Download E. Trow MATH A FINAL FORM S96B

REVIEW for FINAL
Elementary Algebra
Math 070
FORM SP09
Work these problems on separate
paper. NOTE: Show the equation you
used to solve each word problem.
1.
2.
3.
4.
Use substitution or
addition/subtraction to solve the
system:
x + y = 5
3x + 2y = 8
Use the quadratic formula to
solve:
x2 + 5x – 3 = 0
Multiply:
5y  15

9.
Divide:
10.
Simplify:
11.
Find the slope of the line
through (2, –4) and (6, 7)
12. Factor:
7wn 4
3 80  4 5
x2 – 17x + 30
13. Solve for y:
14. Factor:
7x + 2y = 11
25x2 – 49y2
15. Ann can swim 20 laps in 8 min.
How long will it take to swim 9
laps?
Show your equation(s).
Graph: 2x – 5y = 10
(use an x|y chart)
3 y  21
28 w 5 n7  35 wn 5
y2  y  6
y
2
5.
When v = 5 and m = –4,
evaluate: 4v2 – m2
6.
Solve:
7.
Solve by factoring:
y2 = 4y + 12
 49
7(x – 2) = 4x + 1
16. Subtract:
4a  7
a1

3a  10
a 1
17A. Simplify: (5w5y3)4
17B. Graph on a number line:
x < -1
18. Solve:
9x + 7 < 5x + 27
19. Multiply: (4x – 7)(5x + 2)
8.
Solve for c in the right
triangle:
c
10
24
20. Factor:
21.
8b2 – 24b
Find an equation for the line
with slope –4 and y-intercept 5
22. Subtract:
(3y2 – 6y – 7) – (8y2 – 6y + 1)
23. Translate into algebraic notation:
ten less than twice x
x  5 2 x 2  19 x  22
24. Divide:
25. Simplify without negative
exponents:
x 2 y 6
5
x y
26.
4
Almonds worth $8.75 per pound
are mixed with peanuts worth
$4.75 per pound. The mixture is
worth $6.50 per pound. How
many pounds of almonds and
how many pounds of peanuts
must be mixed to make an 80
pound mixture?
Show your equation(s).
27. Solve:
5x – 12 = 3x
28. Translate into algebraic
notation: three divided by
the sum of seven and an
unknown number
29.
Multiply and simplify:
4x5(3x – 11)
30. Suppose you get on a steamboat
at noon in New Orleans and
steam up the Mississippi River
towards St. Louis at 20 mph.
Two hours later your friend gets
in a motor boat in New Orleans
and heads up the river at 30 mph.
At what time does your friend
catch up with you? Show your
equation(s).
31. Solve:
32.
8
x
3
 10
Find an equation for a line
with slope 3 and passing
through (2, 1)
33. Translate into algebraic notation:
7 of an unknown number, less 5
8
34. After receiving a 20% raise, you
now earn $26.40 an hour. What
was your hourly wage before the
raise?
Show your equation(s).
35.
The sum of two numbers is
71. The larger is 6 more than
4 times the smaller. Find the
numbers.
Show your equation(s).
36. Find the slope and y-intercept of:
y = 3x – 11
37. Graph:
y = x2 – 3x
38. Graph:
y = -x2 + 2x
46. Find x.
17
39. The length of one leg of a right
triangle is 4 in. more than the
other. If the length of the
hypotenuse is 8 in., what are the
lengths of the two legs?
40. How long must a guy wire be to
run from the top of a 16-ft pole to
a point on the ground 6 ft from
the base of the pole?
41. The base of a 15-ft ladder is 5 ft
away from a wall. How far above
the floor is the top of the ladder?
42. Solve for x:
3(x – 5)2 = 7
x
8
47. Solve for x:
2x  3 + 1 = 3
48. Solve for z:
2 3z  2 - 1 = 5
49. Simplify:
3 12 - 48
50. Find:
3
43. Solve for x:
2(x – 5)2 = 3
51.
8
9 =
(a) 3
44. Simplify:
8 + 2 27 - 75
(b) -3
(c) 0
(d) not real
52. Graph:
x y < 3
x  2y < 6
45. Find x.
x
5
12
53. Graph:
4 y  3x  12
x 1
54. Solve:
9x  y  9
x  3 y  14
55. The sum of two numbers is 100.
The second is 3 times the first.
Find the two numbers.
56. Solve the system by graphing.
x  3 y  12
2x  3 y  6
1
y x
2
Write the equation of the line passing
through each of the following points
with the indicated slope. Give your
results in slope-intercept form, where
possible.
 0, 5 , m 
58.
 2,3 , m  3
59.
 0, 3 , m  0
71. True or False
x = 4 is vertical.
73. Multiply:
 x  2 y  2 x  3 y 
74. Factor:
 4,3 , m  undefined
61. If
70. True or False
x = 4 is horizontal.
72. True or False
y = -3 is horizontal.
2
3
57.
60.
69. Graph:
3m2 n  6mn2  9mn
f ( x)  2 x 3  x 2  3 x  2
find
62. Solve:
3x + 4 < 5
63. Solve:
-5x + 1

f ( o) .
1
a
1
3
a
3
2
76. Perform the following operations
and simplify.
64. Graph on a number line.
x > -5
65. Find the equation of the line with
slope 2 and y-intercept -4.
3
66. Find the slope of y =
75. Simplify:
5
x7.
3
67. Find the y-intercept of y =
5
x7.
3
68. Find the slope of the line through
the points (-2, 3) and (1, -6).
2w2  11w  21
 (4w  6)
w2  49
77. Multiply and simplify:
6 x 10

5 18 x 2
78. Subtract and simplify:
x2
16

x4 x4
79. Solve:
17
10
2 
x4
x2
What values for x, if any, must be
excluded in each of the following
algebraic fractions?
80.
4
x3
81.
x 1
x 5
82.
5x
( x  3)( x  7)
83.
x3
(3x  1)( x  2)
84. Solve:
x
15
2x

 2
x  4 x  3 x  7 x  12
85. Add:
2
3
 3
2
3x y 4 x
86. Find the LCD of:
5
2
and
x
x 1
90. Simplify:
25 x 2 y 2
5 x 1 y 3
Write the answer without
negative exponents.
91. Factor completely:
5x2 y  15xy  10 xy 2
92. Solve for x:
4( x  7)  ( x  5)
93. Solve:
5( x  2)  5
94. Find the GCF of
15x 2 yz 3 and 25x3 z 4 w
95. Find the x-coordinate of the
vertex of:
y  5x 2  3x  8
96. Write using positive exponents:
x 3
y3
87. Multiply and simplify:
97. Simplify:
88. Multiply and simplify:
98. Multiply:
2 x  6 3x

x2  2x 3  x
3x  15 4 x

x 2  3x 5  x
21x5  28 x 4  14 x3
7x
9a 2 (4a3  7a)
99. Simplify:
89. Simplify:
5(2 x 2 y)0
 2xy 
2 3
100. Graph:
2( x  7)  5x 12