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Algebra I (Grades 8–9) Midterm — Units 5–6

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Math Grades 8–9 20 multiple choice + 1 written

Free printable Algebra I midterm (Grades 8–9): 20 multiple-choice questions plus 1 written response covering Exponents & Exponential Functions, Polynomials, Factoring & Quadratics. Answer key included — customize it in the Midterm Maker.

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Algebra I (Grades 8–9) Midterm — Units 5–6
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Directions: Read each question carefully and choose the best answer. Answer the written response in complete sentences.

Covers: Exponents & Exponential Functions · Polynomials, Factoring & Quadratics

Part 1: Multiple Choice

  1. Simplify: √72
    1. A. 6√2
    2. B. 2√6
    3. C. 4√3
    4. D. 36√2
  2. What is the value of 27^(2/3)?
    1. A. 18
    2. B. 8
    3. C. 9
    4. D. 3
  3. Which table shows an exponential function? Each table lists y for x = 0, 1, 2, 3.
    1. A. y = 3, 6, 9, 12
    2. B. y = 3, 5, 9, 15
    3. C. y = 1, 4, 9, 16
    4. D. y = 3, 6, 12, 24
  4. Simplify: x^5 · x^(-2)
    1. A. x^(-10)
    2. B. x^(-3)
    3. C. x^7
    4. D. x^3
  5. A car is worth $24,000 and loses 15% of its value each year. Which function gives its value V after t years?
    1. A. V = 24,000(1.15)^t
    2. B. V = 24,000(0.15)^t
    3. C. V = 24,000 - 0.85t
    4. D. V = 24,000(0.85)^t
  6. The function y = 200(1.05)^t models a population after t years. What does 1.05 tell you?
    1. A. The population grows 105% each year
    2. B. The population grows 5% each year
    3. C. The population decreases 5% each year
    4. D. The population grows 0.05% each year
  7. A culture starts with 50 bacteria and doubles every hour. How many bacteria are there after 5 hours?
    1. A. 500
    2. B. 3,200
    3. C. 1,600
    4. D. 250
  8. Simplify: (3x^2 y)^3
    1. A. 9x^6 y^3
    2. B. 27x^5 y^3
    3. C. 27x^6 y^3
    4. D. 3x^6 y^3
  9. A value is modeled by y = 1000(0.8)^t. What is y when t = 2?
    1. A. 800
    2. B. 1,280
    3. C. 640
    4. D. 600
  10. Simplify: (2a^3) / (8a^5), with a ≠ 0
    1. A. 1/(4a^2)
    2. B. 1/(4a^8)
    3. C. a^2/4
    4. D. 4a^2
  11. What is the vertex of the graph of y = (x - 2)^2 + 5?
    1. A. (5, 2)
    2. B. (2, -5)
    3. C. (2, 5)
    4. D. (-2, 5)
  12. Factor: x^2 + 7x + 12
    1. A. (x + 2)(x + 6)
    2. B. (x - 3)(x - 4)
    3. C. (x + 1)(x + 12)
    4. D. (x + 3)(x + 4)
  13. Multiply: (x + 4)(x - 3)
    1. A. x^2 - x - 12
    2. B. x^2 - 12
    3. C. x^2 + x - 12
    4. D. x^2 + 7x - 12
  14. How many real solutions does 2x^2 - 4x + 5 = 0 have?
    1. A. No real solutions
    2. B. Two real solutions
    3. C. Three real solutions
    4. D. One real solution
  15. Factor: 2x^2 + 7x + 3
    1. A. (x + 1)(x + 3)
    2. B. (2x + 1)(x - 3)
    3. C. (2x + 1)(x + 3)
    4. D. (2x + 3)(x + 1)
  16. Simplify: (3x^2 + 2x - 5) + (x^2 - 4x + 7)
    1. A. 4x^2 - 2x - 12
    2. B. 4x^2 + 6x + 2
    3. C. 3x^4 - 2x + 2
    4. D. 4x^2 - 2x + 2
  17. Solve: x^2 - 5x - 14 = 0
    1. A. x = 7 or x = -2
    2. B. x = 5 or x = -14
    3. C. x = -7 or x = 2
    4. D. x = 14 or x = -1
  18. Factor: x^2 - 49
    1. A. (x + 7)^2
    2. B. (x - 49)(x + 1)
    3. C. (x + 7)(x - 7)
    4. D. (x - 7)^2
  19. Use the quadratic formula to solve x^2 + 4x - 1 = 0.
    1. A. x = -4 ± √5
    2. B. x = -2 ± √3
    3. C. x = 2 ± √5
    4. D. x = -2 ± √5
  20. What is the axis of symmetry of y = x^2 - 6x + 1?
    1. A. x = 6
    2. B. x = -3
    3. C. x = 1
    4. D. x = 3

Part 2: Written Response

  1. A ball is thrown upward from an 80-foot platform. Its height is h = -16t^2 + 64t + 80, where t is seconds. (a) When does the ball hit the ground? (b) What is its maximum height, and when does it occur? Show your work.

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