PROBLEM SETS # 2

1. At the beginning of Claudia Schaffer’s exercise program, she rides 15 minutes on

the Lifecycle. Each week, she increases her riding time by 5 minutes. Find her
riding time after 7 weeks.
2. Find the ninth term of the arithmetic progression whose first three terms are
3,9,and 15.
3. The second term of a geometric progression is 8 and the sixth term is 128. Find
the 11th term.
4. (ECE Board) Determine the sum of the infinite series : S = 1/3 , 1/9 , 1/27 …
5. Find the sum of the multiples of 3 between 28 and 112. Ans. 1974
6. Find the explicit equation of the terms 0.9,0.09,0.009, etc…
7. Find the sum of the positive terms of the arithmetic sequence 85, 78, 71, … 1
8. Determine the number of terms of the series 5,8,11… of which the sum is 1025.
9. Find the first three terms of the geometric progression whose first term is 3 and a
common ratio of 3.
10. (CE Board) The geometric mean of two numbers is 8 while the arithmetic mean is
4 , the cube of harmonic mean is ____.
11. (CE Board) The geometric mean and the arithmetic mean of the two numbers are
8 and 17, respectively. Find the bigger number.
12. Find the three terms of the geometric progression between 18 and 2/9.
13. Given the numbers 4 and 8. Find the harmonic mean. Ans. 16/3
14. Find the tenth term of the harmonic progression 1/3 , 1/7 , 1/11 …
15. Insert three arithmetic means between 44 and 92.
16. Insert harmonic means between 3 and 7.
17. The first and second terms of a harmonic progression are ‘a” and “b” ,
respectively. What is the third term?
18. What is the geometric mean of 1,3,9,27,and 81 ?
19. Find the twelfth term of the Fibonacci Sequence.
20.Write the following into scientific notation 0.00000032
21. At their closest points, Mars and Earth are approximately 75,000,000 kilometers
apart . Express the distance in meters.
22. According to state census information, the population of LaVergne, Tennessee in
2012 was 3.3777 * 104. The population of Murfreesboro, Tennessee in 2012 was
1.14038 * 105. What was the combined population of both cities?
23. Simplify: (3.4 x 10^6) ÷ (2 x 10^-10 )
24. At that time, the U.S. population was approximately 312,000,000 (312 million),
or 3.12 * 10^8 If the national debt was evenly divided among every individual in
the United States, how much would each citizen have to pay?
25. 5 megavolts to volts .
26. The Memphis Grizzlies play in the FedEx Forum. The FedEx Forum can hold
approximately x 1.5 × 10^4 people. If the Grizzlies play 41 games in the FedEx
Forum and all of the seats were full for all of the games, how many people were
there total?
27. Simplify: (7.245 x 10^9) ÷ (2.1× 10^-3)
28.A computer was used to draw a rectangle with an area of 0.000007 square meter.
Find the area in square centimeters.
29. Toni is 28 years older than Mary. In 6 years, Toni will be three times as old as
Mary. How old is Tony now?
30.Ben is 4 years younger than Harold. Twenty years ago, Harold’s age was 13 years
more than half the age of Ben. How old are they now?
31. Sherry is 13 years younger than Jenny. Nine years from now, the sum of their
ages will be 43. Find the present age of each.
32. The sum of one-fifth of Marrie’s age four years ago and half of her age in six years
is 33. How old is she now?
33. The sum of Andrea and Hanna’s ages is 28. Four years from now, Andrea will be
three times as old as Hanna. Find their present ages.
34. The sum of the ages of Joy and Nena is three times Nena’s age. Seven years ago,
Joy was three less than four times as old as Nena. How old are they now?

35. Suppose one skilled worker can finish painting the entire house in twelve hours,
and the second skilled worker takes eight hours to paint a similarly-sized house.
How long would it take the two skilled workers together to paint the house?
36. One hdpe pipe can fill a water container 1.25 times as fast as a second hdpe pipe.
When both hdpe pipes are opened, they fill the water container in five hours.
How long would it take to fill the water container if only the slower hdpe pipe is
used?
37. Twenty men can cut thirty trees in four hours. If four men leave the job, how
many trees will be cut in six hours?
38.If a duck and a half lays an egg and a half in a day and a half, how many eggs will
five duck lay in six days?
39. A clock is set right at 8 a.m. The clock gains 10 minutes in 24 hours will be the
true time when the clock indicates 1 p.m. on the following day?
40.At what time between 4 and 5 o'clock will the hands of a watch point in opposite
directions?
41. At what time between 5 and 6 o' clock are the hands of a 3 minutes apart?
42. A store owner wants to mix cashews and almonds. Cashews cost 2 dollars per
pound and almonds cost 5 dollars per pound. He plans to sell 150 pounds of a
mixture. How many pounds of each type of nuts should be mixed if the mixture
will cost 3 dollars?

43. Suppose a car can run on ethanol and gas and you have a 15 gallons tank to fill.
You can buy fuel that is either 30 percent ethanol or 80 percent ethanol. How
 much of each type of fuel should you mix so that the mixture is 40 percent
ethanol?
44. In a three digit number, the hundreds digit is twice the units digit. If 396 be
subtracted from the number, the order of the digits will be reversed. Find the
number if the sum of the digits is 17.
Evaluate the following algebraic Expressions
45. Solve for x from √(4−x 2)3 +3 x2 √ 4−x 2=0.

46. Solve for x from

√ (4−x 2 )3 3 x 2 √ 4−x 2
+ =1
x 2 x2
47. Solve for x from √
(4−2 x 3)2 √ 4−x 2
− = √(4−x 2)3
x 2
48.Solve for x from √
√
2
4−x 1
= (4−x 2)3− + 2 x
2 x

49. Solve for y from √

(4 y−2) √ 4−3 y
√
3 2
y2 3
− = (4−3 )
2 2y 2
50.Solve for x from √
√
2
4−x 1
− (4−x 2)3− =2 x
2 x
√(4 y−2) −2

51. Solve for y from 3 √ 4 y−1 =√(4−3 y 2)4 ¿

3 y−¿ −
2y

52. Solve for y from √

√
+ (4−3 ) = √
3
(4 y−2) y2 3 4−3 y 2
+1
2 2 2y

53. Solve for y from √

√
3
(4 y−2) y2 3
= (4−3 )
2 2
54. Solve for y from √(4 y− y ) + √ 4− y =0 .
2 3 2

55. Solve for y from √ (12− y 2)3 + √ 2− y 3=1.

56. Find the 10th term of the arithmetic progression 1, 3.5, 6, 8.5,...
a.22.5 b.23.5 c.34.5 d.24.5
57. Find the eighth term of the sequence 1,3,9 …
a.2,187 b.6,561 c.729 d.19,683
58. A clock is set right at 8 a.m. The clock gains 10 minutes in 24 hours will be the
true time when the clock indicates 1 p.m. on the following day?
a. 45 min. past12 b. 46 min. past12 c. 47 min. past 12 d. 48 min. past 12
59. At what time between 4 and 5 o'clock will the hands of a watch point in opposite
directions?
a. 54 past 4 b. (54 + 8/11) past 4 c. (53 + 7/11) past 4 d. (54 + 6/11) past
4
60.In a three digit number, the hundreds digit is twice the units digit. If 396 be
subtracted from the number, the order of the digits will be reversed. Find the
number if the sum of the digits is 17.
a. 980 b. 548 c. 854 d. 584
61. The digits of a three-digit number are in arithmetic progression. If you divide the
number by the sum of its digits, the quotient is 26. If the digits are reversed, the
resulting number is 198 more than the original number. Find the sum of all the
digits.
a. 9 b. 12 c. 15 d. 18
62. How many three-digit numbers are not divisible by 3?
a. 300 b. 600 c. 900 d. 1,200
63. Solve for x from √ 3−x + √ 4−2 x=√ 3−3 x
a. 2 b. 4 c. 6 d. 8
64. Five years ago, John’s age was half of the age he will be in 8 years. How old is he
now?
a. 8 b. 9 c. 16 d. 18
65. Let x = log2 64
a. x = 1 b. x = 2 c. x = 4 d. x = 6
103
66. i = ____
a. 1 b. -1 c. -i d. i
67. i202 = ____
a. 1 b. -1 c. -i d. i
68.Solve log x (4x – 3) = 2
a. x = 1 b. x = 2 c. x = 4 d. x = 6
69. Solve log4(x2−2x)=log4(5x−12)
a. x = 1 b. x = 2 c. x = 4 d. x = 6
70. Solve ln(x)+ln(x+3)=ln(20−5x)
a. x = 1 b. x = 2 c. x = 4 d. x = 6
71. The sum of Andrea(A) and Hanna’s(H) ages is 28. Four years from now, Andrea
will be three times as old as Hanna. Find their present ages.
a. A = 5, H =23 b. A= 24, H =4 c. A= 4, H =24 d. A= 23, H =5
72. Suppose one skilled worker can finish painting the entire house in twelve hours,
and the second skilled worker takes eight hours to paint a similarly-sized house.
How long would it take the two skilled workers together to paint the house?
a. 4hr&44mins b. 4hr&48mins c. 4hr&52mins d. 4hr&56mins
73. Toni is 28 years older than Mary. In 6 years, Toni will be three times as old as
Mary. How old is Tony now?
a. 36yrs old b. 37 yrs old c. 38yrs old d. 39yrs old
74. Find the ninth term of the arithmetic progression whose first three terms are
3,9,and 15.
a. 45 b. 51 c. 57 d. 63
75. The second term of a geometric progression is 8 and the sixth term is 128. Find
the 11th term.
a. 1,098 b. 2,096 c. 3,098 d. 4,096
76. A clock is set right at 8 a.m. The clock gains 10 minutes in 24 hours will be the true time
when the clock indicates 1 p.m. on the following day?
a. 28min past 12 b. 38min past 12 c. 48min past 12 d. 58min past 12
77. If a is positive and cde is negative, which of the following must be true
a. ab-cde>0 b. ab-(cde)(cde)>0 c. ac+de<0 d. ab/cde <-1
78. If x, y and z are integers. x and y are both even numbers, which of the following
could be an odd integer?
a. xy+z b. xy+y c.y-xz d.y+xz
5 2
79. If f(x) = x – 2x + 3/x, then f(-1) must be equal to:
a. -9 b.-8 c.-7 d.-6
80.If ab = IaI IbI, which of the following relation is true?
a. a=b b. ab>0 c. a>0 and b>0 d. a-b>0
81. In the equation 2x – 1/5 = 4/5, x is most likely equal to
a. 0 b. 1 c. 2 d. ½
82.The exponential form of the term √ w v is 2 3

a. wv b. w2v3 c.wv3/2 d. wv1/3

83.Simply the term √ x ( 4−3 √ x ) (assuming x is positive)
a. 4 √ x −3 x b. 1 c. 4 √ x −3 d. √ x−3 x
84. Twenty men can cut thirty trees in four hours. If four men leave the job, how many trees will
be cut in six hours?
a. 30 trees b. 36 trees c. 40 trees d. 46 trees
85. If f(x) = x5 – 2x2 + 3/x, then f(1) must be equal to:
a. 0 b.1 c.-1 d.2
86.Find the common difference of the arithmetic progression: 2, 5, 8, 11, ...
87. If the first term of an AP is 7 and the common difference is 4, find the 15th term.
88.The sum of the first 10 terms of an AP is 150. If the first term is 8, find the
common difference.
89.In an AP, the 12th term is 45 and the 20th term is 65. Find the common
difference and the first term.
90.Find the sum of the first 25 terms of an AP where the first term is 3 and the
common difference is 6.
91. If the sum of the first n terms of an AP is given by Sₙ = 3n² + 2n, find the first
term and the common difference.
92. The 5th term of an AP is 17 and the 12th term is 44. Find the common difference
and the first term.
93. In an AP, if the 9th term is 28 and the common difference is 3, find the sum of
the first 15 terms.
94. The sum of an arithmetic series is 200. If the first term is 10 and the common
difference is 6, find the number of terms.
95. Find the nth term of an AP if the sum of the first n terms is given by Sₙ = 2n² - n
96. In a GP, the first term is 2 and the common ratio is 3. Find the 8th term.
97. If the first term of a GP is 5 and the common ratio is 2, find the sum of the first 6
terms.
98.The sum of the first 10 terms of a GP is 1023 and the common ratio is 3. Find the
first term.
99. In a GP, the 4th term is 48 and the 6th term is 432. Find the common ratio and
the first term.