SAINT LOUIS UNIVERSITY Name: _____________________________________ Score:

SCHOOL OF ENGINEERING AND ARCHITECTURE Schedule: 12:30-1:30 PM S Class Code: 2752

2nd Sem 2022– 2023 Name of Instructor: Engr. Frederick D. Navo

CE 4251: CE BOARD REVIEW (W/ MOCK BOARD) 7. An amount of P20,000 is paid for the first year, P25,000 for
the second year, and so on increasing at P5,000 per year. What
SUBJECT 1: APPLIED MATHEMATICS, SURVEYING, is the sum of all payments after 12 years?
PRINCIPLES OF TRANSPORTATION AND HIGHWAY a) P 520,000
b) P 570,000
ENGINEERING, CONSTRUCTION MANAGEMENT AND
c) P 630,000
METHODS d) P 610,000
Problem SET 01
8. The process of providing the required water and
Instruction: maintaining a favorable temperature for a period of time after
Choose the best answer. placing concrete is referred to as:
a) Curing
1. Given that y : x = x : 15, find x if y = 4x. b) Screeding
a) 30 c) Troweling
b) 75 d) Finishing
c) 45
d) 60 9. One student can solve a math problem is 6 minutes. Another
student can solve a problem in 5 minutes. How long can they
2. If x/y gives a remainder of 0 and z/y gives a remainder of 3, solve 110 problems?
what is the remainder of xz/y? a) 300 minutes
a) 0 b) 330 minutes
b) 3 c) 270 minutes
c) 2 d) 290 minutes
d) 1
10. A car travelled for p hours with a velocity of magnitude q
4 6 1/4
3. Which of the following is equivalent to [16𝑎 𝑏 ] kph, then travels the same direction for r hours with velocity
a) 3𝑎𝑏 2/3 of magnitude s kph. What is the average velocity during the
b) 2𝑎𝑏 3/2 travel?
c) 4𝑎𝑏 3/2 a) (pq + rs)/(p + r)
d) 4𝑎𝑏 2/3 b) (pr + qs)/(p + r)
c) (pr + qs)/(q + s)
4. The famous pyramid of Egypt having an altitude of 15m has d) (pq + rs)/(q + s)
a weight of 4000 kg. It has a square base at the bottom. At what
distance from its base must it be cut by a plane parallel to each 11. The refractive index of water is 1.33. What is the angle of
base so that the two solids of equal weight will be formed? refraction of light in air strikes water at an angle of incidence
a) 6.8 of 24 degrees?
b) 3.1 a) 17.8 degrees
c) 5.3 b) 18.7 degrees
d) 4.8 c) 23.8 degrees
d) 21.7 degrees
5. The population of bacteria at any time “t” is given by An =
Ao 𝑒 0.584𝑡 . If Ao = 4, find t when An = 2500. 12. A topographic surveying map using a scale 1cm = 40m, and
a) 13.23 with a contour interval of 1.0 m, the distance scaled on the map
b) 6.54 between two adjacent contours is 15 mm. Determine the slope
c) 9.36 of the ground in percent
d) 11.02 a) 1.66%
b) 1.77%
6. The nth term of an arithmetic progression is 𝑎𝑛 = 3n + 5. c) 1.76%
What is the common difference? d) 1.67%
a) 3
b) -3 FOR 13 TO 15: A box contains 24 red balls, 27 green balls, and
c) 5 30 blue balls. If three balls are drawn in succession without
d) -5 replacement, what is the probability that:

13. All three balls are red?

a) 0.024
 b) 0.062 c) 876 ft^2
c) 0.034 d) 852 ft^2
d) 0.048
22. Two ships leave port at the same time, one ship sailing in
14. All three balls are green? the direction of N 23 deg E at a speed of 11mph, and a second
a) 0.062 ship sailing in the direction S 67 deg E at 15mph. Approximate
b) 0.034 the bearing from the second ship to the first, one hour later
c) 0.048 a) N 28 deg E
d) 0.024 b) N 31 deg W
c) N 32 deg W
15. All three balls are blue? d) N 23 deg E
a) 0.062
b) 0.048 23. The interior angles of a triangular lot ABC are A = 80° and
c) 0.024 B = 60°. Which of the following is correct? (Note: a, b, and c
d) 0.034 are the corresponding sides opposite angles A, B, and C,
respectively)
FOR 16 TO 18: A piggy bank has twenty 10-peso coins, thirty a) b < a < c
5-peso coins, and twenty-four 1-peso coin. Three coins are b) c < b < a
drawn without replacement. c) c < b > a
d) a < c > b
16. What is the probability that the three are 10-peso coins?
a) 0.048 24. A right triangle ABC have its right angle at B. If AC = x + y
b) 0.063 and AB = x – y, what is the value of side BC?
c) 0.031 a) 2xy
d) 0.018 b) 4√𝑥𝑦
c) 4xy
17. What is the probability that the three are 5-peso coins? d) 2√𝑥𝑦
a) 0.031
b) 0.018
25. What are the capacity requirement for all scaffoldings?
c) 0.048
a) At least four times its own weight
d) 0.063
b) At least six times its own weight
c) At most six times its own weight
18. What is the probability that the three are 1-peso coins?
d) At most five times its own weight
a) 0.018
b) 0.063
26. If the perpendicular bisectors of two sides of a triangle
c) 0.031
meets on the third side, what kind of triangle is being
d) 0.048
described?
a) Scalene triangle
19. It is described as the expected number of production
b) Obtuse triangle
a) Standard deviation
c) Right triangle
b) Mean
d) Acute triangle
c) Reliability
d) Variance
27. A 6-m long ladder leans against a vertical wall. If the top of
the ladder is 4.8 m above the floor, how far is its foot from the
20. It is the single most important environmental factor in the
wall?
broad field of coastal engineering.
a) 3.6 m
a) Wave
b) 3.8 m
b) Sea
c) 3.4 m
c) Coastal erosion
d) 3.2 m
d) Sand
28. A surveyor is 1190 m and 2290 m away from the two edges
21. A painter needs to find the area of the gable end of a house.
of a lake. If the angle between measurements is 71°, what is
What is the area of the gable if it is a triangle with two sides of
the width of the lake?
42ft. that meet at a 105-degree angle?
a) 2,124.32 m
a) 456 ft^2
b) 2,321.78 m
b) 324 ft^2
c) 2,268.45 m
Page 2 of 5
 d) 2,210.38 m to the edge of the cliff at a point B. Point B is 425 m nearer but
25.6 m lower than A. The angle of elevation was observed to
29. The length of the sides of a triangle are AB = 20 cm, BC = be 36.3° from B. If the elevation of A is 602 m, what is the
24 cm, and AC = 17 cm. What is the angle opposite to side BC? elevation of the top of the cliff?
a) 44.31° a) 885.325 m
b) 83.54° b) 883.075 m
c) 55.26° c) 881.455 m
d) 80.43° d) 880.325 m

30. It provides the detailed requirements for the materials, 36. The distance from A to B is 12 m, from B to C is 4 m, and
equipment, and workmanship to be incorporated into the from C t D is 5 m. What is the minimum distance from A to D?
project. a) 11 m
a) Bid documents b) 0
b) Specifications c) 3 m
c) Estimates d) 7 m
d) Plans
37. Two circles are tangent externally with each other. How
31. A ball is thrown downward from the top of a 180 ft building many possible lines can be drawn that are common tangents
with an initial velocity of 20 ft/s. The height of the ball h after to the two circles?
t seconds is given by the equation h= - 16t^2 20t + 180. How a) 2
long after the ball is thrown will it strike the ground? b) 3
a) 2.8 s c) 1
b) 3.5 s d) 0
c) 1.8 s
d) 4.1 s 38. The basic lane width appropriate for national road
a) 3.35 m
32. When a family of four with a total mass of 200kg step into b) 2.40 m
their 1200 kg car, the cars spring compresses 3cm. assuming c) 1.80 m
they act as a single spring, what is the spring constant of the d) 5.00 m
cars spring? How far will the car lower if loaded with 300kg
rather than 200kg? 39. If all midpoints of the sides of a triangle are connected,
a) 65 kN/m , 0.045m what fraction is the area of the smaller triangle formed to the
b) 63 kN/m , 0.030m area of the original triangle.
c) 62 kN/m , 0.030m a) 1/3
d) 61 kN/m , 0.045m b) 1/4
c) 1/8
d) 1/2
33. A fisherman at sea observed that the angle of elevation of
a cliff is 12°. If the height of the cliff above sea level is 30 m, 40. If the one side of a rectangle is increased by 25%, what is
how far is he from the shore? the effect on the other side to maintain the same area?
a) 141.14 m a) decreased by 80%
b) 163.52 m b) decreased by 20%
c) 124.87 m c) decreased by 30%
d) 104.58 m d) decreased by 10%

34. A man pushes a 50.0 kg box across a level floor at a 41. A rectangular lot has a perimeter of 60 m. Find the area of
constant speed of 1.00 m/s for 10.0 s. If the coefficient of the lot if one ide is 6 m shorter than the other.
friction between the box and the floor is 0.200 determine the a) 224 𝑚2
average power output by man? b) 216 𝑚2
a) 100 watts c) 324 𝑚2
b) 88 watts d) 196 𝑚2
c) 98 watts
d) 105 watts 42. Two wheels, one 60 cm in diameter and the other 40 cm in
diameter are rolling along a straight line with the same linear
35. An inaccessible cliff was sighted from point A. The angle of speed. How many revolutions has the larger wheel made if the
elevation was observed to be 18.45°. The surveyor went closer smaller wheel has made 360 revolutions?
Page 3 of 5
 a) 200 49. A rectangular block have sides measuring 3 cm by 4 cm by
b) 240 12 cm. Determine the perimeter of the triangle formed by the
c) 280 diagonals of three adjacent faces.
d) 300 a) 29.50 cm
43. Given two planes A and B. Line C is perpendicular to plane b) 30.37 cm
A and also perpendicular to plane B. Which of the following is c) 29.20 cm
true? d) 30.02 cm
a) A and B intersect but no perpendicular
b) A and B are perpendicular 50. A rectangular parallelepiped with an altitude of 10 cm have
c) A and B are parallel its width decreasing by 2cm/min and length increasing at 8
d) A and B are skew cm/min. How fast is the total surface area changing when its
width is 16 cm and length is 22 cm?
44. Line A and B intersect at point O. Line C is perpendicular to a) +224 𝑐𝑚2 /min
both A and B at O. Which of the following is true? b) -312 𝑐𝑚2 /min
a) Lines A and B are perpendicular c) -242 𝑐𝑚2 /min
b) Line C in oblique to the plane described by Lines A and d) +288 𝑐𝑚2 /min
B
c) Line C is parallel to the plane described by Lines A and 51. A cubical block of wood 8 cm on each side is cut by a plane
B parallel to one face. What additional surface area is produced?
d) Line C is perpendicular to the plane described by lines a) the same
A and B b) 256 𝑐𝑚2
c) 64 𝑐𝑚2
45. The angle of elevation of top of the tree from point A is 19.9 d) 128 𝑐𝑚2
degrees. From point B, 50 m closer to the tree, the angle of
elevation is 21.8 degrees. Determine the height of the tree. 52. A log 8√2 cm in diameter and 16 cm long is to be cut into
a) 123.63 m equal cubes, if each cube is to be 4 cm on each side, determine
b) 190.63 m the maximum volume of cubes that can be cut from the log.
c) 120.56 m a) 448
d) 180.67 m b) 256
c) 1024
46. A concrete block 70 cm x 80 cm x 90 cm is placed inside a d) 512
tall cylinder tank 1.5 m in diameter containing 1.8 m deep
water. What is the rise in the water level? FOR 53 TO 55: A block of copper having a mass of 70 kg is
a) 24.58 cm drawn out to make 540 m of wire of uniform cross-section.
b) 32.96 cm Given that the density of copper is 8.911 g/𝑐𝑚3 , calculate the
c) 36.54 cm following:
d) 28.52 cm
53. The volume of copper.
47. A rectangular tank 6 m wide, 12 m long and 18 m high is a) 7135.58 𝑐𝑚3
2/3 full of water. If 120 𝑚3 of water is added, how much (in b) 7856.34 𝑐𝑚3
percent) is the tank filled with water? c) 7625.27 𝑐𝑚3
a) 72.45% d) 8547.01 𝑐𝑚3
b) 79.63%
c) 68.57% 54. The cross-sectional area of the wire.
d) 75.93% a) 13.21 𝑚𝑚3
b) 14.55 𝑚𝑚3
48. The opposite faces of a cube are ABCD and EFGH. If the c) 14.12 𝑚𝑚3
edge of the cube is 1 m, what is the distance between the d) 15.83 𝑚𝑚3
midpoint of edge AB and midpoint of edge DH.
a) 1.225 m 55. The diameter of the cross-section of the wire.
b) 1.325 m a) 4.10 mm
c) 1.425 m b) 4.24 mm
d) 1.125 m c) 4.49 mm
d) 4.30 mm

Page 4 of 5
FOR 56 TO 58: A frustum of a sphere have base diameters of
182 cm and 32.9 cm. The thickness of the frustum is 2.6 cm.

56. What is the volume of frustum?

a) 1539.3 𝑐𝑚3
b) 1624.5 𝑐𝑚3
c) 1342.7 𝑐𝑚3
d) 1452.6 𝑐𝑚3

57. What is the radius of the sphere?

a) 32.54 cm
b) 38.51 cm
c) 34.86 cm
d) 40.25 cm

58. What is the curved surface area of the frustum?

a) 629.02 𝑐𝑚2
b) 732.65 𝑐𝑚2
c) 569.43 𝑐𝑚2
d) 601.47 𝑐𝑚2

59. A Particle position in the xy plane at any time t is given by

x=2t^2 + 3 and y=t^4. Find the x-component of the particles
velocity at time t=5.
Hint: Take the derivative with respect to t
a) 23
b) 22
c) 21
d) 20

60. A rectangular box is to be made without a cover. The length

of the base of the box is twice its width. What is the width of
the box to have a minimum surface area if it has a capacity of
2.4 cu.m
a) w = 1.55
b) w = 1.23
c) w = 1.45
d) w = 1.22

Page 5 of 5