KYLO MSTE PSTEST

Question 1

1. Simplify (x-a) (x-b) (x-c) (x-d) … (x-y) (x-z)
   a) x^26 - (abcd…z)^26
   b) 0
   c) x^26 + (abcd…z)^26
   d) 1 -

Answer 1

B

Question 2

2. 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

Answer 2

A

Question 3

3. Two perpendicular chords 5 cm from the center of the circle divided the circle into four parts. If the
   radius of the circle is 13 cm, compute the area of the smallest part using integration.
   a) 31 cm2 b) 38 cm2 c) 32 cm2 d) 35 cm2

Answer 3

A

Question 4

4. Hemispherical bowl 2.5 m radius is filled with water to a depth of 1.8 m. A solid spherical ball 1.8m in
   diameter is placed in a bowl. Find the rise of the water in the bowl.
   a) 0.187 m c) 0.207 m
   b) 0.245 m d) 0.166 m

Answer 4

D

Question 5

5. Groups of surveying students is measuring a certain distance; the result was tabulated as shown.
   Groups Distance Trials
   A 121.34 2
   B 122.56 4
   C 120.97 8
   D 121.87 3
   E 119.99 5

a)100.96 b) 120.56 c) 121.193 d)122.45

Answer 5

C

Question 6

6. From the data of traverse shown
   Which of the following gives the nearest distance?
   Lines Bearings Distance
   1-2 S16’18’W 120.50
   2-3 S13’22’E 185.42
   3-4 N89’28’E 66.46
   4-1
   a)230m b) 243m c) 290m d) 305m

Answer 6

D

Question 7

7. In deep water this normally occurs when wave velocity L is less than seven times the wave height.
   a) breaking wave c) Tsunami
   b) Sea wave d) Knarly Wave

Answer 7

A

Question 8

8. An electrical firm manufactures light bulbs that have a length of life that is normally distributed
   with mean equal to 800 hours and a standard deviation of 40 hours. Find the probability that a
   bulb burns between 778 and 834 hours.

a) 0.08452
b) 0.07845
c) 0.09876
d) 0.05111

Answer 8

D

Question 9

9. From 6 mathematicians, 5 physicists, and 4 chemists, a committee is to be formed consisting of 4
   mathematicians, 3 physicists, and 2 chemists. In how many ways can the committee be formed?
   a) 900
   b) 450
   c) 650
   d) 320

Answer 9

A

Question 10

10. 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 project’s right-of-way is worth 5 million in 40
    years. Construction Cost (includes acquiring right-of-way) =20 million
    Annual Maintenance = 350, 000
    Repaving every 8 years = 3 million
    Annual Value of lives saved = 1 million
    Time savings for commercial traffic = 1.25 million Time savings for commuter and recreational traffic =
    1 million

a) 1.23 b) 1.12 c) 1.33 d) 1.62

Answer 10

A

Question 11

11. From the figure shown, determine the bearing of B from O.
    a) S 57.59° E c) N 22° W
    b) S 67.22° E d) N 66° W

Answer 11

A

Question 12

12. A block weighting 500N is dropped from a height of 1.3m upon spring whose modulus is 20N/mm.
    What velocity will the block have at the instant the spring is deformed 100mm?
    a) 6.35 m/s c) 5.43 m/s
    b) 4.65 m/s d) 1.85 m/s

Answer 12

B

Question 13

13. A compound curve has a common tangent 520m long. The first curve passing through the P.C. is 3-
    degree curve with a central angle of 50 degrees. Find the length of the second curve if its central angle
    is 35 degrees.

a) 233.25m c) 185.37m
b) 125.36m d) 662.37m

Answer 13

D

Question 14

14. Two circles tangent to a third circle internally and are tangent to each other externally. If the distances between their centers are 10cm, 7 cm and 5 cm respectively, compute the radius of the biggest circle.

a) 13 b) 9 c) 15 d) 11

Answer 14

D

Question 15

15. A divided highway goes under a number of bridges, the arch over each lane being in the form of a semi ellipse with the height equal to the 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

Answer 15

B

Question 16

16. A neat computer programmer wears a clean shirt every day. If he drops off his laundry and picks up the previous week’s load every Monday night, how many shirts must he own to keep him going?

a) 8 b) 7 c) 14 d) 15

Answer 16

D

Question 17

17. A simple curve is to be designed for a maximum speed of 90 kph. The coefficient of friction between the tires and the pavement is 0.40. If the superelevation is limited to 12%, determine the degree of
    curvature. Use arc basis.

a) 9.34° b) 3.56° c) 2.65° d) 4.78°

Answer 17

A

Question 18

18. Compute the nominal tension which may be applied to a tape supported over two supports in order to make the tape equal to its nominal length when supported only at end points. The steel tape is 30 m long and weighs 0.84 kg when supported throughout its length under a standard pull of 2x10^6kg/cm^2 and area of 0.06 cm^2

a) 16.45 b) 17.33 c) 18.21 d) 19.06

Answer 18

B

Question 19

19. On top of a 50m hill is a camp of the 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 5 m/s horizontally against the projectile, how far away from the desired target will the bazooka fall?

a) 33.17 b) 36.21 c) 42.93 d) 49.31

Answer 19

D

Question 20

20. A person buys a piece of lot for P100, 000 down payment and 10 deferred semi-annual payments of P8,000 each, starting 3 years from now. What is the present value of the investment if the rate of interest is 12% compounded semi-annually?

a) P 142, 999.08 c) P 142, 189.67
b) P 143, 104.89 d) P 143, 999.08

Answer 20

D

Question 21

21. The moon’s nearly circular orbit around Earth has a radius of about 384, 000 km. and a period of T of 27.3 days. Determine the acceleration of the moon toward the Earth.
    a) 2.72X10−3 m/s² c) 3.52X10−3 m/s²
    b) 9.81X10−3 m/s² d) 0 m/s²

Answer 21

A

Question 22

22. From Point A on level ground, the angle of elevation of the top D and bottom B of a flagpole situated on the top of a hill are measured 47° 54’ and 39° 45’. Find the length of the hill if the height of the
    flagpole is 115.5 ft.

a) 325.36 ft. c) 349.27 ft.
b) 225.36 ft. d) 122.25 ft.

Answer 22

C

Question 23

23. A spiral easement curve has a length of 100 m with a central angle having a radius of 300 m. Determine the degree of spiral at the third quarter point.

a) 4.36° b) 1.25° c) 8.25° d) 2.86°

Answer 23

D

Question 24

24. The Bay of Fundy has the largest tidal range in the world with 38.4 ft. If the high tide in the bay isa 13.4 m, calculate the succeeding low tide.

a) 2.1 m b) 1.7 m c) 2.5 m d) 3.5 m

Answer 24

B

Question 25

25. 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 min. How many minutes will the water in pool B twice that in pool A.

a) 22 b) 2 c) 20 d) None in the list

Answer 25

A

Question 26

26. A rock is thrown upward from the ground. Its height in feet above the ground after t seconds is given
    by the function: f(t)=-16t²+20t. Find the number of seconds it took for the rock to reach its maximum
    height.

a) 0.625 s b) 0.125 s c) 0 s d) 0.245 s

Answer 26

A

Question 27

27. A-2.5% grade is connected to a +1.0% grade by means of 180-m vertical curve. The PL. station is
    100+00 and the P.I. elevation is 100 m above sea level. What is the station of the lowest point on the
    vertical curve?

a) 99+910 c) 100+25.65
b) 100+90 d) 100+38.57

Answer 27

D

Question 28

28. An open top box with a square bottom and rectangular sides is to have a volume of 256 cu. inches.
    Find the minimum amount of material.

a) 192 in2 c) 125 in2
b) 201 in2 d) 350 in2

Answer 28

A

Question 29

29. Rabbits in a lab are to be kept on a strict daily diet that includes 30 grams of protein, 16 grams of
    fat, and 24 grams of carbohydrates. The scientist has only three food mixes available with the following
    grams of nutrients per unit.
    Mix Protein Fat Carbohydrates
    A 4 6 3
    B 6 1 2
    C 4 1 12

a) 2 units of Mix A; 3 units of Mix B; 1 unit of Mix C
b) 1 unit of Mix A; 2 units of Mix B; 1 unit of Mix C
c) 2 units of Mix A; 3 units of Mix B: 2 units of Mix C
d) 4 units of Mix A: 3 units of Mix B; 1 unit of Mix C

Answer 29

A

Question 30

30. A dam will have a first cost of 5,000,000, an annual maintenance cost of 25,000 and minor
    reconstruction costs of 100,000 every five years. At an interest rate of 8% per year, the capitalized cost
    of the dam is nearest to:

a) 5,525,570 c) 525,625
b) 213,125 d) 5,312,500

Answer 30

A

Question 31

31. Find the volume of the parallelepiped whose edges are represented by
    A = 2i-3j+4k
    B = i+2j-k C = 3i-j+2k

a) 4 b) 3 c) 12 d) 7

Answer 31

D

Question 32

SITUATION. From the given closed traverse.
Lines Bearing Distance
AB N 30° E 17.42
BC N 68° E 18.46
CD S 22° E 22.40
DE S 40° W 12.6
EF S 62° W 10.20
FA

32. Compute the bearing of line FA

a) N 50° 18’ W c) N 51° 12’ W
b) N 48° 23’ W d) N 5° 12’ W

33. Compute the distance of line FA

a) 22.31 m c) 21.35 m
b) 18.66 m d) 15.86 m

34. Compute the area of closed traverse in acres
    a) 0.055 b) 0.109 c) 0.21 d) 0.046

Answer 32

A, C, B

Question 33

35. A body moves along a straight line according to the laws
    S= (1/2)t^3 - 2t
    Determine its velocity at the end of 2 seconds.

a) 3 ft/sec c) 4 ft/sec
b) 2 ft/sec d) 5 ft/sec

Answer 33

C

Question 34

36. Determine the angle, the diagonal of a cube makes with one of its edges.

a) 54.74 b) 60.00 c) 63.37 d) 50.77

Answer 34

A

Question 35

37. The population sized y of a community of Lemmings varies according to the relationship: y = yer In
    this formula, t is the time in months y is the initial population at time t = 0.
    Estimate the population after 6 months if there is originally 5000 Lemmings.

a) 13256 b) 14125 c) 15653 d) 12298

Answer 35

D

Question 36

39. For a three-way intersection, determine the number of conflict points.

a) 3 b) 6 c) 9 d) 12

Answer 36

C

Question 37

40. A freeway is to be designed as a passenger car only facility for an AADT of 35000 vehicles per day. t is estimated that the freeway will have a free flow speed of 70mph. The design will be for commuters
    and the peak hour factor is estimated to be 0.85 with 65% of the peak hour 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

Answer 37

A

Question 38

41. A toll bridge from Mandaue to Lapu -Lapu City carries 5000 vehicles per day. The present cost fee is
    P1.50. When the toll fee is increased by PO.25, 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 toll
    charge to maximize revenue.

a) 1 b) 2 c) 3 d) 4

Answer 38

B

Question 39

42. Compute the center of the sphere having equation of x^2+y^2+z^2-2x+8y+16z+65=0

a) (1,4,-8) c) (1,-4,-8)
b) (4,-4,-8) d) (1,4,8)

Answer 39

C

Question 40

43. A point moves in the plane according to the equation x=t^3 +2t, y=2t^2 - 6t find dy/dx.
    When t=0

a) -3 b) 5 c) -8 d) 2

Answer 40

A

Question 41

44. Given the following data measuring a distance of a
    certain line:
    Distance No. of Measurements
    47.23 3
    47.27 2
    47.19 4
    47.22 1
    Determine the most probable value of the measurements.

a) 47.214 b) 46 .230 c) 47.228 d) 47.221

Answer 41

D

Question 42

45. A ___ blank is the loss or displacement of land, or the long-term removal of sediment and rocks along
    the coastline due to action of waves, currents, tides, wind driven water, waterborne ice, or other impacts
    of storms.

a) Coastal erosion c) Land erosion
b) Seashore erosion d) Wave erosion

Answer 42

A

Question 43

47. The surface of a newly placed concrete is stuck of by having a straight edge back and forth with a saw-like motion across the top of the room is known a.

a) Screeding c) Troweling
b) Edging d) Crazing

Answer 43

A

Question 44

48. A mountain climber wants to cut a rope 213 ft long into three pieces. If each piece is to be 2 ft longer than the previous one, where should he make the cuts?

a) 72 b) 73 c) 74 d) 75

Answer 44

B

Question 45

49. A ball of mass m= 2.60 kg, starting from rest, falls a vertical distance h=55cm before striking a vertical coiled spring which it compresses an amount equal to 15cm. Determine the spring stiffness constant k
    of the spring.

a) 1246.96 N/m c) 1055.12 N/m
b) 1342.88 N/m d) 1587.04 N/m

Answer 45

D

Question 46

51. A 0.060 kg tennis ball, moving with a speed of 5.50 m/s has a head on collision with a 0.090 kg ball
    initially moving in the same direction at a speed of 3 m/s. Assuming a perfectly inelastic collision,
    determine the speed of the second ball after collision.

a) 5.0 m/s b) 2.5 m/s c) 4.0 m/s d)3.5 m/s

Answer 46

C

Question 47

52. A symmetrical parabolic curve passes through point A whose elevation is 23.23 m at 54 meters from P.C. The elevation of the P.C. at station 4+100 is 22.56 m. The grade of the back tangent is +2% and the
    length of the curve is 120 m. Determine the grade of the forward tangent.

a) -2.3% b) -1.4% c) -3.3% d) +2.5%

Answer 47

B

Question 48

53. The calculation of the probability that the critical path will be completed by time T.
    I. Assume that activity times are statistically independent
    II. Assume that the total time of the critical path has approximately a beta distribution.
    III. Requires knowledge of the standard deviation for all activities in the network

a) II only
b) I only
c) III only
d) All of these

Answer 48

A

Question 49

54. A mason can do a given job in 4 hours. His helper can do the same job in 9 hours. The mason begins working and after 1 hour is joined by his helper. In how many hours will they complete the job?

a) 2.08 b) 4.64 c) 3.23 d) 7.91

Answer 49

A

Question 50

55. In an experiment that led to the discovery of the atomic structure of matter, Lord Rutherford (1871- 1973) shot high energy alpha particles toward a tin sheet of gold atoms. Because many were reflected, Rutherford showed the existence of the nucleus of a gold atom. The Alpha Rutherford Particle is repelled
    by the nucleus at the origin, it travels along the hyperbolic path given by 4x2 − y2 = 6.
    How close does the particle come to the nucleus?

a. The particle is never closer than 3 units from the nucleus.
b. The particle is never closer than 4 units from the nucleus.
c. The particle is never closer than 1 unit from the nucleus.
d. The particle is never closer than 2 units from the nucleus.

Answer 50

D

Question 51

56. A project is to be evaluated using P.E.R.T. Using the data for the project activities with their threetime estimate, determine the variance of the project.

a) 3.166 b) 2.249 c) 1.249 d) 5.165

Answer 51

D

Question 52

57. A 50 kg block is dropped from a height of 1.2 m upon an unstretched spring. At the instant the spring is deformed by 10o mm, the velocity of the block is 4.417 m/s. Determine the spring modulus, K, of the
    spring in kN/m.

a) 29.98 b) 27.99 c) 20.17 d) 25.46

Answer 52

A

Question 53

58. A satellite orbits around the earth in an elliptical path of eccentricity 0.60 and semi-minor axis of
    length 12000 miles. If the center of the earth is at one of the foci, find the maximum altitude of the
    satellite.

a) 15000 miles c) 24000 miles
b)9000 miles d) 12000 miles

Answer 53

C

Question 54

59. A 10Kn car is approaching a ramp which makes a slope of 20 degrees with a speed of 75 kph. At the foot of the ramp, the engine is turned off. How far does the car travel up the incline before it stops?

a) 64.68ft. c) 255.49ft.
b) 838.25ft. d) 212.21ft.

Answer 54

D

Question 55

60. A spherical ball of radius 3cm was dropped into a conical vessel of depth 8cm and radius of base 6cm. What is the area of the portion of the sphere which lies above the circle of contact with the cone?

a) 25.48cm^2
b) 90.48cm^2
c) 80.48cm^2
d) 75.48cm^2

Answer 55

B

Question 56

61. A small cone is cut “y” meters from the vertex. The volume of the small cone is one-third the volume of the big cone. Solve for the value of y.

a) 2.76 b) 6.24 c) 3.69 d) 5.31

Answer 56

B

Question 57

63. A tank contains 50 gallons of water brine, containing 2 pounds/ gallon of salt, flows into the tank at
    a rate of 2 gallons per minute, and the mixture kept uniform by stirring, runs out at the same rate. How
    long will it take before the quantity of salt in the tank is 50 pounds.

a) 12 min b) 17.33 min c) 30 min d) 20 min

Answer 57

B

Question 58

65. A student was asked to measure a 500m long line using a 25m steel tape that is of standard length at temperature of 28°C. If the average temperature is 12°C, what is the required measurement?

a) 499.907m c) 500.093m
b) 500.156m d) 499.727m

Answer 58

C

Question 59

66. Compute the rate of flow in vehicles per hour if the space mean speed is 20miles per hour and the
    density is 14 vehicles per mi.

a) 120veh/hr c) 280veh/hr
b) 240veh/hr d) 160veh/hr

Answer 59

C

Question 60

68. A section of highway has the following flow-density relationship:
    Where: q is in veh/hr and k is in veh/km. What is the capacity of the highway section?
    a) 2000 veh/hr c) 1900 veh/hr
    b) 1500 veh/hr d) 1700 veh/hr

Answer 60

B

Question 61

SITUATION. A transit system consists of one-way trains running between four stations. The Probabilities
concerning the origin and destination of passengers are summarized in the following matrix.
ORIGIN DESTINATION
1 2 3 4
1 0 0.1 0.3 0.6
2 0.6 0 0.3 0.1
3 0.5 0.1 0 0.4
4 0.8 0.1 0.1 0
The fraction of trips originating from stations 1,2,3 and 4 are 0.25, 0.15, 0.35 and 0.25 respectively.

69. What is the probability that a passenger will leave the train at station 3?

a) 0.256 b) 0.145 c) 0.125 d) 0.350

70. What fraction of the passengers departing the train at Station 3 originated from Station 1?

a) 0.356 b) 0.128 c) 0.521 d) 0.517

71. The number of vertices of a polyhedron is 12 and has 30 edges. Determine how many faces the
    polyhedron has.

a) 18 b) 22 c) 20 d) 24

Answer 61

B, B, D

Question 62

72. It is an application of a low viscosity asphalt to a granular base in preparation for an initial layer (or
    surface course layer) of asphalt.

a) Tack Coat c) Adhesive Coat
b) Prime Coat d) Seal Coat

Answer 62

B

Question 63

73. The structure could be subject to settlement problems The like hood of having a settlement problem
    (event A) depends on the subsoil condition, in particular. whether a weak zone exist in the subsoil or
    not. If there is a small weak zone (event S), the probability of A is 0.2; if the weak zone is large (event L),
    the probability of A becomes 0.6: last. if no weak zone exists (event N), then the probability of A is only
    0.05. Based on their experiences with the geology of the neighborhood and the soil information from
    the preliminary site exploration program, the engineers in this case believe that there is a 70% chance
    of no weak zone in the stratum underlying the structure; however, if there is a weak zone, it would be
    twice as likely to be small than large. What the probability that the structure will have a settlement
    problem.

a) 0.135 b) 0.225 c)0.635 d) 0.897

74. Suppose an additional boring can be performed at the site to gather more information about the
    presence of weak material The engineers judge that: Hf a large weak zone exists; t is 80% likely that the
    boring will encounter it; this encounter probability drops to 30%% for a small weak zone Obviously. the
    boring will not encounter any weak material if the weak: zone does not exist at all, Suppose the
    additional boring failed to encounter any weak material What is the probability of the presence of a large
    weak zone?

a) 0.041 b) 0.098 c) 0.056 d) 0.023

75. (Refer to the previous problem) What is the probability that the structure will have a settlement
    problem?

a) 0.087 b) 0.118 c) 0.005 d) 0.256

Answer 63

A, D, A

Question 64

1. If sin3a=cos6b, then which of the following expression is correct

A. A+B=90
B. A+2B=30
C. A+B=180
D. A+B=270

Answer 64

B

Question 65

2. The sum of the sides of 2 polygon is 12 and their diagonals is 19. Identify one of the polygons

A. Hexagon B. Heptagon C. Octagon D. Nonagon

Answer 65

B

Question 66

3. In a quadratic equation problem, a student made a mistake in copying the coefficient of x2 and got
   roots of 2 and 3. Another student made a mistake in copying the constant term and got roots of 4 and 6
   Find the value of the smaller of the two roots.

a)1.4 b) 10.6 c) 86 d)-1.4

Answer 66

A

Question 67

4. In the quadratic equation ax? +bx+c = 0, when b is equal to 4ac, then the roots are:
   a) equal
   b) real and unequal
   c) imaginary
   d) extraneous

Answer 67

A

Question 68

5. A two rectangular polygons with the same number of sides, find the length of a side of the smaller if
   the lengths of the apothems are 20 and 50 and a side of larger has length of 32.5

a) 13 b) 15 c) 14 d) 16

Answer 68

A