Math 093
Practice Final #4
1
3 x 9  x
1.) Solve for x:
2.) Multiply and simplify:
2
(a) 3 x  7 
(b) (2a 2 b) 3  (3a12b 4 )
3.) Of the four lines below, which two are perpendicular to each other? (explain why!)
(1)
3x  6
3x  2 y  6
(2)
3 x  2 y  12
(3)
2 x  3 y  18
(4)
4.) Solve the inequality:
5.) Graph the inequality:
(2 x  1)( x  3) ≤ 2( x 2  6)
 x  2y < 4
4 x
x 2  16

2 x  12 x 2  10 x  24
6.) Simplify:
7.) Perform the indicated operation and simplify, if possible.
3( 8  2 )
(a)
(b) (2 3  2)( 4 3  5)
8.) Perform the indicated operation and simplify, if possible.
Be sure to rationalize the denominator if necessary.
Assume all variables are positive.
(a)
25 x 3
(b)
2
9.) Subtract and simplify:
3x
2x
 2
x  3 x  10 x  x  6
2
12 x 15 y 6
x 11 y 4
Math 093
Practice Final #4
10.) Solve for x by completing the square:
2
2 x 2  24 x  8
11.) If f ( x)  x 3  2 x 2  4 x  1 , find f (2) .
12.) Factor completely:
(a) 3 x 3  18 x  3 x 2
(b) 12 x 2  11xy  2 y 2
x
4
 2
x4
x4
13.) Solve for x:
14.) A formula for converting the temperature in degrees Celsius (C) to degrees
Fahrenheit (F) is
9
F  C  32 .
5
What is the temperature in degrees Celsius if it is 5° Fahrenheit?
15.) A straight line passes through the points (4, -3) and (-2, 3).
(a) Find the slope of the line.
(b) Find the equation of the line in slope-intercept form.
16.) Simplify. Write your answers without negative exponents.
Assume all variables are positive.
(a)
x 
17.) Solve for x:
3 2
x
8
2( x  3) 2  2  38
(b)
 3 x 12 y 7
 5  2
 x y



2
Math 093
Practice Final #4
18.) Convert each of the following:
(a) 2 × 10 3 to decimal notation
3
(b) 3,800,000 to scientific notation
19.) Simplify: (7 x 3  x 2  5)  (12 x 2  10  15x 3 )
20.) Divide:
20 x 8  12 x 3  4 x 2  6 x
4x 2
21.) Graph the parabola: y   x 2  2 x  8 .
Clearly state the y-intercept, any x-intercept(s), and the vertex.
22.) Consider the equation of the line 5 x  10 y  20 :
(a) Find the slope.
(b) Find the y-intercept. Write your answer as an ordered pair.
(c) Graph the line. Label two points.
23.) Ken invests a total of $18,000 in two different stocks.
After one year, Stock A earns 10% interest while Stock B earns 8% interest.
How much did he invest in each if his total interest was $1580?
24.) For the rational expression:
2( x 2  1)
x 2  5x  4
(a) Find the values of x for which the expression is undefined.
(b) Simplify completely.
25.) Solve the system. If there is no solution or an infinite number of solutions, state this.
 3 y  x  3

 3x  9 y  9
Math 093
Practice Final #4
4
ANSWERS
1.)
x=7
2a.)
2b.)
9 x 2  42 x  49
24a 18b 7
3.)
4.)
x ≥ -3
5.)
x-int (-4,0)
6.)
1
2
9.)
x2  x
( x  5)( x  2)( x  3)
11.)
9
14.)
-15 degrees Celsius
17.)
x = 3 2 5
-8x3 – 13x2 – 15
20.)
5x6 + 3x – 1 +
1
2
23.)
$7000 in Stock A
lines 2 and 4
(slopes are neg. reciprocals)
y-int (0,2)
dotted line
shade below
7a.)
6
7b.)
14  2 3
10.)
x = 6  2 10
8a.)
5x 2 x
2
8b.)
2x 2 y 3
12a.) 3x(x-3)(x+2) 13.)
12b.) (4x-y)(3x-2y)
15a.) m = -1
16a.)
15b.) y = -1x + 1
16b.)
18a.) .002
19.)
no solution
1
x 14
y 10
9x 34
3
2x
18b.) 3.8 × 106
21.)
y-int (0,8)
22a.) m = 
Vertex (1,9) 22b.) (0,2)
x-int (4,0) (-2,0)
opens downward
24a.) x = 4 and 1
2( x  1)
24b.)
x4
25.)
infinite solutions
$11000 in Stock B