CPS Mathematics Benchmark Assessment
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1 Student Name Date 1. What is the solution to the equation? A. x = B. x = C. x = D. x = 5 2. What value for n makes the equation true? A. -6 B. -3 C. 3 D. 6 ( ) 3. How many solutions does the equation have? A. no solutions B. exactly 1 solution C. exactly 2 solutions D. infinitely many solutions 4. The equation has infinitely many solutions. What value should be placed in the box? A. 0 B. 1 C. 3 D. 5 Department of Math SY14-15 Page 1
2 5. The steps Jennifer used to solve an equation are shown below. Given: 7(x 2) = 3x 2 Step 1: 7x 14 = 3x 2 Step 2: 7x 3x = Step 3: 4x = -16 Step 4: x = -4 Which statement explains the error in Jennifer's solution? A. Step 2 is incorrect because she subtracted 3x from 7x instead of multiplying. B. Step 2 is incorrect because 14 should be 14 instead. C. Step 3 is incorrect because 4x should be equal to 12 instead of 16. D. Step 4 is incorrect because she divided 16 by 4 instead of multiplying. 6. Which best represents the solution to the system of equations graphed below? A. (2, 4) B. (-2, 4) C. (4, -2) D. (4, 2) SY14-15 Page 2 Chicago Public Schools
3 7. Which graph shows the solution to the systems of equations given below? x + 2y = 10 -x + y = 2 A. B. C. D. Department of Math SY14-15 Page 3
4 8. What is the solution to this system of equations? A. ( ) B. ( ) C. ( ) y = 4x + 13 y = x + 4 D. ( ) 9. Janice solved the system of equations below by eliminating the variable s. She multiplied Equation B by a factor and added the result to Equation A. Equation A: 9s + 4t = 13 Equation B: 3s 6t = 8 Which factor could Janice have used? A. B. 0. C. D. 3 SY14-15 Page 4 Chicago Public Schools
5 10. Joe solves this linear system correctly: 6x + 3y = 6 y = -2x + 2 These are the last two steps of his work: 6x 6x + 6 = 6 6 = 6 Which statement about this linear system must be true? A. x must equal 6 B. y must equal 6 C. There is no solution to this system. D. There are infinitely many solutions to this system 11. It takes 12 hours to fill a tank with water when pipes A, B, and C are used simultaneously. When used separately, pipe A fills the tank at three times the rate of pipe B, and pipe B fills the tank at twice the rate of pipe C. Which of the following is true regarding the time in hours that pipe C alone takes to fill the tank? A. Solving for x, using the equation, it will take 7 hours. B. Solving for x, using the equation, it will take 12 hours. C. Solving for x, using the equation, it will take 108 hours. D. Solving for x, using the equation, it will take 118 hours. Department of Math SY14-15 Page 5
6 12. Gina wrote this system of linear equations. 2x + y = 7 4x + 5y = 11 Which of the following shows the first four steps that Gina could have used to correctly solve this system for x? A. y = 7 2x 4x + 5(7 2x) = 11 4x x = x = 11 B. y = 7 2x 4x + 5(7 2x) = 11 4x x = x = 11 C. y = 7 2x 4x (7 2x) = 11 2x + 12 = 11 2x = D. x = 11 5y 4x + 5(11 5y) = 11 4x x = 11 4x + 10x = SY14-15 Page 6 Chicago Public Schools
7 13. The drama department was considering two options for the winter production. They used the following equations to represent the profit, y, they would make from the sale of tickets, x, minus the costs. Option A: y = 5x Option B: y = 3x Which graph correctly shows the point when the profits for Option A and Option B are the same? A. B. C. D. Department of Math SY14-15 Page 7
8 14. A laboratory supply company has two concentrations of the same acid solution: a 25% concentration and a 50% concentration. A technician used the following system of equations to determine the number of liters of each concentration he needs to make 25 liters of a 35% concentration for a customer. How many liters of each concentration does the technician need? A. 8 liters of the 25% concentration and 17 liters of the 50% concentration B. 10 liters of the 25% concentration and 15 liters of the 50% concentration C liters of the 25% concentration and 12.5 liters of the 50% concentration D. 15 liters of the 25% concentration and 10 liters of the 50% concentration 15. Geraldo will use the substitution method to solve the system of equations below = = 16 Which expression could he substitute for y in the second equation to determine the y-value of the solution to the system of equations? A. -6x 12 B. -3x 6 C. 2x - 4 D. 3x + 6 SY14-15 Page 8 Chicago Public Schools
9 Read the following and answer the questions below: 16. Anna wants to pick 40 pounds of apples. How much does this cost at David's orchard? Show your calculations. Department of Math SY14-15 Page 9
10 17. Anna wants to pick 40 pounds of apples. How much does it cost at Pam's orchard? Show your calculations. 18. Chris has $30 to spend. How many pounds of apples will he get if he goes to David's orchard? Explain how you figured it out. SY14-15 Page 10 Chicago Public Schools
11 19. Chris has $30 to spend. If Chris goes to Pam's orchard, how many pounds of apples will he get? Explain how you figured it out. 20. How many pounds of apples must Chris pick before Pam's orchard is cheaper than David's? Show your work Department of Math SY14-15 Page 11
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