Math 093
Practice Final #3
1.) Solve for x by using the quadratic formula:
2.) Simplify:
______________
2x 2  2x  5
(3x 2  2 x  4)  (5x  2  8x 2 )
y2  2y  3 y2  6y  9
 2
2 y 2  50
y  2 y  15
3.) Simplify:
4.) Answer TRUE or FALSE for each (explain your answer!):
(a) The line x = 5 has slope 5.
(b) 0.0000054  5.4  10 6
5.) Graph the inequality:
x  x  10  2
6.) Solve for x:
7.) Subtract and simplify:
8.)
 2 x  5 y < 10
y
8y
 2
y  4 y  16
(a) If f ( x)  2 x 3  x 2  4 x , find f (1) .
(b) Is the following a function?:
{ (-3, 1) , (-2, 1) , (0, 3), (1, 9) }
If so, state the domain and the range.
9.) Factor completely:
(a) 6 x 2  3  7 x
(b) 3 x 3  6 x 2  24 x
10.) A rectangle has a perimeter of 64 inches.
Find the dimensions of the rectangle if the length is 8 inches more than the width.
11.) Simplify. Write your answers without negative exponents.
Assume all variables are positive.
 3y 2
(a)  5
 x
12.) Solve for x:



2
(b)
( x  1) 2  8  1
13.) Multiply and simplify:
(a) (4a  5b)(3a  2b)
14.) Divide:
2 x 2 y  3
4 x 7 y 14
18 x 4  15 x 3  3x 2  9 x
3x 2
(b) (2 x 3 y)(7 x 2 y 4 )
1
Math 093
Practice Final #3
______________
2
15.) Consider the equation of the line 2x – 4y – 8 = 0:
(a) Find the slope.
(b) Find the y-intercept. Write your answer as an ordered pair.
(c) Graph the line. Label two points.
16.) Perform the indicated operation and simplify, if possible.
(a) ( 3  2 6 )( 3  4 6 )
(b) 7 3  4 2  5 12
17.) Solve the inequality:
1
8 x  23 ≥ 5 x  1
6
2 3
18.) For the rational expression:
7x
x  4 x  21
2
(a) Find the values of x for which the expression is undefined.
(b) Simplify completely.
19.) A straight line passes through the points (-4, -1) and (-3, 7).
(a) Find the slope of the line.
(b) Find the equation of the line in slope-intercept form.
20.) Solve for x:
2x
4x
3
x 1
x 1
21.) Perform the indicated operation and simplify, if possible.
Be sure to rationalize the denominator if necessary.
Assume all variables are positive.
(a)
2
6 2
(b)
27 x 4 y 9
x11 y 3
22.) Solve the system. If there is no solution or an infinite number of solutions, state this.
3 y  x  6

3x  18  9 y  0
23.) Solve the system. If there is no solution or an infinite number of solutions, state this.
2 x  y  4

2 y  3 x  7
Math 093
Practice Final #3
______________
3
24.) Graph the parabola: y   x 2  2 x  3 .
Clearly state the y-intercept, any x-intercept(s), and the vertex.
25.) Arthur goes to the bank to deposit some cash.
He has 35 bills in all, some of which are $10-bills and some of which are $20-bills.
How many of each does he have if the total deposit amounts to $420?
________________________________________________________________________
ANSWERS
1  11
y 1
 5x 2  7 x  6
1.)
2.)
3.)
2
2( y  5)
y
y4
4.)
both FALSE
6.)
x = -1
7.)
8a.)
8b.)
3
YES
D: -3,-2,0,1
R: 1, 3, 9
9a.)
9b.)
(3x – 1)(2x + 3)
3x(x – 4)(x + 2)
10.)
12 in by 20 in
12.)
x = 4 or -2
13a.)
12a 2  7 ab  10b 2
13b.)
 14 x 5 y 5
16a.)
 45  6 2
11a.)
x10
9y4
11b.)
x5
2 y 17
14.)
6 x 2  5x  1 
17.)
20.)
x ≤ -3
x=3
3
x
1
2
15b.) (0,-2)
15a.)
18a.) x = 7 or -3
1
18b.)
x3
21a.)
21b.)
23.)
(-1,-2)
m
24.)
6 2
2
3
3 y 3x
x4
16b.) 17 3  4 2
19a.)
m8
19b.) y = 8x + 31
22.)
y-int (0,3)
25.)
x-int (3,0) and (-1,0)
vertex (1,4)
opens downward
infinite solutions
28 tens, 7 twenties