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COMPASS Algebra Practice Test DPowerPoint Presentation

COMPASS Algebra Practice Test D

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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.

¡ 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 ?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?

¡ A. 14

¡ B. -14

¡ C. 2

¡ D. -2

¡ E. 19

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

¡ equation A.

¡ B.

¡ C.

¡ D.

¡ E. -1

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

¡ equation 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?Sum of Solutions and the Quadratic Formula equation

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.

¡ equation 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?¡ equation 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

¡ equation 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?¡ equation 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?¡ equation 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?¡ equation 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?☺

¡ equation 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?¡ equation 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?¡ equation 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?☺

¡ equation 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?¡ equation 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?D8. For all x equation ≠ 2,

¡ A. (x + 5)

¡ B. (x - 2)

¡ C. (x + 2)

¡ D. (x - 3)

¡ E. (x + 3)

Factor the numerator.

D8. For all x equation ≠ 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.

¡ equation 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 = ?¡ equation 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?
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