Algebra 2 by Richard Wright

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3-Review

Take this test as you would take a test in class. When you are finished, check your work against the answers.

    3-01

    Evaluate.

  1. \(\sqrt{-75}\)

    2. Simplify.

  2. (2 + 3i) − (3 − i)
  3. (2 + 3i)(3 − i)

    4. 3-02

    Factor.

  4. 2x2 + x − 1
  5. 6x2 + x − 12

    6. Solve by factoring.

  6. x2 − 5x + 4 = 0

    7. 3-03

    Solve by graphing.

  7. x2 − 2x − 15 = 0

    8. Solve using square roots.

  8. 3x2 + 48 = 0

    9. 3-04

    Solve by completing the square.

  9. x2 – 6x + 4 = 0

    10. Rewrite in standard form.

  10. y = x2 + 2x − 2

    11. 3-05

    Use the descriminant to classify the types of solutions.

  11. 0 = 2x2 − 3x + 5
  12. x2 + 4x − 4 = 0

    13. Solve by using the quadratic formula.

  13. 2x2 − 3x − 2 = 0

    14. 3-06

    Determine most efficient method to solve.

  14. 2x2 + 36 = 0
  15. 2x2 + 11x + 5 = 0
  16. x2 – 4x – 3 = 0

    17. Solve by any method.

  17. 3x2 – 4 = 2x2 – 28
  18. 2x2 + 4 = 9x
  19. A hot-air balloon is 20 feet above the ground while taking place in a competition. The pilot drops a weighted bag and a team member on the ground is supposed to catch it before it hits the ground. The model h = −16t2 + h0 gives the height of the bag t seconds after being dropped from the initial height h0. How much time does the team member on the ground have to catch the bag?

    20. 3-07

    Solve.

  20. x2 – 4x + 3 ≤ 0
  21. 3x2 > 27

Answers

  1. \(5\sqrt{3}i\)
  2. −1 + 4i
  3. 9 + 7i
  4. (2x − 1)(x + 1)
  5. (2x + 3)(3x − 4)
  6. 1, 4
  7. −3, 5
  8. ±4i
  9. \(3±\sqrt{5}\)
  10. y = (x + 1)2 − 3
  11. −31; two imaginary solutions
  12. 32; two real solutions
  13. \(-\frac{1}{2}\), 2
  14. square roots
  15. factoring or quadratic formula
  16. quadratic formula
  17. \(±2\sqrt{6}i\)
  18. \(\frac{1}{2}\), 4
  19. 1.12 s
  20. 1 ≤ x ≤ 3
  21. x < −3 or x > 3