MATH 45

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```					          MATH 45, Elementary Algebra                       12)   Given that a = 2, b = 3, and c = 1, evaluate
Review Problems for Comprehensive                           b 2  4ac .
Final Exam
{Scientific Calculators allowed, No Graphing
Calculators}                           13)   Given that x = 2, y = 1, evaluate
xy  y 2  x 2 .
3 5 3
1)               
7 14 4
14)   Given that x = 1, y = 1, evaluate 3x  2y.

2)        (13  4) + (7 + 2) =
15)   Write an algebraic expression to represent
2                                     "11 more than one half of a number k."
10  5(2)  2
3)                              
52
16)   Translate the following into an algebraic
78   78                                               expression: "The quotient of a number x
4)                                                               divided by 5 is decreased by 15."
5
17)   Name the property illustrated by the
8  4(2)  2 2                                          statement: 3 (5 + 9) = (5 + 9) 3
5)                              
4  22
18)   Name the property illustrated by the
statement: (x + y) + 4 = x + (y + 4)
5 1 2
6)                                                       19)   Name the property illustrated by the
6 3 5                                                   statement: 7 (a − w) = 7a − 7w

5                                                                           5            2
7)        3     6                                                                   a3   6a9 
8                                             20)   Simplify:                    
          

8)        You have 60 ounces of dough to make
21)   Simplify:           5y 6  2y 3
      
5                                          
4
ounces of dough, how many breadsticks can
you make?
22)   Simplify:           xz   2y 2 z 




4   2
9)        2     6 
5   3
23)   Simplify:          5y  3  y
10)       In the following figure, what is the total area
in square feet?
3 ft                     24)   Solve for the variable h in the expression:
1
A  bh
6 ft                       2
3 ft

9 ft                    25)   Solve for the variable x in the expression:
ax + by = c

11)       In the expression 25y, what is the
coefficient?                                      26)   Write the number 1,637,000,000 in scientific
notation.
2
27)   Solve for x in the equation:
5x  10 = 4x  10
39)       Greg has three times as many pencils as he
has erasers and five fewer rulers than
28)   Solve for x in the equation:                               pencils. He has 30 items in all. How many
1          2      3         1                     rulers does he have?
x               x   
4          3      4         3
40)       William has 20 coins. All are nickels and
29)   Solve for x in the equation:
dimes. The combined value is \$1.60. How
6(2  3x) =  5(2x  8)                            many nickels does he have?

30)   Solve for x in the equation:
5x  3 = 13                              41)       Find h.

31)   Solve for x in the inequality, then graph the
solution.
7  3x  22
h

32)   Solve for z in the inequality, then graph the
solution.                                                                               6 ft
 2 (z  1)  3 (z  1)
|             100 ft                |   8 ft   |

33)   Solve for x in the equation:
10  x       x4
                             42)       Graph the equation y =  2
2           5
43)       Graph the equation y = 6

34)   What is the area of a circle that has a          44)       Graph the equation x = 3
diameter of 18 feet? (round to nearest tenth)
45)       Graph the equation y  5x = 1

35)   Eight is subtracted from five times a number.
46)       Graph.    x  y  2
The result is two more than six times the
number. What is the number?                      47)       Graph. 2x  y  6

48)       Determine the slope and y-intercept of the
line 3x + 4y + 12 = 0.
36)   The width of a swimming pool is four feet
less than its length. The perimeter of the       49)       Given 2x + y = 5, determine the slope and y-
pool is 112 feet. What is the width of the                 intercept.
pool?
50)       Find the equation (in slope-intercept form) of
the line that passes through the points (2, 3)
37)   Two cars start at the same point and travel in
(4, 6).
opposite directions at average speeds of 40
and 55 miles per hour. How much time must
51)       Write an equation of the line perpendicular to
elapse before the two cars are 170 miles
the line y = 6x 1 which has y-intercept 8.
apart?
52)       Find the equation (in slope-intercept form) of
38)   The price of a pair of ski boots is \$98. What              the line that passes through the point (5, 1)
will be the sale price of the boots during a               and has slope 2.
60% off sale?
3
53)   Determine whether the lines given by the          68)   Simplify and write with no negative
equations y = 1/3x  1 and y = 3x + 7 are                                   xy 2
parallel, perpendicular or neither.                     exponents.
y 3 x 3
54)   Find the sum of 7x 2  3x  10 and
69)   Simplify and write with no negative
 9x 2  4x  6.                                                                                2
exponents.          4z 6  5z3 
            
            
55)   Subtract and simplify.
 5x 2  4x  3    x 2  3x  5 
                                      70)   Simplify and write with no negative
                                
1
exponents.           2s1t 2 
            
56)   Multiply and simplify.        (6  2x) (4x + 3)                                        

71)   Simplify and write with no negative
57)   Expand and simplify.          5  x 2                                                   3
 x 3 y 4 
exponents.                   
58)   Multiply and simplify.                                                      5 
          

.      3x 2 y 6xy  4xy 5  7z 
                                        72)   Simplify and write with no negative
                  
2x 3
exponents.
59)   Simplify.
4x 2 y 3                                                5x 1
 6 xy 9
73)   Factor completely, if possible.             7f 2  7f
60)   Divide and simplify.
74)   Factor completely, if possible.             4x 3  36x
4a  9b
2       2

12ab                                            75)   Factor completely, if possible.             100  49x 2

61)   Divide and simplify.                              76)   Factor completely, if possible.             x 2  25

 30a 2 b 2  15a 2 b  10ab 2                    77)   A binomial factor of both
 10ab                                      x2  x  6   and      x 2  x  12 is

62)   Divide and simplify.                              78)   Factor completely, if possible.
x 3  x 2  2x
6x  11x  2
2

3x  1                                         79)   Factor completely, if possible.
c 2  6c  10
63)   Divide and simplify.
80)   Factor completely, if possible.
2x  7 x  4x  3
3       2
6y 2  5 y  6
2x  3
81)   Factor completely, if possible.
64)   Write in Scientific Notation. .000000302                        3z 2  8z  5

65)   Evaluate.           50                           82)   Factor completely, if possible.
4z 2  12z  40
4
66)   Evaluate.          1
83)   Factor completely, if possible.
0 1
67)   Evaluate.          7 6                                          x 2  5x  x  5
4
84)   Factor completely, if possible.                  98)    Solve for x and y. 2x  5y = 1

xy + 3y + 2x + 6                                                        x+ y= 3

85)   Factor completely, if possible.
game for \$1. The admission for non-
students is \$2. If 350 tickets are sold and the
x3  8                                         total receipts are \$450, how many student
tickets are sold?
86)   Factor completely, if possible.
100)   Simplify and reduce to lowest terms (if
125a 3  27                                    possible):
9  3t
t 3
87)   Factor completely, if possible.
101)   Simplify and reduce to lowest terms (if
2t  128t
5         2                                                   x4
possible):
x
88)   Solve for x.      x (x  3) (x + 25) = 0
102)   Simplify and reduce to lowest terms (if
89)   Solve for x.         2
3x  x                                                        x2  9
possible):
x 2  4x  3
90)   Solve for x.      x 2  x  20
103)   Simplify and reduce to lowest terms (if
91)   Solve for x.      4x 2  1  0                                                 x 2  7x
possible):
x 2  8x  7
92)   Solve for x.      3x 2  8x  5  0
25 x 2       8xy 2
104)   Multiply and simplify:                  
93)   Find two consecutive positive odd integers
8xy 10         5x
whose product is 323.

94)   The length of a rectangle is 1 centimeter                                             x x  7 x 1
105)   Multiply and simplify:              
more than 3 times its width. If its area is 52                                        7   x    x 7
square centimeters, find the dimensions of
the rectangle.                                   106)   Multiply and simplify:
y 2  8y  7       y 2  3y  10
95)   Solve.            x  2y = 1                                          
y 2  3y  4       y 2  9y  14
6x + 4y = 3
x2  x  2
107)   Divide and simplify:                      (2  x )
x2
96)   Solve for y.      xy=6
x 2  y 2 x  y 2
108)   Divide and simplify:                   
x+y=2                                                                  xy        xy

2y 2    6y
109)   Divide and simplify:               
97)   Solve for x.       x  y = 6                                                         y3 y  2  3y

x + y = 2                                     3y  2 2 y  5
y3    y3

7 x  7 2x  7
111)   Subtract:                   
5y     5y
5

3y    x   yx
    
x 5 x 5 x 5
113)   Find the length of x of the triangle shown.

3 in                              5 in

x

114)   What is the slope of the line shown?

10
8

6
4

2

-10 -8    -6 -4   -2             2   4   6   8   10
-2

-4

-6
-8

-10

```
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