Sample Questions for College Level Mathematics
1.
Simplify the exponential expression. Write your answer using only positive exponents:
1
 3ab 2 
 1 2  =
 9a b c 
2.
Factor each polynomial completely:
x 4  13x 2  36 =
a)
3 x 5  48 x =
b)
x6 1 =
c)
3.
Given
a)
b)
c)
d)
4.
f ( x)   x 4  3x  2 , find:
f(2)=
f(-x)=
f( a 2 )=
Is f(x) even, odd or neither?
Solve each of the following equations for exact values:
a)
2x  1  3
b)
c)
d)
e)
11  x  1  x
2x
4
 6  0
x3 x
2  3 x 1  18
log 2 ( x  1)  3
5.
Simplify and write as a single logarithm:
2 log 2 x  log 2 y + 3 log 2 z =
6.
Evaluate:
log b (log b b b ) =
7.
Solve each of the inequalities:
 x 2  3x  2  0
a)
x 2  3x  22  0
b)
c)
2x  1  3
8.
Write equation of the line that is parallel to the line 2y + 3x = 6 and passes through point A (0, 7).
9.
Write the equation of the line pictured below:
Revised November 13, 2006
10.
Given f ( x)  x 2  1 and g ( x)  3 x  1 , find f ( g ( x)) =
11.
Evaluate:
7!
=
5!
12.
Given the graph of y = f(x) below, sketch the graph of y = f (x) :
13.
Perform the operations on the given complex numbers. Write your results in standard form:
i  (2  i ) =
a)
1  3i
=
2i
b)
14.
Shade the region { ( x, y) x  0 and y  x }:
Error!
15.
Solve system of equations:
3x 2  2 y 2  5
x  y  2
1
16.
Given f ( x)  3 x  2 , find f
17.
If
18.
What is the period and amplitude of f(x) = 3sin(2x)
19.
Simplify:

2
 x   and sin(x) = ½, find cos(x) =
cot( x) 
20.
( x) =
sin( x)
1  cos( x)
Find all solutions of sin( x)  tan( x)  sin( x) on the interval 0,2  .
2
Answers:
3b 4 c
1.
a2
2. a) ( x  3)( x  3)( x  2)( x  2)
b) 3x( x  2)( x  2)( x 2  4)
c) ( x  1)( x  1)( x 2  x  1)( x 2  x  1)
3. a) -12 b) f ( x)   x 4  3x  2 c) f (a 2 )  a 8  3a 2  2 d) neither even nor odd
4. a) {-1, 2} b) 2 c)
5. log 2
11  73
4
d) 1 e) 7
x2  z3
y
6. 1
7. a) (,1)  (2, )
8. y  
9. y 
b) No solution (empty set)
c) (,1)  (2, )
3
x7
2
1
x 1
2
10. y  9 x 2  6 x  2
11. 42
12.
13. a) 1+ 2i
1
5
b)  
7
i
5
14.
3
 3 7 
 5 5 

15.   ,  ,  1,1 
16. f
17.
1
( x) 

x2
3
 3
2
18. Period is  ; amplitude is 3
19. csc(x)
5 
 
, , 
4 
 4
20 . 0,
4