Compass D

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COMPASS Practice Test D: 

COMPASS Practice Test D Quadratics This PowerPoint presentation will present 10 sample problems with answers. You can save this file to your computer and use it offline if you have PowerPoint installed on your computer.

Quadratics: 

Quadratics This slide presentation will focus on quadratics. Quadratics will always have a variable raised to the second power, like x2. Factoring is a skill that will help you find solutions to quadratic equations. 0 = x2 - 6x - 16 0 = (x - 8)(x + 2) x = {-2, 8}

Quadratic Formula: 

Quadratic Formula If you do not like to factor you can always use the quadratic formula. 0 = x2 - 6x - 16 a = 1 b = -6 c = -16

D1. If x = -1 and y = -2, what is the value of the expression 2x2y- 3xy ?: 

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

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 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}

D2. What are the solutions to the quadratic x2 - 2x - 48 = 0?: 

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 Or you could find the answer with the quadratic formula. a = 1 b = -2 c = 48

D2. What are the solutions to the quadratic x2 - 2x - 48 = 0?: 

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 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 Thus we can eliminate answers A and D This process of elimination is a good strategy if you get stuck.

D3. What is the sum of the solutions to the quadratic x2 - 2x - 48 = 0?: 

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 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

D4. What is the sum of the solutions of the quadratic equation x2 + 3x = 28?: 

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 First write the equation in standard form. x2 + 3x - 28 = 0 Using the quadratic formula. a = 1 b = 3 c = -28

D5. What is the sum of the solutions of the quadratic equation 2x2 - x = 15?: 

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 Using the quadratic formula. a = 2 b = -1 c = -15

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 D6. If the equation x2 - x = 6 is solved for x, what is the sum of the solutions? First write the equation in standard form. x2 - x - 6 = 0 Using the quadratic formula. a = 1 b = -1 c = -6

D7. What are the solutions to the quadratic x2 - 5x = -6?: 

¡ 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? First write the equation in standard form. x2 - 5x + 6 = 0 Using the quadratic formula. a = 1 b = -5 c = 6

D8. For all x ≠ 2,: 

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

D8. For all x ≠ 2,: 

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

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

D10. What are the solutions to the quadratic x2 - 10x + 24 = 0?: 

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 x2 - 10x + 24 = 0 (x - 4)(x - 6) = 0 x - 4 = 0 x = 4 x - 6 = 0 x = 6 x = { 4, 6}

The End Compass D: 

The End Compass D