Math 8 (Grade 8) Midterm — Units 5–6

Part 1: Multiple Choice

1. Which system has the solution (1, -2)?
   1. A. y = x + 3 and y = -2x
   2. B. y = 2x - 4 and y = x + 1
   3. C. y = -x - 1 and y = 3x
   4. D. y = x - 3 and y = -2x
2. In the system 2x + 3y = 12 and x = 3, what is the value of y?
   1. A. 3
   2. B. 2
   3. C. 6
   4. D. 4
3. What is the solution to the system 3x + 2y = 16 and x - 2y = 0?
   1. A. (4, 2)
   2. B. (2, 4)
   3. C. (4, -2)
   4. D. (2, 5)
4. When a system of two linear equations is graphed, what represents the solution?
   1. A. The point where each line crosses the x-axis
   2. B. The point where the two lines intersect
   3. C. The y-intercept of the first line
   4. D. The slope of each line
5. How many solutions does the system y = -x + 4 and 2y = -2x + 8 have?
   1. A. Exactly one solution
   2. B. Infinitely many solutions
   3. C. Exactly two solutions
   4. D. No solution
6. What is the solution to the system x + y = 10 and x - y = 4?
   1. A. (8, 2)
   2. B. (7, 3)
   3. C. (6, 4)
   4. D. (3, 7)
7. The sum of two numbers is 30 and their difference is 8. What is the larger number?
   1. A. 22
   2. B. 19
   3. C. 11
   4. D. 15
8. How many solutions does the system y = 3x + 2 and y = 3x - 5 have?
   1. A. Infinitely many solutions
   2. B. No solution
   3. C. Exactly two solutions
   4. D. Exactly one solution
9. What is the solution to the system y = 2x and x + y = 9?
   1. A. (2, 7)
   2. B. (6, 3)
   3. C. (3, 6)
   4. D. (4, 5)
10. A school sold 20 tickets to a play for $127. Adult tickets cost $8 and student tickets cost $5. How many adult tickets were sold?
    1. A. 9
    2. B. 15
    3. C. 11
    4. D. 12
11. The point (3, -2) is translated 4 units left and 5 units up. What is the new point?
    1. A. (-1, 3)
    2. B. (-1, -7)
    3. C. (7, -7)
    4. D. (7, 3)
12. A line of fit for test scores is y = 2.5x + 60, where x is hours studied. What score does it predict for 8 hours?
    1. A. 85
    2. B. 20
    3. C. 80
    4. D. 68
13. The point (2, -1) is dilated by a scale factor of 3 centered at the origin. What is the image?
    1. A. (5, 2)
    2. B. (2/3, -1/3)
    3. C. (6, 3)
    4. D. (6, -3)
14. The point (4, 5) is reflected over the x-axis. What is the image?
    1. A. (-4, 5)
    2. B. (4, -5)
    3. C. (-4, -5)
    4. D. (5, 4)
15. What is the volume of a cylinder with radius 3 cm and height 10 cm?
    1. A. 60π cubic cm
    2. B. 30π cubic cm
    3. C. 900π cubic cm
    4. D. 90π cubic cm
16. The point (2, 3) is rotated 90° counterclockwise about the origin. What is the image?
    1. A. (3, -2)
    2. B. (-2, -3)
    3. C. (2, -3)
    4. D. (-3, 2)
17. What is the volume of a sphere with radius 3 m?
    1. A. 108π cubic meters
    2. B. 12π cubic meters
    3. C. 36π cubic meters
    4. D. 27π cubic meters
18. A scatter plot shows that students who studied more hours tended to earn higher test scores. What type of association is this?
    1. A. Negative association
    2. B. Nonlinear association with scores falling
    3. C. No association
    4. D. Positive association
19. What is the volume of a cone with radius 3 inches and height 4 inches?
    1. A. 36π cubic inches
    2. B. 12π cubic inches
    3. C. 48π cubic inches
    4. D. 4π cubic inches
20. Which transformation does NOT always produce a figure congruent to the original?
    1. A. Translation
    2. B. Rotation
    3. C. Reflection
    4. D. Dilation

Part 2: Written Response

21. Triangle ABC has vertices A(1, 1), B(4, 1), and C(1, 3). Reflect it over the y-axis, then translate the image 2 units down. Give the final coordinates and explain whether the area changes. Show your work.