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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