COMPASS Practice Test D

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COMPASSPractice Test D

• Quadratics
• This PowerPoint presentation will present 10
  sample problems with answers.
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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

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QuadraticFormula

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

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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.
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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

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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

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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.
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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

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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

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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

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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
• Using the quadratic formula.
• a 1 b -1 c -6

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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

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

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

• x2 - 10x 24 0
• (x - 4)(x - 6) 0
• x - 4 0
• x 4
• x - 6 0
• x 6
• x 4, 6

• A. 4 and 6
• B. -4 and 6
• C. -4 and -6
• D. 2 and -12
• E. -2 and 12

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The End Compass D