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COMPASS Practice D - PowerPoint PPT Presentation

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.

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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.

• 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?

D8. For all x equation ≠ 2,

¡ A. (x + 5)

¡ B. (x - 2)

¡ C. (x + 2)

¡ D. (x - 3)

¡ E. (x + 3)

¡ 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?

B equation

C

C

B

A

D

B

D

B

A

¡ 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

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

a = 1 b = -2 c = -48

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?

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

a = 1 b = 3 c = -28

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

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

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

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?