Math 8 (Grade 8) Midterm — Units 3–4

Part 1: Multiple Choice

1. Solve: 0.5x - 1.2 = 0.3x + 0.4
   1. A. x = 0.8
   2. B. x = 2
   3. C. x = 4
   4. D. x = 8
2. Solve: 5x + 3 = 2x + 18
   1. A. x = 3
   2. B. x = 7
   3. C. x = 5
   4. D. x = 15
3. How many solutions does 4(x + 2) = 4x + 8 have?
   1. A. No solution
   2. B. Infinitely many solutions
   3. C. Exactly one solution, x = 0
   4. D. Exactly one solution, x = 2
4. What is the slope of the line through (2, 3) and (6, 11)?
   1. A. 2
   2. B. 1/2
   3. C. 4
   4. D. -2
5. Which equation has the solution x = -2?
   1. A. 3x + 10 = 4
   2. B. 5 - x = 3
   3. C. x + 6 = 4x
   4. D. 2x - 4 = 0
6. Gym A charges $30 per month plus $5 per visit. Gym B charges $10 per visit. For how many visits in a month do the gyms cost the same?
   1. A. 3 visits
   2. B. 2 visits
   3. C. 30 visits
   4. D. 6 visits
7. Which equation describes a line with slope -3 and y-intercept 5?
   1. A. y = 3x + 5
   2. B. y = -3x - 5
   3. C. y = 5x - 3
   4. D. y = -3x + 5
8. How many solutions does 2x + 7 = 2x - 3 have?
   1. A. Exactly one solution, x = 5
   2. B. No solution
   3. C. Exactly one solution, x = 0
   4. D. Infinitely many solutions
9. Solve: 3(x - 2) = 2(x + 4)
   1. A. x = 10
   2. B. x = 14
   3. C. x = 2
   4. D. x = -14
10. Which equation describes the line with slope 4/3 that passes through (0, -2)?
    1. A. y = -2x + 4/3
    2. B. y = (4/3)x - 2
    3. C. y = (4/3)x + 2
    4. D. y = (3/4)x - 2
11. Which set of ordered pairs represents a function?
    1. A. {(1, 2), (1, 3), (2, 4), (3, 5)}
    2. B. {(2, 1), (3, 1), (2, 5), (4, 6)}
    3. C. {(0, 0), (5, 1), (5, -1), (6, 2)}
    4. D. {(1, 2), (2, 4), (3, 6), (4, 8)}
12. A line passes through (0, 4) and (2, 0). Which equation describes it?
    1. A. y = 4x - 2
    2. B. y = 2x + 4
    3. C. y = -0.5x + 4
    4. D. y = -2x + 4
13. A graph shows a car's speed over time: the speed rises, stays level, then falls to zero. Which story fits the graph?
    1. A. A car cruises at a steady speed, speeds up, then parks
    2. B. A car slows down, stops, then speeds up
    3. C. A car stays parked the entire time
    4. D. A car speeds up from a stop, cruises at a steady speed, then slows to a stop
14. Which function is nonlinear?
    1. A. y = -x
    2. B. y = x^2 + 1
    3. C. y = 4x - 2
    4. D. y = x/2 + 3
15. Function A is y = 2x + 7. Function B has these values: when x = 1, 2, 3, y = 4, 9, 14. Which statement is true?
    1. A. Function B has the greater rate of change, 4
    2. B. Function A has the greater rate of change, 7
    3. C. Function A has the greater rate of change, 2
    4. D. Function B has the greater rate of change, 5
16. If f(x) = 3x - 4, what is f(5)?
    1. A. -11
    2. B. 19
    3. C. 3
    4. D. 11
17. A linear function has these values: when x = 0, 1, 2, 3, y = 5, 8, 11, 14. What is the rate of change?
    1. A. 3
    2. B. 5
    3. C. 8
    4. D. 1/3
18. A plumber charges a $65 fee plus $40 per hour. In a function for the total cost, what is the initial value?
    1. A. $65
    2. B. $40
    3. C. $105
    4. D. $25
19. A linear function has these values: when x = 1, 2, 3, 4, y = 7, 9, 11, 13. Which rule fits?
    1. A. y = 2x + 7
    2. B. y = x + 6
    3. C. y = 7x
    4. D. y = 2x + 5
20. The graph of a linear function goes down from left to right. What does this tell you?
    1. A. The rate of change is positive
    2. B. The rate of change is undefined
    3. C. The rate of change is zero
    4. D. The rate of change is negative

Part 2: Written Response

21. A tank holds 500 gallons of water and drains at a constant 20 gallons per minute. (a) Write a function W(t) for the water left after t minutes. (b) Name the rate of change and initial value. (c) How much water is left after 12 minutes? (d) When is the tank empty? Show your work.