Math 093
Practice Final #2
1.) Multiply and simplify:
(a) (2 x  3 y ) 2
1
(b) ( x  3)( x 2  4 x  2)
2.) Consider the equation of the line 4x – 3y = 12:
(a) Find the x-intercept. Write your answer as an ordered pair.
(b) Find the y-intercept. Write your answer as an ordered pair.
(c) Find the slope
(d) Graph the line. Label two points.
(8x 3  32 x 2  x  11)  ( x 3  12 x 2  11  7 x)
5
3 1
 
4.) Solve for x:
2x x 6
5  x 1  x
5.) Solve for x:
3.) Simplify:
6.) Solve for x by completing the square:
x 2  10 x  1  0
( x  2) 2  4  14
2
8
(1  x)  x 
8.) Solve the inequality:
3
3
8 6
5 4
2 2
10 x y  x y  5 x y  15 xy
9.) Divide:
5x 2 y 2
7.) Solve for x:
10.) Simplify:
y2  5y
y 2  y  30

y 2  6 y  16 y 2  8 y  12
11.) Perform the indicated operation and simplify, if possible.
Assume all variables are positive.
(a) 5 12  6 8  2 27
12.) For the rational expression:
(b)
28a15b12
3 x
x  2 x  15
2
(a) Find the values of x for which the expression is undefined.
(b) Simplify completely.
13.) Factor completely:
(a) 2 x 2 y  18 y
(b) 6 x 2  14 x  12
14.) A right triangle has hypotenuse
find the missing side.
15.) Graph the inequality:
29 inches. If one of the other sides is 3 inches,
y > -3x + 1.
Math 093
Practice Final #2
2
16.) A straight line passes through the points (2, -1) and (-1, -7).
(a) Find the slope of the line.
(b) Find the equation of the line in slope-intercept form.
17.) Simplify. Write your answers without negative exponents.
Assume all variables are positive.
5 x 2 y 4
(a) (2 x 4 ) 3  (5 x 2 )
(b)
15 x 4 y 7
18.) Perform the indicated operation and simplify, if possible.
Be sure to rationalize the denominator if necessary.
Assume all variables are positive.
(a)
6
(b)
5 3
2x5 y 8
5x 3 y 9
19.) A formula in physics which relates kinetic energy E (in Joules),
mass m (in kilograms), and velocity v (in meters per second) is
1
E  v2m .
2
Find the mass of an object with a kinetic energy of 40 Joules if it is traveling at a
velocity of 4 meters per second.
20.) Solve the system. If there is no solution or an infinite number of solutions, state this.
x+1–y=0
10x + 4y = -24
21.) Solve the system. If there is no solution or an infinite number of solutions, state this.
2y – x = 5
2x – 4y = 5
22.) Ken invests a total of $30,000 in two different stocks.
One year later, Stock A pays 12% interest while Stock B pays 10% interest.
How much did Ken invest in each if his total interest for the year was $3320?
23.) Graph the parabola: y  2 x 2  4 x  6 .
Clearly state the y-intercept, any x-intercept(s), and the vertex.
24.) If f ( x)  x 3  3x 2  7 x  4 , find f (2) .
25.) Add and simplify:
x
1
 2
x  10 x  16 x  x  2
2
Math 093
Practice Final #2
3
ANSWERS
1a.)
b.)
4x2 – 12xy + 9y2
x3 + x2 – 14x + 6
2a.)
b.)
c.)
(3,0)
(0,-4)
m = 4/3
3.)
7x3 + 44x2 + 6x
4.)
x=3
5.)
x=8
6.)
x = 2 6 5
7.)
x = 3 2 2
8.)
x≥2
10.)
y
y 8
11a.)
16 3  12 2
9.)
2x 6 y 4 
x3 y 2
3
1
5
xy
b.)
13a.) 2y(x – 3)(x + 3)
12a.) x = -5, 3
1
b.)
x5
15.) y-int (0,1)
b.)
slope = -3
16a.) m = 2
b.)
y = 2x – 5
14.)
2a 7 b 6 7a
x= 2 5
2(3x + 2)(x – 3)
dotted line
shade above the line
17a.)
40
x 10
18a.)
b.)
1y 3
3x 6
b.)
30  3 2
2
x 10 y
5y
19.)
m = 5 kg
20.)
(-2,-1)
21.)
no solution
22.)
$16,000 @ 12%
$14,000 @ 10%
23.)
y-int (0,-6)
x-int (3,0) (-1,0)
Vertex (1,-8)
Opens upward
24.)
22
25.)
x4
( x  8)( x  1)