Republic of the Philippines

GILLESANIA Engineering Review and Training Center

Cebu

BOARD OF CIVIL ENGINEERING

PRACTICE PROBLEMS LEVEL 4

Wednesday, June 24, 2020

Structural Situation 3 – The rigid bars ABC and CD are supported by pins at
A and D and by a steel rod at B. There is a roller connection
Situation 1 – The bar ABC is supported by a pin at A and a steel between the bars at C. The load P = 40 kN. neglect all weights.
wire at B. The cross-sectional area of the wire is 2 mm² and 7. Compute the reaction (kN) at A.
the modulus of elasticity of steel is 200 GPa. A. 15 kN (upward) C. 10 kN (upward)
1. If P = 200 N, compute the elongation (mm) of the wire. B. 15 kN (downward) D. 10 kN (downward)
A. 2.4 C. 1.2 8. Determine the tensile stress (MPa) of the steel rod.

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B. 3.6 D. 0.6 A. 125 C. 75
2. If P = 150 N, compute the horizontal displacement (mm) of B. 150 D. 100
point C. 9. Compute the vertical displacement (mm) of point C.
A. 1.44 C. 2.15 A. 3.25 C. 2.50
B. 1.92 D. 2.36 B. 2.25 D. 2.75
3. If the horizontal displacement at C is 1 mm, compute the value
of P (N).
A. 154.6 C. 126.3

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B. 104.2 D. 115.7
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Situation 4 – The structure in the figure is composed of two rigid
bars (AB and CD) and two vertical rods made of aluminum and
steel. All connections are pin joints. Neglect the weights of the
members.
10. If P = 40 kN, determine the stress (MPa) in the steel rod.
A. 20 C. 80
B. 40 D. 50
Situation 2 – The rigid bar AB, attached to aluminum and steel 11. If P = 40 kN, determine the strain in the aluminum rod.
rods, is horizontal before the load P = 45 kN is applied. Neglect
E
A. 0.0012 C. 0.0019
all weights. B. 0.0005 D. 0.0025
4. Determine the stress (MPa) in the steel rod. 12. Determine the maximum force P (kN) that can be applied to
A. 52.5 C. 72.5 the structure if the vertical displacement of its point of
B. 62.5 D. 42.5 application is limited to 5 mm.
5. Determine the strain in the aluminum rod. A. 49.88 C. 65.32
A. 0.00068 C. 0.00026 B. 59.85 D. 87.96
B. 0.00057 D. 0.00089
6. Find the vertical displacement (mm) of point C.
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A. 1.518 C. 2.154
B. 1.729 D. 1.228
Situation 5 – The rigid bars AB and CD are supported by pins at A Situation 7 – Figure shows a copper rod that is placed in an
and D. The vertical rods are made of aluminum and bronze. aluminum tube. The rod is 0.13 mm longer than the tube.
Neglect the weights of the members. Given the following data:
13. Determine the elongation (mm) of the aluminum rod. Copper: A = 1290 mm²
A. 1.96 C. 2.12 E = 117 GPa
B. 1.81 D. 1.42 Allowable stress = 138 MPa
14. Determine the vertical displacement (mm) of point C. Aluminum: A = 1940 mm²
A. 4.84 C. 6.86 E = 69 GPa
B. 2.03 D. 8.66 Allowable stress = 69 MPa
15. Determine the vertical displacement of the point where the
force P is applied. 18. If P = 200 kN, compute the stress (MPa) in the copper rod.
A. 3.43 C. 1.01 A. 32.6 C. 45.8
B. 4.33 D. 2.42 B. 67.4 D. 55.3
19. If P = 200 kN, compute the stress (MPa) in the aluminum tube.
A. 55.3 C. 32.6

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B. 45.8 D. 67.4
20. Find the maximum safe load P (kN) that can be applied to the
bearing plate.
A. 325.6 C. 254.2
B. 212.8 D. 277.9

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m

Situation 6 – The concrete post is reinforced axially with four

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symmetrically placed steel bars, each of cross-sectional area
900 mm². The moduli of elasticity are 200 GPa for steel and 14
GPa for concrete. Situation 8 - The square wooden column shown in Figure ME45-
16. Compute the stress (MPa) in concrete. M01F carries an axial load P. The column is glued along the
A. 7.26 C. 9.12 shaded section. The allowable compressive and shearing
B. 8.65 D. 6.35 stresses of the glue are 6.5 MPa and 3.4 MPa, respectively.  =
17. Compute the stress (MPa) in steel. 35 and w = 175 mm.
A. 165.2 C. 124.5 21. Find the maximum load P based on compressive stress on the
B. 95.4 D. 103.6 glue.
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A. 463 kN C. 584 kN
B. 605 kN D. 316 kN
22. Find the maximum load P based on shearing stress on the glue.
A. 424 kN C. 325 kN
B. 221 kN D. 287 kN
23. Find the angle of the plane of maximum shear.
A. 90 C. 45
B. 35 D. 30
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Situation 9 – In the figure shown, w1 Situation 12 – A crane supports the load W as shown.
= 36 N/m, w2 = 30 N/m, w3 = 15 32. If W = 28 kN find the total reaction at B (kN) neglecting the
N/m, a = 4.5 m, b = 3 m, c = 2.m. weight of the boom.
Calculate the following: A. 42.65 C. 40.12
24. The magnitude of the resultant B. 48.25 D. 45.96
force in N. 33. If the allowable tension of cable AC is 52 kN, find the maximum
A. 232 value of W in kN. Neglect the weight of boom.
B. 263 A. 65.8 C. 60.1
C. 246 B. 69.3 D. 62.4
D. 251 34. If the boom (mast) weighs 10 kN and the allowable tension of
25. The moment about O in N-m. the cable AC is 52 kN, find the maximum value of W.
A. 956.32 A. 61.8 C. 57.4
B. 972.75 B. 52.3 D. 59.4
C. 986.25
D. 825.75

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Situation 10 – For the shaded area shown, a = 450 mm, b = 200
mm, c = 130 mm, d = 300 mm, e = 120 mm, f = 120 mm, g = 100
mm, r = 60 mm. Calculate the following:
26. The total area in mm2.
A. 105509.7 C. 82890.3
B. 95236.7 D. 80124.7
27. The x-coordinate of the centroid in mm.
A. 181.76 C. 164.23

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B. 176.35 D. 154.21
28. The y-coordinate of the centroid in mm.
A. 132.65 C. 118.24
B. 124.27 D. 125.43

Situation 13 – The
portable seat shown
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is braced by a cable
FG with permissible
tension of 1920 N.
Surfaces C, D, and E
are frictionless.
Given the following
data:
x = 0.60 m; x1 =
0.20 m; x2 = 0.30 m
E
H1 = 0.40 m; H2 =
0.20 m; H3 = 0.20 m
35. Calculate the safe
Situation 11 – The archer load W (in N) than the
pulls his bowstring back seat can safely carry.
"c" by exerting a force A. 1200
that increases uniformly B. 1280
from zero to 486 N at C. 1320
point A as shown in D. 1380
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Figure ME25-362. In this 36. If W = 1320 N, what is the reaction at D in Newtons?

problem a = 300 mm, b = A. 460 C. 500
400 mm and c = 220 mm. B. 420 D. 440
29. Find the tension (N) at 37. If W = 1320 N, what is the reaction at E in Newtons?
the top chord AB. A. 900 C. 880
A. 470 B. 860 D. 600
B. 428
C. 432 Figure ME25‐362
D. 450
30. Find the tension (N) at the bottom chord AC.
A. 428 C. 450
B. 470 D. 432
31. What is the force (N) exerted by the archer at the front hand
D?
A. 523 C. 486
B. 468 D. 632
38. A smooth 20-kg cylinder is placed in between members AB 46. A welded connection has an effective length of 180 mm. 12 mm
and CDB as shown in Figure ANM 12.225. Determine the fillet welds are used. It is to resist 400 kN of applied load. If the
contact force at C in Newtons. ultimate strength of the weld is 485 MPa and its allowable
A. 147 C. 120 shearing stress is 60% of Fuw. Determine the required weld
B. 164 D. 153 thickness in mm.
A. 9 C. 10
B. 12 D. 11

Situation 15 – A load of 8.9 kN is applied to a 6-mm-thick steel
plate, as shown. The steel plate is supported by a 10-mm-
diameter steel pin in a single shear connection at A and a 10-
mm-diameter steel pin in a double shear connection at B. The
ultimate shear strength of the steel pins is 280 MPa, and the
ultimate bearing strength of the steel plate is 530 MPa.

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47. Determine the factor of safety for pin A with respect to the
Figure ANM 12.225 ultimate shear strength.
A. 3.41 C. 2.76
Situation 14 – Two 200-mm wide plate, 12 mm thick are to be B. 3.09 D. 4.48
joined together (lap joint) and welded. The steel is A36 with 48. Determine the factor of safety for pin B with respect to the
Fy = 250 MPa. The weld has an allowable shearing stress of ultimate shear strength.
124 MPa. A. 2.11 C. 3.41
39. What is the gross capacity of the plates, in kN? B. 2.84 D. 3.09

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A. 360 C. 340 49. Determine the factor of safety with respect to the ultimate
B. 350 D. 380 bearing strength for the steel plate at pin B.
40. Using the result in part 1, what size of fillet weld is required if A. 2.04 C. 2.24
the length of weld is 490 mm? B. 2.90 D. 2.67
A. 5.9 mm C. 9.6 mm
B. 10.5 mm D. 8.4 mm Situation 16 – A 20-mm-thick steel plate will be used as an axial
member to support a dead load of 150 kN and a live load of
41. A plate is loaded with an axial dead load of 230 kN and an axial 220 kN. The yield strength of the steel is 250 MPa.
live load of 280 kN. Fy for steel is 250 MPa. Load factors: 1.2 50. Use the ASD method to determine the minimum plate width b
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for dead load and 1.6 for live load. Determine the ASD total required for the axial member if a factor of safety of 1.67 with
load to be used for analysis in kN. respect to yielding is required.
A. 510 C. 276 A. 370 C. 123
B. 724 D. 448 B. 149 D. 124
51. Use the LRFD method to determine the minimum plate width
42. A plate is loaded with an axial dead load of 230 kN and an axial b required for the axial member based on yielding of the gross
live load of 280 kN. Fy for steel is 250 MPa. Load factors: 1.2 section using the LRFD method. Use a resistance factor of 𝛷t =
for dead load and 1.6 for live load. Determine the LRFD total 0.9 and load factors of 1.2 and 1.6 for the dead and live loads,
load to be used for analysis in kN. respectively.
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A. 510 C. 276 A. 119 C. 236
B. 724 D. 448 B. 532 D. 117

43. A plate is loaded with an axial dead load of 230 kN and an axial
live load of 280 kN. Fy for steel is 250 MPa. Load factors: 1.2 Fluid Mechanics
for dead load and 1.6 for live load. If the thickness of the plate
is 10 mm and the resistance factor used is 0.9, determine the Situation 17 – A wooden buoy (sp. gr. = 0.75) cylindrical in shape
required width of the plate using LRFD. has a diameter of 0.5m and a height of 1.1m is submerged in a
A. 204 C. 322
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liquid having a specific gravity of 0.85.

B. 290 D. 227 52. Determine the volume percentage exposed.
A. 13.33% C. 14.44%
44. A plate is loaded with an axial dead load of 230 kN and an axial B. 15.33% D. 20.10%
live load of 280 kN. Fy for steel is 250 MPa. Load factors: 1.2 53. If the volume exposed is 0.035m3, what is the total volume of
for dead load and 1.6 for live load. If the thickness of the plate the wooden buoy considering 20% of the total volume is
is 10 mm, the resistance factor used is 0.9 and the safety factor exposed?
is 1.67, determine the required width of the plate using ASD. A. 5.71 C. 0.18
A. 184 C. 484 B. 0.632 D. 0.45
B. 204 D. 341 54. Referring to the first question, what additional weight to make
it fully submerged?
45. Twelve mm fillet welds are used. It is to resist 480 kN of A. 250 N C. 420 N
applied load. If the ultimate strength of the weld is 485 MPa B. 530 N D. 300 N
and its allowable shearing stress is 60% of Fuw. Determine the
required effective length of the weld in mm.
A. 83 C. 117
B. 138 D. 195
Situation 18 - A barge with a flat bottom and square ends has a
draft of 1.8 m. when fully loaded and floating in an upright
position. The barge is 7.6 m. wide and 12.8 m. long and a height p = -15.49 kPa Figure FM-543
of 3 m. The center of gravity of the barge is 0.30 m. above the
water surface if the barge is stable. A
Oil, s = 0.8
55. Determine the distance of the metacenter above the center of
buoyancy.
A. 1.87 m C. 0.90 m
8m
B. 2.03 m D. 2.67 m 6m
56. Determine the distance of the metacenter above the barge
center of gravity.
A. 1.47 m C. 1.74 m
B. 1.87 m D. 1.78 m B P 2m
57. What is the righting moment in water when the angle of heel
is 12˚?

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A. 475 kN-m C. 630 kN-m Situation 22 – The quarter-
B. 526 kN-m D. 415 kN-m cylindrical gate shown is 6
m long perpendicular to
Situation 19 – A right circular cylinder having a diameter of 1.00 the paper. For this
m and weighing 900 N is held in position by an anchor block h1
problem, r = 1.4 m and h1 Water
such that 0.30 m of the cylinder is below the surface of the = 1.6 m. Determine the
water with its axis vertical. The anchor block has a volume of following:
0.50 cubic meter and weighs 24 kN per cubic meter in air. 67. The horizontal
B
Assume sea water to have a specific gravity = 1.03. Neglecting

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component of the total
the weight and volume of the cable, pressure acting on the
r
58. Evaluate the buoyant force on the cylinder for the position gate, in kN.
described, in kN; A. 252.71
A O
A. 2.38 C. 2.98 B. 189.53
B. 2.87 D. 3.12 C. 195.46
59. Evaluate the tensile force in the wire for the given draft of the D. 157.94
cylinder, in kN; 68. The location of the horizontal component of the total pressure
A. 1.48 C. 1.14 measured from O, in cm.
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B. 1.64 D. 6.95 A. 62.90 C. 58.76
60. evaluate the rise in the tide that will lift the anchor from the B. 63.67 D. 60.12
bottom of the sea, in meter(s). 69. The vertical component of the total pressure acting on the
A. 0.754 C. 0.989 gate, in kN.
B. 0.821 D. 0.689 A. 150.34 C. 208.81
B. 156.60 D. 130.50
Situation 20 - A steel pipe 275 mm in diameter and 5 mm thick is 70. The location of the vertical component of the total pressure
used convey water. measured from O, in cm.
61. Calculate for the tensile stress in the pipe when the pressure A. 75.92 C. 74.32
head is 400 m of water, in MPa?
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B. 77.88 D. 76.12
A. 107.9 C. 102.6 71. The total hydrostatic pressure acting on the gate in kN.
B. 112.3 D. 97.5 A. 245.85 C. 327.81
62. If the allowable tensile stress in steel is 124 MPa, determine B. 204.88 D. 234.89
the required pipe thickness in mm if the pressure head is 550
m of water. Assume that the efficiency of the pipe joint is 80%. Situation 23 – Answer the following translation problems:
A. 6.78 mm C. 7.48 mm 72. An open rectangular tank 6 m long, 2.2 m wide and 1.8 m tall
B. 8.32 mm D. 7.81 mm contains 1.4 m deep of water and accelerated horizontally
63. Using the thickness in part 2, determine the actual wall stress along its length. What is the maximum horizontal acceleration
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in MPa when the pressure head is 400 m of water. (in m/s2) without spilling any water?
A. 78.2 MPa C. 72.1 MPa A. 1.308 C. 1.124
B. 89.4 MPa D. 68.3 MPa B. 1.456 D. 1.005
73. For the tank in Part 1, how much water is spilled when the
Situation 21 - The gate AB shown in Figure FM-543 is hinged at A acceleration is 2 m/s2?
and kept closed by a force P at B. A. 2564 L C. 2968 L
64. Determine the nearest value to the total force exerted by oil on B. 2796 L D. 2238 L
the gate, in kN. 74. For the tank in Part 2, what is the total hydrostatic force acting
A. 321 C. 256 on the frond end of the tank in kN?
B. 285 D. 268 A. 8.675 C. 12.563
65. Determine the nearest value to the location of this total force B. 10.231 D. 3.584
from A, in meters.
A. 3.543 C. 3.991
B. 4.299 D. 3.762
66. Determine the nearest value to the force P needed to keep the
gate closed, in kN.
A. 156.76 C. 189.59
B. 175.87 D. 231.64
Situation 24 – An open cylindrical tank has a base diameter of 0.9 87. Solve for the non-integral solution to equation:
meter contains 2.55 meters deep of water. The tank is rotated 1 10
3
about its vertical axis at 90 rpm. 2𝑝 4 2𝑝 4
75. What is the minimum height of the tank so that no water can A. -1/3 C. -7/6
be spilled at 90 rpm? B. -3 D. -6/7
A. 4.5 m C. 3.0 m
B. 3.5 m D. 4.0 m a4 b5 c4
76. If  = 130 rpm, how much water is spilled in liters? 88. Simplify 3
 1 2 .
c a b
A. 567 C. 723
a3b3 a3b7
B. 508 D. 609 A. C.
77. If  = 150 MPa, what will be the pressure at the center bottom c c
5 3
of the tank in kPa? ab
B. D. a3b7c7
A. 5.48 C. 9.45 c
B. 4.52 D. 4.38 89. If 3x = 54, then 3x-2 is equal to:
A. 6 C. 8

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B. 5 D. 9
Algebra
90. If 2x = y, then 2x - 4 =
A. y × 24 C. 24/y
78. Solve: 4(x – 4) + 4(x – 1) = 5(x – 1)(x – 4).
B. y/24 D. y4
A. {5} C. {5/8, 5}
B. {8/5} D. {8/5, 5}
91. Factor the equation: m2 – am – 3m + 3a
A. (m - a)(m - 3) C. (m + 3)(m - a)
79. An arrow is shot directly upward from the top of a 112-foot

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B. (m + a)(m - 3) D. (m - 3a)(m - 1)
tall building with an initial velocity of 96 feet per second. The
height of the arrow above the ground after t seconds is given
92. Factorise x3 + 3x2 − x − 3
by the position function s(t) = -16t² + 96t + 112. After how
A. (x - 3)(x2 - 1) C. (x2 + 1)(x - 3)
many seconds will the arrow strike the ground?
B. (x + 3)(x2 + 1) D. (x + 3)(x2 - 1)
A. 5 seconds C. 7 seconds
B. 6 seconds D. 8 seconds
93. Which of the following is a factor of x3 – 11x + 6?
A. x2 – 3x -2 C. x2 – 3x + 2
80. Find the values of p for which 𝑥 𝑝 𝑥 3 𝑝 𝑥 3
B. x – 3x + 3
2 D. x2 + 3x – 2
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has a remainder of 4.
A. {5} C. {5, -16/3}
94. If (x2 + 9x + 14)/(x2 - 49) is divided by (3x + 6)/(x2 + x - 56),
B. {16/3} D. {-5, 16/3}
the quotient is:
A. x + 8 C. (x + 8)/3
81. By synthetic division, determine the quotient and remainder
B. x + 3 D. (x + 3)/8
in the following.
3𝑥 4𝑥 5𝑥 8𝑥 25 𝑥 2
95. Simplify: (x2 y3 + x y2) / (xy).
A. 3𝑥 2𝑥 𝑥 2𝑥 12 A. xy2 + y C. x2 y + y
B. 3𝑥 2𝑥 𝑥 2𝑥 12 B. xy + y2 D. x2 y2 + y
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C. 3𝑥 2𝑥 𝑥 2𝑥 12
96. Without dividing out, find the remainder when 2x2 −3x + 4 is
D. 3𝑥 2𝑥 𝑥 2𝑥 12 divided by (x − 2).
A. 8 C. 4
82. Solve: B. 5 D. 6
𝑥 3 𝑥 2 1
4 3 4 97. When the expression ax4 + bx3 + cx2 + 5x - 8 is divided by (x +
A. 𝑥 7 C. 𝑥 14 1), the remainder is -4, when it is divided by (x - 2) the
B. 𝑥 7 D. 𝑥 14 remainder is 26, one of its factors is (x – 1). What is the
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remainder when it is divided by (x + 2)?

83. Solve: √2𝑥 5 √2𝑥 3. A. 24 C. 32
A. 2/3 C. 2/7 B. 68 D. 54
B. 2/5 D. 2/9
84. Which of the following gives the greatest common factor of 98. logx 146 = 5, find log x
9x⁴y² and 12x³y³? A. 0.4329 C. 0.9967
A. 36 x³y² C. 3x³y² B. 2.209 D. 1.0822
B. 36x⁴y³ D. 36x³y²
99. If Log(x - y) = 3 and Log(x + y) = 4, then what is x/y?
85. Which of the following is not a zero of the polynomial equation A. 0.818 C. 0.143
4x⁵ + 12x⁴ - 41x³ - 99x² +10x + 24 = 0? B. 1.222 D. 1.325
A. -1/2 C. -3
B. -2 D. -4 100. Describe the roots of the equation 7x2 - 6x + 12 = 0.
A. real and unequal C. imaginary
86. Which of the following is a factor of x⁴ - 2x³ -5x² + 8x + 4? B. real and equal D. none of these
A. x² - 2x + 1 C. x² + 2x - 1
B. x² - 2x - 1 D. x² + 2x + 1
101. What is the sum of the possible values of x from the
equation x  2 2x  3  3  0 ? Situation 26 – A parcel of land is defined as follows:
A. -20 C. 20
Corner Northings Eastings
B. 26 D. -26
1 9835 9765
2 9700 9840
102.The curve y = x2 + bx + 256 cuts the x axis at (h, 0) and (k, 0). 3 9640 9572
If h and k are integers, what is the least value of b? 4 9735 9483
A. -40 C. -130
B. -68 D. -257 112.What is the length of line 1-2, in meter?
A. 154.4 C. 132.4
5x  1 B. 148.7 D. 127.5
103.What are the numerators of the partial fraction of ?
x  x 2
2
113.What is the azimuth of line 4-1?
A. 1 and 2 C. 2 and -2 A. 109.52° C. 70.48°
B. 2 and 3 D. 1 and -3 B. 160.48° D. 250.48°
114.Find the area of the lot in square meters.

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104.Find B if (x + 7)/(x2 - 7x + 10) = A/(x - 2) + B/(x - 5). A. 36 467 C. 38 185
A. -4 C. 4 B. 35 852 D. 37 572
B. 3 D. -3
115.Two stations A and B are 540m apart. From the following
triangulation stations C and D on opposite sides of AB angles
Trigo/Traverse/Geometry are observed.
∠ACD = 54° 12’; ∠DCB = 41° 24’
105.A tower cast a 49-meter shadow when the angle of elevation ∠ADC = 49° 18’; ∠BDC = 47° 12’

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of the sun is 54. How long will its shadow be when the angle Find the distance BC to the nearest meter.
of elevation of the sun is 32? A. 534 m C. 353 m
A. 84.35 m C. 95.46 m B. 335 m D. 333 m
B. 121.87 m D. 107.93 m
116.A corner lot of land is 35 m on one street and 25 m on the other
106.Two stations A and B were setup to determine the height of a street. The angle between the two lines of the street is 82°. The
mountain. The angles of elevation to the top of the mountain other two lines of the lot are respectively perpendicular to the
measured from stations A and B were 27.25 and 30.21, lines of the streets. Determine the area of the lot.
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respectively. Station A is 55 m above station B. Station B is A. 602.33 m² C. 753.62 m²
310 m closer to the mountain. If the elevation of station A is B. 640.71 m² D. 520.36 m²
421.63 m, what is the elevation of the top of the mountain?
A. 2154.87 m C. 2368.74 m 117.A, B and C are three known control stations and P is the
B. 2226.15 m D. 2663.54 m position of a sounding vessel which is to be located. If AC =
6925.50 m and AB = 6708.40 m, ∠BAC = 112°45’25”, ∠BPA =
107.From the top of a vertical cliff 80.0m high the angles of 25°32’40”, ∠APC = 45°35’50”, determine the distance AP if A
depression of two buoys lying due west of the cliff are 23◦ and is nearer to P than B and C.
15◦, respectively. How far are the buoys apart? A. 4225.32 m C. 4222.35 m
A. 134.2 m C. 123.4 m B. 4325.23 m D. 4335.43 m
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B. 117.6 m D. 110.1 m
118.PA and PB are tangents at A and B respectively of a circle
108.A circle of radius 9 cm is circumscribed about a triangle whose having a diameter AC. If AC and PB is prolonged, it will
area is 48.23 square cm. If one side of the triangle measure 18 intersect outside the circle at Q. If the value of the angle PQA is
cm, determine length of the shortest side of the triangle. 20°, find the value of the angle BAQ.
A. 4.37 m C. 5.64 m A. 56° C. 53°
B. 6.64 m D. 2.34 m B. 65° D. 35°
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Situation 25 – From a window “O” of a tall building 78 meters Situation 27 – Given the following field data:
above a level ground, the angle of depression of the top of a Coordinate of A (600m, 1500m)
tower is 38. From the base of the building, the angle of Coordinate of B (430m, 1680m)
elevation of the top of the tower is 22. Determine the Bearing of AP = S 82° 30’ W
following: Distance of AP = 85.32 m
109.The height of the tower in meters. 119.Determine the distance AB in meters.
A. 28.63 C. 25.47 A. 231.24 C. 220.47
B. 26.59 D. 30.65 B. 247.59 D. 210.42
110.The distance from the tower to the building in m. 120.Determine the distance PB in meters.
A. 68.54 C. 65.81 A. 209.35 C. 238.42
B. 75.85 D. 96.32 B. 232.14 D. 225.65
111.The angle subtended by the tower from point O in degrees. 121.Determine the bearing of line PB.
A. 12.54 C. 11.85 A. N 24° 5’ W C. N 20° 32’ W
B. 13.86 D. 10.54 B. N 21° 15’ W D. N 25° 09’ W
 125.Two sides of a parallelogram measure 68 ft and 83 ft and the
122.Each interior angle of a regular nonagon is: shorter diagonal is 42 ft. Determine the length of the longer
A. 135° C. 120° diagonal in cm.
B. 150° D. 140° A. 3888 C. 4633
B. 3999 D. 4444
123.When mixing a quantity of paints, dyes of four different
colours are used in the ratio of 7 : 3 : 19 : 5. If the mass of the 126.The sides of a triangular lot are 130 m, 180 m, and 190 m. The
first dye used is 3½ g, determine the total mass of the dyes lot is to be divided by a line bisecting the longest side and
used. drawn from the opposite vertex. The length of this dividing
A. 16.5 g C. 17.5 g line is:
B. 17 g D. 18 g A. 125 m C. 115 m
B. 156 m D. 110 m
124.Determine the 6th term of the sequence 8, 12, 18, …
A. 78.25 C. 80.50
B. 60.75 D. 65.25

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PLEASE SUBMIT THIS TEST QUESTIONNAIRE TOGETHER WITH YOUR ANSWER SHEET TO YOUR PROCTOR.

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Answer Key
1 C 11 C 21 B 31 C 41 A 51 A 61 A 71 A 81 A 91 A 101 B 111 C 121 A
2 A 12 A 22 B 32 D 42 B 52 A 62 C 72 A 82 D 92 D 102 D 112 A 122 D
3 B 13 B 23 C 33 D 43 C 53 C 63 C 73 B 83 D 93 D 103 B 113 D 123 B
4 A 14 C 24 C 34 C 44 D 54 B 64 B 74 D 84 C 94 C 104 C 114 C 124 B
5 D 15 A 25 B 35 B 45 D 55 D 65 C 75 C 85 C 95 A 105 D 115 C 125 D
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6 B 16 A 26 C 36 D 46 D 56 A 66 C 76 D 86 B 96 D 106 B 116 B 126 A
7 D 17 D 27 A 37 C 47 A 57 B 67 B 77 B 87 C 97 D 107 D 117 A
8 D 18 D 28 D 38 A 48 D 58 A 68 A 78 D 88 C 98 A 108 C 118 D
9 B 19 C 29 A 39 A 49 C 59 A 69 B 79 C 89 A 99 B 109 B 119 B
10 B 20 D 30 D 40 D 50 D 60 D 70 D 80 C 90 B 100 C 110 C 120 A
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