COMPASS Algebra Practice Test 3 This practice test is 10 items long. Record your responses on a...

COMPASS AlgebraPractice Test 3

• 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.

1. If x = -2 and y = -3, what is the value of the expression 4x3 - 2xy ?

A. 36

B. 20

C. -20

D. -36

E. -44

2. Which of the following expressions represents the product of four more than twice x and six less than x? A. x2 – 4x – 12

B. 2(x2 – 4x – 12)

C. 8x2 – 48x

D. 2x2 +16x + 24

E. 2x2 – 16x – 24

3. A student earned scores of 85, 76, and 78 on three of four tests. What must the student score on the fourth test to have an average (arithmetic mean) of exactly 80?

A. 79

B. 80

C. 81

D. 82

E. 83

D.

E.

A.

B.

C.

4. Which of the following is an equation of the line that contains the points (2, 3) and (4 , 6)?

xy2

3 xy

3

2

xy2

3 6

3

2 xy

62

3 xy

5. For all x ±6, ?36

302

2

x

xx

A.

B.

C.

D.

E.

6

5

x

x

6

6

x

x

6

5

x

x

6

5

x

x

6

5

x

x

6. Each circle has a diameter of 6. What is the location of point B the center of the bottom circle.?

A. (6, -15)

B. (6, -18)

C. (3, -15)

D. (3, -18)

E. (1, -3)

B (3, -15)B

7. For all x, (x2 + 3x + 9)(x - 3) is

A. x3 + 3x2 - x - 3

B. x2 + 2x - 3

C. 3x - 3

D. x3 - 27

E. x3 - x2 + 3x - 3

8. If A ° B = 2A + 3B, find 4 ° 5

A. 20

B. 23

C. 17

D. 9

E. 5

9. What is the perimeter of ABC?

A. 8

B. 10

C. 14

D. 24

E. 28

B C

6

4

2

-2

-4

-5 5

C

B

A

10. What is the value of 642/3?

A. 4

B. 16

C. 21.3

D. 96

E.

3

128

Answers Algebra Practice Test 3

1. E2. B3. C4. B5. D

6. C7. D8. B9. D10.B

1. If x = -2 and y = -3, what is the value of the expression 4x3 – 2xy ?

A. 36

B. 20

C. -20

D. -36

E. -44

4x3 – 2xy

4(-2)3 – 2(-2)(-3) =

4(-8) – 2(-2)(-3) =

-32 – 2(6) =

-32 – 12 =

-32 + (-12) = -44

Answer E

2. Which of the following expressions represents the product of four more than twice x and six less than x? A. x2 – 4x – 12

B. 2(x2 – 4x – 12)

C. 8x2 – 48x

D. 2x2 +16x + 24

E. 2x2 – 16x – 24

(2x + 4)(x – 6)

2x2 – 12x + 4x – 24

2x2 – 8x – 24

Factor the common 2

2(x2 – 4x – 12)

Answer B

3. A student earned scores of 85, 76, and 78 on three of four tests. What must the student score on the fourth test to have an average (arithmetic mean) of exactly 80?

A. 79

B. 80

C. 81

D. 82

E. 83

804

787685

x

4804

7876854

x

320787685 x

320239 x239320 x 81

Answer C

D.

E.

A.

B.

C.

4. Which of the following is an equation of the line that contains the points (2, 3) and (4 , 6)?

xy2

3 xy

3

2

xy2

3 6

3

2 xy

62

3 xy

bmxy

If we can find m and b then we will be able to select the correct response.

4. Which of the following is an equation of the line that contains the points (2, 3) and (4 , 6)?

12

12

xx

yym

Find slope

24

36

m

2

3m

Now find b

bmxy

b

2

2

3)3(

b33

b0

02

3 xy

Answer B

bmxy If we can find m and b then we will be able to select the correct response.

bmxy

xy2

3

4. Which of the following is an equation of the line that contains the points (2, 3) and (4 , 6)?

A.

B.

xy2

3

xy2

3

)2(2

3)3(

Another way to work this problem is to plug the points into each equation.

Try A

3)3(

Try B)2(

2

3)3(

33 True

To be the correct equation it must also work for the other given point.

)4(2

3)6(

66 True

False

Answer B

5. For all x ±6, ?36

302

2

x

xx

A.

B.

C.

D.

E.

6

5

x

x

6

6

x

x

6

5

x

x

6

5

x

x

6

5

x

x

5. For all x ±6, ?36

302

2

x

xx

)6)(6(

)5)(6(

xx

xx

36

302

2

x

xx

)6(

)5(

x

x

Pay close attention to the signs. Every possibility is covered in the distracters.

AnswerD

Step 1. Factor

Step 2. Cancel

6. Each circle has a diameter of 6. What is the location of point B the center of the bottom circle.?

A. (6, -15)

B. (6, -18)

C. (3, -15)

D. (3, -18)

E. (1, -3)

B (3, -15)B

6

6

3

3

-15

(3, -15)

7. For all x, (x2 + 3x + 9)(x - 3) is

A. x3 + 3x2 - x - 3

B. x2 + 2x - 3

C. 3x - 3

D. x3 - 27

E. x3 - x2 + 3x - 3

(x2 + 3x + 9)(x - 3) =

x3 + 3x2 + 9x

-3x2 - 9x - 27

7. For all x, (x2 + 3x + 9)(x - 3) is

x3 - 27 Answer D

1st Distribute the x through the trinomial.

2nd Distribute the -3 through the trinomial.

8. If A ° B = 2A + 3B, find 4 ° 5

A. 20

B. 23

C. 17

D. 9

E. 5

Substitute

2A + 3B =

2(4) + 3(5) =

8 + 15 = 23

Answer B

9. What is the perimeter of ABC?

A. 8

B. 10

C. 14

D. 24

E. 28

B C

6

4

2

-2

-4

-5 5

C

B

A

9. What is the perimeter of ABC?

B C

6

4

2

-2

-4

-5 5

C

B

ANow use the PythagoreanTheorem to find the length of the hypotenuse.

Count the blocks tofind the lengths of the legs.AC = 8 AB = 6

222 cba 222 68 c23664 c

2100 cc10

Add the three sidesto find the perimeter.

8 + 6 + 10 = 24

8

610

Answer D

9. What is the perimeter of ABC?

• Another way to find the

distance from B to C is to

use the distance formula.

• First identify the coordinates.

C (-4, 4) and B (4, -2)

B C

6

4

2

-2

-4

-5 5

C

B

A

212

212 )()( yyxxD

22 ))4()2(())4(4( D

22 )6()8( D 3664 100 10

10

8

6

10. What is the value of 642/3?

A. 4

B. 16

C. 21.3

D. 96

E.

3

128

233

2

6464

Note that the denominatorbecomes the index of the radical

232

3 44464

164 2