ESSEX COUNTY COLLEGE
DIVISION OF MATHEMATICS & PHYSICS
MATH 086
Final Exam Review
FALL 2013
Perform the indicated operation(s)
(Any fraction in your final answer must be in its simplest form)
1. Find the sum of 2395 , 4568 and 749 .
2. Find 40031 less 37685
3. 1895 × 908 =
4. Find the quotient and the remainder of 104 divided into 52509.
5. If 235,894 is divided by 79, what is 989 less than the result?
6. Find the total of 49.785 , 384 and 7.93 .
7. Find 259.857 less than 300.13
8. Find the product of 49.7 and .984
9. Divide 52.798 by 6.1 and round the quotient to the nearest hundredth.
10.
3 5 5
+ +
=
16 12 24
11.
7 5
− =
15 12
12. 3
13.
3 6 2
⋅ ⋅1 =
10 11 3
8 12
÷
=
15 25
14. 54
15. 6
2
1
1
− 39 + 5
3
6
2
2
5
÷3 =
3
9
16. −17 − ( −31) =
17. 2.25 ( −4.5)( −3)( −1) =
18. −6 − 8 ⋅ 4 ÷ ( −2 ) =
19. −6 − 8 ÷ 4 ⋅ ( −2 ) =
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20.
6
⎛ 7⎞
−5−⎜− ⎟ =
5
⎝ 2⎠
21. −
5 ⎛ 2⎞
÷⎜− ⎟ =
6 ⎝ 3⎠
Simplify
(Any fraction in your final answer must be in its simplest form)
22. 17 − ( −3) =
2
23. −4 (3 − 6) + 3( 4 − 7 ) =
2
2
24. ( −2)( −3) − ( −5)( −4 ) =
3
25. 4 − ( −4 ) − −4 − 4 =
−62 + ( −4 )
26.
=
−5
2
−51
=
3
6
7
27.
1 2
+
28. 6 3 =
5 1
−
8 4
3
5=
29.
1
5+
4
4 −1
100 − 64 =
30.
31. 4 16 − 9 4 =
⎛ 1⎞
⎝ 2⎠
2
32. ⎜ 1 ⎟ −
49
=
144
2
⎛1⎞ 4 1
33. ⎜ ⎟ + ÷ 1 =
⎝5⎠ 5 3
⎛
⎝
34. ⎜ 3 −
3⎞
9
=
⎟÷
10 ⎠
25
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Simplify the following variable expressions
(Any fraction in your final answer must be in its simplest form)
35. −3 z 4 ⋅ 4 z 3 =
36. −
9 x 27 x
÷
16 24
37.
( −2x )
38.
( −3x )
4 3
4 2
39. 9 − 2 ( −3x + 4 )
40. −8 + 3 ( −4 x + 5)
41. 7 x − 8 x 2 − 3x + 4 x 2
42. −3 ⎡⎣−2 ( x − 1) + 3 ( −4 x + 2 )⎤⎦
(
)
43. 6 x −2 x 2 + 5x − 1
44. Evaluate 4 x 2 − 2 y 3 for x = −3 and y = −2
45. Evaluate 2x − ( y − x ) for x = −3 and y = 2
2
46. Evaluate 7 x − 2 xy − 8 z for x = −2 , y =
47. Evaluate 4a ÷ b − 4c 2 for a =
1
and z = −3
4
1
2
1
, b = and c = − (Your answer must be simplified)
9
3
2
Solve the following equations
(Any fraction in your final answer must be in its simplest form)
48. x + 5 = −3
49. −10 + x = −18
50. −15 x = −75
51.
x
=2
−6
52. 6 = x − 5
53. 7 − x = 2
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54. x −
4 3
=
7 14
55. x +
3
=1
5
56.
15 20
=
12 x
57.
−9 0.6
=
x 1.8
Percent and Rate
58. Complete the following table
Fraction
Decimal
Percent
Decimal
Percent
1
5
1
1
10
59. Complete the following table
Fraction
3.3
0.875
60. Complete the following table
Fraction
Decimal
Percent
54%
3
5 %
4
61. 8% of what number is 16?
62. 105 is what percent of 70?
63. What is 75% of 24?
64. Write as a simplified unit rate: “300 miles on 15 gallons of gas”
Word Problems
65. After purchasing a new computer, John’s bank account is $8041 less $1478. How much does he now have in
his account?
66. Debbie earns $1,859 a month. Her husband earns $583 a week. How much do they earn together in one year?
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67. Cindy’s bank statement showed a balance of $375 at the beginning of the month. During the month she made
the following deposits: $194 and $259. During the same month she wrote the following checks: $59 and $91.
She also made a donation to her charity for the amount $178. Find her balance at the end of the month.
68. Find the class average on a history test if two students score 90, one student scored 85, four students scored
70, and one student scored 55.
69. A town has 7,598 habitants who pay property taxes. If the average tax paid is $593, what is the town’s
income from property taxes?
70. An organization membership list shows that 1600 members have cable TV and 1000 members don’t have
cable TV. What is the ratio of members who don’t have cable TV to the total number of members? ”
71. The ratio of men to women in a party is exactly 3:2. If there are a total of 120 people at the party,
how many of them are women?
72. A recipe for eggnog calls for 2 eggs for every 3 cups of milk. If there are 4 cups in a quart, how
many eggs will be needed to mix with 6 quarts of milk?
73. A softball player has hit 9 home runs in 32 games. At the same rate, how many home runs will the player hit
in a 160-games schedule?
74. Find the discount rate when the original price is $124.00 and the amount of the discount is $24.80.
75. Find the sale price when the original price is $76.00 and the discount rate is 41%.
76. The Powell family paid 21% of the purchase price of a $188,000 home as a down payment. What is the
amount of the down payment?
77. 70 nurses from the local hospital were diagnosed with the flu. If this was 28% of the total number of nurses,
how many nurses are there at the hospital?
78. A union contract calls for a 7.7% salary increase for all employees. Determine the new salary for a worker
who is currently making $25,130.
79. Find the simple interest on a 2-year loan of $5,000 if the annual simple interest rate is 8.4%.
80. Translate to an algebraic expression: “Five less than the product of three and a number”
81. Translate to an algebraic expression: “Seven more than the quotient of twice a number and nine”
82. Convert 17 ft. to yards.
3
lbs to ounces.
4
4
1
84. A large truck can carry 10 tons of lettuce. If the truck is
full, how many tons of lettuce is it carrying?
5
2
1
3
85. The monthly rainfall for a city was 2 inches in January, 6 inches in February, 10 inches in March and
2
4
1
7 inches in April. What was the average monthly rainfall for the four-month period?
2
83. Convert 2
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86. A car rental agency charges $12.00 a day and 15 cents a mile to rent their cars. How much would it
cost to rent a car for a week if you drove 875 miles?
87. At a convenience store, you buy two gallons of milk at $3.94 per gallon and three loaves of bread at
$2.47 per loaf. You give the clerk a 20-dollar bill. How much change will you receive?
88. Find the perimeter of the shape below in feet.
3
10 yd
4
8 ft
89. Plot the ordered pairs below.
( –1, –2 ) , (3, 0 ) , ( –2,1) , ⎛⎜
5 ⎞
,1⎟ , ( 4, –3)
⎝2 ⎠
5
y
4
3
2
1
-5
-4
-3
-2
-1
x
1
2
3
4
5
-1
-2
-3
-4
-5
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ESSEX COUNTY COLLEGE
DIVISION OF MATHEMATICS & PHYSICS
MATH 086
2013
Answer Key (Final Exam Review sheet)
1.
2.
3.
7712
2346
1,720,660
23.
24.
25.
-9
34
0
44.
45.
46.
4.
504 r 93
26.
4
47.
5.
1997
27.
6.
441.715
28.
7.
40.273
29.
8.
9.
10.
48.9048
8.66
30.
31.
32.
13
16
1
20
11.
12.
3
13.
14.
33.
1
34.
35.
1
9
21
15.
1
36.
37.
7
8
FALL
52
-31
11
68.
69.
70.
75
$4,505,614
71.
48 women
48.
1
3
x = −8
72.
16 eggs
2
9
16
35
49.
x = −8
73.
45 home runs
50.
x=5
74.
20%
2
-2
51.
52.
53.
x = −12
x = 11
x=5
75.
76.
77.
$44.84
$39,480
250 nurses
54.
78.
$27,065.01
79.
$840
56.
11
14
2
x=
5
x = 16
80.
3x − 5
1
2
− 8x12
57.
x = −27
81.
61.
200
82.
2x
+7
9
2
5 yards
3
62.
150%
83.
63.
18
84.
−7
14
15
2
2
3
16
25
1
4
2
− 12z 7
1
−
55.
−
x=
5
13
16.
14
38.
17.
-30.375
39.
9x 8
6x + 1
18.
10
40.
− 12 x + 7
64.
20 miles per gallon
85.
19.
-2
41.
65.
$6563
86.
$215.25
20.
3
10
1
1
4
42.
4x2 + 4x
42 x − 24
66.
$52,624
87.
$4.71
43.
− 12 x 3 + 30 x 2 − 6 x
67.
$500
88.
1
80 feet
2
−
21.
22.
44 ounces
2
tons of lettuce
5
3
26 inches
4
8
8
58.
Fraction
1
5
59.
Decimal
Percent
0.2
20%
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60.
Page 7
1
1
10
1.1
110%
Fraction
3
10
7
8
3
Prepared by Emmanuel ADEPO
Decimal
Percent
3.3
330%
0.875
87.5%
Fraction
27
50
23
400
Decimal
Percent
0.54
54%
3
5 %
4
0.0575
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