Intermediate Algebra – Final Exam Review
1.
Solve the following equation: x  4  9
2.
Find the domain and range of
3.
Suppose your yearly pay is $6000.00 plus 4% of your sales, how much do you need to
sell in one year to earn $42,000.00?
y  x2  4
4.
Find the slope of the line passing through points 3,  1 and  1, 0.
5.
Give an equation of the line passing through the point  5,  12 with slope m 
6.
Let
7.
Solve the system of equations
3 x  2 y  6 and y  2 x  3
8.
Solve the system
How many gallons of 30% solution and 50% solution must be mixed together
to create 15 gallons of 40% solution?
9.
Find the x and y intercepts for 5x – 10y = 30
10.
Solve by graphing: x + y < 4 and 3x + y  9
11.
Expand: (8  i ) 2
12.
Solve 5 y  3  4  6 y  1  5 y
13.
Re-write in terms of i:
14.
Multiply and simplify: 3 5( 5  4 5)
f x  7 x  1 and g x   1  6 x 2 .
Evaluate f 2  g  2
9  169
3
Rev. Fall 2007
1
7
.
2
15.
Solve by substitution: (t  5) 2  4(t  5)  13  0
16.
Solve: 5x  3  4  20
17.
Solve: 3x  3  4  8
18.
Solve by completing the square: x 2  6 x  3  0
19.
The current of a river is 5 miles per hour. A boat travels between two points on
5
the river. If it takes 2 hours to travel in one direction and
hours to travel in the
2
other direction, what is the speed of the boat in still water?
20.
Simplify, assuming that all variables represent non-negative integers.
27a b
64a b 
6
3
21.
1
3
2
2 3
Simplify, assuming all variables represent non-negative real numbers.
24a 8 b 4  16ab 2
4ab 
2
Rev. Fall 2007
2
22.
Rationalize the denominator, assuming the variables represent positive numbers.
44 x 4 y
16 z 3
23.
Simplify, assuming all variables represent non-negative numbers.

24.
w2

2
Rationalize the denominator.
x 5
x 5
25. Solve for the variable.
w  4  7w  2
26.
1
For the following question: Suppose f x   2 and g  x    
 3
Evaluate g  2 and f  1
x
Rev fall 2007
3
x
27.
 x 
Expand: log 2  
 yz 
28.
Write as one log: logb x  3logb x  4logb x
29.
Solve for x
log 3 x  3
30.
Solve for x
log 2 x  log 2 4 = 1
31.
The annual rate of depreciation, r, on a car that is purchased for P dollars and is worth
W dollars t years later can be found from:
1
W
log 1  r   log
t
P
Find the annual rate of depreciation on a car that is purchased for $14,650
and sold 3 years later for $9,500.
Enter your answer to 3 decimal places.
32.
The population of a city can be estimated by the equation:
P  108,000e 0.05t
Where t is the number of years from the present time,
how many years will it take the population to reach 324,000?
Enter your answer to the 1st decimal place.
Rev. Fall 2007
4
Answers – Final Exam Review
1.
2.
13, -5
D: (-, )
R: [-4, )
3.
$900,000.00
4.
1

4
5.
6.
y
7
11
x
2
2
x  3 or x  5
18.
x  3  2 3
19.
45 miles per hour
20.
3
16b
21.
6a 6 b 2 
 10
7.
12, 21
8.
x  7.5, y  7.5
9.
x-int: (6,0)
y-int: (0,-3)
10.
17.
22.
First: Dashed, shaded below
Second: Solid, shaded below
Final answer is the overlapping
region
4
a
x 2 11yz
2z 2
23.
4 w4 w
24.
x  25  10 x
x  25
25.
w  14
26.
9 and
27.
log 2 x  log 2 y  log 2 z
1
2
11.
63 – 16i
12.
y  5
13i
3
3
28.
log b ( x 2 )
29.
x  3 3 
14.
45
30.
x=8
15.
t  7  3i
19
13
x
or x 
5
5
31.
0.134 or 13.4%
32.
22.0 years
13.
16.
rev. Fall 2007
5
1
27