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COMPASS Algebra Practice Test D

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  1. COMPASS AlgebraPractice Test D • This practice test is 10 items long. • Record your responses on a sheet of paper. • The correct answers are on the slide after the last question. • Complete solutions follow the answer slide. • Click the mouse or use the spacebar to advance to the next question.

  2. ¡ A. -24 ¡ B. -10 ¡ C. -2 ¡ D. 2 ¡ E. 10 D1. If x = -1 and y = -2, what is the value of the expression 2x2y- 3xy ?

  3. D2. What are the solutions to the quadratic x2 – 2x – 48 = 0? ¡ A. 6 and 8 ¡ B. -6 and -8 ¡ C. -6 and 8 ¡ D. 6 and -8 ¡ E. 3 and 16

  4. D3. What is the sum of the solutions to the quadratic x2 – 2x – 48 = 0? ¡ A. 14 ¡ B. -14 ¡ C. 2 ¡ D. -2 ¡ E. 19

  5. D4. What is the sum of the solutions of the quadratic equation x2 + 3x = 28? ¡ A. 3 ¡ B. -3 ¡ C. 11 ¡ D. -11 ¡ E. 10

  6. ¡ A. ¡ B. ¡ C. ¡ D. ¡ E. -1 D5. What is the sum of the solutions of the quadratic equation 2x2 - x = 15?

  7. ¡ A. 3 ¡ B. 2 ¡ C. 5 ¡ D. 1 ¡ E. -1 D6. If the equation x2 – x = 6 is solved for x, what is the sum of the solutions?

  8. ¡ A. -2, -3 ¡ B. 2, 3 ¡ C. 1, 6 ¡ D. -1, -6 ¡ E. -2, 3 D7. What are the solutions to the quadratic x2 - 5x = -6?

  9. D8. For all x ≠ 2, ¡ A. (x + 5) ¡ B. (x - 2) ¡ C. (x + 2) ¡ D. (x - 3) ¡ E. (x + 3)

  10. ¡ A. 16 ¡ B. 28 ¡ C. -28 ¡ D. 60 ¡ E. -60 D9. If x = -4 is a solution to the equation x2 + 11x + K = 0, then K = ?

  11. ¡ A. 4 and 6 ¡ B. -4 and 6 ¡ C. -4 and -6 ¡ D. 2 and -12 ¡ E. -2 and 12 D10. What are the solutions to the quadratic x2 - 10x + 24 = 0?

  12. B C C B A D B D B A Answers Algebra Practice Test D

  13. ¡ A. -24 ¡ B. -10 ¡ C. -2 ¡ D. 2 ¡ E. 10 2x2y – 3xy = 2(-1)2(-2) – 3(-1)(-2) = 2(1)(-2) – 3(-1)(-2) = -4 – 6 = -10 Answer B D1. If x = -1 and y = -2, what is the value of the expression 2x2y- 3xy ?

  14. ¡ A. 6 and 8 ¡ B. -6 and -8 ¡ C. -6 and 8 ¡ D. 6 and -8 ¡ E. 3 and 16 x2 – 2x – 48 = 0 (x – 8)(x + 6) = 0 Set each factor to 0 x – 8 = 0 x = 8 x + 6 = 0 x = -6 x = { 8, -6} Factoring D2. What are the solutions to the quadratic x2 – 2x – 48 = 0?

  15. ¡ A. 6 and 8 ¡ B. -6 and -8 ¡ C. -6 and 8 ¡ D. 6 and -8 ¡ E. 3 and 16 Or you could find the answer with the quadratic formula. a = 1 b = -2 c = -48 Quadratic Formula D2. What are the solutions to the quadratic x2 – 2x – 48 = 0?

  16. ¡ A. 6 and 8 ¡ B. -6 and -8 ¡ C. -6 and 8 ¡ D. 6 and -8 ¡ E. 3 and 16 Another way to find the solution is to check each of the answers back into the original equation. This would take a long time, but remember this test is not timed. Try x = 6 Working Backwards D2. What are the solutions to the quadratic x2 - 2x - 48 = 0? (6)2 – 2(6) – 48 = 0 36 – 12 – 48 = 0 24 – 48 = 0 -24 = 0 • Thus we can eliminate answers A and D This process of elimination method is a good strategy if you get stuck. False

  17. ¡ A. 14 ¡ B. -14 ¡ C. 2 ¡ D. -2 ¡ E. 19 To prevent people from using the process of elimination discussed on the previous slide the questions are sometimes written this way. Find the solution set {-6, 8} Add the solutions -6 + 8 = 2 D3. What is the sum of the solutions to the quadratic x2 – 2x – 48 = 0?

  18. Sum of Solutions and the Quadratic Formula The formula represents the two solutions to any quadratic. If we add the two solutions we will have a general solution for the sum. Sum of solutions shortcut.

  19. ¡ A. 14 ¡ B. -14 ¡ C. 2 ¡ D. -2 ¡ E. 19 Using the general solution from the previous slide. Sum of Solutions Formula D3. What is the sum of the solutions to the quadratic x2 – 2x – 48 = 0?

  20. ¡ A. 3 ¡ B. -3 ¡ C. 11 ¡ D. -11 ¡ E. 10 First write the equation in standard form. x2 + 3x – 28 = 0 List all of the factors of 28. Since the last term (-28) is negative find the difference (subtract) in the factors. (x – 4)(x + 7) = 0 x = {-7 , 4} -7 + 4 = - 3 Factoring D4. What is the sum of the solutions of the quadratic equation x2 + 3x = 28? 27 12 3

  21. ¡ A. 3 ¡ B. -3 ¡ C. 11 ¡ D. -11 ¡ E. 10 First write the equation in standard form. x2 + 3x – 28 = 0 Using the quadratic formula. a = 1 b = 3 c = -28 Quadratic Formula D4. What is the sum of the solutions of the quadratic equation x2 + 3x = 28?

  22. ¡ A. ¡ B. ¡ C. ¡ D. ¡ E. -1 Write the equation in standard form. 2x2 – x – 15 = 0 (2x + 5)(x – 3) = 0 Factoring D5. What is the sum of the solutions of the quadratic equation 2x2 - x = 15?

  23. ¡ A. ¡ B. ¡ C. ¡ D. ¡ E. -1 First write the equation in standard form. 2x2 – x – 15 = 0 Identify a, b, and c for the quadratic formula. a = 2, b = -1, c = -15 Quadratic Formula D5. What is the sum of the solutions of the quadratic equation 2x2 – x = 15?

  24. ¡ A. ¡ B. ¡ C. ¡ D. ¡ E. -1 First write the equation in standard form. 2x2 – x – 15 = 0 Identify a, b, and c for the quadratic formula. a = 2, b = -1, c = -15 Sum of Solutions Formula D5. What is the sum of the solutions of the quadratic equation 2x2 – x = 15? ☺

  25. ¡ A. 3 ¡ B. 2 ¡ C. 5 ¡ D. 1 ¡ E. -1 First write the equation in standard form. x2 – x – 6 = 0 (x – 3)(x + 2) = 0 x = {-2, 3} -2 + 3 = 1 Factoring D6. If the equation x2 – x = 6 is solved for x, what is the sum of the solutions?

  26. ¡ A. 3 ¡ B. 2 ¡ C. 5 ¡ D. 1 ¡ E. -1 First write the equation in standard form. x2 – x – 6 = 0 Identify a, b, and c for the quadratic formula. a = 1, b = -1, c = -6 Quadratic Formula D6. If the equation x2 – x = 6 is solved for x, what is the sum of the solutions?

  27. ¡ A. 3 ¡ B. 2 ¡ C. 5 ¡ D. 1 ¡ E. -1 First write the equation in standard form. x2 – x – 6 = 0 Identify a, b, and c for the quadratic formula. a = 1, b = -1, c = -6 Sum of Solutions Formula D6. If the equation x2 – x = 6 is solved for x, what is the sum of the solutions? ☺

  28. ¡ A. -2, -3 ¡ B. 2, 3 ¡ C. 1, 6 ¡ D. -1, -6 ¡ E. -2, 3 First write the equation in standard form. x2 – 5x + 6 = 0 (x – 3)(x – 2) = 0 x ={3, 2} Factoring D7. What are the solutions to the quadratic x2 – 5x = -6?

  29. ¡ A. -2, -3 ¡ B. 2, 3 ¡ C. 1, 6 ¡ D. -1, -6 ¡ E. -2, 3 First write the equation in standard form. x2 – 5x + 6 = 0 Identify a, b, and c for the quadratic formula. a = 1, b = -5, c = 6 Quadratic Formula D7. What are the solutions to the quadratic x2 – 5x = -6?

  30. D8. For all x ≠ 2, ¡ A. (x + 5) ¡ B. (x - 2) ¡ C. (x + 2) ¡ D. (x - 3) ¡ E. (x + 3) Factor the numerator.

  31. D8. For all x ≠ 2, ¡ A. (x + 5) ¡ B. (x - 2) ¡ C. (x + 2) ¡ D. (x - 3) ¡ E. (x + 3) Another way to work this problem is to just make up a number for x. Let x = 5 Now plug x = 5 into each of the answers until you find a match.

  32. ¡ A. 16 ¡ B. 28 ¡ C. -28 ¡ D. 60 ¡ E. -60 First substitute x = -4 into the given equation. Then solve for K. x2 + 11x + K = 0 D9. If x = -4 is a solution to the equation x2 + 11x + K = 0, then K = ?

  33. ¡ A. 4 and 6 ¡ B. -4 and 6 ¡ C. -4 and -6 ¡ D. 2 and -12 ¡ E. -2 and 12 x2 - 10x + 24 = 0 (x - 4)(x - 6) = 0 x - 4 = 0 x = 4 x - 6 = 0 x = 6 x = { 4, 6} D10. What are the solutions to the quadratic x2 - 10x + 24 = 0?