Republic of the Philippines

GILLESANIA Engineering Review and Training Center

Cebu

BOARD OF CIVIL ENGINEERING

FINAL PREBOARD - MSTHC & HPGE 1

Friday, September 9, 2022 Test 14

INSTRUCTION: Select the correct answer for each of the following questions. Mark only one answer for each item by shading the box
corresponding to the letter of your choice on the answer sheet provided. STRICTLY NO ERASURES ALLOWED. Use pencil no. 2 only. NOTE:
WHENEVER YOU CAN ENCOUNTER A CARET (^) SIGN, IT MEANS EXPONENTIATION

11. An inspection procedure at a manufacturing plant involves'

MSTHC picking three items at random and then accepting the whole
lot if at least two of the three items are in perfect condition. If
1. A 3-meter-long steel pipe has its upper end leaning against a
in reality 90% of the whole lot are perfect, what is the
vertical wall and tower and on a level ground. The lower end
probability that the lot will be accepted?
moves away at a constant rate of 2 cm/s. How fast is the pipe
A. 0.243 C. 0.810
rotating when the lower end is 2 m from the wall in rad/sec?
B. 0.667 D. 0.927
A. 0.00968 C. 0.00754
12. An earth satellite has an apogee of 2450 miles and a perigee of
B. 0.00105 D. 0.00894
410 miles. Assuming that the earth’s radius is 400 miles, what
2. The slope of the curve y = x3 + 6x – 4 as it passes through (0, -
is the value of the eccentricity of ellipse, which form with the
4) is equal to:
center of the earth at one focus and whose apogee and perigee
A. -6 C. 6
satisfy the condition above?
B. -4 D. 4
A. 0.431 C. 0.688
3. A contractor estimates that he could finish a project in 15 days
B. 0.557 D. 0.715
if he has 20 men. At the start, he hired 10 men then after 6
13. In 1626, Peter Minuit persuaded the Wappinger Indians to sell
days, 10 more men are added. How many days was the project
him Manhattan Island for $24. If the Native Americans had put
delayed?
the $24 into a bank account paying 5% interest, how much
A. 5 C. 6
would the investment have been worth in the year 2005 if
B. 3 D. 4
interest were compounded continuously?
4. What is the derivative with respect to y = 2 cos (2 + x³)?
A. $4,277,927,533 C. $4,074,662,794
A. 6x² sin (2 + x³) C. -6x² sin (2 + x³)
B. $4,069,378,018 D. $4,283,575,223
B. 3x² sin (2 + x³) D. -3x² sin (2 + x³)
14. Find the sum of all even integers from 2 through 100.
5. Solve for n, given nP4 = 30 nP2.
A. 2500 C. 2600
A. 6 C. 8
B. 2550 D. 2650
B. 7 D. 9
15. A student plans to deposit $600 each year in a savings account,
6. Find a value of k so that the sequence 2k - 5, k - 4, 10 - 3k forms
over a period of 10 years. If the bank pays 6% per year,
a G.P.
compounded annually, how much money will have
A. 2 C. 22/7
accumulated at the end of the 10-year period?
B. -3 D. 15/8
A. $7,105.90 C. $7,772.55
7. Of the microcomputers manufactured by a certain process, 5%
B. $7,908.50 D. $7,458.67
are defective. Four of the microcomputers are chosen at
16. Find the second term of the binomial expansion of (2x + 3y²)⁴.
random. Assume they function independently. What is the
A. 69x³y² C. 87x³y²
probability that they all work?
B. 96x³y² D. 78x³y²
A. 20% C. 81.45%
17. If two cards are drawn from a deck, what is the probability that
B. 76.41% D. 93.75%
at least one of the cards will be a face card?
8. An engineer bought a dump truck costing $25,000 payable in
A. 26% C. 41%
5 years, semi-annual payment, each installment payable at the
B. 36% D. 69%
beginning of each period. If the nominal rate of interest is 12%
18. A series of 10 annual payments of P2,000 is equivalent to two
per year, compounded semi-annually, determine the amount
equal payments, one at the end of 15 years and the other at the
of each installment.
end of 20 years. The interest rate is 8%, compounded annually.
A. $3,198.42 C. $3,311.98
What is the amount of the two equal payments?
B. $3,204.43 D. $3,400.25
A. P21,532 C. P23,531
9. A lathe machine in a mechanical shop breaks down at an
B. P21,253 D. P25,331
average of 4 times per year. Using Poison’s distribution, find
19. A machine costing P100,000 has an estimated scrap value of
the probability that at most one breakdown will occur each
P10,000 at the end of its economic life of 10 years. Determine
year.
the book value at the end of 5 years using double declining
A. 0.0733 C. 0.0377
balance method.
B. 0.0916 D. 0.0619
A. P31,623 C. P34,958
10. What rate of interests compounded monthly is equivalent to
B. P32,768 D. P35,015
an interest rate of 14% compounded quarterly?
A. 12.79% C. 14.21%
B. 13.84% D. 14.92%
20. A baseball team consists of nine players. Find the number of are on level ground. If the height of the building B is 100 m,
ways of arranging the first four positions in the batting order how far apart are the buildings in m?
if the pitcher is excluded. 8*7*6*5 A. 69.1 C. 61.9
A. 1680 C. 1860 B. 67.5 D. 63.8
33. A mountain climber wants to cut a rope 213 feet long into
B. 1790 D. 1970
three pieces. If each piece is to be 2 feet longer than the
21. Suppose five cards are drawn from a standard deck of 52 previous one, where should he make the cuts?
playing cards. Approximate the probability that all five cards A. 70 and 73 C. 69 and 73
are hearts. B. 71 and 75 D. 68 and 70
A. 1/1000 C. 1/2000 34. At the NLEX, a tourist bus is capable of an acceleration of about
B. 1/1500 D. 1/2500 1.6 m/s2. At this rate, how long would it take to accelerate from
22. Find the values of x and y, where x and y are real numbers: 80 kph to 110 kph.
ሺ2‫ ݔ‬− 4ሻ + 9݅ = 8 + 3‫݅ݕ‬ A. 2.5 s C. 4.5 s
A. x = 4; y = 3 C. x = 6; y = 3 B. 3.5 s D. 5.2 s
35. Line AB has point A(4, 5) and point B(-3, -2). Find point C along
B. x = 3; y = 4 D. x = 3; y = 6 line AB if distance BC is three times the distance AC.
23. Find the vertical asymptote of the graph of the function A. (3.00, 4.00) C. (-3.25, 2.25)
‫ݔ‬ଶ − 9 B. (3.25, 2.25) D. (2.25, 3.25)
݂ሺ‫ݔ‬ሻ =
2‫ ݔ‬− 4 36. Find the area in square centimeters of the largest square that
A. x = -2 C. x = -3 can be cut from a sector of a circle radius 8 cm and central
B. x = 2 D. x = 3 angle 120°?
24. Air handling equipment that costs $12,000 has a life of 8 years A. 54.5 m C. 33.5
with a $2000 salvage value. Determine the book value after 3 B. 34.6 m D. 45.6
years. 37. A frustum of a sphere has base diameters of 20 cm and 12 cm
and thickness of 3.6 cm. What is the volume of the frustum?
A. $8000 C. $8750 A. 783.5 cu.cm. C. 773.5 cu.cm.
B. $8250 D. $9000 B. 793.5 cu.cm. D. 763.5 cu.cm.
25. At what rate must funds be continuously added to a savings 38. From the set of numbers; 14, 8, 6, 2. Find the range, mean
account in order to accumulate Php10 000 in 15 years, if absolute deviation and standard deviation.
interest is paid at 5% per year, compounded continuously? A. 12, 4.1, 4.33 C. 12, 5.3, 4.55
A. Php495.21 per year C. Php459.01 per year B. 12, 3.5, 4.33 D. 12, 4.90, 3.65
B. Php474.36 per year D. Php447.63 per year 39. Off-ramp traffic must stop at a single tollbooth. The arrival rate
26. A group of hikers from Tulsa hiked down into the Grand at the tollbooth is 45 vehicles per hour. If the service rate is 60
Canyon in 3 hours 30 minutes. Coming back up on a trail that vehicles per hour, determine the number of vehicles waiting
excluding the vehicles being served.
was 4 miles shorter, they hiked 2 mph slower and it took them A. 4.65 vehicles C. 3.75 vehicles
1 hour longer. What was their rate going down? B. 5.50 vehicles D. 2.25 vehicles
A. 3 mph C. 5 mph 40. Given data of a simple curve
B. 4 mph D. 6 mph I = 44°
27. Assume that a population is growing continuously at a rate of R = 400 ft
4% per year. Approximate the amount of time it takes for the Sta. PC = 11 + 10.57
population to double its size-that is, its doubling time. Sta. PI = 12 + 72.18
A. 13.7 years C. 14.8 years Sta. PT = 14 + 17.75
B. 17.3 years D. 18.4 years Compute the total deflection angle at station 13 + 50
A. 19°08’52” C. 21°08’52”
28. How much money must be deposited at the end of each year B. 17°08’52” D. 23°08’52”
in a savings account that pays 9% per year, compounded 41. A spring has a natural length of L = 1 m. A force of 24 newtons
annually, in order to have a total of $10 000 at the end of 14 stretches the spring to a length of 1.8 m. Find the spring
years? constant k.
Compound Amount Factor Present Worth Factor A. 30.00 C. 50.00
(F/A, 9%, 14) = 26.0192 (P/A, 9%, 14) = 23.8708 B. 13.33 D. 14.44
Capital Recovery Factor Sinking Fund Factor 42. A sag parabolic curve has the data:
(A/P, 9%, 14) = 0.12843317 (A/F, 9%, 14) = 0.03843317 g1 = -2%
A. $1284.33 C. $418.92 g2 = +1.6%
B. $384.33 D. $207.29 L = 800 ft
29. Suppose 3 items are inspected and if at least one defective is PV1 = 87 + 00
found, the lot will be 100% inspected. Otherwise, the lot will Elev. PV1 = 743.00 ft
be passed on. How likely it is that a lot containing 5 defectives Compute the distance from BVC to the lowest point of the
curve.
will be passed on? A. 333.33 C. 444.44
A. 0.90859 C. 0.855999 B. 555.55 D. 222.22
B. 0.76927 D. 0.796802 43. The clearance to an obstruction is 50 m and the desirable sight
30. The population of a city in 1970 was 153,800. Assuming that distance when rounding a horizontal curve is 600 m.
the population increases continuously at a rate of 5% per year, Determine the minimum radius of horizontal curve if the
predict the population of the city in the year 2000. length of curve is 500 m long.
A. 629,884 C. 682,498 A. 859 m C. 900 m
B. 642,889 D. 689,284 B. 875 m D. 1218 m
31. Triangle ABC is inscribed in a circle with side a = 50 cm, and 44. If the position of a particle at a time t is given by the equation
angle BAC = 20° and angle ABC = 40°. Find the area of the circle x(t) = t³ – 11t² + 24t, find the velocity and the acceleration of
in sq.cm. the particle at time t = 5.
A. 16,785 C. 16,975 A. -10 and -8 C. -12 and 9
B. 17,118 D. 17,811 B. -11 and 8 D. -13 and -9
32. From the top of the building A the angle of elevation of the top
of the building B is 46°. From the foot of the building B the
angle of elevation of the top of building A is 28°. Both buildings
45. Find two angles such that the angles are vertical and Determine the space mean speed.
complementary. A. 75 kph C. 81 kph
A. 90° each C. 60° each B. 72 kph D. 62 kph
B. 45° each D. 30° each 57. The area bounded by the waterline of a reservoir and the
46. A child in a boat throws a 6.4 kg package out horizontally with contours at an interval of 1.7 m. are as follows:
a speed of 10 m/s. Calculate the velocity of the boat A1 = 15430 m² A2 = 12980 m² A3 = 10650 m²
immediately after, assuming it was initially at rest. The mass A4 = 8540 m² A5 = 5270 m² A6 = 2180 m²
of the child is 26 kg and that of a man is 45 kg. Ignore water Calculate the volume of the reservoir by prismoidal formula in
resistance. cu.m.
A. -0.801 m/s C. -0.707 m/s A. 78911 C. 74681
B. -0.901 m/s D. -0.606 m/s B. 75108 D. 77290
47. The equation of an asymptote of a hyperbola equal to y = 2x 58. A circular cone having an altitude if 9 m is divided into 2
which passes through (5/2, 3). Determine the length of the segments having the same vertex. If the smaller altitude is 6 m,
latus rectum. find the ratio of the volume of small cone to the big cone.
A. 12 C. 20 A. 0.926 C. 0.629
B. 16 D. 24 B. 0.296 D. 0.692
48. Find the value of (8Cis 40˚)(2Cis -40˚). 59. From station 0+040 with center height of 1.2 m in fill, the
A. 20 C. 16 ground line makes a uniform slope of +6.5% to station 0+100
B. 22 D. 18 whose center height in cut is 3.5 m. Find the grade of the
49. To fight a forest fire, the forest dry department plans to clear finished roadway.
a rectangular fire break around the fire. Crews are equipped A. -1.33% C. +1.09%
with mobile communications with a 3,000-yard range. If point B. +1.33% D. -1.09%
‫ ܣ‬is 2400 yards east of point ‫ ܥ‬and point ‫ ܤ‬is 1000 yards north 60. The toll booth in the toll bridge of San Juanico Strait in
of point ‫ܥ‬, can crews at point ‫ ܣ‬and ‫ ܤ‬remain in radio contact? Tacloban City controls the traffic flow of traffic thru the bridge.
A. Yes, because two crews are 2,500 yards apart, it is less than The toll plaza consists of two booths, each of which can handle
the range of radios. on vehicle every 6 seconds. The volume of traffic and its
B. Yes, because two crews are 2,600 yards apart, it is less than corresponding times during morning peak period is tabulated
the range of the radios. as shown.
C. No, because two crews are 2,500 yards apart, it is more Time 15 min. Cumulative
than the range of radios. Period volume Volume
D. No, because two crews are 2,600 yards apart, it is more 7:00-7:15 200 200
than the range of radios. 7:15-7:30 250 450
50. In triangle ‫ܦܥܤ‬, ‫ = ܥܤ‬25݉ and ‫ = ܦܥ‬10݉. Compute the 7:30-7:45 350 800
probable perimeter of the triangle. 7:45-8:00 400 1200
A. 72 C. 70 8:00-8:15 250 1450
B. 71 D. 69
8:15-8:30 200 1650
51. A car weighing 800 kg runs at 60 kph around an unbanked
Determine the total delay in vehicle-minute.
circular curve with a radius of 100 m. What force of friction on
A. 4500 C. 5500
the tires should there be to prevent the car from sliding?
B. 5000 D. 4300
A. 2222 N C. 2666 N
B. 3333 N D. 3666 N
52. During peak hours, 4400 vehicles pass through a certain
highway from 9:00 am to 11:00 am, with a space mean speed
of 20 kph. What is the traffic density in vehicles per kilometer? HPGE
A. 110 C. 105
B. 100 D. 90 61. Soils having size larger than 75 mm.
53. The observed interior angles of a quadrilateral and their A. Gravel C. Loam
corresponding number of observations are as follows: B. Rock D. Boulders & Cobbles
No. of 62. A tank containing 0.6 m deep of water is transported by an
Corner Angle
observations elevator. What is the pressure at the bottom of the tank when
1 67° 5 the elevator accelerates 2 m/s2 downward?
2 132° 6 A. 7.09 kPa C. 4.69 kPa
3 96° 3 B. 6.32 kPa D. 5.25 kPa
4 68° 4 63. Given the unit of air to be constant at 12 N/m^3, determine
Determine the corrected angle at corner 3. the approximate height of a mountain, in meters, if a mercury
A. 94°56.84’ C. 97°3.16’ barometer at its base reads 760 mm and at the same instant
B. 96°32.12’ D. 95°45.9’ another barometer at the top of the mountain reads 300 mm.
54. A line on a map was drawn at a scale of 5:100,000. If a line in A. 5085 C. 5736
the map is 290 mm long, the actual length of the line is: B. 5670 D. 5114
A. 5.8 km C. 2.9 km 64. A cube, 270 mm on each side is to be held in equilibrium under
B. 4.8 km D. 6.4 km water by attaching a lightweight foam buoy to it. The specific
55. Using arc basis, a 3.2-degree curve with central angle of 18° weight of the cube and foam are 20 kN/m3 and 0.81 kN/m3,
has an external distance of: respectively. Evaluate the minimum volume of the foam
A. 4.46 m C. 5.55 m required, in m3. Neglect the attachments in the calculations.
B. 6.32 m D. 8.98 m A. 0.0432 C. 0.0337
56. The following data were taken on five cars traversing a 1.5-km B. 0.0223 D. 0.0248
highway.
Time Situation 1 – A pump draws water from a reservoir M and delivers
Car
(minutes) it to reservoir A, as shown in the figure. If the losses from M to
A 1.3 point 1 is five times the velocity head in the 250 – mm pipe and
B 1.1 from point 2 to A is twenty times the velocity head in the 200
C 1.4
– mm pipe. The discharge is 6,056 liters per minute.
D 1.0
E 1.2
65. Find the pressure at point 1.
A. -12.69 kPa C. 85.34 kPa
B. -28.06 kPa D. 9.33 kPa
66. Find the pressure at point 2.
A. 943.02 kPa C. 856.07 kPa
B. 845.62 kPa D. 935.44 kPa
67. Find the horsepower of the pump.
A. 103.31 hp C. 118.48 hp
B. 116.50 hp D. 127.68 hp

Situation 2 – In order to provide irrigation, water has to be

pumped to an elevation 150 m through a 650-mm pipe where
the pressure required at the higher elevation is 178 kPa. The
source of the water and the discharge point are at atmospheric Situation 4 – A rectangular gate 3.20 m wide rests against a
pressure. Irrigation requirements dictate that water must be smooth wall at A. It is hinged at B located at 5.2 m below the
pumped at the rate of 1.5 m^3/sec. The loss of head due to water surface. A is 2.92 m to the right of B and 2.2 m above B.
friction and other factors is estimated to be 3.79 m. 74. Determine the force on the gate due to sea water pressure.
68. Determine the velocity of the water inside the pipe for the A. 376.46 kN C. 260.96 kN
B. 482.07 kN D. 150.17 kN
required discharge.
A. 3.32 m/s C. 52.18 m/s 75. Determine the horizontal force exerted by the wall at point A.
B. 4.52 m/s D. 5.31 m/s A. 196.69 kN C. 433.51 kN
B. 387.66 kN D. 364.73 kN
69. Determine the amount of energy, in meters, that the pump
76. Determine the reaction at hinged B.
must furnish.
A. 392.19 kN C. 605.14 kN
A. 266 m C. 173 m
B. 406.61 kN D. 243.56 kN
B. 254 m D. 232 m
70. The rating of the pump in horsepower if it is only 80%
efficient.
A. 5735 hp C. 65595 hp
B. 4267 hp D. 6277 hp

Situation 3 – Given the following data of a circular footing:

Footing diameter = 7 m
Depth of footing = 2 m
Unit weight of soil = 18 kN/m^3
Soil cohesion = 0
Angel of friction of soil = 20 deg.
71. Obtain the contribution of footing of footing embedment of
ultimate bearing capacity.
A. 172.3 kPa C. 210.4 kPa
B. 238.1 kPa D. 267.8 kPa
72. Obtain the contribution of footing dimension to ultimate
bearing capacity.
A. 232.9 kPa C. 174.7 kPa
B. 183.5 kPa D. 137.6 kPa
73. Obtain the gross allowable pressure if the factor of safety is Situation 5 – FIGURE SMSC – 1 shows the sieve analysis of soil
3.0. samples A, B, and C. See chart UCS 08 – 1 and FIGURE SMSC –
A. 135.1 kPa C. 84.71 kPa 1.
B. 150.4 kPa D. 405.4 kPa 77. Classify soil A in accordance with Unified Soils Classification
System.
A. SW C. SM
B. SP D. SC
78. Classify soil B in accordance with Unified Soils Classification
System.
A. SM C. SP
B. SC D. SP
79. Classify soil C in accordance with Unified Soils Classification
System.
A. GP C. CL
B. SM D. OH
 100

Situation 6 – After 24 hours of pumping at 60 liters/sec, the water

90
level in an observation well at a distance of 100 m from the
80 test well is lowered 0.50 m. At another observation well
Soil C
located 50 m from the test well, the water level dropped by 1.0
70
m.
80. Estimate the rate of flow in cubic meters per day.
Percent finer by weight

60
A. 3456 C. 4852
50
Soil B Soil A B. 5184 D. 4215
81. Evaluate the coefficient of permeability of the aquifer in
40
meters per day.
30 A. 34.23 C. 43.57
B. 29.05 D. 52.36
20 82. Compute the transmissibility of the aquifer in square meters
per day.
10
A. 1025 C. 763
0
B. 1144 D. 989
0.01 0.1 1 10
Figure SM-52 Grain Size, mm