1.P
Let f  x   4 x / 2 . Find f 1 .
Soln:
1.1
1.2
x  y  2z  4

Find the ordered triple that satisfies the system  x  y  2 z  0 .
x  y
0

Expand
Soln: 1,1,1
2x  5
into partial fractions.
x  5x  6
2
Soln:
1.3
1
2
1
1

x2 x3
Let f  x   5  3x2 and g  x   3x  1 . Find  f g  x  .
Soln: 27 x 2  18 x  2
1.4
For the sets A  1,3,5,6,8 , B  2,3,6,7 , and C  6,8,9 , find  B  C   A .
Soln:
1.5
6
If the point  1, 2  is on the graph of f  x   ax 2  4 , find a.
Soln: -2
1.6
Simplify
sec x
.
csc x
Soln: tan x
1.7
Determine the domain of the function f  x  
1
1
1


.
x x 1 x  2
Soln:
1.8
 , 2   2, 1   1,0   0,  
Find the length of x.
25
x
30
Soln: 12.5 or
1.9
25
2
Find the area of the parallelogram in the plane with vertices A 1,0 , B  0,1 , C  1,0 , and D  0, 1 .
Soln: 2
1.10
Solve for y: log5 y  log5  y  4  1 .
Soln: 5
1.11
Find the arc length corresponding to a central angle of
3
on a circle with radius 7 cm.
14
3
cm.
2
Soln:
1.12
Calculate sin 30 cos 60  sin 60 cos 30 .
Soln: 1
2.P
Simplify log 2 16  log 2 4  log 2
1
.
32
Soln: 11
2.1
Simplify e3ln 2 x1 .
Soln:
 2 x  1
3
OR 8 x3  12 x 2  6 x  1
ln e m  2 m  24
Simplify
.
m 2  36
2
2.2
Soln:
2.3
Let g  x   2 x  3 . Find
m4
m6
g a  b  g a
.
b
Soln: 2
2.4
Find the exact value of log 3 9 .
Soln: 4
2.5
What are the next two terms in the sequence A, c, E, g, …
Soln: I, k
(Case matters)
2.6
Find the center of the ellipse 4 x 2  y 2  16 x  6 y  21  0
Soln:
2.7
Find the roots of x3  4 x 2  9 x  36  0 .
2.8
If log a 4  .6021 , log a 7  .8451 , and log a 9  .9542 , find log a
 2,3
Soln: 4, 3 OR 4,3, 3
63
.
4
Soln: 1.1972
2.9
Find the next term of the sequence 20, 17, 13, 8, …
Soln: 2
2.10
According to the rational root theorem, what are the possible rational roots of x 6  4 x5  3x 4  x 2  4 x  3  0 ?
Soln: 3, 1
2.11
If z  4  3i , find z .
Soln: 5
2.12
For what intervals of x does
x2 y 2

 1 produce real y values?
16 9
Soln:
3.1
 , 4  4, 
The area of an equilateral triangle varies directly with the square of the length of a side. Find the constant of
proportionality.
Soln:
3.2
3
4
  
Solve tan 2 x  tan x  2  0 in the interval   ,  .
 2 2
 

 

Soln:   , tan 1 2  OR   , arctan 2 
 4

 4

1
1
OR tan  1 , tan  2  OR arctan  1 ,arctan 2
3.3
Calculate  2  3i  6  2i  .
Soln: 18  14i
3.4
Find the length of CD in terms of x.
C
30
D
x
45
45
A
B
Soln:
3
x OR
2
3x
2
100
3.5
Evaluate
6.
1
Soln: 600
3.6
 1 1 
Find the inverse of 
.
 1 0
 0 1
Soln: 

1 1
3.7
Find the polar equation for the Cartesian equation x 2  y 2  7 .
Soln: r  7
3.8
  
Evaluate tan 1  3 on the interval   ,  .
 2 2


Soln: 
3.9

3
 1 2
5 1
Let A  
and B  

 . Find det  BA .
 1 1 
3 0 
Soln: 9
3.10
Find the coefficient of x3 y 4 in the expansion of  x  y  .
7
Soln: 35
3.11
How many times can the face 5 be expected to occur in a sequence of 2016 throws of a fair die?
Soln: 336
3.12
If u  3, 2 and v  1, 3 , find u v .
Soln: -9
4.1
x2
.
x 2 x 2  4
Find lim
Soln: 
4.2
4.3
Several logs are stored in a pile with 20 logs on the bottom layer, 19 on the second layer, 18 on the third, and so
on. If the top layer has one log, how many logs are in the pile?
Soln: 210
Let r   
12


4

3

1
4
. Find r '   .
Soln: 
4.4
1
4
12

2

12

4

4
5
Find the sum of the first five multiples of 4.
Soln: 60
4.5
4.6
A couple is planning their wedding. They can select from 2 different chapels, 4 soloists, 3 organists, and 2
ministers. How many different wedding arrangements are possible?
Soln: 48
Find the distance between the points P  2, 4,3 and Q  4,7, 3 .
Soln:
4.7
161
If P  A  .3 and P  B A   .6 , find P  A  B  .
Soln: .18
4.8
Find lim 1  cos   csc x  .
x 
6
Soln:
2
4.9
1 
Find c in the interval  , 2 
2 
1
f  2  f  
 2  if f x  x  1 .
such that f '  c  
 
1
x
2
2
Soln: 1
4.10
Evaluate
  2 x  5 dx .
0
2
Soln: 6
4.11
Find the slope of the tangent line to the graph of f  x   x2  2 at the point  1,3 .
Soln: -2
4.12
A gum manufacturer randomly puts a coupon in 1 of every 5 packages. What is the probability of getting at
least one coupon if 4 packages are purchased?
Soln:
369
625