Download mth:140 practice final examination

MTH:140 PRACTICE FINAL EXAMINATION
(Revised Nov. 2010)
1.
Factor completely: 24x2 + 8x +4
2.
Factor completely: 25x2 + 10x +1
3.
Factor completely: 16x2 – 16y2
4.
Factor completely: 6x2 – x – 2
5.
Factor completely: x3 + 8
6.
Factor completely: x  2 x  3 x  6
7.
Simplify:
8.
2 x
Simplify:
9.
Solve for x and write your answer in interval notation:
10.
Rationalize the denominator and simplify:
11.
Solve: (x – 1) 2 = 9
12.
The formula C 
13.
How many ml. of distilled water must be added to 60 ml. of 70% alcohol solution to obtain a 60% solution?
14.
If f ( x)  2 x 2
3
Then
2
3 8  32
y 1 / 3
b0 x 2 y
2/5

5
x2  4
2x2  4x

x  3x  2
x 1
15.
Simplify:
16.
Divide 3x  x  3 by
2
2
1
3 2
5
( F  32) relates Fahrenheit and Centigrade Temperature measures. Solve for F.
9
f ( x  b) 
3
 9  5  2x  6
x2
17.
Simplify:
18.
Simplify:
4
4


x2 x2
x2  4x  3
x 1
19.
Simplify:
1 1

x y
x 1  y 1
20.
Solve for x:
3x  1  3x  4
21.
Perform the indicated operation:
22.
Solve for x:
2x  a  3a
23.
Solve for x:
2x  3
7
x 1
24.
Solve for x:
2x2  x  3  0
25.
Solve for x:
4 x  x2
26.
Find the domain for the following function: g ( x ) 
27.
Solve for x and write your answer in interval notation: 2 x  7  1
28.
Solve the system
29.
Write the equation of the line that passes through the points (1, 2) and (0, 5).
30.
The length of a rectangle is 2 more than 3 times its width. If the perimeter is 120 cm, what is the width of the rectangle?
31.
Draw the graph of y = 2 – x2
32.
Write the equation of the line that passes through the point (1, 2) with slope 3. Write your answer in Standard Form.
33.
Solve the following system: 3x  y  7
34.
Simplify:
35.
Simplify:
2
2


x2 x2
x  y  1

x  y  1

2x  3y  7
25
x2
x2  9
1
2

3 12  2 27
36.
Solve for x:
37.
Simplify:
2x  3  5
x
1
1
x

1
3
6x

 2
x2 x2 x 4
38.
Solve:
39.
Factor completely: 4 x 4  16 x 2
40.
Rationalize the denominator and simplify:
41.
Solve for x: 2x  (5x + 7) < (4  2x)
42.
Solve for x:
43.
A person can drive from town A to town B in 6 hours. If she increases her speed by 20 mph she can make the trip in 4 hours.
5 x ,x>0
32 x
x2 + 5 = 0
How far is town A from town B?
4 9 
44.
Simplify:
45.
If f(x) = x3 , then f (x + h) =
46.
Solve for x: x4  1 = 0
47.
Given i is the imaginary unit, multiply and write in the form of
48.
Solve for x:
49.
Divide and simplify:
50.
Two planes leave St. Louis at the same time and fly in opposite directions. If one flies at 840 kmph and the other at 510 kmph,
a  bi : (2  3i )( 4  5i)
x2 + x + 1 = 0
x2  4
x 2  4x  4

x2  x  6
x3
how long will it take them to be 3500 km. apart?
51.
The speed of Lazy River’s current is 5 mph. If the boat travels 20 miles downstream in the same time that it takes to travel 10
miles upstream, find the speed of the boat in still water.
52.
Solve for x:
x x2  2
53.
Solve for x:
54.
Solve for x:
5x 2  14 x
6x
2


x 2  7 x  12 x  4 3  x
2 x  1  10  0
Answer Key
1. 4  6 x 2  2 x  1
5x  15x 1
16  x  y  x  y 
3x  2 2x 1
 x  2  x2  2x  4
6.  x  2   x 2  3
2.
3.
4.
5.
7. 2 2
32
8. 8 3
y
1
9.   , 7 
 2
22. 2a
23. 2
3
24.  ,  1
2

25.
26.
27.
28.
29.
30.
31.
3
32.
33.
34.
35.
36.
3 x  y  1
x | All Reals, x  3
(3, 4)
(1, 0)
y  3x  5
14.5
3 2
7
11. 4,  2
9
12. F  C  32
5
10.
13. 10 ml.
14. 2 x 2  4 xb  2b 2
1
15.
2x
16. 3x 2  7 x  14 
17.
18.
19.
20.
8x
2
x 4
x3
yx
yx
5

6
8
21. 2
x 4
31
x2
(2 , -1)
5
0
x  4 or x  1
x2
x 1
38. 2 , extraneous
39. 4x2  x  2 x  2
37.
10 x  15 x
9  4x
41. x  11
42. i 5, i 5
40.
43. 240 miles
44. 6
45. x3  3x 2 h  3xh 2  h3
46. 1,  i
47. 23  2i
1
2
3
i
2
x2
49.
 x  2  x  2 
70
hours
50.
27
48.  
51.
52.
53.
54.
15 mph
2, 3
2
no solution