Download 6311 FINAL REVIEW ESSENTIALS OF MATH 1

MATH 099
FINAL EXAM REVIEW
ELEMENTARY ALGEBRA I
1. Add:  4  7  (10)
2. Subtract:  16  (25)  4
3. Multiply: (2)(3)( 4)
4. Divide: (60)  (12)
7 11  1 
     (Express answer in lowest terms)
12 16  3 
5. Subtract:
6. Divide:
5 3

12 2
 9  8  3 
7. Multiply:       (Express answer in lowest terms)
 16  27  2 
3
 2
8. Simplify:  3    (Express answer in lowest terms)
 3
2
9. Simplify: (25 )  (3  5)2  (3)
10. Simplify:  2 4
11. Simplify  2 
4
12. Evaluate: a  3b 2 when a  4 and b  2
13. Evaluate: b 2  (a  b) 2 when a  4 and b  1
14. Simplify: 8a  12b  9a
15. Simplify:
1
(9 a )
3
 5
16. Simplify:   (32b)
 8
17. Simplify: (4)(2 y 2  5 y  8)
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Final Exam Review
18. Simplify:  4 x  3(2 x  5)
19. Simplify: 3(4 x  1)  7( x  2)
20. Simplify: 3x  2[ x  4(2  x)]
21. Simplify: 3[4 x  2( x  4 y )]  5 y
22. Is 2 a solution of the following equation? 4  2 x  x 2  2  4 x
23. Solve: 9  x  12
24. Solve: 8  5x  7
25. Solve: 6  2x  6  2x
26. Solve:  6 x  4(3  2 x)  4 x  8
27. Solve:
2 3 1
  x
3 4 2
28. Solve: 2.4x  3.7  1.1
29. Solve the following inequality and graph the solution set: 5x  3  2x  3
30. Solve the following inequality and graph the solution set: 5x  6  8x  3
31. 40% of what number is 18?
32. Translate: “the difference between six and the product of a number and twelve” into a
variable expression.
33. Translate and simplify: “the total of five and the difference between a number and seven.”
34. Translate “the sum of eight times a number and twelve is equal to the product of four and the
number” into an equation and solve to determine “the number”.
35. The manager of a department store buys a chain necklace for a cost of $8 and sells it for $14.
Determine the markup rate as a percentage.
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Final Exam Review
36. The regular price for a carpet sweeper is $126. What is the sale price if there is a 22%
discount on the sweeper.
37. Find three consecutive integers whose sum is 75.
38. Find three consecutive even integers such that three times the second is 14 more than the sum
of the first and third integers.
39. A piggy bank contains 100 coins, consisting of just dimes and quarters. If the total value of
the coins is $18.55, how many coins are dimes and how many are quarters?
40. The perimeter of a rectangle is 42 inches. The length is three more than the width. Find the
length and width of the rectangle.
41. The perimeter of a triangle is 38 inches. The length of the first side is 14. The length of the
second side is twice the length of the third side. Find the lengths of the second and third
sides.
42. Graph and label the ordered pairs A(-3,2), B(5,-4), C(3,-1), D(0,7) and E(6,0).
MATH 099 (Spring 2010)
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Final Exam Review
43. Find the coordinates of each point. H( ,
), I(
,
), J(
, ), K(
, )
H
J
I
K
44. Graph the equation y  2 x  3 by first establishing a table of (x,y) ordered pairs
x
y
MATH 099 (Spring 2010)
(x,y)
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Final Exam Review
45. Graph the equation 3 x  2 y  12 by first determining the x-intercept and y-intercept.
Write intercepts as ordered pairs
x-intercept:
_________
y-intercept:
_________
46. Graph the equation y 
2
x  5 by using the slope and y-intercept.
3
Slope (m):
_________
y-intercept (b):
_________
47. Is (2,-3) a solution of y  x  5 ?
48. Write the equation 5 x  2 y  8 in the form y  mx  b .
49. Determine the slope of the line containing the points (2,5) and (-3,8)
50. Determine the slope of the line containing the points (3,8) and (-7,8)
MATH 099 (Spring 2010)
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Final Exam Review
51. Determine the equation of the line which has a slope of 5 and a y-intercept of -3
52. Determine the equation of the line which has a slope of -2 that contains the point (2,-3).
53. Determine the equation of the line which passes through the points (10,5) and (5,8).
54. In right triangle ABC side a = 12 and side b = 8, find side c.
55. In right triangle ABC side c = 10 and side a = 6, find side b.
56. Find angle A if sin A = .6691
57. Find angle B if tan B = .4877
58. Given right triangle ABC in the figure, find sin B, cos B, and tan B
59. In right triangle ABC side a = 8 and angle B = 35º, set up the
equation that could be used to find side c.
60. In right triangle ABC side b = 5 and side a = 8, set up the equation
that could be used to find angle A.
Figure for
Problem #58
only
61. A 16 foot ladder leans against a wall. The ladder makes an angle of 65 degrees with the
ground. How far up the side of the wall does the ladder reach?
For 62-69 arrange answers in descending power order starting with the highest power of x
62. Add (5x3  4 x 2  7)  (3x 2  8x  3)
63. Subtract (5x 2  2 x  1)  (3x 2  5x  8)
64. Add (8x 2  8x  3)  (5x 2  3x  9)


65 Multiply 5x 2 y 3x 3 y 2 z

66. Multiply 2 x( x 2  2 x  4)
67. Multiply (3x  5)( 2 x  3)
68. Multiply (3x  4)(5x 2  2 x  3)
69. Multiply (2 x  y )( 2 x  y )
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Final Exam Review
70 Simplify into an expression which does not have negative exponents
71. Simplify
x 2 y 3
x 3 y  2
 12a 3b 2
3ab
15 y 2  12 y
 3y
72. Divide
73. Simplify
27 x 6 y 3
3x 4 y 3
74 Simplify
36 x 5 y 5
24 x 7 y 2
75. Simplify (2 x 2 y 4 )3 (3xy3 )2

76 Simplify 3x 2 y
 2 xy
0
2
77. Simplify (3a 2b)(2ab3 )  (ab2 )(4a 2b2 )
78. Divide
12b 2  36b5  3b 4
(Provide answer in descending power order)
3b 2
79. Simplify (2a12b3 )(9b2c6 )(3ac)
80. Perform the following Long Division Problem. Express your remainder as a fraction:
3x 2  2 x  1
x2
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Final Exam Review
MATH099 Review Answer Key
1.
2.
3.
4.
-7
5
24
5
5.
11
48
6.
7.
8.
9.
10.
11.
12.
13.
14.
15.
16.
17.
18.
19.
20.
21.
22.
23.
24.
25.
26.
27.
28.
29.
30.
5
18
1
4
8
3
-5
-16
16
-8
-24
(#29)
(#30)
31.
32.
45
6 - 12x
33.
5  n  7  n  2
34.
35.
36.
37.
38.
39.
40.
41.
42.
8x + 12 = 4x, x = -3
75%
$98.28
24, 25, 26
12, 14, 16
43 dimes, 57 quarters
9 inches by 12 inches
8, 16
Graph and label the ordered pairs A(-3,2), B(5,-4),
C(3,-1), D(0,7) and E(6,0).
 a  12b
3a
20b
-8y2 + 20y + 32
D
 10x  15
5x  17
13x - 16
6x + 29y
No
-3
-3
3
-10
1
6
2
E
A
C
B
43. H( -7 , 5 ), I( -3 , -3 ), J( 6 , 3 ), K( 5 , -6 )
x  2 (see graph)
x  3 (see graph)
MATH 099 (Spring 2010)
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Final Exam Review
MATH099 Review Answer Key
44.
Graph y  2 x  3 using ordered pairs
x
0
1
2
y
-3
-1
1
See Graph on the right
(x,y)
(0,3)
(1,-1)
(2,1)
45.
x-intercept: (-4,0); y-intercept (0,-6)
See Graph on the right
46.
Slope =
47.
yes
48.
5
y   x4
2
49.
Slope = m=
50.
51.
y  5x  3
2
, y-intercept = 5.
3
See Graph on the right
3
5
Slope = m= 0
52.
y  2 x  1
53.
y
54.
c  208  14.42
55.
56.
57.
b=8
A = 42º
B = 26º
58.
59.
60.
61.
3
x  11
5
3
4
3
sin B = , cos B = , tan B =
4
5
5
8
cos 35º =
c
8
tan A =
5
14.5 feet
MATH 099 (Spring 2010)
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Final Exam Review
MATH099 Review Answer Key
62.
5x 3  x 2  8x  4
63.
2x 2  7x  9
64.
3 x 2  11x  12
65.
15x 5 y 3 z
66.
2 x 3  4 x 2  8x
67.
6 x 2  x  15
68.
15 x 3  26 x 2  17 x  12
69.
4x 2  y 2
70.
x5
y
71.
 4 a 2b
72.
 5y  4
73.
9x 2
74
3y3
2x 2
75.
72 x8 y18
76.
4x 2 y 2
77.
10a 3b 4
78.
4  12b 3  b 2  12b 3  b 2  4
79.
 54a13b5c 7
80.
3x  4 
9
x2
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Final Exam Review
MATH 099 FORMULA SHEET
EQUATIONS OF LINES:
ORDER OF OPERATIONS: PEMDAS
Slope given two points:
y  y1
m 2
x 2  x1
Slope – Intercept form:
y  mx  b
Point – Slope form:
y  y1  mx  x1 
m
EXPONENT RULES:
x x  x
m
n
 x
xm

 
 y
ym
m n
xm
 x m n
n
x
x0  1
x 
x m 
m n
 x mn
1
xm
 xy m  x m y m
TRIGONOMETRY RATIOS:
sin A 
opp a

hyp c
a
A  sin 1  
c
cos A 
adj b

hyp c
b
A  cos 1  
c
tan A 
opp a

adj b
a
A  tan 1  
b
PYTHAGOREAN THEOREM: Given right triangle ABC with right angle at C: a 2  b 2  c 2
PERIMETER:
The perimeter, P, of a rectangle is P = 2W + 2L
The perimeter P, of a triangle is P = a + b + c
The perimeter P, of a square is P = 4s
MARKUP AND DISCOUNT:
S = C + rC
S=Selling Price, C = Cost, r = Markup rate
S = R – rR
S = Sale Price, R = Regular Price, r = Discount rate