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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

1.85 D. 678.2°.5 m B.74cm long.33 m B. 3318. Two balls A and B. 3845. units 13. 2. 2011. how far is the target? A. where m is the slope and b is the y-intercept.51 cm² D. units B. 254. 921.99 cm² 15.5m/s². 89.54 11. 1021. A. 498. 1200m apart are moving towards each other. 512.23 m C.32 C.3 m 17.23 m 14. Find the area between the circles inscribed in the hexagon and the circle circumscribed about the hexagon.27 is tangent to the coordinate axes.23 cm² D. A circle having an area of 50.75 seconds? A. 23. units D. how far apart are the missiles after 0.5. 957.98 cm C. units C.3 m D.3 m/s².77 cm² 16.98 m D.02 sq. 98.9 m C. y=20. 1. A.45 sq. What is the total distance travelled by C? Neglect the sizes of the balls. Find the slope of the line for the following conditions: If x=7. 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.6 A. 67. 3265. If their velocities are 64.98 sq. 1.32 m C. A. 67. 78. He heard the bullet hit the target 2.54 m D. 43.5 seconds later. A marksman fires a bullet to a target. Find the area between the circumscribed and inscribed circles of the square. 74.21 cm² C.5. Ball B has an initial velocity of 15m/s and an acceleration of 1.52 cm² 10. Find the area of the smaller circle that is tangent to the given circle and to the coordinate axes. Ball A has an initial velocity of 40m/s and acceleration of 0.62 m . The slope-intercept form of a line is y=mx+b.79 cm D. 1. Two missiles are fired simultaneously at different directions.C. y=12.21 cm² D.48 sq. Find the depth of the strongest beam that can be cut from a log of whose cross-sectional area is 4212cm². 59.54 m B. A. 103.32 cm² B. The side of a square is 65 cm. If the speed of the bullet is 900 m/s and the speed of sound is 300 m/s.43 cm² B. The side of a regular hexagon is 9.62 B. 103. A. 1.5 If x=12.32 cm B. 1. 54. 289. 1.54m/s and 76.32 cm² C.89 cm 12. The strength of a rectangular beam varies directly to the product of its width and the square of its depth. 562. The angle between their directions is 61. 876.98m/s.

2 .75 m D. what is its width? A. 15. A rectangular lot is 12m long and 5m wide. 2.Two sides of a triangle measure 2.8° 24.54m and their included angle is 48. If the area of the pathway is 11.3 meters wide and its height at the center is 12.9° SITUATION 2. A solid spherical steel ball has a volume of 1500cm³. what is the corrected length of the line? A.563 m D. 13. 18.034 m B.3° C. The outside perimeter of the lot is to be provided with a pathway of uniform width.56m side? A.1° B. Find the radius of the inscribed circle.84 m 19.72 m B. A Quonset hut 18 meters long has a parabolic cross. 34 m C. A 20-m chord of a simple curve subtends an angle of 2.53 grams per cubic centimetre. A. 0.56 m and 3.78m. The vertical distance between the ends of the line is 0. 85. 417. What is the angle facing the 2. A. 42.432. 82. A flat horizontal ceiling 12.98 m Situation 1.89 D. 16. Density of steel is 8. 2. 15.9° D.2° C. What is the volume of steel in cubic centimetre? A.2 square meter. 53. 5. 15.12 m 20. 3. 46.46 m B.2 B. 27. 53. 46. 5. 4. How high is the ceiling above the base? A.673 m C.94 m long. 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.98 cm C.171. 387.32 m D.892 m C.87 B.34 m D.272 m C. 0. What is the radius of the curve? A. 14.18.65°. 4. What is the angle facing the 3.3° B.344 m D.28 m C.318 m B. 85. The sides of a triangle measures 59. 18. 3. 13.65 C. 0. A line was measured on a sloping ground to be 15.2 meters wide is constructed inside the hut.338 m 25.A solid steel weighing 155 kg is remoulded into a wire of uniform diameter and length of 1500m.1° D. 5.376 m 22. What is the measure of the third side of the triangle? A.61 21. 82. 2.1° 26. Its base is 16. and 64. 2.54m side? A. 402.921 m D.743 m 23.4 meters.01 m B. 4.456. 0.834 m B.

15.37 B.945.834. What is the cross-sectional area of the wire in square millimeters? A. 18. 12.41 B. 13. 4.24 D.93 C. 3.8 D.11 C.17 D. 18. 17.84 . 4.C.68 29. What is the diameter of the wire in mm? A.5 28. 4.

4 KN C. 1177 m/s C. 1. Calculate the discharge on the canal. 19. What weight of lead (lead=110KN/m³) must be placed inside in order for the cylinder to float with 2. 2.24KN.67 square meter B. 1.678 X10⁹ Pa B. What additional load can be placed on top of the cylinder for it to be submerged completely in water? A. 16.1 square meter C. 19.3 KN SITUATION 2. A. 25. 21. 23. 1421 m/s B. 15. 1935 kPa B. 21. 1. 1m in diameter and 3m tall weighs 3.45 KN C.32 KN 2. 23.8 square meter D. 600mm in diameter.3 KN D. What weight of lead must be fastened to the outside bottom in order for the cylinder to float with 2. 20.6 KN B. 1. 1.1 KN B. 1876 kPa SITUATION 3.384 X10⁹ Pa 5. 18.013.Water flows on a straight 150m pipe.002 and roughness coefficient is 0. A.2x10⁹. 1256 m/s D. The velocity of flow is 1. 2365 kPa D. 0.24 C. Modulus of elasticity of pipe material is 1.21 8.2 square meter 9. 17.291 X10⁹ Pa D. 0. Pipe thickness is 16mm. 2118 kPa C. 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.76 KN B. 18. 1.2 KN 3.5 meters below the water surface? A. The canal laid on a uniform slope of 0.2 meters depth. 1382 m/s 6. Bulk modulus of elasticity of water is 2.3 KN D.02 KN D.34 B.5 meters below the water surface? A.21 cubic meter B. What is the composite modulus of elasticity of water? A. 15. 1.A cylindrical tank.8m/s. in m³/S A.45 cubic meter . 0. 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.112X10⁹ Pa C. Determine the water hammer pressure assuming instantaneous closure. 16.4x10¹¹ Pa. 19.HYDRAULICS & GEOTECHNICAL ENGINEERING SITUATION 1. 4.76 D.9 KN C.A rectangular canal is 6.2 meters wide and 1. 7. Determine the celerity of pressure wave of water.

A.7 C.70. 400 12. the soil weighs 975 grams. Laboratory test shows the soil particles have specific gravity of 2. 600 11. 95 15. 200 cubic meter B. 18. 500 C. 18.44 Void ratio at its loonsest state=0. 43. 34 C.98 D.63 B.2 B. Determine the dry unit weight of the soil in kn/m³ A. 32. Determine the nearest value to the moisture content of the soil in percent. 16. 13. 104 C. A. what is the volume at 2000hrs? A. 300 cubic meter C.62 16.350 grams.5 14.67 cubic meter D. 112 D. 59 B. Determine the minimum reservoir capacity in cubic meter.A sample of saturated soil taken from the field weighs 1. After oven drying for 24 hours. What is the minimum requirement from the reservoir in cubic meter? A.66 Void ratio at its densest state=0. What is the porosity of the soil in percent? A.Water is pumped into a reservoir at 600m³ every 4 hours. 51 D.67 .39 cubic meter SITUATION 4. 40. 700 D. 17. 100 cubic meter D. 65 SITUATION 6. 900 B. What is the void ratio of the soil in percent? A.6 D. 108 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. 38.C. 400 cubic meter SITUATION 5. 600 C. 0.34 C. 800 D. 500 B. 0. If the volume of water in the tank at 0800hrs is 700m³.Given the following soil properties of a road grading works Moist unit weight=1900kg/m³ Moisture content=12% Specific gravity of solids=2.

1000 D. 55. 800 SITUATION 8.3% 18.9° C. 19. 59.23 D. 63. 76.8% B. in kPa. 62. What is the approximate settlement of the foundation? A.2 C. Compute for the compression inside of the clay. 0.7 D. L2=1. L1=1. 123 mm D.8° D.5° B.qu=180kPa. L=9m.8m.5 B. 167. that is the effective pressure at the midheight of the consolidating clay layer.9 C.4° 21.2 B.3% C.2° C. Determine the in situ void ratio of the soil. 145. B.8 SITUATION 7. Determine the relative density of the soil in percent.7Mm. 99 mm 130 mm C.33 B. 131. A. What is the nearest value to the maximum principal stress in kPa? A. 68. What is the nearest value to the angle of internal friction of the soil? A.1% D. 43. 39. A.17. 56.28 24. 157. 1100 B. 65. 0. 36. 900 C.7° D.45 C. A. the normal stress is 400 kPa and the shearing stress is 300 kPa. What is the nearest value to the angle of failure plane? A.FS=3 22.9° 20.5 23. 22. Compute for the overburden pressure. 157 mm . 43. 32. 28. 0. A.A triaxial test was conducted on a cohesionless soil.A group of friction piles is shown in the figure. 0.5° B. 32. The total load on the pile less the soil displaced by the footing is 1600 Kn.7 D. At failure plane.

3 kPa C.25 C. 210. 22. 104.62 m/day B.L=2km.SITUATION 9. A.12 m/day D.76 m³/day C. 0. 28. 18.0025 30.21 m³/day STUCTURAL ENGINEERING & CONSTRUCTION . Compute for the value of the unit weight of sand above water table. 27. in kPa.A 5.82 kPa D. Compute for the value of the effective stress at a depth of 10m from the ground surface.4 kPa D.98 kPa B. 167.32 Kpa SITUATION 10. 26.35 kn/m³ 26. 3.A confined aquifer underlies an unconfined aquifer as shown in the figure.97 kn/m³ B.45 m/day 29. 189.93 m/day C. A. GIVEN THE FOLLOWING: d1=52M. The water table is 2. Compute for the value of the total stress at a depth of 10m from the ground surface.5 D. Calculate the flow of water from one stream to another per meter width. Calculate the hydraulic gradient.74 kPa C. 127. 0. The sand have void ratio of 52% and the degree of saturation above water table is 37%. 3.66 m³/day B. A.32 kn/m³ C.5m below the ground (sand) surface.H2=30m. 138.29 m³/day D. 19.5 kPa 27. 2. 18. D2=47m. 25. 0. K2=25m/day. 2. A.5 meter thick sand is overlying a very thick clay layer. A. 115. H1=35m. The clay has moisture content of 42%.025 B. 173.K1=28m/day. Assume specific gravity of solids for both sand and clay equal to 2. Calculate the equivalent coefficient of permeability in horizontal direction A.65 25. 4. 17.2 kPa B. in kPa.45 kn/m³ D.

5° 3. 5. At what angle will the resultant make with the horizontal? A.The ring moulding shown in Figure 004 is 2m in diameter and supported by six steel cables spaced equally along its perimeter.59 mm B.23 B. Minimum weight W to prevent uplift with a factor of safety of 1.78 KN SITUATION 2.45 C. What is the minimum diameter of cable if its allowable stress is 124 MPa? A. 6 mm C. 5.SITUATION 1. 5.5KN.56 5.32 D.66 KN B. 5 mm D. 67. 2.87 2. 1.98 mm .3° B. 8. 51. 0. 5. Determine the vertical displacement of moulding if the diameter of the cable wire is 10mm. 0. 1. 3. A.17 mm C.76 D. The ring weighs 2. Determine the force in each cable in KN.78 C. 7 mm B.98 KN D.25 A.2° C. 58. The tension in the wires are T1=3KN and T2=7. 6. 2.12 B. 4.4° D. A. 4. 4 mm 6. 46.Two tension wires are supported by a concrete block shown in Figure 002. What is the resultant of the forces in the wires. 6. in KN? A.34 mm D. 4.5 kn//m along its circumferential length. 1.12 KN C.

The superimposed load on the floor due to ceiling.75 m SITUATION 4. A. 5. 3.The concrete slab shown in Figure 005 is subjected to uniform loads 7.5 m C. 2.SITUATION 3. 62 KN D. 38 KN-m C. The girders are spaced 3 meters on centers. floor finish (including weight of joint) is 2. What is the maximum bending stress in the beam using 3-m long joist? A.5 m. Determine the maximum moment in the slab. 1. Determine the maximum shear in the slab. 40 KN-m B. 58 KN C. A.4 kPa.3m o.The timber floor joist shown in the figure has dressed dimension of 40mm x 190mm and spaced 0. A. Determine the location of zero bending moment measured from the left end of the slab. 1 m B. 36 KN-m D. 48 KN 8.45 MPa B.c.5 m D. 42 KN-m 9. 50 KN B. 10. The joists to be used have lengths of 3m and 3.37 MPa . 3.

1200 Pa Live load pressure…………………….5-m long joist? A. The trusses are spaced 3 meters on centers.8x10³ mm³ Sy=11.32 MPa 11.. Fbx=Fby=138 MPa . 0.8x10³ mm³ Weight. 6. w=71N/m Allowable bending stress.18 MPa B.2 Leeward…………………………….78 MPa C. What is the maximum bending stress in the beam using 3.1000 Pa Wind pressure……………………………….21 MPa C. 5. 0.65 MPa D.67 MPa D. 0.C.74 MPa D.1400 Pa Wind pressure coefficients: Windward……………………………0.…. 0. The roof loads are as follows: Dead load pressure………………….The channel shown in Figure 001 is used as a purlin on a roof truss with slope of 3H to 1V.. 4...32 MPa SITUATION 5.43 MPa 12.0.…. What is the maximum shearing stress in the beam using 3-m long joist? A. 3..60 Channel properties: Sx=48.45 MPa B. 1. 2.

453 D.58 C. The Euler critical load is P=πEI/(Le)² where Le is the effective length of the column. 0.72 15. 0. A. Determine the value of interaction equation due to load combination 0. 1.A 6 meter long simply supported reinforced concrete beam has a width of 350mm and an overall depth of 400mm. 0.56 B. 312 C. 387 B. 83 C. 86 KN SITUATION 7. Determine the value of interaction equation due to dead load and live load if sag rods are provided at the midspan of each purlin. 45 KN D. 0.7 MPa.87 B. 16. 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.98 D.71 SITUATION 6. 0. each located 70mm from the extreme concrete fiber.28 mm tension bars at the bottom. The properties of the column section are as follows: . and steel yield strength fy=415 MPa. A. The beam is reinforced with 2. Depth of compression block assuming both tension and compression steel yields. 0. What is the ultimate moment capacity of the beam in KN-m? A.94 C.13. 123 KN C. 0.An 8-m long steel column is pinned at the top and fixed at the bottom.87 C.45 D.28mm compression bars on top and 4. A. A. 73 KN B. 1.86 D. 0. 532 18. The column is provided with lateral support at midheight of its weak axis. 98 B. Concrete strength f’c=20.02 14. 71 D.32 B. 0. 132 17.75(DL+LL+WL) A. 0. Determine the value of interaction equation due to dead load and live load.

3 m B. 456 KN 23. Determine the mean reaction based on bending at a distance k from the X axis of the web. A. 118 20.8 m SITUATION 8. 2320 KN 21.The steel beam shown in Figure 006 is resting on a 200-mm thick concrete wall. The wall is provided with 300mmx200mmx25mm steel base plate. 198 KN B.70 19. 1980 KN C. Allowable bearing strength of concrete is 0. 98 B. Determine the beam reaction based on web crippling at a distance N+25k A. 83 D.6 m D. 504 KN B. 11. 570 KN . The steel are A-36 with Fy=248MPa. 153 KN D. 430 KN C.35 f’c. 620 KN B. Allowable compressive stress in the web at the toe of fillet is 0. 78 C.66Fy. 179 KN C. 2750 KN D. Allowable bending stress of steel base plate is 0. Determine the beam reaction based on bearing on concrete wall.0. Concrete strength Fx= 24 MPa. 6.5 Fixed and one end and pin on the other end…………. Iy= 18. Determine the maximum length of the column if the proportional limit is 320 MPa. 372 KN D. 112 KN 24.0.75Fx Properties of beam: B=225mm t=12mm D=600mm k=36mm T=18mm 22... 576 KN C. 9. 7. A. 510 KN D.5 m C.8x10⁶ mm⁴ Ix= 178. What is the critical effective slenderness ration of the column? A.0 Fixed at both ends………………………………………………. A.…. 3170 KN B.1x10⁶ mm⁴ A= 8129 mm² Effective length factors: Pin at both ends………………………………………………………1. What is the critical load P that will cause an initial buckling? A.

36 kPa including its own weight. Determine the nominal balanced moment of the column in KN-m A. It is required to determine the moment in girder BEHK 28. 1480 27. Determine the nominal balanced load of the column in KN.6 KN B. in KN.SITUATION 9. 146 D. f’c=21MPa. 560 B. 1190 C. 450mm x 450mm. 4620 26. 176 C. 4415 D. 234 B.The slab shown in Figure 007 carries uniform factored load of 12.3 KN 30. 380 C. A. What is the factored load by beam GHI t H in girder BEHK? A.6 KN D. 440 SITUATION 10. 198.7 KN B. What is the factored load included by beam BEF at E in girder BEHK? A. 1850 D. 211. 25. 211. 198.2 KN 29. 174. 4185 C. 194 . reinforced with 8. 174. 4890 B. fy=415 MPa. 270 D. A.2 KN D. Concrete protective cover is 40mm.3 KN C.7 KN C. stirrup used is 12mm in diameter. What is the maximum positive moment in beam BEHK in KN/m? A. 154. Determine the nominal axial load capacity of the column.28mm bars spaced evenly on all sides.Concrete column. 154. 1530 B.