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COMPASS
Practice Test A
Algebra Test
A1. If x = -1 and y = 3, what is the
value of the expression 3x3 - 2xy ?
A.
B.
C.
D.
E.
-9
-3
3
9
21
3(-1)3 - 2(-1)(3) =
3(-1) - 2(-1)(3) =
-3 - (-6) =
-3 + 6 =
3
Answer C
A2. Which of the following expressions
represents the product of three less than
x and five more than twice x ?
A.
B.
C.
D.
E.
2x2
+ 11x + 15
2x2 - 11x + 15
2x2 + x - 15
2x2 - x - 15
2x2 + 22x + 15
• This question asks you to
multiply the binomials
• “3 less than x” (x - 3)
• “five more than twice x”
(2x + 5).
(x - 3)(2x + 5)
= 2x2 + 5x - 6x - 15
= 2x2 - x – 15
Answer D
A3. A student earned scores of 83, 78, and
77 on three of four tests. What must the
student score on the fourth test to have an
average (arithmetic mean) of exactly 80?
A. 80
83  78  77  x
 80
B. 82
4
C. 84
238  x
 80
D. 85
4
E. 86
 238  x 
4
  80  4
 4 
x  82
238  x  320
x  320  238
A4. What is the equation of the line that
contains the points (2, 3) and (14 , - 6)?
A.
B.
C.
3
y
x5
4
3
9
y
x
4
2
3
y  x5
4
D.
E.
4
17
y
x
3
3
1
5
y
x
2
2
A4. What is the equation of the line that
contains the points (2, 3) and (14 , - 6)?
y 2 - y1
3 - (-6)
9
3
m =
=
=
=2 - 14
-12
4
x 2 - x1
3
m 
4
Click one
3
y
xb
4
With this information we
can finish the problem with
3
either the slope intercept or y  y 

x  x1 
1
the point slope.
4
A4. What is the equation of the line that
contains the points (2, 3) and (14 , - 6)?
3
3
y
xb
(3)   b
4
2
Click here to
see different
3
6 3
(3) 
(2) method.
b


b
4
2
Click here 2
3
(3) 
b
2
finish the
problem.
9
b
2
3
m
4
9
b
2
3
9
y
x
4
2
A4. What is the equation of the line that
contains the points (2, 3) and (14 , - 6)?
3
x  x1 
y  y1 
4
33
  xx22 4
4yy33
44
4 y  12  3x  6
4 y  3x  18
4
3
18
y  x
4
4
4
3
9
y  x
4
2
A4. What is the equation of the line that
contains the points (2, 3) and (14 , - 6)?
A.
B.
C.
3
y
x5
4
3
9
y
x
4
2
3
y  x5
4
D.
E.
4
17
y
x
3
3
1
5
y
x
2
2
3
9
y
x
4
2
x  x  20
A5. For all x  ±4,

?
2
x  16
2
A.
B.
C.
x5
x4
x4
x4
x5
x4
D.
E.
x5
x4
x5
x4
x  x  20
A5. For all x  ±4,

?
2
x  16
2
( x  5)
x  x  20 ( x  4)( x  5)


2
( x  4)( x  4)
( x  4)
x  16
2
Pay close attention to the
signs. Every possibility
is covered in the
distracters.
Answer
e
A6. A rope 36 feet long is cut into three pieces, the
second piece is four feet longer than the first, the
last peace is three times as long as the second. If x
represents the length of the first peace, then which
equation determines the length of the first peace?
A.
B.
C.
D.
E.
36 = 5x + 8
36 = x + (x + 4) + (3x)
36 = 3x + 12
36 = x + (x + 4) + 3(x + 4)
36 = 3x + 16
• Let x represent the first length.
• Then (x + 4) represents the
second.
• The third length is 3 times the
second (not three times the
first) 3(x + 4).
• Therefore the equation is D
x + (x + 4 ) + 3(x + 4) = 36
A7. The product
A. x3 + 3x2 - x - 3
B. x2 + 2x - 3
C. 3x - 3
D. x3 - 3
E. x3 - x2 + 3x - 3
2
(x
+ 3)(x - 1) is
• This is just a
binomial times a
binomial, FOIL
problem.
(x2 + 3)(x - 1)
= x3 - x2 + 3x - 3
A8. In n is an integer which
expression must be an even integer?
A.
B.
C.
D.
E.
2n + 1 •
2n - 1
n+1 •
2n2
n2
•
Most people will do a problem like this
by process of elimination.
If you plug any number into A or B you
always get an odd number so we can
eliminate them as possible answers.
If you plug 3 into C you get an even
number, but if you plug 4 into C you get
an odd number, so eliminate it.
A8. In n is an integer which
expression must be an even integer?
A.
B.
C.
D.
E.
2n + 1 •
2n - 1
n+1 •
2n2 •
n2
If you plug any odd number into E you
get an odd number.
Therefore the only answer possible is D.
Some people will think about the
definition of even (any integer divisible
by 2) and see that since 2n2 is a product
of some number (n2) and 2 that it will
always be even.
A9. If x = -3, what is the value of
2x2 + 3x - 5 ?
A. -22
B. -6
C. -5
D.
4
E. 22
2(-3)2 + 3(-3) - 5 =
2(9) + 3(-3) - 5 =
18 - 9 - 5 =
4
Answer D
A10.Which of the following is the
complete factorization of 2x2 - 13x - 24 ?
A. (2x - 6)(x + 4)
B. (x - 6)(2x + 4)
C. (2x - 3)(x - 8)
D. (2x + 3)(x - 8)
E. 2(x + 3)(x - 4)
Answer D
If you cannot factor just
multiply out each of
the distracters.
End COMPASS
Practice Test A
Algebra Test