Preboard - Set A

PHILIPPINE INSTITUTE OF CIVIL ENGINNERS SPLBE – PREBOARD – EXAM MATHEMATICS, SURVEYING & TRANSPORTATION ENGINEERING INSTRUCTION: Select the correct answer for each of the following questions. Mark only one answer for each item by shading the circle corresponding to the letter of your choice on the answer sheet provided. 1. Given the following elements of a circular curve: middle ordinate = 2 m; length of long chord = 70 m. Find its degree of curve, use arc basis. a. 4.5° b. 5.3° c. 2.9° d. 3.7° 2. A truncated prism having a square base has a volume of 1000 cubic meters. The height of the prism at each corner is respectively 7m, 7m, 10m, and 10m. What is the area of the base? a. 132.85 m2 b. 109.95 m2 c. 120.45 m2 d. 117.65 m2 3. A grade line AB having a slope of +5% intersect another grade line BC having a slope of –3% at B. The elevations of points A, B and C are 95 m, 100 m and 97 m respectively. Determine the elevation of the summit of the 100 m parabolic vertical curve to connect the grade lines. a. 98.32 m b. 99.06 m c. 97.32 m d. 96.86 m 4. Determine the impact factor for a highway curve having a radius of 600m and maximum speed of 100kph. a. 0.28 b. 0.51 c. 0.13 d. 0.37 5. Find the largest area of a rectangle which can be inscribed in the ellipse, 4𝑥 2 + 9𝑦 2 = 36. a. 12 b. 24 c. 6 d. 48

PHILIPPINE INSTITUTE OF CIVIL ENGINNERS SPLBE – PREBOARD – EXAM MATHEMATICS, SURVEYING & TRANSPORTATION ENGINEERING 6. A right circular cone with an altitude of 9 m is divided into two segments. One is smaller circular cone having the same vertex with an altitude of 6m. Find the ratio of the volume of the two cones. a. 2:3 b. 8:27 c. 2:5 d. 1:3 7. Determine the capacity of a single lane road in vehicle’s per hour if the speed of the car moving in a single lane is 50kph. Length of car is 4.80m. Reaction time =0.80sec. a. 3567 b. 3560 c. 3225 d. 3142 8. Identify the quadrant/s of an angle that satisfies the given condition cos θ < 0, sec θ < 0. a. II, IV b. II, III c. II d. III 9. The edges of the bases of a frustum of a regular square pyramid are 10 m and 20 m, respectively and the altitude is 7 m. calculate its lateral surface area. a. 516.14 m2 b. 502.76 m2 c. 498.25 m2 d. 480.34 m2 10. Find the radius of the spherical wedge whose volume is 12 m3 with a central angle of 1.8 radians. a. 2.45 m b. 2.33 m c. 2.63 m d. 2.15 m 11. From the top of a tower 120 ft. high, the angle of depression of a point A is 15°, and of another point B is 11°. The bearings of A and B from the tower are 205° and 137° respectively. If A and B lie in a horizontal plane through the base of the tower, calculate the distance AB. a. 610ft b. 611ft c. 612ft d. 613ft

PHILIPPINE INSTITUTE OF CIVIL ENGINNERS SPLBE – PREBOARD – EXAM MATHEMATICS, SURVEYING & TRANSPORTATION ENGINEERING 12. Given the following cross section notes of an earthwork on a rolling terrain. If the width of the road is 12m and the side slope is 2.5:1, compute the volume using end area with Prismoidal correction. STA 5+000 +10 31

+5 0

+3 13.5

STA 5+020 +14 41 a. b. c. d.

+7 0

+4.50 17.25

4050.42 cu. m. 4055.42 cu. m. 4060.42 cu. m. 4065.42 cu. m.

13. Three sides of a cyclic quadrilateral measure 252 m, 368 m and 280 m, consecutively. If the angle measurement from the first to second side is 107°, calculate the area of the quadrilateral. a. 23.11 ha b. 13.22 ha c. 21.13 ha d. 11.23 ha 14. In a two peg test on a dumpy level, the following observations were taken. What is the true difference in elevation between A & B if point C is equidistant from A and B and D is 12m from A and 72m from B?

Rod Reading on A Rod Reading on B a. b. c. d.

Instrument at C 1.103 0.991

Instrument at D 0.568 0.289

0.175 0.112 0.135 0.276

15. Given the corrected latitudes and departure of a closed traverse LINES

1-2

LATITUDE +80.16

DEPARTURE -40.12

PHILIPPINE INSTITUTE OF CIVIL ENGINNERS SPLBE – PREBOARD – EXAM MATHEMATICS, SURVEYING & TRANSPORTATION ENGINEERING

2-3 3-4 4-5 5-6 6-1

-40.13 +70.18 -30.14 +60.20 -140.27

-36.82 +50.42 +30.36 -52.34 +48.50

Compute the DMD of line 3-4. a. +103.46 b. -103.46 c. +190.28 d. -190.28 16. Compute the area of the lot in the previous problem. a. 175 sq. m. b. 180 sq. m. c. 185 sq. m. d. 190 sq. m. 17. Calculate the central angle of the sector if its area is 32% of the circle. a. 115.2° b. 123.5° c. 105.3° d. 132.1° 18. Given is the area in the first quadrant bounded by 𝑥 2 = 8𝑦 , the line 𝑥 = 4 and the 𝑥 − 𝑎𝑥𝑖𝑠. What is the volume generated by revolving this area about the y-axis? a. 50.26 b. 52.26 c. 53.26 d. 51.26 19. The sides of a square lot having an area of 2.25 hectares were measures using a 100m tape that was 0.04 too short. Compute the error in square meter. a. 18 b. 20 c. 22 d. 24 20. Find the area in the first quadrant bounded by the parabola 𝑦 2 = 4𝑥, 𝑥 = 1 and 𝑥=3 a. 9.555 b. 5.955 c. 5.595

PHILIPPINE INSTITUTE OF CIVIL ENGINNERS SPLBE – PREBOARD – EXAM MATHEMATICS, SURVEYING & TRANSPORTATION ENGINEERING d. 9.955 1

21. Determine the period of the function 𝑦 = 2𝑠𝑒𝑐 2 𝑥. a. b. c. d.

4π 2π π π/2

22. Two hills A and C have elevations of 600m and 800m respectively. In between A and C is another tower B which has an elevation of 705m and is located 12km from A and 10km from C. Determine the clearance or obstruction of the line of sight at hill B if the observer is at A so that C will be visible from A. a. 2.95m b. 3.95m c. 4.95m d. 5.95m 23. A solid has a circular base of base radius 20 cm. Find the volume of the solid if every plane section perpendicular to a certain diameter is an isosceles right triangle with one leg in the plane of the base. a. 22333.33 cm3 b. 23333.33 cm3 c. 21333.33 cm3 d. 20333.33 cm3 𝜋

24. Evaluate integral of 12 ∫02 𝑠𝑖𝑛5 𝑥𝑐𝑜𝑠 5 𝑥𝑑𝑥 . a. 0.20 b. 0.50 c. 0.25 d. 0.35 25. What is the book value of an electronic test equipment after 8 years of use if it depreciates from its original value of P120 000 to its salvage value of 13% in 12 years. Use straight line method. a. P20,794.76 b. P50,400 c. P40,794.76 d. P50,794.76 26. A steel drum manufacturer incurs a yearly fixed operating cost of P200,000. Each drum manufactured cost P160 to produce and sells for P200. What is the manufacturers break-even sales volume in drums per year? a. 1250 b. 2500 c. 1000

PHILIPPINE INSTITUTE OF CIVIL ENGINNERS SPLBE – PREBOARD – EXAM MATHEMATICS, SURVEYING & TRANSPORTATION ENGINEERING d. 5000 27. Find the distance between the lines 3𝑥 + 𝑦 − 12 = 0 and 3𝑥 + 𝑦 − 4 = 0. 16 a. 10 b. c. d.

√ 12 √10 4 √10 8 √10