45 Minutes 27 Questions YOU MAY WRITE ON THIS
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1 Algebra 2 Chapter 3.3/3.4 Review NAME 45 Minutes 27 Questions YOU MAY WRITE ON THIS DIRECTIONS: Solve each problem, choose the correct answer, and then fill in the corresponding oval on your answer document. Refer to the formula sheet when needed. You are permitted to use a calculator on this test. Illustrative figures are NOT necessarily drawn to scale. 1. Identify the solution to the system of linear equations which is graphed below. 3. Identify the solution to the system of linear equations which is graphed below. A. (1, 2) B. ( 3, 1) C. (2, 1) D. No Solution 2. Graph the linear system of equations. y = x 2 y = 2x + 1 A. (6, 2) B. (2, 4) C. (3, 1) D. No Solution 4. Graph the linear system of equations. y = x + 1 y = 2 A. B. A. B. C. D. C. D.
2 5. Solve the system using Substitution. x = 3 y = 2x 5 7. Solve the system using Substitution. y = x 1 3x y = 5 A. (3, 1) B. (3, 1) C. ( 1, 3) D. ( 1, 1) E. No Solution A. (1, 3) B. (5, 3) C. (2, 4) D. (2, 1) 6. Solve the system using Substitution. y = x + 2 2x + y = 8 8. Solve the system using Substitution. y = 2x + 3 y = 2x 5 A. (2, 4) B. (2, 1) C. ( 1, 3) D. ( 2, 1) A. (3, 1) B. (3, 1) C. ( 1, 3) D. ( 1, 1) E. No Solution 2
3 9. Solve the system using Elimination. 2x + y = 3 5x y = Solve the system using Elimination. 4x + 5y = 2 5x 4y = 23 A. ( 2, 1) B. ( 3, 7) C. ( 1, 4) D. (4, 1) E. ( 2, 4) A. (1, 3) B. (5, 3) C. (2, 4) D. (2, 1) 10. Solve the system using Elimination. 2x + y = 6 3x + 5y = Solve the system using Elimination. 2x + 3y = 7 2x 3y = 11 A. (7, 7) B. (3, 0) C. ( 1, 4) D. (3, 4) E. (2, 3) A. (3, 1) B. (3, 1) C. ( 1, 3) D. ( 1, 1) E. No Solution 3
4 13. Tell which ordered triple is the solution to the system. 2x 3y + z = 0 2x y + 2z = 3 x + y + z = Tell which ordered triple is the solution to the system. x + 4y 2z = 1 4x 3y + z = 11 5x 3y + z = 14 A. (0, 1, 3 ) B. (1, 1, 1 ) C. ( 1, 0, 4 ) D. (2, 1, 0 ) A. (3, 2, 5 ) B. (0, 2, 3 ) C. ( 1, 0, 2 ) D. ( 3, 2, 1 ) 14. The function f of the 2 variables x and y is defined by: f(x, y) = 2x 2 5y 16. The function f of the 2 variables x and y is defined by: 3x 2y + 5z = 16 What is f(3, 2)? What is f(1, 1)? A. 7 B. 1 C. 2 D. 8 E. 26 A. 1 B. 1 C. 3 D. 5 E. 16 4
5 17. Use the given point (3, 5, 2) to find the volume of the rectangular prism. 19. Use the given point (4, 2, 6) to find the volume of the rectangular prism. A. 3 u 3 B. 5 u 3 C. 15 u 3 D. 30 u 3 E. 40 u 3 A. 4 u 3 B. 6 u 3 C. 24 u 3 D. 30 u 3 E. 48 u Tell which ordered pair is a solution to the system of linear inequalities. 20. Tell which ordered pair is a solution to the system of linear inequalities. x + y > 2 y 4 A. ( 2, 3) B. (2, 1) C. (4, 5) D. (0, 3) E. None of the Above A. (0, 3) B. (3, 1) C. (2, 5) D. ( 1, 2) E. None of the Above 5
6 21. Graph the linear system of inequalities. y 2x + 1 y 1 x Graph the linear system of inequalities. y > 2 x 4 3 y < 2 x 1 3 A. A. B. B. C. C. D. D. E. None of the Above 6
7 23. Graph the linear system of inequalities. x 2 y 2 y x Soldier Johnson is on a field expedition. He needs to determine his location. He can see two mountains in the distance. From his map, he can determine the coordinates of Mount Thor as (2, 3) and the equation of the line through Mount Thor to his location as y = 1 2 x + 2. The other mountain, Mount Loki, has the coordinates (12, 2) and the equation of the line through Mount Loki to Soldier Johhson s location is y = 1x + 14 Use the two equations and graph to triangulate the coordinates of the mountains to determine Soldier Johnson s location. 7
8 Name Hour 25. Tickets to the movies are $5 for children and $8 for adults. The total number of tickets sold on Sunday was 400 tickets and the total receipts were $2900. Solve for how many of each ticket were sold. (2 points) 26. Business A charges $55 for a service call, plus an additional $30 per hour for labor. Business B charges $25 for a service call, plus an additional $40 per hour for labor. Write and solve a system of equations to find the break-even point where both businesses would cost the same amount. (2 points) 27. Solve the system. (2 points) x 2y + 3z = 11 y z = 3 2y + z = 0 8
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