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NOVEMBER 2010

MATHEMATICS, SURVEYING & TRANSPORTATION ENG’G

1. AB is directly proportional to BC and BC is directly proportional to CD. The ratio of AB to BC and BC to
CD is 13/17. Find AB when CD=26.
A. 15.204 C. 16.932
B. 12.219 D. 10.334

2. Given that x varies inversely with y. If x=8 when y=2, find x when y=4.
A. 2 C. 6
B. 4 D. 1

3. An airplane flying with the wind took 1.5 sec to travel 500m and 1.6 sec flying against the wind. What
is the speed of the airplane in still air?
A. 1198.2 kph C. 1237.4 kph
B. 1162.5 kph D. 1032.5 kph

4. An observer measured the angle of elevation of a building form X on a level ground as 32°. Moving
100m closer to the building, the angle of elevation was 47°. Find the height of the building.
A. 157.23 m C. 132.98 m
B. 149. 74 m D. 165.22 m

5. From the third floor window of 9m above the ground, an observer measured the angle of elevation of
the top of a nearby building to be 68° and the angle of depression of its base to be 8°. What is the height
of the building?
A. 162.3 m C. 167.5 m
B. 154.9 m D. 136.8 m

6. From a point A 20m above the ground, the angle of elevation of the top of the tower is 29.33°. From a
point B on the ground 150 m horizontally from A, the angle of elevation of the top of the tower is 63.56°.
What is the height of the tower?
A. 232.98 m C. 216.89 m
B. 267.32 m D. 210.16 m

7. An observer measured the angle of elevation of a mountain from a point on a level ground as 8.23°.
Moving 450m closer to the mountain, the angle of elevation is 9.44°. All points are on the same vertical
plane. What is the height of the mountain?
A. 500.32 m C. 621.78 m
B. 534.22 m D. 574.93 m

8. A chord of a circle 0.65m from the center is 1.25 meters long. What is the area of the circle?
A. 2.555 m² C. 3.672 m²
B. 6.236 m² D. 4.975 m²

9. A sphere having a volume of 7238 cm² is cut by a plane 7.2cm from the center. Find the area of the
circle formed by the cutting plane.
A. 128.98 cm² B. 378.76 cm²

876.3 m/s². 289. Find the area between the circles inscribed in the hexagon and the circle circumscribed about the hexagon.77 cm² 16.32 cm² C. 1. how far apart are the missiles after 0.9 m C. 254. The side of a square is 65 cm. 921.21 cm² C.98m/s.23 cm² D.23 m C. where m is the slope and b is the y-intercept. Ball B has an initial velocity of 15m/s and an acceleration of 1.2°. The slope-intercept form of a line is y=mx+b. Find the slope of the line for the following conditions: If x=7.75 seconds? A. units C.21 cm² D. 498.5m/s². 74. how far is the target? A.98 sq.98 cm C.32 m C.54 m D. Ball A has an initial velocity of 40m/s and acceleration of 0.85 D.5.54 11. 59.98 m D. 98. What is the total distance travelled by C? Neglect the sizes of the balls. He heard the bullet hit the target 2. 678.3 m 17.27 is tangent to the coordinate axes. 3845.5. Find the area of the smaller circle that is tangent to the given circle and to the coordinate axes. units B.6 A. y=12. 2011. A marksman fires a bullet to a target. 1. 67.99 cm² 15.62 m . The strength of a rectangular beam varies directly to the product of its width and the square of its depth. A third ball C travels continuously back and forth from A to B at uniform speed of 50m/s until balls A and B collide. A.32 cm² B.3 m D. y=20.54 m B. 78.48 sq. 43. Find the depth of the strongest beam that can be cut from a log of whose cross-sectional area is 4212cm².32 cm B.33 m B. 562.52 cm² 10. 23. 54. 1. 103.74cm long. 89. 1.5 m B. A. 2.45 sq.5 If x=12.43 cm² B. If the speed of the bullet is 900 m/s and the speed of sound is 300 m/s. Two missiles are fired simultaneously at different directions.32 C. 3318. 67. 1.5 seconds later. 957.54m/s and 76. units 13.02 sq. 1. If their velocities are 64.62 B.23 m 14. 1021. A. The angle between their directions is 61. 1. A.C. 103.89 cm 12. 512. A. Two balls A and B. A circle having an area of 50. Find the area between the circumscribed and inscribed circles of the square. units D. The side of a regular hexagon is 9. 1200m apart are moving towards each other. 3265.51 cm² D.79 cm D.

What is the angle facing the 2.A solid steel weighing 155 kg is remoulded into a wire of uniform diameter and length of 1500m.2 B.65°. 4. The outside perimeter of the lot is to be provided with a pathway of uniform width. 0.272 m C. Its base is 16.3° B.28 m C. 15. 5. 15.338 m 25. 417.2 square meter.2 meters wide is constructed inside the hut.98 cm C. 18. what is the corrected length of the line? A.61 21. 14. 3. 82. A line was measured on a sloping ground to be 15. Find the thickness of hallow spherical steel ball of the same volume and with inside diameter equal to the diameter of the solid ball.Two sides of a triangle measure 2.034 m B.87 B.8° 24. The vertical distance between the ends of the line is 0.171. 15.456.834 m B. 34 m C. What is the radius of the curve? A.9° D.2 .54m and their included angle is 48. 46.78m. If the area of the pathway is 11. 402.3° C. 82.01 m B.318 m B. 0. 3.1° D.75 m D.34 m D. 0.344 m D.3 meters wide and its height at the center is 12. 5.2° C.54m side? A. What is the measure of the third side of the triangle? A.53 grams per cubic centimetre.743 m 23.18. 18. 16.56m side? A.432.98 m Situation 1. How high is the ceiling above the base? A.673 m C. A.84 m 19. 42. A rectangular lot is 12m long and 5m wide. 53. 15. 4.563 m D. 2.46 m B. 2. 13. A solid spherical steel ball has a volume of 1500cm³.72 m B. What is the volume of steel in cubic centimetre? A. 27.1° B. 2.89 D. 2.56 m and 3. and 64. A flat horizontal ceiling 12.1° 26.9° SITUATION 2. 4. 13.32 m D.376 m 22. 0. A 20-m chord of a simple curve subtends an angle of 2. What is the angle facing the 3. A. 46. 85. 53. Find the radius of the inscribed circle. Density of steel is 8. what is its width? A.892 m C.4 meters. 85.12 m 20.94 m long. 5. The sides of a triangle measures 59.65 C. 387. A Quonset hut 18 meters long has a parabolic cross.921 m D.

37 B.834.84 . 3. What is the cross-sectional area of the wire in square millimeters? A. What is the diameter of the wire in mm? A.24 D. 17.41 B.8 D.93 C. 18. 4.945. 4.5 28.17 D. 13.C. 12. 15.68 29. 4.11 C. 18.

5 meters below the water surface? A.8 square meter D. 2365 kPa D.2 square meter 9. A. What additional load can be placed on top of the cylinder for it to be submerged completely in water? A.5 meters below the water surface? A.34 B. 1935 kPa B. 1256 m/s D.3 KN SITUATION 2. 16. 2.A rectangular canal is 6. 1.6 KN B.8m/s. 1.21 8.678 X10⁹ Pa B. 1. 25. 18. 18.76 KN B. What is the composite modulus of elasticity of water? A.02 KN D.2x10⁹. Determine the celerity of pressure wave of water. 0. 19. 1177 m/s C. Modulus of elasticity of pipe material is 1. Pipe thickness is 16mm.A cylindrical tank. 1. 4.1 KN B. Determine the water hammer pressure assuming instantaneous closure.384 X10⁹ Pa 5. 1. 1. 1. 1876 kPa SITUATION 3.112X10⁹ Pa C. 19. What weight of lead must be fastened to the outside bottom in order for the cylinder to float with 2. What savings in lining per meter length of canal could have been effected if the most efficient rectangular section were used for the same discharge and slope? A. 1382 m/s 6. What savings in earth excavation per meter length of canal could have been effected if the most efficient rectangular section were used for the same discharge and slope? A.Water flows on a straight 150m pipe.9 KN C.3 KN D.4x10¹¹ Pa. in m³/S A.21 cubic meter B.1 square meter C. Bulk modulus of elasticity of water is 2.24KN. 19.2 KN 3. 21. The canal laid on a uniform slope of 0. Calculate the discharge on the canal. What weight of lead (lead=110KN/m³) must be placed inside in order for the cylinder to float with 2.45 cubic meter .3 KN D. 16.013. 20. 1421 m/s B.002 and roughness coefficient is 0. 17.67 square meter B. 1m in diameter and 3m tall weighs 3. 0. 21. 15.24 C. The velocity of flow is 1. 0. 600mm in diameter. A.32 KN 2.76 D.2 meters wide and 1. 2118 kPa C.HYDRAULICS & GEOTECHNICAL ENGINEERING SITUATION 1.2 meters depth. 7. 23.291 X10⁹ Pa D.45 KN C.4 KN C. 23. 15.

900 B. Determine the nearest value to the moisture content of the soil in percent. 400 12. Laboratory test shows the soil particles have specific gravity of 2. 112 D. Determine the minimum reservoir capacity in cubic meter. 0. A.2 B. 500 B. 104 C. 16. 108 B. 51 D. 300 cubic meter C. 32. 65 SITUATION 6.Water is pumped into a reservoir at 600m³ every 4 hours. 18. what is the volume at 2000hrs? A.98 D. 200 cubic meter B.63 B. 800 D.39 cubic meter SITUATION 4. the soil weighs 975 grams. 59 B. The demand every 4 hour interval is as follows: Time` Demand 0400 200 0800 800 1200 1100 1600 700 2000 500 2400 300 10.70. A. 43.62 16.67 cubic meter D.67 . 400 cubic meter SITUATION 5. What is the porosity of the soil in percent? A. 700 D.7 C. 95 15. 40.44 Void ratio at its loonsest state=0.5 14.350 grams. What is the minimum requirement from the reservoir in cubic meter? A. 34 C. 18. 500 C.6 D.66 Void ratio at its densest state=0. 100 cubic meter D.34 C. What is the void ratio of the soil in percent? A. Determine the dry unit weight of the soil in kn/m³ A.C.Given the following soil properties of a road grading works Moist unit weight=1900kg/m³ Moisture content=12% Specific gravity of solids=2. After oven drying for 24 hours. 17. 38.A sample of saturated soil taken from the field weighs 1. 600 11. 600 C. 13. 0. If the volume of water in the tank at 0800hrs is 700m³.

What is the nearest value to the angle of failure plane? A.5 B.8° D. L1=1. 36. 43.A triaxial test was conducted on a cohesionless soil. At failure plane. 32.45 C.3% 18.33 B. 68.7Mm. 900 C.28 24. that is the effective pressure at the midheight of the consolidating clay layer.2 C. 22. 167. 0.5° B.1% D. L2=1.7 D.8m.4° 21. 56.5° B. 99 mm 130 mm C. 0. 59. A. 131.7 D.A group of friction piles is shown in the figure. Compute for the compression inside of the clay. B.qu=180kPa. 157. 65. A. 55. 145. 157 mm . 62. What is the nearest value to the maximum principal stress in kPa? A. in kPa. 123 mm D.FS=3 22. 0. 800 SITUATION 8.7° D. A.9 C. 0.5 23. What is the nearest value to the angle of internal friction of the soil? A.2° C.9° 20. A. 39.8% B. 43. Determine the relative density of the soil in percent. the normal stress is 400 kPa and the shearing stress is 300 kPa.17.8 SITUATION 7.23 D. 63.2 B. Compute for the overburden pressure. 32. 1100 B. The total load on the pile less the soil displaced by the footing is 1600 Kn.3% C. What is the approximate settlement of the foundation? A. L=9m. 76.9° C. 1000 D. Determine the in situ void ratio of the soil. 19. 28.

3 kPa C. 27. A. A. 19. D2=47m. 173.74 kPa C.32 Kpa SITUATION 10. 0. 2.98 kPa B. 115. Compute for the value of the unit weight of sand above water table.66 m³/day B. The water table is 2.4 kPa D. 189.0025 30. 0. The sand have void ratio of 52% and the degree of saturation above water table is 37%.35 kn/m³ 26.A confined aquifer underlies an unconfined aquifer as shown in the figure. 18. 25.45 kn/m³ D. 17. 0.76 m³/day C. Calculate the hydraulic gradient. 3. A. 138.5 meter thick sand is overlying a very thick clay layer.21 m³/day STUCTURAL ENGINEERING & CONSTRUCTION .025 B.5 kPa 27. A. Calculate the flow of water from one stream to another per meter width. The clay has moisture content of 42%.H2=30m. Compute for the value of the total stress at a depth of 10m from the ground surface. K2=25m/day. 210. 18.32 kn/m³ C.5m below the ground (sand) surface. 28. 2. A. 26. 167. 22. Calculate the equivalent coefficient of permeability in horizontal direction A.82 kPa D. 4. 104.2 kPa B. 3. Compute for the value of the effective stress at a depth of 10m from the ground surface.25 C. in kPa.93 m/day C.62 m/day B.K1=28m/day. in kPa.L=2km. 127.A 5.65 25. GIVEN THE FOLLOWING: d1=52M.5 D.SITUATION 9. H1=35m.12 m/day D.97 kn/m³ B. Assume specific gravity of solids for both sand and clay equal to 2.29 m³/day D.45 m/day 29.

6. 5. 3.4° D. A. 5.5° 3.34 mm D. 7 mm B.45 C.The ring moulding shown in Figure 004 is 2m in diameter and supported by six steel cables spaced equally along its perimeter. Determine the force in each cable in KN. 51.56 5.2° C.23 B.5 kn//m along its circumferential length. 6 mm C. What is the minimum diameter of cable if its allowable stress is 124 MPa? A. 8.66 KN B. 5 mm D. 4. 1. Determine the vertical displacement of moulding if the diameter of the cable wire is 10mm.25 A. 1.59 mm B. 4.12 KN C. What is the resultant of the forces in the wires. 0. 2.3° B. 58. At what angle will the resultant make with the horizontal? A.78 KN SITUATION 2. 2. 67. 4. 0.87 2.98 KN D. 1.17 mm C.12 B. 5.5KN. Minimum weight W to prevent uplift with a factor of safety of 1. 5. 6. in KN? A.76 D. The ring weighs 2.Two tension wires are supported by a concrete block shown in Figure 002. A.32 D.78 C. 4 mm 6.98 mm . The tension in the wires are T1=3KN and T2=7.SITUATION 1. 46.

1 m B. A. 5. 3. A. 62 KN D. 38 KN-m C. Determine the maximum shear in the slab. 58 KN C.4 kPa.5 m D. 1.3m o. 48 KN 8. Determine the location of zero bending moment measured from the left end of the slab.The concrete slab shown in Figure 005 is subjected to uniform loads 7. What is the maximum bending stress in the beam using 3-m long joist? A.c. 3.5 m. floor finish (including weight of joint) is 2. 42 KN-m 9.37 MPa . Determine the maximum moment in the slab. A. 50 KN B. The superimposed load on the floor due to ceiling.45 MPa B. 2. 40 KN-m B.SITUATION 3. The joists to be used have lengths of 3m and 3. 10.5 m C.75 m SITUATION 4.The timber floor joist shown in the figure has dressed dimension of 40mm x 190mm and spaced 0. The girders are spaced 3 meters on centers. 36 KN-m D.

.67 MPa D.60 Channel properties: Sx=48. 5. 4.5-m long joist? A.74 MPa D.….2 Leeward……………………………. What is the maximum bending stress in the beam using 3.32 MPa SITUATION 5. 6.21 MPa C. 0. 0. 2.The channel shown in Figure 001 is used as a purlin on a roof truss with slope of 3H to 1V. The roof loads are as follows: Dead load pressure………………….C. w=71N/m Allowable bending stress. 1.18 MPa B.8x10³ mm³ Sy=11. 0. 3.78 MPa C. Fbx=Fby=138 MPa .8x10³ mm³ Weight....65 MPa D. The trusses are spaced 3 meters on centers. 0.43 MPa 12.0.1400 Pa Wind pressure coefficients: Windward……………………………0.45 MPa B.….32 MPa 11.1000 Pa Wind pressure………………………………. What is the maximum shearing stress in the beam using 3-m long joist? A..1200 Pa Live load pressure…………………….

28 mm tension bars at the bottom. 312 C. 387 B.94 C. 0. 0. The properties of the column section are as follows: . A. 453 D.28mm compression bars on top and 4.02 14. 0. each located 70mm from the extreme concrete fiber. What is the ultimate moment capacity of the beam in KN-m? A. 123 KN C. 0.32 B. A. The Euler critical load is P=πEI/(Le)² where Le is the effective length of the column. 71 D.98 D. 0.75(DL+LL+WL) A.72 15. 0. 16.An 8-m long steel column is pinned at the top and fixed at the bottom. The column is provided with lateral support at midheight of its weak axis. 0. Determine the value of interaction equation due to dead load and live load if sag rods are provided at the midspan of each purlin.71 SITUATION 6. 1. 98 B. 73 KN B. The beam is reinforced with 2.86 D.13. A.58 C. 0. 0. 1. 83 C. and steel yield strength fy=415 MPa. Determine the value of interaction equation due to load combination 0. Concrete strength f’c=20. A.56 B. Determine the additional concentrated live load that can be applied at midspan if the dead load including the weight of the beam is 20 kn/m. 86 KN SITUATION 7. Determine the value of interaction equation due to dead load and live load. 132 17.A 6 meter long simply supported reinforced concrete beam has a width of 350mm and an overall depth of 400mm.45 D.7 MPa.87 B. 45 KN D.87 C. Depth of compression block assuming both tension and compression steel yields. 532 18. 0.

3170 KN B. 430 KN C.…. 6. 198 KN B. 11.35 f’c.8x10⁶ mm⁴ Ix= 178. Concrete strength Fx= 24 MPa. 576 KN C.The steel beam shown in Figure 006 is resting on a 200-mm thick concrete wall. 456 KN 23. A. 98 B. 118 20.5 m C. Allowable bearing strength of concrete is 0. 504 KN B. The wall is provided with 300mmx200mmx25mm steel base plate. Determine the maximum length of the column if the proportional limit is 320 MPa.0 Fixed at both ends……………………………………………….70 19. Allowable bending stress of steel base plate is 0. 7. Determine the beam reaction based on bearing on concrete wall. What is the critical load P that will cause an initial buckling? A.1x10⁶ mm⁴ A= 8129 mm² Effective length factors: Pin at both ends………………………………………………………1. What is the critical effective slenderness ration of the column? A. 179 KN C. Determine the mean reaction based on bending at a distance k from the X axis of the web.66Fy. 153 KN D. A. The steel are A-36 with Fy=248MPa.8 m SITUATION 8. 78 C.75Fx Properties of beam: B=225mm t=12mm D=600mm k=36mm T=18mm 22. 1980 KN C.5 Fixed and one end and pin on the other end…………. 2750 KN D.6 m D. 570 KN . 83 D. A. 2320 KN 21.. Determine the beam reaction based on web crippling at a distance N+25k A. 112 KN 24. 9.0. 620 KN B. 510 KN D. Allowable compressive stress in the web at the toe of fillet is 0. 372 KN D.3 m B.0. Iy= 18..

reinforced with 8.28mm bars spaced evenly on all sides.7 KN B. 270 D.3 KN 30. 440 SITUATION 10. 198. It is required to determine the moment in girder BEHK 28.3 KN C. 154. 211. 154. What is the factored load by beam GHI t H in girder BEHK? A. 176 C. 25. 211.7 KN C. What is the maximum positive moment in beam BEHK in KN/m? A. in KN. 174. Determine the nominal axial load capacity of the column. 560 B. 4890 B. 4620 26.6 KN D. 234 B.2 KN 29.36 kPa including its own weight. Concrete protective cover is 40mm. 450mm x 450mm.The slab shown in Figure 007 carries uniform factored load of 12. A. Determine the nominal balanced load of the column in KN. fy=415 MPa. Determine the nominal balanced moment of the column in KN-m A. f’c=21MPa.Concrete column. stirrup used is 12mm in diameter. 194 . A.SITUATION 9. 146 D. 380 C. 1480 27. 174. 4415 D. 198. What is the factored load included by beam BEF at E in girder BEHK? A. 1850 D.2 KN D. 4185 C. 1530 B.6 KN B. 1190 C.