MONTGOMERY COLLEGE
Department of Mathematics
College Mathematics Practice Test
Review the following questions only if you have already successfully completed second year algebra or a higher
level mathematics course.
1.
( x + y) + ( x − 3y)
2
a)
b)
c)
2.
3.
=
2 x 2 + 8 xy + 10 y 2
2 x 2 + 10 y 2
2 x2 + 7 y 2
If
f ( x) =
a)
1
d)
e)
2 x2 − 8 y 2
2 x 2 − 4 xy + 10 y 2
x −5
and g ( x ) = x 2 − 2 x then g ( f ( −1) ) =
2
b)
3
c)
15
d)
9
A rectangle has a length of N − 3 and a width of 3N 2 + 4 N . What is its perimeter?
a)
b)
c)
4.
2
3N 3 − 5 N 2 − 12 N
3N 3 + 4 N 2 − 3
3N 2 + 5 N − 3
d)
e)
3N 3 − 12 N
6 N 2 + 10 N − 6
8x
x2 − 4
⋅
=
3x − 6 2 x + 4
a)
4
− ( x − 1)
3
d)
4
x
3
b)
4 x ( x − 2)
3( x + 2)
e)
x 2 + 8x − 4
5x − 2
c)
4 x 3 − 16 x
6 x 2 − 12
e)
–3
2
5.
Which of the following could be the graph of
a)
y = cos x for 0 ≤ x ≤ π ?
b)
c)
1
1
y
y
1
y
-1
1 x
2
3
d)
1 x
2
3
1 x
2
3
1 x
2
3
e)
1
y
1
y
1 x
-1
2
3
-1
4
6.
∑ n(n − 1) =
n =1
a)
b)
c)
7.
d)
e)
144
22
Which of the following equations could represent
the graph at right?
a)
b)
c)
8.
20
12
0
y = 3x 3 -18 x -12
y = x2 − 4
y = x3
y = −2 x − 4
y = − x3 + 3x 2 − 4
4
Simplify
a)
d)
e)
y
4 + 14
1
1 + 14
b)
8 − 2 14
c)
8 + 2 14
15
d)
1 − 14
− 13
e)
2 2
3
x
3
9.
Which of the following is NOT equal to zero?
a)
b)
c)
10.
14.
15.
e)
cos −1 (1)
⎛π ⎞
⎛π ⎞
cos ⎜ ⎟ − sin ⎜ ⎟
⎝4⎠
⎝4⎠
–1 only
b)
–3 only
c)
1, –3
d)
e)
cot θ − sin 2 θ
sin 2 θ
c)
5
d)
–1, 3
e)
1, 3
cos 2 θ
tan θ − sin 2 θ
secθ − sin 2 θ
d)
–18
e)
1
log x + log 20 = 2 . Then x =
a)
13.
sin −1 (π )
sin θ ( cscθ − sin θ ) =
a)
b)
c)
12.
d)
The x-value(s) of all intersection points of y = 6 − 2 x and y = x 2 + 3 is (are)
a)
11.
⎛π ⎞
cos ⎜ ⎟
⎝2⎠
tan ( 0D )
1
10
b)
80
x 2 + 1 is a factor of f ( x ) . Which of the following is TRUE?
a)
f ( −1) = 0
d)
f ( x ) has an x-intercept of 1
b)
f ( x ) has a y-intercept of -1
e)
f ( 0) = 1
c)
f ( i ) = 0 where i = −1
2−5 ⋅ 64
2
a)
512
3
=
b)
1
512
What is the least common denominator for
a)
2 ( x2 − 9)
b)
3x ( 2 x + 6 ) + 4 ( x 2 − 9 )
c)
2 ( x − 3)
c)
16
d)
3x
4
and
?
x −9
2x + 6
2
d)
2 ( x + 3) ( x − 3)
e)
(x
2
2
− 9) ( 2x + 6)
1
e)
1
2
4
16.
17.
18.
Which of the following could be the graph of y = − ( x + a ) where a > 0 ?
2
a)
b)
d)
e)
Find the equation of the line passing through ( 2, −4 ) and parallel to 3 x + 2 y = 4 .
a)
3
y = − x +1
2
b)
y=
c)
2
8
y =− x−
3
3
π
Solve
a)
π 3π
b)
2
Solve for y:
a)
20.
3
x−7
2
d)
3
y = − x −1
2
e)
y=
3
x+8
2
Solve tan 2 x = 1 where 0 ≤ x ≤ π . Then x =
a)
19.
c)
1
+
y +1
2
a
4
a
=
,
4
c)
1, –1
d)
0
e)
π
4
3
y +1
b)
2−a
a
c)
2a − 1
d)
2−a
e)
b)
−9 < x < 9
c)
x <1
d)
x>9
e)
a −3
2 x − 8 < 10
x<9
−1 < x < 9
5
Answers to College Mathematics Practice Test
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
15.
16.
17.
18.
19.
20.
e
c
e
d
d
a
a
b
d
c
a
c
c
e
a
a
d
b
b
e