 4 min: f( 1, 5) = 6 Solve the given system of equations. 13. 3a = 36 10a + 3c = 9 2b + 5c = 23 a. a = 12, b = 96, c = 43 c. a = 12, b = 96, c = 43 b. a = 12, b = 43, c = 96 d. a = 43, b = 12, c = 96 6
Name: I: 14. 11a + 2c = 10 2a = 32 8b + 10c = 18 a. a = 16, b = 114, c = 93 c. a = 16, b = 93, c = 114 b. a = 16, b = 114, c = 93 d. a = 93, b = 16, c = 114 hocos is a dish made from wheat, sugar, and cocoa. ertha 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 ertha purchased. a. 5w + 3s + 4c = 48 w + s + c = 12 c = 2s b. 5w + 3s + 2c = 48 w + s + c = 12 c = 2s c. 5w + 3s + 4c = 12 w + s + c = 48 c = 2s d. 5w + 3s + 4c = 48 w + s + c = 12 s = 2c Short nswer hoco pies are cookies made from chocolate (c), sugar (s), and flour (f). hocolate 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.. 7
I: lgebra 2 Honors hapter 3 Test nswer Section MULTIPLE HOIE 1. NS: Graph the equations and find their point of intersection. What is the x-coordinate of the intersection? id you graph both equations correctly? Write the coordinates of the intersection carefully. PTS: 1 IF: verage REF: Lesson 3-1 OJ: 3-1.1 Solve systems of linear equations by graphing. TOP: Solve systems of linear equations by graphing. KEY: System of Linear Equations Graphs 2. NS: Graph the equations and find their point of intersection. ST: M.912..3.14 M.912..3.15 id you plot the graphs correctly? id you read the intersection of the graphs correctly? What is the x-coordinate of the intersection? PTS: 1 IF: verage REF: Lesson 3-1 OJ: 3-1.1 Solve systems of linear equations by graphing. TOP: Solve systems of linear equations by graphing. KEY: System of Linear Equations Graphs 3. NS: Graph the equations and check the number of solutions. ST: M.912..3.14 M.912..3.15 id you check the number of solutions? re the y-intercepts equal? id you find the slope of each line? PTS: 1 IF: verage REF: Lesson 3-1 OJ: 3-1.2 etermine whether a system of linear equations is consistent and independent, consistent and dependent, or inconsistent. ST: M.912..3.14 M.912..3.15 TOP: etermine whether a system of linear equations is consistent and independent, consistent and dependent, or inconsistent. KEY: System of Linear Equations onsistent System Inconsistent System 1
I: 4. NS: Graph the equations and check the number of solutions. re the slopes equal? re the y-intercepts equal? id you plot the graphs correctly? PTS: 1 IF: verage REF: Lesson 3-1 OJ: 3-1.2 etermine whether a system of linear equations is consistent and independent, consistent and dependent, or inconsistent. ST: M.912..3.14 M.912..3.15 TOP: etermine whether a system of linear equations is consistent and independent, consistent and dependent, or inconsistent. KEY: System of Linear Equations onsistent System Inconsistent System 5. NS: y 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. id you calculate the values correctly? Recalculate the value of x. Recalculate the value of y. PTS: 1 IF: verage REF: Lesson 3-2 OJ: 3-2.1 Solve systems of linear equations by using substitution. ST: M.912..3.14 M.912..3.15 TOP: Solve systems of linear equations by using substitution. KEY: System of Linear Equations Substitution 6. NS: y 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. Recalculate the value of s. id you calculate correctly? Recalculate the value of r. PTS: 1 IF: verage REF: Lesson 3-2 OJ: 3-2.1 Solve systems of linear equations by using substitution. ST: M.912..3.14 M.912..3.15 TOP: Solve systems of linear equations by using substitution. KEY: System of Linear Equations Substitution 2
I: 7. NS: oth the inequalities should be plotted and the region common to both should be shaded. You have plotted the first inequality incorrectly. You have plotted the second inequality incorrectly. You have plotted the inequalities incorrectly. PTS: 1 IF: verage REF: Lesson 3-3 OJ: 3-3.1 Solve systems of inequalities by graphing. ST: M.912..3.14 M.912..3.15 TOP: Solve systems of inequalities by graphing. KEY: System of Inequalities Graphs 8. NS: Plot the first inequality. Then, plot the positive and negative values of y and shade the common region. What is the y-intercept of the first related equation? id you plot the second equation correctly? id you plot all the equations? PTS: 1 IF: verage REF: Lesson 3-3 OJ: 3-3.1 Solve systems of inequalities by graphing. ST: M.912..3.14 M.912..3.15 TOP: Solve systems of inequalities by graphing. KEY: System of Inequalities Graphs 9. NS: Solve the system of inequalities by graphing the inequalities on the same coordinate plane. The solution set is represented by the intersection of the graphs. id you plot the inequalities correctly? id you check the sign of the coordinates? You have interchanged the coordinates. PTS: 1 IF: dvanced REF: Lesson 3-3 OJ: 3-3.2 etermine the coordinates of the vertices of a region formed by the graph of a system of inequalities. ST: M.912..3.14 M.912..3.15 TOP: etermine the coordinates of the vertices of a region formed by the graph of a system of inequalities. KEY: System of Inequalities Graphs 3
I: 10. NS: Solve the system of inequalities by graphing the inequalities on the same coordinate plane. The solution set is represented by the intersection of the graphs. You have interchanged the coordinates. id you check the sign of the coordinates? id you plot the inequalities correctly? PTS: 1 IF: dvanced REF: Lesson 3-3 OJ: 3-3.2 etermine the coordinates of the vertices of a region formed by the graph of a system of inequalities. ST: M.912..3.14 M.912..3.15 TOP: etermine the coordinates of the vertices of a region formed by the graph of a system of inequalities. KEY: System of Inequalities Graphs 11. NS: Plot all the four graphs and shade the feasible region. Then find the coordinates of the feasible region, maximum value, and minimum value. The first inequality is plotted incorrectly. You have not plotted all the inequalities. id you use the correct sign for the coefficient of x? PTS: 1 IF: verage REF: Lesson 3-4 OJ: 3-4.1 Find the maximum and minimum values of a function over a region. ST: M.912..3.14 M.912..3.15 TOP: Find the maximum and minimum values of a function over a region. KEY: Maximum Values Minimum Values 12. NS: Plot all the four graphs and shade the feasible region. Then find the coordinates of the feasible region, maximum value, and minimum value. You have not plotted all the inequalities. id you check the graph properly? You have plotted the first equation incorrectly. PTS: 1 IF: verage REF: Lesson 3-4 OJ: 3-4.1 Find the maximum and minimum values of a function over a region. ST: M.912..3.14 M.912..3.15 TOP: Find the maximum and minimum values of a function over a region. KEY: Maximum Values Minimum Values 4
I: 13. NS: Solve three equations simultaneously. heck whether the values of the variables have been interchanged. Only two of the values are correct. The values of a, b, and c are interchanged. PTS: 1 IF: verage REF: Lesson 3-5 OJ: 3-5.1 Solve systems of linear equations in three variables. ST: M.912..3.14 M.912..3.15 TOP: Solve systems of linear equations in three variables. KEY: System of Equations Three Variables 14. NS: Solve three equations simultaneously. Only two of the values are correct. heck whether the values of the variables have been interchanged. The values of a, b, and c are interchanged. PTS: 1 IF: verage REF: Lesson 3-5 OJ: 3-5.1 Solve systems of linear equations in three variables. ST: M.912..3.14 M.912..3.15 TOP: Solve systems of linear equations in three variables. KEY: System of Equations Three Variables 15. NS: efine variables for each of the ingredients and write a system of equations. What is the price of cocoa? You have interchanged the price and quantity of the food. id you interchange the values of cocoa and sugar? PTS: 1 IF: verage REF: Lesson 3-5 OJ: 3-5.2 Solve real-world problems using systems of linear equations in three variables. ST: M.912..3.14 M.912..3.15 TOP: Solve real-world problems using systems of linear equations in three variables. KEY: System of Equations Three Variables Real-World Problems 5
I: SHORT NSWER 16. NS: 5c + 3s + 2f = 50 c + s + f = 18 f = 2s efine variables for each ingredient and write a system of equations. PTS: 1 IF: verage REF: Lesson 3-5 OJ: 3-5.2 Solve real-world problems using systems of linear equations in three variables. ST: M.912..3.14 M.912..3.15 TOP: Solve real-world problems using systems of linear equations in three variables. KEY: System of Equations Three Variables Real-World Problems 6