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

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.

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

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

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

A.

B.

C.

D.

E. -1

2

1

2

1

2

11

2

11

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?

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 ≠ 2, ?2

652

x

xx

A. (x + 5)

B. (x - 2)

C. (x + 2)

D. (x - 3)

E. (x + 3)

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 = ?


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

Answers Algebra Practice Test D

1. B2. C3. C4. B5. A

6. D7. B8. D9. B10. A

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



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



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

)1(2

)48)(1(4)2()2( 2 x

2

19242

2

1962

2

142

2

142 x

2

16 8

2

142 x 6

2

12

}6,8{ x

Quadratic Formula


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 method is a good strategy if you get stuck.

(6)2 – 2(6) – 48 = 0

36 – 12 – 48 = 0

24 – 48 = 0

-24 = 0

False

Working Backwards



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

Sum of Solutions and the Quadratic Formula

a

acbbx

2

42

The formula represents the two solutions to any quadratic.

If we add the two solutions we will have a general solution for the sum.

a

acbb

a

acbb

2

4

2

4 22

a

acbbacbb

2

44 22

a

bb

2

a

b

2

2

a

b

a

bSum of solutions shortcut.



A. 14

B. -14

C. 2

D. -2

E. 19

• Using the general solution from the previous slide.

a

b)1(

)2( 2

Sum of Solutions Formula



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

Factors Diff

1 28

2 14

4 7

27

12

3

Factoring



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

)1(2

)28)(1(4)3()3( 2 x

2

11293

2

1213

2

113

42

8

2

113

x

}7,4{ x

72

14

2

113

x 3)7(4

Quadratic Formula

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

A.

B.

C.

D.

E. -1

Write the equation in standard form.

2x2 – x – 15 = 0

(2x + 5)(x – 3) = 0

2

1

2

1

2

11

2

11

Factoring

052 x52 x

2

5x

03 x3x

3,2

5x

2

53

2

5

2

6

2

1

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

A.

B.

C.

D.

E. -1


2x2 – x – 15 = 0Identify a, b, and c for the quadratic formula.

a = 2, b = -1, c = -15

)2(2

)15)(2(4)1()1( 2 x

4

12011

4

1211

4

111

2

5

4

10

4

111

x

2

1

2

53

2

1

2

1

2

11

2

113

4

12x

Quadratic Formula

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

A.

B.

C.

D.

E. -1


2x2 – x – 15 = 0Identify a, b, and c for the quadratic formula.

a = 2, b = -1, c = -15

a

bsum

)2(

)1(

2

1

2

1

2

11

2

11


2

1

☺

A. 3

B. 2

C. 5

D. 1

E. -1



x2 – x – 6 = 0

(x – 3)(x + 2) = 0

x = {-2, 3}

-2 + 3 = 1

Factoring

A. 3

B. 2

C. 5

D. 1

E. -1



x2 – x – 6 = 0Identify a, b, and c for the quadratic formula.

a = 1, b = -1, c = -6

)1(2

)6)(1(4)1()1( 2 x

2

2411

2

251

2

51

22

4

2

51

x 123

32

6

2

51

x

Quadratic Formula

A. 3

B. 2

C. 5

D. 1

E. -1



x2 – x – 6 = 0Identify a, b, and c for the quadratic formula.

a = 1, b = -1, c = -6

a

bsum


)1(

)1( 1

1

1

☺

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?


x2 – 5x + 6 = 0

(x – 3)(x – 2) = 0

x ={3, 2}

Factoring

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?


x2 – 5x + 6 = 0Identify a, b, and c for the quadratic formula.

a = 1, b = -5, c = 6

)1(2

)6)(1(4)5()5( 2 x

2

24255

2

15

2

15

32

6

2

15

x

}3,2{x2

2

4

2

15

x

Quadratic Formula

D8. For all x ≠ 2, ?2

652

x

xx

A. (x + 5)

B. (x - 2)

C. (x + 2)

D. (x - 3)

E. (x + 3)

)2(

)3)(2(

x

xx

Factor the numerator.

)3( x

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

D8. For all x ≠ 2, ?2

652

x

xx

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

235)3( xD

25

6)5(5)5( 2

23

6

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

0)4(11)4( 2 K

04416 K

028 K28K


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}

Documents

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