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REVIEW INNOVATIONS MANILA – CEBU - DAVAO PHILIPPINES FINAL PREBOARD FOR CIVIL ENGINEERING CIVIL ENGINEERS Final Preboard Examination Saturday, October 20, 2018 08:00 a.m. — 12:00 p.m. ---------------------------------------------------------------------MATHEMATICS, SURVEYING & TRANSPORTATION ENGINEERING

SET A

INSTRUCTION: Select the correct answer for each of the following questions. Mark only one answer for each item by shading the box corresponding to the letter of your choice on the answer sheet provided. STRICTLY NO ERASURES ALLOWED.GOOD LUCK. NOTE:

A times B is represented by A × B or A*B. A raised to the power n is expressed as A^n. All problems are 1 point each.

1.

The distance of the highest point of a vertical curve is 70.59m from the PC. If the length of curve is 120m and the slope of the forward tangent is -1.4%, determine the slope of the back tangent. A. -2% C. +2% B. -1% D. +1%

2.

A building has a salvage value of P1M after 50 years. Annual depreciation is P2M. Using straight line depreciation, how many years after should you sell the building for P31M. A. 28 C. 33 B. 31 D. 35

3.

During baseball practice, a batter hits a very high fly ball and then runs in a straight line and catches it. Which of the following statements is true? A. The batter and the ball has the same displacement. B. The batter has a greater displacement than the ball. C. The ball has a greater displacement than the batter. D. The ball and the batter has the same distance travelled.

4.

The offset distance of the simple curve from the PT to the tangent line passing through the PC is equal to 120.20 m. The simple curve has an angle of intersection of 500. Find the radius of the simple curve. A. 165.69 m C. 168.25 m B. 336.49 m D. 331.38 m

5.

A rectangular field was measured using a 100m tape, which was actually 10cm too short. The recorded area was 4500m2. What is the true area of the field? A. 4504.50 m2 C. 4509.0035 m2 2 B. 4495.50 m D. 4491.0045 m2

6.

What is the page number on the last page if there is a total of 2457 digits used in the page numbers of a book starting with page numbered 1? A. 845 C. 955 B. 855 D. 745

7.

Find the area of a piece of land with an irregular boundary as follows: STATION 0+000 0+015 0+030 0+045 0+060

OFFSET DISTANCE (m) 5.59 3.38 2.30 3.96 4.80

The stations are on a straight-line boundary. Find the area of the land using Simpson’s One-Third Rule. A. 222.53 m2 C. 222.35 m2 B. 221.75 m2 D. 221.57 m2 Page 1 of 8

CIVIL ENGINEERS Final Preboard Examination Saturday, October 20, 2018 08:00 a.m. — 12:00 p.m. MATHEMATICS

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8.

An equipment costs P400,00 and has a life of 30,000 hours, at the end of which has a salvage value of “x” pesos. In the 1st year, it was used for 6,240 hrs, 8,360 hrs in the 2nd year and 7,400 hrs in the third year. The book value at the end of 1st year was P325,120. Find the depreciation reserved for the 2nd year. A. 200,750 C. 91,250 B. 100,320 D. 40,000

9.

An army of troops is marching along a road at 5 kph. A messenger on horseback was sent from the front to the rear of the column and returns immediately back. The total time taken being 10 minutes. Assuming that the messenger rides at the rate of 10 kph, determine the length of the column. A. 526 m C. 854 m B. 1 km D. 625 m

10. A man and his wife invite 8 of their friends to a dinner. They are to be seated around a round table. How many arrangements can be made if the man and his wife are to sit side by side? A. 80,640 C. 362,880 B. 10,080 D. 40,320 11. Two men are walking toward each other alongside a railway. A freight train overtakes one of them in 20 seconds and exactly 10 minutes later meets the other man coming from the opposite direction. The train passes this man in 18 seconds. How long after the train has passed the second man will the two men meet? Constant speeds are to be assumed throughout. A. 1 hr, 42 min, 32 sec C. 1 hr, 32 min, 42 sec B. 1 hr, 24 min, 23 sec D. 1 hr, 23 min, 24 sec 12. The repair costs for some handheld equipment in the office of NAIA is estimated to be P12,000 for the first year, increasing by P3,000 per year in subsequent years. Determine the amount that the office will need to de posit into a bank account paying 4% interest, to provide the repair cost for the next 4 years. A. 68,790 C. 59,360 B. 93,650 D. 79,068 13. What is the probability of getting at least 1 one in 2 throws of a die? A. 5/6 C. 11/36 B. 5/18 D. 25/36 14. A and B working together can do a job in 4 days, B and C together can do the job in 3 days, and A and C together can do it in 2.4 days. In how many days can A do the job working alone? A. 6 C. 4 B. 12 D. 8 15. It takes 2 hours to row 9 miles with the current and 6 hours to return against the current. Determine the rate of the current. A. 1.5 mi/hr C. 2.5 mi/hr B. 3 mi/hr D. 2 mi/hr 16. Divide 253 into 4 parts proportional to 2, 5, 7, 9. largest part? A. 88 C. 77 B. 111 D. 99

What is the value of

17. What is the angle between the hands of a clock at 3:35 pm? A. 102.5° C. 87.5° B. 124.3° D. 98.6° 18. Franco is a tile installation contractor. He estimated that one of his two tilers would take 9 hours to complete a certain floor area and the other 10 hours. He knew from experience that when these two tilers worked together, 10 fewer tiles got laid per hour. Since he has a deadline to beat, he put both men on the job and it took them exactly 5 hours to cover the entire area. How many tiles did this floor area contain? A. 800 C. 850 B. 900 D. 950 Page 2 of 8

CIVIL ENGINEERS Final Preboard Examination Saturday, October 20, 2018 08:00 a.m. — 12:00 p.m. MATHEMATICS

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19. A freely falling body, starting from rest, falls 16 ft during the 1st second, 48 ft during the 2nd second, 80 ft during the 3rd second, etc. Calculate the distance it falls during the 15th second. A. 464 ft C. 644 ft B. 3600 ft D. 6300 ft 20. A catapult is placed 100 ft from the castle wall, which is 35 feet high. The soldier wants the burning bale of hay to clear the top of the wall and land 50 feet inside the castle wall. If the initial velocity of the bale is 70 feet per second, then at what angle should the bale of hay be launched so that it travels 150 feet and pass over the castle wall. A. 58.8 C. 50.8 B. 53.8 D. 54.8 21. A conical hole with a 70mm diameter opening at 50 degrees is checked by a spherical ball 40mm in diameter. Determine the height of clearance or obstruction. A. 7.74mm obstruction C. 13.76mm obstruction B. 7.74mm clearance D. 13.76mm clearance 22. In order for Iñigo to walk a kilometer in his rectangular backyard, he must walk the length 25 times or walk its perimeter 10 times. What is the area of the rectangular backyard? A. 100 m2 C. 400 m2 B. 200 m2 D. 800 m2 23. Two years ago, a man was six times as old as his daughter. In 18 years, he will be twice as old as his daughter. How old is his daughter? A. 8 C. 10 B. 7 D. 9 24. If 8 men take 12 days to assemble 16 machines, how many days will it take 15 men to assemble 50 machines? A. 18 C. 20 B. 22 D. 24 25. A chord of a circle 0.65m from the center is 1.25m long. What is the area of the circle? A. 2.555 m2 C. 3.672 m2 2 B. 6.236 m D. 4.975 m2 26. Find the volume generated by revolving about the line x – 2 = 0, the area in the first and fourth quadrants, bounded by the curve x^2 + y^2 – 4 = 0 and the line x = 0. A. 45.4 C. 61.8 B. 55.7 D. 23.8 27. Find the maximum product of three positive numbers whose sum is 150. A. 175000 C. 150000 B. 125000 D. 210000 28. An isosceles triangle has legs 10 cm, the base decreases at the rate of 4 cm/s, find the rate of change of the angle at the apex when its base is 16 cm. A. 4/3 rad/s C. 5/6 rad/s B. 7/2 rad/s D. 2/3 rad/s 29. A ball is dropped from a height of 120 m. Each time it strikes the ground, it bounces up to 1/3 of its previous height. What is the total displacement travelled by the ball before coming to rest assuming a straight line motion? A. 60 m C. 240 m B. 120 m D. 360 m 30. An engineering student takes a 5-item multiple choice exam. He can only pass the exam if he can score at least 3 correct answers. What is his probability to pass if he relies only in guessing from 4 choices for every question? A. 0.0156 C. 0.0954 B. 0.0879 D. 0.1035 Page 3 of 8

CIVIL ENGINEERS Final Preboard Examination Saturday, October 20, 2018 08:00 a.m. — 12:00 p.m. MATHEMATICS

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31. Find dy/dx at (0, –2) if x3 – xy + y2 = 4. A. 0.667 C. –0.333 B. 0.8 D. 0.5 32. While visiting Cape Kennedy, we came upon an engineer digging a hole. “How deep is that hole?” we asked. “Guess,” said the engineer, being evasive. “My height is exactly 5 feet 10 inches.” “How much deeper are you going?” we inquired. “I am one-third done,” was the answer, “and when I am finished my head will be twice as far below the ground as it is now above the ground.” How deep will that hole be when finished? A. 10 feet 6 inches C. 12 feet 4 inches B. 11 feet 5 inches D. 9 feet 7 inches 33. Find the function f(x) whose derivatives is sin x and whose graph passes through the point (0,2). A. f(x) = cos x + 3 C. f(x) = cos x – 3 B. f(x) = –cos x + 3 D. f(x) = –cos x – 3 34. A body is projected vertically upward such that is height from the ground in feet is h = 50t – 16.1t^2 where t = time in flight in seconds. After how many seconds will the velocity be 12 fps? A. 1.18 C. 0.75 B. 0.88 D. 1.16 35. An ice cream cone is filled with ice cream and a surmounted ice cream in the form of a hemisphere on top of the cone. If the hemispherical surface is equal to the lateral area of the cone, find the total volume in cu in of ice cream if the radius of the hemisphere is equal to 1 inch and assuming the diameter of the hemisphere is equal to the diameter of the cone. A. 3.45 C. 4.12 B. 3.91 D. 0.5 36. The diameter of a tumor D in mm, t in D(t) = 10e^0.0277t. How long until the A. 30 C. B. 27 D.

days after diagnosis is given by diameter is doubled? 25 21

37. From a tank filled with 240 gallons of alcohol, 60 gallons are drawn off and the tank is filled up with water. Then 60 gallons of the mixture are removed and replaced with water, etc. How many gallons of alcohol remain in the tank after 5 drawings of 60 gallons each are made? A. 55 gallons C. 56 gallons B. 58 gallons D. 57 gallons 38. In a certain barangay, 80% of the population have cellphone. Two people from the barangay were selected at random. Find the probability that one has cellphone and the other has none. A. 0.64 C. 0.08 B. 0.08 D. 0.32 39. The kinetic energy E of a body is proportional to its weight W and to the square of its velocity v. An 8 lb body moving at 4 ft/sec has 2 ft-lb of kinetic energy. Find the kinetic energy of a 6000 lb truck speeding at 88 ft/sec. A. 627,000 ft-lb C. 672,000 ft-lb B. 762,000 ft-lb D. 726,000 ft-lb 40. The following notes are for irregular cross-section. Compute the crosssectional area. Width of roadway is 12 m with side slopes of 1V:2H. C2.67 11.34 A. 43.14 m2 B. 67.14 m2

C8.00 8.00

C4.00 4.00

C2.83 0

C2.33 5.00

C. 34.41 m2 D. 76.41 m2

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C1.67 9.34

CIVIL ENGINEERS Final Preboard Examination Saturday, October 20, 2018 08:00 a.m. — 12:00 p.m. MATHEMATICS

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41. One edge of regular hexahedron is 24 cm long. Find the ratio of its volume to its surface area. A. 0.5 C. 0.125 B. 4 D. 2 42. Three identical circles are tangent to one another. The radius is 20 cm. Find the area enclosed by the three circles but outside each of the three circles in sq. cm. A. 74.3 C. 64.5 B. 82.1 D. 50.7 43. A vein has a dip of 570 W. The bearing of a drift of 5% with the plane of the vein. Determine the A. N 360 0’ W C. N 350 9’ B. N 360 4’ W D. N 350 2’

is N 370 W having a grade bearing of the strike. W W

44. The length of the spiral curve is 82 m and the radius of the central curve of the spiral curve is 260 m. Compute the length of throw. A. 4.31 m C. 2.16 m B. 1.08 m D. 0.54 m 45. The areas in respectively. volume of cut A. 3449.69 B. 3446.96

cut of two irregular sections 65m apart are 36m 2 and 72m2 Base width is 10m, sideslope of 3H:2V. Find the corrected in cubic meter, using Prismoidal Correction. m3 C. 3434.09 m3 m3 D. 3459.09 m3

46. A pavement with a width of 12 m is to be super-elevated to allow safe negotiation of 2030’ circular curve at a design speed of 60 kph. What will be the theoretical difference in elevation between the opposite edges of the pavement? A. 0.37 m C. 1.48 m B. 0.74 m D. 0.56 m 47. A vehicle traveling at 40 kph was stopped within 1.8 seconds after the application of brakes. Determine the average skid resistance. A. 0.39 C. 0.54 B. 0.46 D. 0.63 48. Twelve vehicles are observed in a 400 m section of the extension of SCTEX. Average time of headway is 4 seconds. Determine the space mean speed. A. 20 kph C. 30 kph B. 40 kph D. 60 kph 49. Determine the equation of the curve such that any point of the curve from two points whose (3,0) is always equal to 8. A. 7x2 + 16y2 = 112 C. 49x2 + B. 16x2 + 7y2 = 112 D. 16x2 +

the sum of its distances of coordinates are (-3,0) and 16y2 = 112 49y2 = 112

50. The distance from point A [(√6)cosθ, (√2)sinθ] to the center of ellipse is equal to 2. If the equation of ellipse is 2x2 + 6y2 = 12, find the value of θ. A. 150 C. 450 B. 300 D. 600 51. What is the angle between an asymptote of the hyperbola x 2 – 4y2 – 2x – 63 = 0 and the x-axis? A. 26.570 C. 53.140 0 B. 63.43 D. 31.720 52. Compute the area of the curve having a polar equation of r = 2sinθ + 2cosθ. A. 12.57 u2 C. 8.89 u2 2 B. 4.44 u D. 6.28 u2 53. AB is a diameter of a circle. BC is a chord 10 cm long.CD is another chord. Angle BDC = 18°. What is the area of the circle in cm2. A. 856.4 C. 789.8 B. 904.1 D. 822.5 Page 5 of 8

CIVIL ENGINEERS Final Preboard Examination Saturday, October 20, 2018 08:00 a.m. — 12:00 p.m. MATHEMATICS

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54. The eccentricity of an ellipse having its major axis parallel to the xaxis and center at (0, 0) is equal to 0.60. The distance between the foci of the ellipse is equal to 12. Compute the distance between directrices. A. 16.67 units C. 8.34 units B. 33.33 units D. 25.34 units 55. The coordinate axes are asymptotes of the equilateral hyperbola whose vertex in the first quadrant is 3√2 units from the origin. What is the equation of the hyperbola? A. xy = 18 C. xy = 10 B. xy = 9 D. xy = 16 56. The vertices of a triangle has polar coordinates of (0,00), (6,300), and (9,700). Find the area of the triangle. A. 27.00 u2 C. 17.36 u2 2 B. 13.50 u D. 25.37 u2 57. Two perpendicular chords both 5 cm from the center of the circle, which divides into four parts. If the radius of the circle is 13 cm, find the area (cm2) of the smallest part. A. 36 C. 31 B. 12 D. 24 58. A circle is inscribed in a triangle ABC, and it touches AC at P. If AB = 14, AC = 10, and AP = 4, what is the length of side BC A. 16 C. 12 B. 14 D. 28 59. The volume of the spherical is 6.67 cubic meters and its radius is 2 m. Determine the surface area (m3 )of the lune. A. 11 C. 9 B. 10 D. 8 60. The surface area of a regular tetrahedron is 173.2 cm2. What is its volume? A. 122.9 C. 117.8 B. 88.0 D. 98.6 61. The bases of a right prism are pentagons with each side 6 cm long. the bases are 14 cm apart. What is the volume of the prism in cm3? A. 802 C. 756 B. 795 D. 867 62. A liquor vendor borrowed P2,400 and agreed to pay P3,200 after 6o days. What is the simple interest rate per annum? A. 30% C. 300% B. 20% D. 200% 63. A man wishes to have P50,000 in a certain fund at the end of 10 years that will pay nominal rate of 6% compounded continuously. What is the value of the compound amount factor for this rate? A. 1.616 C. 0.549 B. 1.822 D. 0.619 64. An engineer’s level uses level tube with a radius of curvature of 4m. During observation the bubble is off centered through 4 spaces. What is the error on the observed vertical distance on a station 120m away if one space on the tube is 0.5mm long? A. 0.06 m C. 0.04 m B. 0.05 m D. 0.03 m 65. An employee is earning P40,000 a month wants to buy a Mitsubishi Mirage 2018 model with a cash value of P717,000. He can only afford to purchase the car with a down payment and a monthly amortization of 30% of his monthly salary. What is the required down payment if the seller agree that the remaining balance can be paid for 5 years at 18% per year payable on monthly basis? The first payment will be due at the end of first month. A. P244,500 C. 266,700 B. P200,000 D. 198,000

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CIVIL ENGINEERS Final Preboard Examination Saturday, October 20, 2018 08:00 a.m. — 12:00 p.m. MATHEMATICS

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66. A man bought a government bond which cost P200,000 and will pay P10,000 interest each year for 20 years. The bond will mature at the end of 20 years and he will receive the original P200,000. If there is a 2% annual inflation during this period, what rate of return will the investor receive after considering the effect of inflation. A. 2.94% C. 3.00% B. 5% D. 3.65% 67. A machine which cost P50,000 when new has a 10-year lifetime and salvage value equal to 10% of its original value. Determine the capital recovery, based upon an interest rate of 8% per year compounded annually. (Hint: capital recovery is a constant annuity, annually, needed to regain the investment over the life of an investment). A. 4,000 C. 6,720 B. 5,325 D. 7,106 68. An asset is purchased for 9,000 has a book value of P7,545.45 after 1 year. Its estimated life is 10 years. Find its salvage value if sum of the year’s digits method is used. A. P3,000 C. P1,000 B. P2,000 D. P500 69. Objects A and B with the same mass m = 2 kg undergo a direct central impact. A is moving to the right with a velocity of 4 m/s and B is stationary. Determine the velocity of A after impact if the impact is perfectly elastic. A. 4 m/s to the left C. 2 m/s to the right B. 4 m/s to the right D. none of the above 70. A particle moves along a horizontal path with a velocity of v = (3t 2 6t) m/s, where t is the time in seconds. If it is initially located at the origin O, what will be the distance traveled after 3.5 s? A. 6.13 m C. 14.13 m B. 8.13 m D. 10.13 m 71. The crate, which has a mass of 100 kg, is subjected to the action of the two forces. If it is originally at rest, determine the distance it slides in order to attain a speed of 6 m/s. The coefficient of kinetic friction between the crate and the surface is μk = 0.2. A. 1.35 m C. 1.64 m B. 1.09 m D. 0.95 m 72. A tennis tournament has 8 players. The number a player draws from a hat decides his first-round rung in the tournament ladder. See diagram below. If the best player always defeats the rest of the players and the second best player always defeats all the rest except the best, what is the probability that the second best wins the runner-up trophy? 1

First round

Second round

Finals

2 3 4 5 6 7 8 A. 1/2 B. 4/7

C. 2/3 D. 3/7

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Winner

CIVIL ENGINEERS Final Preboard Examination Saturday, October 20, 2018 08:00 a.m. — 12:00 p.m. MATHEMATICS

Page 8 SET A

73. The big block of granite shown in the figure has as lower base the horizontal triangle CDE. The upper edge AB is horizontal and point D lies in the plane ABC. Find the volume. A. 39.60 m3 C. 53.50 m3 B. 44.72 m3 D. 80.71 m3 74. A grocer bought a number of items for P 1440. Later the price increased by P 2.00 per item and as a result he received 24 fewer items for the same amount. Find the number of items bought first. A. 150 C. 162 B. 130 D. 144 75. The areas bounded by the waterline of a reservoir and the contours at an interval of 1.7m are as follows: A1 = 15,430m2, A2 = 12,980m2, A3 = 10,650m2, A4 = 8,540m2, A5 = 5,270m2 and A6 = 2,180m2. Calculate the volume of the reservoir by Prismoidal Formula. A. 78,616.50 m3 C. 78,911.17 m3 3 B. 72,578.67 m D. 72,875.70 m3

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WARNING:

Failure to submit your Test Questions (Complete) set will cause the cancellation of your Test-Results for the subject.

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