COMPASS Algebra Practice 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.

D1. If x = -1 and y = -2, what is the value of the expression 2x2y- 3xy ? ¡ B. -10 ¡ C. -2 ¡ D. 2 ¡ E. 10 We start this practice with a substitution problem, not a quadratic. COMPASS often starts with a substitution problem.

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

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

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

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

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

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

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

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

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

Answers Algebra Practice Test D

D1. If x = -1 and y = -2, what is the value of the expression 2x2y- 3xy ? ¡ B. -10 ¡ C. -2 ¡ D. 2 ¡ E. 10 2x2 y – 3xy = 2(-1)2 (-2) – 3(-1)(-2) = 2(1) (-2) – 3(-1)(-2) = -4 – 6 = -10 Answer B We start this practice with a substitution problem, not a quadratic. COMPASS often starts with a substitution problem.

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

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

D2. What are the solutions to the quadratic x2 - 2x - 48 = 0? Working Backwards D2. What are the solutions to the quadratic x2 - 2x - 48 = 0? 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 ¡ A. 6 and 8 ¡ B. -6 and -8 ¡ C. -6 and 8 ¡ D. 6 and -8 ¡ E. 3 and 16 Process of Elimination/working backwards from the distractors. (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

D3. What is the sum of the solutions to the quadratic x2 – 2x – 48 = 0? 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 ¡ A. 14 ¡ B. -14 ¡ C. 2 ¡ D. -2 ¡ E. 19 Same quadratic that was used in D2 but asked in a different style.

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 formula Sum of solutions shortcut.

Sum of Solutions Formula 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 Using the general solution from the previous slide. Using the sum of solutions formula.

First write the equation in standard form. Factoring D4. What is the sum of the solutions of the quadratic equation x2 + 3x = 28? 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 ¡ A. 3 ¡ B. -3 ¡ C. 11 ¡ D. -11 ¡ E. 10 Factoring. Factors Diff 1 28 2 14 4 7 27 12 3

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

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

Quadratic Formula D5. What is the sum of the solutions of the quadratic equation 2x2 – x = 15? ¡ 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 to find the solutions and then addition to find the sum of solutions.

Sum of Solutions Formula D5. What is the sum of the solutions of the quadratic equation 2x2 – x = 15? ¡ 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. ☺

First write the equation in standard form. Factoring D6. If the equation x2 – x = 6 is solved for x, what is the sum of the solutions? ¡ 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 to find the solutions and then addition to find the sum.

Quadratic Formula D6. If the equation x2 – x = 6 is solved for x, what is the sum of the solutions? ¡ 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 to find the solutions and then addition to find the sum of solutions.

Sum of Solutions Formula D6. If the equation x2 – x = 6 is solved for x, what is the sum of the solutions? ¡ 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. ☺

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

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

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

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 Substitution and the process of elimination. Now plug x = 5 into each of the answers until you find a match.

First substitute x = -4 into the given equation. Then solve for K. D9. If x = -4 is a solution to the equation x2 + 11x + K = 0, then K = ? ¡ 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 Substitution.

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