MATHEMATICS AND SURVEYING
MAY 2013 1. Find the sum of the first 7 terms of the series 2, 5, 12 ½ . . . . .
order to determine the exact number of each
a. 822.50 b. 812.50 c. 802.50 d. 800.50 2. Determine the sum to infinity of the series 4, 2, 1 . . . . .
kind of animals in the barn, the former o wner told a visiting Civil Engineer graduate to simply count the total number of heads and legs, the
a. 6 b. 7 c. 8 3. Find the sum to infinity of the series
d. 9
a. 5/3 b. 3/5 c. -5/3 d. -3/5 4. Meriam and Lilia decided to eat pizza hut. Meriam ordered 3 slices of pizza and 3 soft drinks. Meriam paid P600 while Lilia paid P525. How much did one pizza size cost? b.140
visitor did so and reported 60 heads and 140 legs. How many pigs were there?
2 ½, -1 ¼, 5/8 . . . . .
a. 150
11. A country barn house chickens and pigs. In
a. 40 b. 30 c. 20 d. 10 12. If the domain of y = 2x + 1 is {x|-2 ≤ x ≤ 3}. Which of the following is not in the r ange. a. -4 b. 0 c. -2 d. 7 13. If a is positive integer, then the n which of the following mathematical statements must be
c. 130
d. 120
Situation 1:
true of (a - 1), (a), (a + 1). a. It is always negative
A certain physical characteristic of solid yields the
b. It is always odd
following equation. c = a + bt when c = 52,
c.
t = 100 and when c = 172, t = 400.
d. It is always divisible by 4
5. Find “a” a. 22 6. Find “b” a. -0.4
14. Find – Find – 4|d|, 4|d|, given that d is not equal to 0. b. 10
c. 12
d. 14
b. 0.2
c. 0.40
d. 0.8
Situation 2:
The electrical circuit analysis resulted in the following governing equations.
7. Find the value of I 1. a. 4.62 b.5.62 8. Find the value of I 2. a. 6.47
b. 6.74
c. 3.62
d. 2.62
c. 7.64
d. 7.46
Situation 3:
The resistance R ohms of a length of wire at t degrees centigrade is given by the formula,
where R is the resistance at 0° o
centigrade and α is the temperature coefficient of resistance in degrees centigrade. If R = 30 ohms at 50°C and R = 35 ohms at 100°C, determine the following: a. 0.003 b. 0.004 10. Find the value of R o b. 23
a. – a. – 4|d| b. 4|d| c. – c. – 4|-d| d. 4|-d| 15. If ab is divisible by c, which of t he following can not be true? a. a is not divisible by c b. b is divisible by c c.
a is a prime number
d. ab + c is odd and c is even 16. Find the product of two numbers such that their sum multiplied by the sum of their squares is 5,500, and their differences multiplied by the difference of their squares is 352. a. 114 b. 115 c. 116 d. 117 17. Martin buys a pen for P75.00, he then marks up the price by 80% consequently sells it for a discount of 20%. If the transaction tr ansaction was paid in cash, what was his profit from the deal? a. 30 b. 31 c. 32 d. 33 18. In what time would Peter, Paul P aul and Mary together do a piece of work if Peter could do it in 6 hours more, Paul alone in one hour more
9. Find the value of α
a. 22
It is always divisible by 3
c. 0.005
d. 0.006
c. 24
d. 25
and Mary alone in twice the time? a. 20 min
b. 30 min
c. 40 min
d. 50 min
19. If you are to multiply the expressions (-2)
1/2
and
29. Find the area bounded by the curve
,
the x-axis, the vertical line x = -2 and x = 2.
, what will be the result?
a. 1/2 b. -1/2 c. 2/3 d. -2/3 20. Two thirds of people in a party are lawyers,
a. 2π/3 b. 4π c. π d. π/2 30. Find the area bounded by the parabola
whose average I.Q. is 120. The rest are
and .
engineers, whose I.Q. is 180. What is the
a. 34/6
average I.Q. of all persons in the room? a. 140 b. 145 c. 150 d. 155 21. Daniel and Nathan belong to the same baseball
b. 64/3
c. 46/3
d. 36/4
Situation 5:
A drill bit apparatus is bought at one million pesos and is rated to produce 2,500 drill bits per year. It
team. After so many swings, Daniel recorded 8
has an expected minimum output of 10,000 bits
hits out of 20 times at bat. Judging on his
before replacement, and will fetch a scrap value of
present performance record, what is the
P50,000. The machine has the following operations
probability that both will get a hit next at bat?
and maintenance costs:
a. 4/20 b. 5/20 c. 8/20 d. 3/20 22. If a log x = y where b is the base of logarithm,
Cost of lease of space . . . . . P25,000 per year Cost of electricity required per drill bit produced . . . . . . . . . . . . . . . . . P9.00
then what value of x is equal to what form? b
y
a. x = y b. x = b c. x = yb d. x = by 23. A few books are laid out on a desk in a library. Two are Hydraulics, three are Mathematics, one
Rated maintenance cost per unit produced . . . . . . . . . . . . . . . . . P7.00 Cost of labor per unit produced
is Design and four are Surveying. Student A
. . . . . . . . . . . . . . . . . P35.00
selects a hydraulics book and student B then
Assume a depreciation by Sinking Fund Method
selects a surveying book. Both students took
at 12% discount rate.
their selections to the classroom to study. If student C then selects a book at random, what is the probability that he selects a hydraulics book? a. 3/8 b. 4/8 c. 1/8 d. 1/4 24. In order to find the volume of a certain very small cube, Panfilo measured an edge using a ruler and found it to be 2 cm. he later found that the actual length of the cube is 2.1 cm.
31. To the nearest peso, what is the fixed cost per unit? a. P51 b. P15 c. P61 d. P16 32. What is the total production cost per unit? a. 170.51 b. 160.51 c. 150.51 d. 140.51 33. How many years will it take to produce 6000 units? a. 1.2 yrs b. 2.4 yrs 34. Given the equation
c. 2.1 yrs
d. 4.2 yrs
, use
What is the relative error in his volume
algebraic operations to determine the solution
computation?
set.
a. 0.21
b. 0.61
c. 0.10
d. 0.16
Situation 4:
a. 7 b. 6 c. 5 d. 4 35. As of the moment, Procopio has a selection of
A circle is described algebraically by t he equation
98 DVDs. He plans to expand his collection by
.
buying x DVDs each week for y weeks.
25. Determine the coordinate of the center
Determine the total number of DVDs that he
a. (-3,4) b. (3,4) c. (4,3) 26. Determine the radius of the circle
d. (3,-4)
will have?
a. 4 b. 2 c. 3 27. Determine the area of the circle
d. 1
raising his average commission by P100. Ernie’s
a. 4π b. 5π c. 6π d. 7π 28. Find the area bounded by the parabola and the line
.
a. 3/2
b. 1/3
a. 98(x+y) b. 98y+x c. 98+xy d. 98x+y 36. Ernie earned a P2,000 commission n a big deal,
new average commission now is P900. How many sales has he made so far? a. 12
c. 2/9
d. 9/2
b. 10
c. 8
d. 4
37. The population of weeds in a particular idle field
3
44. A sphere has a volume of 2000 m . There exists
doubles every year. If there are 2,000 weeds
a small circle of the sphere, the plane of which
now, in approximately how many years will it
is 6.5 m from the center. Calculating the area of
take the population to grow to a million or
the small circle of the sphere in m. 2
more?
2
2
2
a. 69 m b. 89 m c. 79 m d. 59 m 45. A new engineer who just passed the Board
a. 8 yrs b. 9 yrs c. 10 yrs d. 11 yrs 38. In about 4 years from now, the population of
Exam decided he will not work and will just do
mosquitos doubles every 2 years, if the
some stock market instead. He acquired a
7
population now is 2 x 10 , what was the
portfolio comprising of stocks in GHG which has
population 4 years ago?
an annual gain of 10%, and stocks in Apollo and
5
2
5
6
a. 2 x 10 b. 5 x 10 c. 6 x 10 d. 5 x 10 39. The population of germs in an open wound if
Praxedes, Inc., with annual gain of 20%. If the total combined stock portfolio gained 14%
left untreated doubles every two days. If these
overall, which of the following is true?
were 200 germs in the wound six days ago, how
a.
many germs will there be in the same wound 4
There are more stocks of GHG than Apollo and Praxedes, Inc.
days from now?
b. There is not enough information to
a. 6,200 b. 6,300 c. 6,400 d. 6,500 40. A bowler’s average score for 6 games is 150. He
determine the numbers. c.
wants to raise his total average score by 10% by
There are more stocks of Apollo and Praxedes, Inc. than GHG.
scoring more in the remaining two games left.
d. GHG and Apollo and Praxedes, Inc. have
What must be the average in the two games in order to attain this?
equal number of stocks. Situation 6:
a. 210 b. 110 c. 300 d. 120 41. If left alone, a certain specie of grass expands
The monitor in a nuclear research laboratory showed a cyclical curve which follows the following
the ground if covers following the e quation
function,
, where A is the area originally
covered by the grass in million sq.m. and t is the number of years since 1998. In what year will
46. Determine the amplitude
the area covered reach 10 million for the first
a. 1/2 b. 2 47. Determine the period
time? a. 2013 b. 2014 c. 2015 d. 2016 42. Along EDSA, two billboards were erected. They are of dissimilar sizes with their sides having a
d. 2π
a. 0.64 49. If
c. 0.16
d. 0.08
c. a/7
d. a/8
2
2
a. a/5
much material, in m , is needed for the smaller 50. 2
2
2
2
a. 130 m b. 140 m c. 150 m d. 160 m 43. A surveyor measures a distance of 25.07 m
plumb bob end was 1.03m lower than it should be. Find the correct distance. a. 27.05
b. 24.05
c. 26.05
d. 25.05m
51.
b. a/6
, given that r < s < 0 < w < t. what is the sign of . a. negative b. positive
using break chaining. The tape was not actually accurately levelled at that time, and at the
b. 1.27
( ) , what is the
value of x in terms of a.
m of material to cover the entire billboard. How one?
d. 4
a. π/4 b. π/2 c. 4π 48. Determine the frequency
ratio of 5:4. The bigger billboard required 250
c. 1/4
c. imaginary d. cannot be define , given that K < 0 and h and m is
not equal to zero. What is the sign of
. a. negative b. positive
c. imaginary d. cannot be define
52. What should be the length of r adius of the circle described by the equation
26.5° respectively. Find the height of the building if the distance between x and y is
a. 6 b. 5 c. 4 d. 3 53. How many three-letter arrangements can be
330m. a. 31.62 b. 61.32 c. 62.31 d. 32.61 61. Determine the total surface area of a 4 cm by 6
made with letters that comprise the word
cm rectangular pyramid of perpendicular height
ANGLE if no letter may be repeated.
of 12 cm.
a. 60 b. 50 c. 65 d. 55 54. A series of numbers or terms is defined by the parametric formula
, where n
a. 176.9 b. 166.9 c. 156.9 d. 146.9 62. If you are doing a survey, which method of collecting data would most likely result in an
is the order in the series, what maybe the
unbiased random sample.
common ratio of the terms in this series?
a.
a. 1.2 b. 1.5 c. 1 d. 15 55. N is the normally distributed variable with an
how they voted in the last 2010 elections. b. Selecting every third teenager leaving a mall
average or mean of zero. Approximately 2% of the observations are -10 or smaller. Determine
Placing a survey in a local newspaper on
to answer survey about shopping. c.
Survey dean’s lister taking concrete design
approximately what fraction of the observation
to determine the average amount of the CE
lie between 0 and 5.
students study each night.
a. 3/2 b. 1/3 c. 2/3 d. 3/4 56. The position of a particle moving along a straight line is given by
. The distance is increasing for: a. 1 < t < 3 c. t > 2 b. t < 2 d. all except t = 2 57. The displacement from the origin of a particle moving on a line is given by
.
Determine the maximum displacement during the time interval -2 ≤ t ≤ 4. a. 3 b. 16 c. 27 d. 0 58. If a particle moves along a line according to the law
, find time it reverses
direction. a. 3 b. 16 c. 27 d. 0 59. If the three positive number x, y, z are in G.P., which of the following is true? a.
2 log y = log x + log z
b. log (x + y) = log 2z c.
(log x)(log z) = 2 log y
d. log x – log y = log z 60. Two points x and y are on opposite side of a building which lies on the same straight line connecting them. Measurements were made from those two points and records the angle of elevation of the top of the building and the following figures were recorded as 16 .5° and
d. Selecting students by the last digit of t heir school student number to participate in a survey about cafeterias food. 63. A 4.2 cm by 4.2 cm square pyramid whose sloping edges are each 15 cm. Find the total surface area. a. 122.38 b. 132.38 c. 142.38 d. 152.38 64. A pyramid having an octagonal base of side 5cm and a perpendicular height of 20 cm. Find the total surface area. a. 337.8 b. 437.8 c. 537.8 d. 637.8 65. A set has 5 items and it has a range of 7. The set is composed of the following: 2
{1, 2, m, 5, m } with m > 0 Find the average number in the set. a. 3.76 b. 4.76 c. 5.76 d. 6.76 66. Electric resistance of metal are dependent on temperature. For a certain given wire at t degrees C, the resistance R in ohms maybe computed as
where R is the o
resistance at 0° centigrade and α is the temperature coefficient of resistance in degrees centigrade. Solve the value of Ro in ohms if R = 30 ohms at 50°C and R = 35 ohms at 100°C. a. 25
b. 35
c. 45
d. 55
67. The molar heat capacity of a solid component is defined by the equation c = a + bT. When c = 52, T = 100 and when c = 172, T = 400. Calculate the value of b. a. 0.40 b. 0.50 c. 0.60 d. 0.70 68. A student is given a simple set which contains only two integers, 15 and 16 and is written as set {15, 16}. The set is equivalent to: a.
{x|15 < x ≤ 16, where x is an integer}
75. Determine the area of a regular hexagon which has sides 25mm. a. 1723.8 b. 1623.8 c. 1523.8 d. 1423.8 76. The major axis of an ellipse is 200 mm and the minor axis is 100mm. determine the approximate perimeter of the ellipse. a. 124.71 b. 424.71 c. 174.24 d. 471.24 77. Four numbers are such that the sum of the first, third and fourth exceeds the second by 8, the
b. {x|15 < x < 16, where x is an integer}
sum of the squares of the first and second
c.
{x|14 ≤ x < 16, where x is an integer}
exceeds the sum of the squares of the third and
d. {x|14 < x ≤ 16, where x is an integer}
the fourth by 36, the sum of the products of the
69. In a steel tape survey, the sides of a triangular
first and second and third and fourth is 42, the
lot were determined to have the following
cube of the first equals the sum of the cubes of
values: 255.5 m, 301.4 m and 212.5 m .
the second, third and fourth. Which if the
Determine the angle opposite the longest side?
following is not any of the four numbers?
a. 69.6° b. 79.6° c. 89.6° d. 99.6° 70. A triangular lot ABC is surveyed and gave the
a. -5 b. 6 c. 5 d. 4 78. A sphere of radius 1 is totally submerged in a
following measurements. Angle A = 30°, side a =
cylindrical tank of radius 4. The water level in
8m, and side b = 12m. How many triangular lots
the tank rises a distance h. What is the value of
maybe formed with these measurements?
h?
a. 1 b. 2 c. 3 d. 4 71. A survey instrument was set up at A, with a known elevation of 563.80m above sea level, the angle of elevation of the top of the hill was measured as 34.66°. The instrument was moved
a. 0.083 b. 0.163 c. 0.0234 d. 0.038 79. A cube has a surface area of 6x. What is the volume of the cube? 4/3
3/4
3/2
a. x b. x c. x d. x 80. A sphere has a radius of r. if this radius is
2/3
to B, 450m nearer to the mountain nut 25m
increased by b, then what is the increased
lower in elevation than A, and the angle of
surface area of the sphere?
elevation was 43.22°. Determine the elevation
a.
of the top of the hill. a. 983.8 b. 1610.83 c. 1710.8 d. 1810.83 72. A huge sporty sail boat has two sails that are in
b.
c.
d.
Situation 7:
Given an angle in standard position. Determine which quadrant does the terminal side of the angles
the shape of similar triangles. The larger sail
given fall.
measures 10m by 24m by 26m. if you measured
81. tan c > 0 and sec c > 0
the dimension of the shortest side of t he
a. I b. II 82. csc D < 0 and cos D > 0
c. III
d. IV
a. I b. II 83. tan y > 0 and sin y < 0
c. III
d. IV
c. III
d. IV
smaller sail and found it to be 6m long, what is the perimeter of the smaller sail? a. 16 b. 25 c. 36 d. 49 73. A chord, 7.49 m long, is 4.2 m from the center of a circle. Find the area of the circle. a. 99.47 b. 100.47 c. 101.47 d. 102.47 74. Calculate the area of a rectangular octagon if each side is 20 mm and the width across the flat is 48.3 mm. a. 2032
b. 1932
c. 1832
d. 1732
a. I
b. II
Situation 8:
Given the following inequalities, determine which quadrant does the terminal side of the angle in standard position falls. 84. cos A < 0 and tan A > 0 a. I b. II 85. sec x > 0 and sin x > 0 a. I
b. II
c. III
d. IV
c. III
d. IV
86. tan B < 0 and sec B > 0 a. I
b. II
97. c. III
d. IV
b. 1
c. -1
d. 0
Situation 9:
For the different trigonometric expressions below, find the respective values. 88.
89.
b. 2/3
a. 0 90.
c.
c.
a. 0
√
d. -1/2
√
d. -1/2
√
b. 2/3
have?
a.
b. It does not have any symmetry It is symmetrical with respect to y-axis
d. It is symmetrical with respect to both x and y-axis 2
92. The graph of f(y) = y is translated 2 units left and reflected over the x-axis. The resulting graph is then represented by g(y). What is the value of g(4)? a. -4 b. -16 c. -25 d. -36 93. You are given the word “absolute”. Calculate how many three letter arrangements can be formed out of the letters in that word if each letter is used only once. a. 666 94. If
b. 633
c. 336 d. 363 , when y = -3, what is the
value of b? a. -1 only b. -3 only
d. ( ) c.
Using a levelling instrument, a surveyor
measures the angle of depression of a building elevation of its top is recorded as 56.7°. If the height of the instrument is 7.54m from the level ground, determine the height of the building.
It is symmetrical with respect to x-axis
c.
b. ( )
and found it to be 14.54° while the angle of
d. -1/2 c. 91. What kind of symmetry, if any, does the graph of
√
a. a + c is odd c. abc is odd b. abc is even d. b + c is even -3/2 99. Determine the equivalent expression of x
100. b. 2/3
d.
the following must be false.
a.
√
where x > 0.
a. 0
c.
98. If a, b, c are integers and ab + c is odd, which of
2
87. Find the min. value of f(x) = 2x +x . a. 2
, find the sine. √ b. √ a.
c. -1 and 1 only d. 1 only
Situation 10:
From the following angles in standard position, find the values of the trigonometric functions asked if the given points are on the terminal sides of the angles.
√ , find the cosine. √ b. √ √ a. c. 96. find the sine. √ b. √ √ a. c. 95.
d.
√
d.
√
a. 91.57
b. 75.19
c. 15.79
d. 51.79
01. A
14. B
27. A
40. A
53. A
66. A
79. C
92. D
02. C
15. D
28. D
41. B
54. A
67. A
80. B
93. C
03. A
16. D
29. C
42. D
55. B
68. C
81. A
94. D
04. A
17. D
30. B
43. D
56. C
69. B
82. D
95. B
05. C
18. C
31. A
44. D
57. C
70. B
83. C
96. D
06. C
19. B
32. D
45. A
58. D
71. D
84. C
97. A
07. A
20. A
33. B
46. A
59. A
72. C
85. A
98. C
08. A
21. D
34. D
47. B
60. B
73. A
86. D
99. A
09. B
22. B
35. C
48. A
61. D
74. B
87. C
100. D
10. D
23. C
36. A
49. C
62. A
75. B
88. D
11. D
24. D
37. B
50. B
63. C
76. D
89. C
12. A
25. A
38. D
51. A
64. C
77. A
90. A
13. C
26. B
39. C
52. D
65. A
78. A
91. C
