DE

dy 1
1. Solve dx
+ y
ey²+3 = 0 , y ≠ 0

2 +3
a. ey dx = ex c. y2 + e dx = ex
1 −y2 1 y2 + e
b. 2
e = 3 e3x + c d. y
dx = ex

2. xy3 dx + (y+1)e-x dy = 0
y+1
a. y3
dy + C c. (y-2 + y-3) + C
1 1 1 1
b. (y+1)ex = y
+ 2y2
+C d. (x-1)ex = y
+ 2y2
+C

dy
3. dx
= (x+y)2
a. x + y = tan(x + C) c. v2 + 1 = tan(x + C)
b. tan-1v = x + C d. tan-1 (x + y) = 1 + C

4. (y + 2xy2) dx + (2x + 3x2y) dy = 0

a. x2y + x2y3 = C c. xy2 + x3y2 = C
b. xy2 + x2y3 = C d. x2y + x3y2 = C

5. (3x4 + y) dx + (2x2y - x) dy = 0
y y
a. x2 + y3 - x
=C c. x3 + y2 - x
=C
b. 3x2dx + 2ydy = C d. 2x2dx + 2ydy = C

STATIC
6. The vertical force P of magnitude 100kN is applied to the frame shown in the
figure. Resolve P into components that are parallel to the members AB and AC of
the truss.

a. PAB = 100kN, PBC = 186.3kN c. PAB = 100kN, PBC = 183.6kN

b. PAB = 100kN, PBC = 163.8kN d. PAB = 100kN, PBC = 136.8kN
7. The screw eye in the figure is subjected to two forces F1 and F2. Determine the
magnitude and direction of the resultant force.

a. R = 231N, θ = 54.8ᵒ c. R = 231N, θ = 39.8ᵒ

b. R = 213N, θ = 39.8ᵒ d. R = 213N, θ = 54.8ᵒ
8. Determine the magnitude of the resultant force FR if FR is directed along the
positive y axis.

a. 629 N c. 786 N
b. 678 N d. 875 N

9. Determine the magnitudes of the projection of the force F in the figure onto the u
and v axis.

a. Fu = 96.6 N, Fv = 70.7 N c. Fu = 108.5 N, Fv = 84.3 N

b. Fu = 70.7 N, Fv = 96.6 N d. Fu = 84.3 N, Fv = 108.5 N
10. Determine the tension in cables BC necessary to support the 60-kg cylinder.

a. 420 N c. 476 N
b. 649 N d. 585 N

11. The 200-kg crate is suspended using ropes AB and AC. Each rope can withstand
a maximum force of 10kN before it breaks. If AB always remains horizontal,
determine the smallest angle θ to which the crate can be suspended before one of
the ropes breaks.

a. 13.6ᵒ c. 10.8ᵒ
b. 11.3ᵒ d. 12.5ᵒ

12. Determine the resultant moment of the four forces acting on the rod shown in the
figure about point O.

a. 334 N.m c. 284 N.m

b. 465 N.m d. 637 N.m
13. Determine the vertical component at point B of the reaction on the beam caused
by the pin at B and the rocker at A. Neglect the weight of the beam.

a. 319 N c. 405 N
b. 424 N d. 378 N

14. The box wrench is used to tighten the bolt at A. If the wrench does not turn when
the load is applied to the handle, determine the torque or moment applied to the
bolt.

a. 62.3 N.m c. 43.5 N.m

b. 74.0 N.m d. 32.6 N.m

15. The uniform 10-kg ladder rests against the smooth wall at B, and the end A rests
on the rough horizontal plane for which the coefficient of static friction is u = 0.3.
Determine the angle of inclination θ.

a. 60ᵒ c. 50ᵒ
b. 48ᵒ d. 59ᵒ
16. A 10-kg steel wheel has a radius of 100mm and rests on an inclined plane made
of soft wood. If θ is increased so that the wheel begins to roll down the incline
with constant velocity when θ = 1.2ᴼ, determine the coefficient of rolling
resistance.

a. 2.09 mm c. 2.29 mm
b. 2.19 mm d. 2.39 mm

17. What is the centroid of the plate area shown in the figure.

a. x = - 0.438 ft, y = 2.12 ft c. x = - 0.348 ft, y = 1.22 ft

b. x = - 0.834 ft, y = 2.12 ft d. x = - 0.483 ft, y = 1.22 ft

18. What is the moment of inertia for the cross-sectional area of the member shown
in the figure about x centroidal axis.

a. Ix = 5.6x109 mm4 c. Ix = 9.2x109 mm4

b. Ix = 2.9x109 mm4 d. Ix = 6.5x109 mm4
SURVEYING
19. The readings obtained from two-peg test carried out on an automatic level with a
single level staff set up alternately at two pegs A and B placed 50m apart were as
follows:

Calculate the collimation error of the level per 50m of sight

a. - 0.10m per 50m c. - 0.20m per 50m
b. - 0.40m per 50m d. - 0.30m per 50m

20. Reciprocal leveling gives the following readings in meters from a set up near A:
on A,2.558; on B, 1.883, 1.886, and 1.885. At the set up near B: on B, 1.555; on
A, 2.228, 2.226, and 2.229. The elevation of A is 158.618m. Determine the
elevation of B.
a. 159.291m c. 176.381m
b. 160.291m d. 183.451m

21. Reciprocal leveling across canyon provides the data listed (in meters). The
elevation of Y is 2265.879ft. The elevation of X is required. Instrument at X:
+3.182, -S = 9.365, 9.370, and 9.368. Instrument at Y: +S = 10.223, -S = 4.037,
4.041, and 4.038. Determine the misclosure.
a. - 6.18, - 6.20 c. - 7.21, - 7.23
b. - 6.16, - 6.18 d. - 7.46, - 7.47

22. Determine the azimuth of the side CD if the corner of the lot have the following
X and Y coordinates (in ft.): A(5000.00, 5000.00); B (5289.67, 5436.12);
C(4884.96, 5354.54); D(4756.66, 5068.37)
a. 223ᵒ10’58” c. 258ᵒ36’12”
b. 204ᵒ08’54” d. 33ᵒ35’31”

23. Compute the length of the side BC of a closed-polygon traverse whose corners
have the following X and Y coordinates (in meters): A(8000.00, 5000.00); B
(2650.00, 4702.906); C(1752.028, 2015.453); D(1912.303, 1511.635)
a. 7016.32 m c. 2833.51 m
b. 5358.24 m d. 528.70 m
ESECON
24. What lump-sum amount of interest will be paid on a $10,000 loan that was made
on August 1, 2012, and repaid on November 1, 2016, with ordinary simple
interest at 10% per year?
a. $ 6,437 c. $ 8,250
b. $ 7,230 d. $ 8,870

25. How long does it take (to the nearest whole year) for $1,000 to quadruple in value
when the interest rate is 15% per year?
a. 15 years c. 8 years
b. 10 years d. 12 years

26. Your spendthrift cousin wants to buy a fancy watch for $425. Instead, you
suggested that she could buy an inexpensive watch for $25 and save the
difference of $400. Your cousin agrees with your idea and invests $400 for 40
years in an account earning 9% interest per year. How much will she accumulate
in this account after 40 years have passed?
a. $ 12,673.86 c. $ 12,365.67
b. $ 12,763.36 d. $ 12,563.76

27. An economy is experiencing inflation at an annual rate of 6%. If this continues,

what will $100 be worth five years from now, in terms of today's dollars?
a. $74.73 c. $47.37
b. $73.74 d. $47.34

28. Suppose that a man lends $1000 for four years at 12% per year simple interest. At
the end of the four years, he invests the entire amount which he then has for 10
years at 8% interest per year, compounded annually. How much money will he
have at the end of the 14-year period?
a. $ 3195.21 c. $ 3591.21
b. $ 3951.21 d. $ 3159.21
DYNAMICS
29. If a particle has an initial velocity of v0 = 12 ft/s to the right, at s0 = 0, determine
its position when t = 10 s, if a = 2 ft/s2 to the left.
a. 20 ft c. 40 ft
b. 30 ft d. 50 ft

30. The conveyor belt is moving downward at 4 m/s. If the coefficient of static
friction between the conveyor and the 15-kg package B is us = 0.8, determine the
shortest time the belt can stop so that the package does not slide on the belt.

a. 1.98 sec c. 3.47 sec

b. 2.11 sec d. 2.75 sec

31. Block A has a weight of 8 lb and block B has a weight of 6 lb. They rest on a
surface for which the coefficient of kinetic friction is uk = 0.2. If the spring has a
stiffness of k = 20 lb/ft, and it is compressed 0.2 ft, determine the acceleration of
each block just after they are released.

a. aA = 15 ft/s2 , aB = 9.66 ft/s2 c. aA = 10.8 ft/s2 , aB = 12 ft/s2

b. aA = 9.66 ft/s2 , aB = 15 ft/s2 d. aA = 12 ft/s2 , aB = 10.8 ft/s2

32. The acceleration of a rocket traveling upward is given by a = (6 + 0.02s) m/s2,

where s is in meters. Determine the time needed for the rocket to reach an altitude
of s = 100 m. Initially, v = 0 and s = 0 when t = 0.
a. 4.38 sec c. 6.45 sec
b. 8.74 sec d. 5.62 sec
33. The collar has a mass of 20 kg and slides along the smooth rod. Two springs are
attached to it and the ends of the rod as shown. If each spring has an
uncompressed length of 1 m and the collar has a speed of 2 m/s when s = 0,
determine the maximum compression of each spring due to the back-and-forth
(oscillating) motion of the collar.

a. 0.837 m c. 0.730 m
b. 0.305 m d. 0.394 m

34. The velocity of a car is plotted as shown. Determine the total distance the car
moves until it stops.

a. 500 m c. 600 m
b. 700 m d. 800 m

35. Determine the maximum constant speed at which the pilot can travel around the
vertical curve having a radius of curvature p = 800 m, so that he experiences a
maximum acceleration an = 8g = 78.5 m/s2. If he has a mass of 70 kg, determine
the normal force he exerts on the seat of the airplane when the plane is traveling
at this speed and is at its lowest point.

a. v = 265 m/s , N = 8.91 kN c. v = 251 m/s , N = 6.18 kN

b. v = 274 m/s , N = 9.76 kN d. v = 281 m/s , N = 7.04 kN
DEFORMABLE BODIES
36. The beam AB is fixed to the wall and has a uniform weight of 80 lb ft. If the
trolley supports a load of 1500 lb, determine the moment at point C acting on the
cross sections.

a. - 38.5 kip.ft c. - 0.36 kip.ft

b. - 47.5 kip.ft d. - 2.71 kip.ft

37. Determine the moment at D on the cross section of the Beam. Assume the
reactions at the supports A and B are vertical.

a. 3.94 kN.m c. 2.81 kN.m

b. 4.85 kN.m d. 6.89 kN.m

38. The bolt shank is subjected to a tension of 80 lb. Determine the moment at C
acting on the cross section.

a. - 350 lb.in c. - 560 lb.in

b. - 720 lb.in d. - 480 lb.in
39. Determine shear at point C acting on the cross section. Assume the reactions at
the supports A and B are vertical.

a. 31.5 kip c. 4.5 kip

b. 9.7 kip d. 18 kip

40. If the block is subjected to the centrally applied force of 600 kN, determine the
average normal stress in the material.

a. 10 Mpa c. 8 Mpa
b. 5 Mpa d. 12 Mpa

41. Determine the average shear stress developed in pin A of the truss. A horizontal
force of P = 40KN is applied to joint C. Each pin has a diameter of 25 mm and is
subjected to double shear.

a. 50.9 Mpa c. 25 Mpa

b. 8.96 Mpa d. 72.9 Mpa
42. The 20-kg chandelier is suspended from the wall and ceiling using rods AB and
BC, which have diameters of 3 mm and 4 mm, respectively. Determine the angle
θ so that the average normal stress in both rods is the same.

a. 46.5ᵒ c. 60.8ᵒ
b. 65.3ᵒ d. 58.4ᵒ
43. The driver of the sports car applies his rear brakes and causes the tires to slip. If
the normal force on each rear tire is 400 lb and the coefficient of kinetic friction
between the tires and the pavement is , determine the average shear stress
developed by the friction force on the tires. Assume the rubber of the tires is
flexible and each tire is filled with an air pressure of 32 psi.

a. 16 psi c. 18 psi
b. 17 psi d. 19 psi

44. The lever is attached to the shaft A using a key that has a width d and length of
25 mm. If the shaft is fixed and a vertical force of 200 N is applied perpendicular
to the handle, determine the dimension d if the allowable shear stress for the key
is tallow = 35 MPa.

a. 7.68 mm c. 6.85 mm
b. 8.42 mm d. 5.71 mm
45. The joint is fastened together using two bolts. Determine the required diameter of
the bolts if the failure shear stress for the bolts is Tfail = 350Mpa. Use a factor of
safety for shear of F.S. = 2.5.

a. 19.61 mm c. 10.47 mm
b. 13.5 mm d. 15.85 mm

46. The two aluminum rods AB and AC have diameters of 10 mm and 8 mm,
respectively. Determine the largest vertical force P that can be supported.The
allowable tensile stress for the aluminum is 150 MPa.

a. 7.54 kN c. 17.21 kN
b. 8.95 kN d. 23.18 kN

47. If the allowable bearing stress for the material under the supports at A and B is
determine the maximum load P that can be applied to the beam. The bearing
plates and have square cross sections of 150 mm * 150 mm and respectively.

a. 67.4 kN c. 87.3 kN
b. 52.8 kN d. 72.5 kN
48. A specimen is originally 1 ft long, has a diameter of 0.5 in., and is subjected to a
force of 500 lb. When the force is increased from 500 lb to 1800 lb, the specimen
elongates 0.009 in. Determine the modulus of elasticity for the material if it
remains linear elastic.
a. 7.54x103 ksi c. 8.83x103 ksi
b. 6.63x103 ksi d. 9.61x103 ksi

49. A bar having a length of 5 in. and cross-sectional area of 0.7 in.2 is subjected to
an axial force of 8000 lb. If the bar stretches 0.002 in., determine the modulus of
elasticity of the material. The material has linear-elastic behavior.

a. 14.96x103 ksi c. 46.28x103 ksi

b. 28.6x103 ksi d. 39.15x103 ksi
50. The joint is made from three A992 steel plates that are bonded together at their
seams. Determine the displacement of end A with respect to end B when the joint
is subjected to the axial loads shown. Each plate has a thickness of 5 mm.

a. 0.491 mm c. 0.639 mm
b. 0.836 mm d. 0.386 mm

51. The copper pipe has an outer diameter of 40 mm and an inner diameter of 37 mm.
If it is tightly secured to the wall at A and three torques are applied to it as shown,
determine the absolute maximum shear stress developed in the pipe.

a. 67.8 Mpa c. 26.7 Mpa

b. 87.38 Mpa d. 37.6 Mpa
ESMAN
52. One of the project stages which involves the architectural and engineering design
of the entire project. It culminates in the preparation of final working drawings
and specifications for the total construction program.
a. Planning and Definition c. Procurement and Construction
b. Design d. Bidding

53. This refers to the ordering, expediting, and delivering of key project equipment
and materials, especially those that may involve long delivery periods. This
function may or may not be handled separately from the construction process
itself.
a. Planning c. Procurement
b. Design d. Construction

54. This refers to the overlapping accomplishment of project design and construction.
As the design of progressive phases of the work is finalized, these work packages
are put under contract, a process also commonly referred to as phased
construction.
a. Fast Tracking c. Construction Services
b. Construction Contract Services d. Design-Construct

55. The term is applied to the provision of professional management services to the
owner of a construction project with the objective of achieving high quality at
minimum cost.
a. Project Planning c. Project Quality
b. Project Manager d. Construction Management

56. The person organizes, plans, schedules, and controls all the work of the project
and is responsible for getting the project completed within the time and cost
limitations.
a. Contractor c. Architect
b. Project Manager d. Engineer
TERMS
57. The bending effect at any section of a structural element equal to the algebraic
sum of the moments of the vertical and horizontal forces, with respect to the
centroidal axis of a member, acting on a freebody of the member.
a. Bending Moment c. Deflection
b. Moment Diagram d. Tension

58. It is a force (and hence has a magnitude and direction) which refers to the
gravitational attraction of the earth on a quantity of mass m.
a. Volume c. Weight
b. Mass d. Force

59. This type of survey establish a network of horizontal and vertical monuments that
serve as a reference framework for initiating other surveys.
a. Cadastral Survey c. Topographic Survey
b. Control Surveys d. Construction Survey

60. A science that deals with the production and consumption of goods and services
and the distribution and rendering of these for human welfare.
a. Sociology c. Psychology
b. Political Science d. Economics

61. It is a branch of the physical sciences that is concerned with the state of rest or
motion of bodies subjected to the action of forces.
a. Dynamics c. Kinematics
b. Mechanics d. Kinetics

62. It is the quantitative measure of the inertia or resistance to change in motion of a

body. It may also be considered as the quantity of matter in a body as well as the
property which gives rise to gravitational attraction.
a. Gravity c. Mass
b. Weight d. Force

63. It is a body whose changes in shape are negligible compared with the overall
dimensions of the body or with the changes in position of the body as a whole.
a. Rigid Bodies c. Plastic Bodies
b. Elastic Bodies d. Fluid Bodies

64. It is defined as something made up of interdependent parts in a definite pattern of

organization, an interrelation parts as determined by the general character of the
whole.
a. Mechanism c. Structure
b. System d. Machine