1
Q
- The Calculation of the probability that the Critical Path will be completed by time T.
I. Assumes that activity times are statistically independent.
II. Assumes that total time of critical path has approximately a BETA distribution.
III. Requires knowledge of the standard deviation for all activates in the network.
A. II only
B. I only
C. III only
D. All of the Above
A
B
2
Q
- The Process of Bringing each roadway layer to its final grade.
A. Ground Modification
B. Trimming
C. Grading
D. Earthworks
A
B
3
Q
- Bringing of a Concrete surface to true grase with enough mortar to provide the desired finish.
A. Floating
B. Sreening
C. Leveling
D. Troweling
A
C
4
Q
- Wearing away of the pavement surface caused by dislodging of aggregate particles and the loss of asphalt binder. This is usually a result of insufficient asphalt binder in the mix or stripping of asphalt from the paticles of aggregates.
A. Block Cracking
B. Transverse Cracking
C. Longitudinal Cracking
D. Raveling
A
D
5
Q
- Simplify (x-a)(x-b)(x-c)(x-d)…(x-y)(x-z)
a. [ π₯^26 - (ππππ… π¦π§)^26 ]
b. 0
c. [ π₯^26 + (ππππ… π¦π§)^26 ]
d. 1
A
B
6
Q
- A father is three times as old as his twin sons. If the sum of their ages in two years will be 81, how old is the father now?
a. 45
b. 40
c. 35
d. 30
A
A
6
Q
- If the altitude and base of a parallelogram are increased by 5 inches, the area will increase by 50 in^2. if the altitude is increased by 3 in. and the base is decreased by 2 in., the area will increase by 5 in^2 . Determine the original value of the base of the parallelogram
a. 3.2 in.
b. 4.2 in.
c. 3.8 in.
d. 5.2 in.
A
B
7
Q
- The segment from (-1, 4) to (2, -2) is extended three times its own length. Find the terminal point.
a. (11, -24)
b. (11, -18)
c. (-11, -20)
d. (11, -20)
A
D
8
Q
- A tank in a shape of a frustum of a cone is 10m high with an upper radius of 3m and inner radius of 1m. It is filled with 6m height of water. If pump is located 1m above the top , find the work done by the pump to empty the tank.
A. 3239.7
B. 2379.3
C. 9733.2
D. 2337.9
A
A
9
Q
- In a certain college, 4% of the men and 1% of the women are taller than 6ft. Furthermore, 60% of the students are women. If a student is selected at random and is taller than 6ft, find the probability that it’s a woman.
A. 5/11
B. 9/11
C. 3/11
D. 7/11
A
C
9
Q
- Sand falling from a chute forms a conical pile whose altitude is always equal to 4/3 the radius of the base. How fast is the volume increasing when the radius of the base is 3 ft. and is increasing at the rate of 3 in/min?
a) 3Ο ft/min
b) 36Ο ft/min
c) 30Ο ft/min
d) 3.6Ο ft/min
A
A
10
Q
- A test consists of 6 questions, and to pass the test, a student has to answer at least 4 questions correctly, each question has 3 possible answers of which only one is correct. If a student guesses on each question, what is the probability that the student will pass the test?
A. 0.08
B. 0.10
C. 0.90
D. 0.98
A
B
11
Q
- A parking lot charges x for the first hour of fraction of an hour and 2/3 x for each hour or fraction thereafter. Smith parks 7 times as long as Jones but pays only 3 times as much. How long did each park? (The clock registers only 5-minute intervals)
a) 3.5 & 0.5
b) 3.0 & 1.0
c) 4.0 & 0.5
d) 2.5 & 2.0
A
A
12
Q
- A farmer wants to fence an area of 1.5 million square feet in a rectangular field and then divide it in half with a fence parallel to one of the sides of the rectangle. What would be the dimension of the field so as to minimize the cost of the fence?
a) 1000 ft x 1500 ft
b) 2000 ft x 750 ft
c) 1250 ft by 1200 ft
d) 1224.74 ft by 1224.74 ft
A
A
13
Q
- The difference between the highest and the lowest data is called _____.
a) Standard Deviation
b) First Quartile
c) Range
d) Interquartile Range
A
C
13
Q
- A basketball team is composed of 3 point guards, 4 shooting guards, 2 small forwads,1 power forward and 3 centers. How many groups of 5 can be formed if the group should be composed of players with different positions?
a) 13
b) 36
c) 30
d) 72
A
D
14
Q
- Charlie Meyer paid $24 for the rights to Manhattan Island in 1626. What are the corresponding values in 2006 if i=5%?
a) $2,704,860,603
b) $2,740,860,602
c) $2,860,704,602
d) $2,860,407,602
A
A
15
Q
- A credit charge interest at 1.5% per month. What is the nominal interest rates?
A. 18.00%
B. 1.51%
C. 15.1%
D. 19.56%
A
A
15
Q
- CGNIES office may buy a patent with 14 years of life left. If CGNIES spends $1.5M to implement the technology, it expects net revenues of $650,000 per year for the patent’s life. If MoreTech’s discount rate for money’s time value is 10%, what is the maximum price that MoreTech can pay for the patent?
A. 3.3 M
B. 4.4 M
C. 5.5 M
D. 6.6 M
A
A
16
Q
- An engineer has received $10 000 from his employer for a patent disclosure. He has decided to invest the money in a 15-year savings certificate that pays 8% per year, compounded annually. What will be then final value of his investment, in terms of today’s dollars, if inflation continues at the rate of 6% per year?
A. 13,362
B. 13,423
C. 13,236
D. 13,342
A
C
17
Q
- UM purchased a new service van. A van is depreciated over a 10-year period with salvage value β±500,000. If the van will worth β±870,550 after six years, using Declining Balance Method, how much did UM pay to purchase the van?
A. β±2,500,000
B. β±1,500,000
C. β±2,000,000
D. β±3,000,000
A
C
18
Q
- Calculate the benefit/cost ratio for a highway project with the following benefits and costs. The project life is 40 years, the interest rate is 10%, and the projectβs right-of-way is worth 5M in 40 years.
Construction cost (includes acquiring right-of-way) = 20M
Annual maintenance = β±350,000
Repaving every 8 years =3M
Annual value of lives saved =1M
Time of savings for commercial traffic = 1.25M
Time of savings for commuter and recreational traffic= 1M
a) 1.23
b) 1.12
c) 1.33
d) 1.62
A
A
19
Q
- From the figure shown, determine the bearing of B from O.
a) S 57.59Β° E
b) S 67.22Β° E
c) N 22Β° W
d) N 66Β° W
A
A
20
Q
- A divided highway goes under a number of bridges, the arch over each lane being in the form of a semi-ellipse width. A truck is 6 ft wide and 12 ft high. What is the lowest bridge under which it can pass?
A. 12
B. 13.5
C. 12.5
D. 13
A
B
21
25. A neat computer programmer wears a clean shirt everyday. If he drops off his laundry and picks up the previous weekβs load every Monday night, how many shirts must he own to keep him going?
A. 8
B. 7
C. 14
D. 15
D
22
26. Write the equation of the circle going through the points P(2,-1) , Q(-3,0), & R(1,4)
A. 3x2 + 3y2 + x β 7y β 24 = 0
B. 3x2 + 3y2 β x + 7y - 24 = 0
C. 3x2 + 3y2 + x β 7x + 24 = 0
D. 3x2 + 3y2 β x + 7y + 24 = 0
A
23
27. A piece of wire 10m long is cut into two pieces. One piece is bent into a square and the other is bent into an equilateral triangle. What is the perimeter of the square so that the total area enclosed is minimum?
a. 4.35
b. 6.98
c. 7.53
d. 5.65
A
24
28. A satellite camera takes a rectangular shaped picture. The smallest region that can be photographed is a 5km x 7km rectangle. As the camera zooms out, the length L and width W of the rectangle increase at a rate of 3 km/sec. How long does it take for area A to be at least 7 times its original size?
a. 3.63 s
b. 3.23
c. 3.66
d. 3.33
B
24
29. Water is being poured into a hemispherical bowl of radius 3 in at the rate of 1 in3/s. How fast is the water level rising when the water is 1 in deep?
a. 0.0763
b. 0.0736
c. 0.0673
d. 0.0637
D
25
30. Fourier equation: f(t)=5cos(20Οt)+2cos(40Οt)+cos(80Οt). What is the frequency?
A. 10
B. 20
C. 40
D. 30
A
26
31. A multiple-choice examination has 200 questions, each with 4 possible answers, of which only one is correct answer. What is the probability that sheer guesswork yields from 25 to 30 correct answer for 80 of the 200 problems about which the student has no knowledge?
A. 0.125
B. 0.1193
C. 0.11321
D. 0.2122
B
27
32. Solve the problem using normal approximation
A. 0.1243
B. 0.1318
C. 0.1197
D. 0.2219
C
28
33. The scores in an examination are normally distributed with a mean of 48 and a standard deviation of 8. Approximately what percent of the scores fall between 40 and 56?
A. 64%
B. 68%
C. 95%
D. 72%
B
29
34. A monic polynomial f(x) of degree 5 is such that f(1)=1, f(2)=3, f(3)=6, f(4)=10, f(5)=15. What is f(6)?
A. 141
B. 120
C. 21
D. 60
A
30
SITUATION. The number of accidents in a week on a stretch of road is known to follow a poisson distribution with a parameter 2.1. Find the probability that
35. In a given week there is 1 accident
A. 0.257
B. 0.066
C. 0.132
D. 0.099
36. In two weeks period there are 2 accidents.
A. 0.257
B. 0.066
C. 0.132
D. 0.099
37. There is 1 accident in each two successive weeks
A. 0.257
B. 0.066
C. 0.132
D. 0.099
A, C, B
31
SITUATION: From the given closed traverse:
LINES BEARING DISTANCE
AB N20E 17.42
BC N68E 18.46
CD N22E 22.40
DE S40W 12.60
EF S62W 10.20
FA
56. Compute the bearing of the line FA.
A. S 50Β°18β W
B. S 48Β°23β W
C. S 51Β°12β W
D. S 51Β°8β W
57. Compute the distance of line FA
A. 22.31 m
B 21.35 m
C 18.66 m
D. 15,86 m
58. Compute the area of the closed traverse in acres.
A. 0.055 c. 0.0121
B. 0.169 d. 0.046
A, C, B
31
38. A student whirls a bucket of water in a vertical circle of radius 0.8m. Determine the frequency of rotation required for the bucket to completely negotiate the top of the loop without water spilling out of the bucket.
A. 47.3 rpm
B. 23.7 rpm
C. 33.4 rpm
D. 16.7 rpm
C
32
43. The Bay of Fundy has the largest tidal range in the world with 38.4 ft. If the high tide in the bay is 13.4 m, calculate the succeeding low tide.
a. 2.1 m
b. 1.7 m
c. 2.5 m
d. 3.5 m
B
33
39. A projectile is shot from the edge of a cliff 115m above the ground with an initial velocity of 65 m/s at an angle of 35Β° with the horizontal. Determine the magnitude of the velocity as it hits the ground.
A. 80.51
B. 60.38
C. 37.28
D. 53.24
A
33
45. A rotating vessel coming to rest makes 300 revolutions in the first minutes and in each minute thereafter makes β
as many revolutions as the preceding minutes. For how many revolutions the wheel makes before it comes to rest.
A. 450 rev
B. 500 rev
C. 600 rev
D. 620 rev
B
33
47. A cask containing 20L of wine was emptied of β
of its content and then filled with water. If this is done 18 times, how many liters of wine remains in the cask?
A. 0.24
B. 0.18
C. 0.36
D. 0.05
C
34
42. On top of a 50 m hill is a camp of Philippine Army. The general aims at 60 degrees from horizontal using a bazooka that can go 50 m/s when fired to hit a target. The general, however, neglected the air resistance in his approximation. If the wind at the top of the hill is blowing at 5 m/s horizontally against the projectile, how far away from the desired target will the bazooka fall?
a. 33.17 m
b. 36.21 m
c. 42.93 m
d. 49.31 m
D
34
44. There are 84 tons of water in pool A and 36 tons of water in pool B. If the water flows from pool A to pool B at a rate of 2 tons per minute. How many minutes will the water in pool B twice that in pool A?
a. 22
b. 2
c. 20
d. None of the list
A
34
55. A 80m spiral curve has an external distance of 20.5m. Determine the radius of the central curve if the intersection angle was 40 degrees.
A. 304.92
B. 504.3
C. 310.12
D. 298.57
D
34
40. Consider the two circular arches in the figure, taking the axes as shown. Compute the height of the column.
A. 7.82ft
B. 8.82ft
C. 8.02ft
D 9.02ft
C
35
41. Compute the normal tension which may be applied to a tape supported over two supports in order to make the tape equal to its nominal when supported only at end points. The steel tape is 30m long and weighs 0.84 kg when supported throughout its length under a standard pull of 5.67 kg with E = 2x10^6 kg/cmΒ²
A. 16.45
B. 17.33
C. 18.21
D. 19.06
B
36
49. A surveyor setup a transit at point P which is at the inner portion of a four-sided tract of land ABCD. He then reads the bearing and measures the distances as follows
LINE
PA
PB
PC
PD
BEARING
N 40Β°30β W
N 38Β°00β E
S 70Β°00β E
S 60Β°00β W
DISTANCE
420.35
530.15
480.75
695.10
What is the area of the tract in hectares?
A. 50.14
B. 45.58
C. 48.62
D. 47.28
36
50. At Sta. 2+500 at elevation 50m of a railroad, a +8% grade meets a -0.4% grade. The maximum allowable change in grade per station is 0.2%. Determine the length of the curve.
A. 120
B. 100
C. 110
D. 130
A
36
46. A horse and rider are racing to the right with a speed of 21m/s when they pass the finish line and begin slowing down. The horse slows for 52m with constant acceleration before it drops. What was the acceleration of the horse as it came to a stop?
A. 4.24
B. -4.24
C. 3.34
D. -3.34
B
37
48. A ball is thrown vertically onto the air so that its height (s) after t seconds is given by s= -127t2+ 4t. Find its maximum height.
A. 9
B. 8
C. 6
D. 7
A
38
62. A 3-lane expressway (one direction) in a portion of the extension of the North Expressway is carrying a total volume of 4,000 vehicles per hour when the incident occurs resulting in the closure of two lanes. The highway capacity is 2,000 vehicles per hour per lane. If it takes 0.5 hours to clear the obstruction, determine the maximum queue.
A. 1000 vehicles
B. 2000 vehicles
C. 3000 vehicles
D. 4000 vehicles
38
60.) A freeway is to be designed as a passenger-car-only facility for an AADT of 35,000 vehicles per day. It is estimated that the freeway will have a free flow speed of 70 mph. The design will be for commuters and the peak are factor is estimated to be 0.85 with 65% of the peak of traffic traveling in the peak direction. If the k factor for this freeway is 0.148, determine the directional design hourly volume.
A. 3367
B. 4403
C. 2862
D. 5015
A
38
51. Determine the corrected distance of line AB. Given:
βLAT = -0.44
βDEP = -0.37
Perimeter = 2915.80
Total Departure = 1945.73
Total Latitude = 1897.40
Line AB = 483.52 m
Departure = 356.30 E
Latitude = 326.87 N
A. 483.25 m
b. 483.61
C. 484.25 m
d. 482.98 m
B
38
53. The tangent distance of a 3-degree curve is only half of its radius. Compute the length of the curve.
A. 362.12
B. 354.20
C. 367.67
D. 398.50
B
39
52. If the sensitivity of a bubble tube is 30β per 2mm division, what would be the error in tape reading on a vertically held staff at a distance of 200m when the bubble is out of the center by 2.5 divisions.
A. 0.056
B. 0.069
C. 0.073
D. 0.086
C
39
54. The design speed of a car passing through an easement curve is equal to 180 kph (dili ni 80?). The radius of the central curve of the spiral curve is equal to 260 m long. Compute the length of the easement curve.
A. 80.34m
B. 80.34m
C. 70.89m
D. 75.62m
C
40
59. For a three-way intersection, determine the number of conflict points.
A. 3
b. 6
c. 9
d. 12
C
41
61. A toll bridge from Mandaue to Lapu-Lapu carries 5000 vehicles per day. The present cost fee is P1.50 when the toll fee is increased by P0.25 pesos, traffic volume will decrease by 500 vehicles per day. It is desired to increase the toll fee to a point where the revenue will be maximized determine the tall charge to maximize revenue.
A. 1
B. 2
C. 3
D. 4
B
41
64. The maximum speed limit for urban roads is
A. 70 kph
B. 40 kph
C. 60 kph
D. 50 kph
41
63. Localized upward buckling and shattering of the slabs at traverse joints or cracks. They can occur when transverse joints are field with incompressible solid materials.
A. Blowups
B. Raveling
C. Spalling
D. Faulting
A
42
66. Applying full brakes at a speed of 60 kph, the car traveled 40 m until it stopped. Determine the average skid resistance.
A. 0.53
B. 0.35
C. 0.42
D. 0.24
B
42
70. It is the process of bringing earthwork to the desired shape and elevation
a. Grading c.Balancing
b Compacting d. Trimming
A
43
65. Wilson Tiu, an architect, is designing an airport for small planes. One kind of airplane that might use this airfield must reach a speed before takeoff of at least 100 kph and can accelerate at 2 m/s^2. What minimum length must the runway have, in m?
A. 122.9
B. 199.9
C. 192.9
D. 199.2
C
43
SIT. For a concrete mixture, the following data were recorded:
WATER: 600/L
CEMENT: 34 BAGS @40KG/BAG
SPECIFIC GRAVITY = 3.15
FINE AGGREGATES:
3000KG ON A DRY BASIS
SPECIFIC GRAVITY = 2.67
2% ABSORPTION
COARSE AGGREGATES:
6000KG ON A DRY BASIS
SPECIFIC GRAVITY = 2.64
1.5% EXCESS MOISTURE
67. Solve for the volume of fine aggregates.
A. 1.12 cu.m.
B. 2.12 cu.m.
C. 0.14 cu.m.
D. 1.24 cu.m.
68. Solve for the volume of yield concrete.
A. 4.01 cu.m.
B. 4.14 cu.m.
C. 3.12 cu.m.
D. 3.10 cu.m.
69. Solve for the volume of water needed
a. 0.57cu.m c. 0.45cu.m
b. 0.63 cu.m d. 0.65 cu.m
A, A, A
44
73. ) Estimate activity times in PERT networks.
I. MAKE USE OF THREE ESTIMATES
II. PUTS THE GREATEST WEIGHT ON MOST LIKELY TIME ESTIMATE
III. IS MOTIVATED BY BETA DISTRIBUTION
A. III only
B. I only
C. II only
D. All of these
D
44
68. Solve for the volume of yield concrete.
A. 4.01 cu.m.
B. 4.14 cu.m.
C. 3.12 cu.m.
D. 3.10 cu.m.
A
44
67. Solve for the volume of fine aggregates.
A. 1.12 cu.m.
B. 2.12 cu.m.
C. 0.14 cu.m.
D. 1.24 cu.m.
A
45
69. Solve for the volume of water needed
a. 0.57cu.m c. 0.45cu.m
b. 0.63 cu.m d. 0.65 cu.m
A
45
71. Find the swell and shrinkage of a soil that weighs 1661 kg/mΒ³ in its natural state, 1186 kg/mΒ³ after excavation and 2077 kg/mΒ³ after compaction.
a. 60%, 80%
b. 40%, 20%
c. 50%, 50%
d. 60%, 40%
B
46
72. Calculate the volume of plastic concrete that will be produced by mix given in the table below.
COMPONENT SPECIFIC G. KG
CEMENT 3.15 154
SAND (SD) 2.65 426
GRAVEL 2.66 549
WATER 1.9 95
A. 0.51 M
B. 0.15 M
C. 0.55 M
D. 0.11 M
A
47
SITUATION.
A reverse curve has a perpendicular distance between two parallel tangents equal to 6 m, the central angle being equal to 7α΅ and the radius of curvature of the first curve is 163.8m.
74. ) Find the offset distance from back tangent to PRC.
A. 1.98m
B. 1.39m
C. 0.75m
D. 1.22m
75. ) Compute the radius of the second curve.
A. 641.28m
B. 578.32m
C. 614.16m
D. 498.25m
D, A
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