Name: ________________________ Class: ___________________ Date: __________
Algebra I Chapter 6 Practice Test Multiple Choice Identify the choice that best completes the statement or answers the question. Find a solution of the system of linear inequalities. 1. y < 3x + 12 y ≥ 5x + 7 a. (1, 2)
b.
(0, –1)
c.
(2, 17)
Short Answer 2. Use substitution to solve the following system of equations. d + e – f = 11 e=f+d+5 f = 2e – 12 Graph the inequality. 3. 4x + 6y ≥ 10
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d.
(–2, –5)
ID: A
Name: ________________________
ID: A
4. 3x − 7y < −21
Write the linear inequality shown in the graph. 5.
6. An ice skating arena charges an admission fee for each child plus a rental fee for each pair of ice skates. John paid the admission fees for his six nephews and rented five pairs of ice skates. He was charged $32.00. Juanita paid the admission fees for her seven grandchildren and rented five pairs of ice skates. She was charged $35.25. What is the admission fee? What is the rental fee for a pair of skates?
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Name: ________________________
ID: A
7. At the local ballpark, the team charges $5 for each ticket and expects to make $1,400 in concessions. The team must pay its players $2,000 and pay all other workers $1,600. Each fan gets a free bat that costs the team $3 per bat. How many tickets must be sold to break even? 8. The sum of two numbers is 82. Their difference is 24. Write a system of equations that describes this situation. Solve by elimination to find the two numbers. Solve the system using elimination. 9. 5x = –25 + 5y 10y = 42 + 2x 10. 3x – 4y = 9 –3x + 2y = 9 Solve the system of equations using substitution.
1 11. 3y = – x + 2 2 y = –x + 9 12. 3x + 2y = 7 y = –3x + 11 13. Find a solution to the following system of equations. −5x + y = −5 −4x + 2y = 2 14. Find the value of b that makes the system of equations have the solution (3, 5). y = 3x – 4 y = bx + 2
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Name: ________________________
ID: A
15. Graph the following equation. y ≥ |x − 2| − 2
16. Graph the following linear inequalities on the same coordinate plane. What figure does the solution to all three inequalities make?
y ≥ −5 y ≤ 2x + 5 y ≤ −2x + 5
4
Name: ________________________
ID: A
Solve the system of linear inequalities by graphing. 17. y ≤ x + 4 2x + y ≤ −4
Essay 18. Write the inequality y is less than x plus 4. Explain how to graph the inequality. Then graph the inequality. 19. Ronald is setting up an aquarium in his new office. At one pet store, fish cost $2 each and an aquarium cost $40. At another pet store, fish cost $3 each and an aquarium cost $36. Write and solve a system of equations to represent the cost of x fish and an aquarium at each store. Solve this the system. What does this solution represent? If Ronald wants 5 fish, from which pet store should he buy his aquarium? Explain. Other 20. Tickets to a local movie were sold at $6.00 for adults and $4.50 for students. There were 240 tickets sold for a total of $1,155.00. Write a system of equations to model the situation. a. Solve the system to find the number of adult tickets sold and the number of student b. tickets sold. Explain the method you used to solve the system. c. 21. Without graphing, decide whether the system has one solution, no solution, or infinitely many solutions. Explain.
y = −3x + 4 y = 3x + 8
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ID: A
Algebra I Chapter 6 Practice Test Answer Section MULTIPLE CHOICE 1. ANS: C
DIF: L2
SHORT ANSWER 2. ANS: d = 3, e = 4, f = –4 DIF: L4 3. ANS:
DIF: L3 4. ANS:
DIF: L3
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ID: A 5. ANS: y > 4x − 3 DIF: L3 6. ANS: admission fee: $3.25 skate rental fee: $2.50 DIF: L3 7. ANS: 1,100 DIF: L3 8. ANS: x + y = 82 x – y = 24 53 and 29 DIF: L3 9. ANS: (–1, 4) DIF: L3 10. ANS: (–9, –9) DIF: L3 11. ANS: (10, –1) DIF: L3 12. ANS: (5, –4) DIF: L3 13. ANS: (2, 5) DIF: L3 14. ANS: 1 DIF: L3
2
ID: A 15. ANS:
DIF: L4 16. ANS:
The figure is an isosceles triangle. DIF: L4
3
ID: A 17. ANS:
DIF: L2 ESSAY 18. ANS: y < x+4 [4] Draw a dashed line at y = x + 4. The line is dashed because the value of y cannot be equal to x + 4. Shade the y values below the line since y should be less than x + 4.
[3] [2] [1]
minor error in graph minor error in equation correct graph without explanation
DIF: L3
4
ID: A 19. ANS: y = 2x + 40 [4] y = 3x + 36 The solution is (4, 48). If Ronald buys 4 fish and an aquarium, it will cost $48 in either pet store. Five fish will cost 2(5) + 40, or $50, in the first store, and 3(5) + 36, or $51 in the second store. To spend less, he should buy at the first store. [3] [2] [1]
minor computational error correct equations and solution, error in interpretation correct equations only OR correct choice of pet store without explanation
DIF: L3 OTHER 20. ANS: 6a + 4.5s = 1,155 a. a + s = 240 There were 50 adult tickets and 190 student tickets. b. Methods may vary. Sample: By multiplying the second equation by 6, it becomes 6a + c. 6s = 1,440. You can then use subtraction to eliminate a. DIF: L3 21. ANS: The system has one solution. A system of linear equations has no solution when the equations are of parallel lines and infinitely many solutions when the equations are of the same line. The slopes of the lines are not equal, so neither case applies. DIF: L3
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