1. COMPASS Practice Test D
Quadratics
This PowerPoint presentation will present 10 sample problems with answers.
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2. 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}

3. 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

4. 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.

5. D2. What are the solutions to the quadratic x2 - 2x - 48 = 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

6. 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

7. 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
Thus we can eliminate answers A and D
This process of elimination is a good strategy if you get stuck.

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

9. 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

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

11. 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
First write the equation in standard form.
x2 - x - 6 = 0
Using the quadratic formula.
a = 1 b = -1 c = -6

12. 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
¡ A. -2, -3
¡ B. 2, 3
¡ C. 1, 6
¡ D. -1, -6
¡ E. -2, 3

13. 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.

14. 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.

15. 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

16. 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

17. The End Compass D