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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

The side of a regular hexagon is 9. 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. 43. A marksman fires a bullet to a target. 1. 921.5 seconds later.32 cm B. 103. 98. A.21 cm² C. 2. 498. A. how far apart are the missiles after 0.21 cm² D. Find the area between the circumscribed and inscribed circles of the square. y=12. The side of a square is 65 cm. 678.9 m C. Find the slope of the line for the following conditions: If x=7.32 cm² C. 67. 3845. 78. 54.98m/s.5m/s². A.54 m B.89 cm 12. A.02 sq.3 m/s². Find the depth of the strongest beam that can be cut from a log of whose cross-sectional area is 4212cm².6 A.74cm long. 67. 1.27 is tangent to the coordinate axes.62 m . 957. where m is the slope and b is the y-intercept.5. 1. 23.98 sq.75 seconds? A. 289.98 cm C. units D.2°. The strength of a rectangular beam varies directly to the product of its width and the square of its depth. Ball A has an initial velocity of 40m/s and acceleration of 0.32 cm² B. y=20.54 m D.99 cm² 15. The slope-intercept form of a line is y=mx+b. 1. 1. 1. A circle having an area of 50.5.77 cm² 16. 74.33 m B. 254. 3318. 876. He heard the bullet hit the target 2.C.54m/s and 76.5 m B. 1200m apart are moving towards each other.79 cm D. how far is the target? A. 1.43 cm² B.48 sq.45 sq.32 C.98 m D.3 m 17.23 cm² D. units B. If their velocities are 64. 103. 3265. 2011. The angle between their directions is 61. Two missiles are fired simultaneously at different directions. What is the total distance travelled by C? Neglect the sizes of the balls.23 m 14.52 cm² 10. 562. units C. Find the area of the smaller circle that is tangent to the given circle and to the coordinate axes.3 m D. Two balls A and B. 512.85 D.62 B. Ball B has an initial velocity of 15m/s and an acceleration of 1.23 m C. 1021.51 cm² D. units 13. 59. Find the area between the circles inscribed in the hexagon and the circle circumscribed about the hexagon. 89.5 If x=12. A.32 m C.54 11. If the speed of the bullet is 900 m/s and the speed of sound is 300 m/s.

5. 34 m C.034 m B.344 m D.65 C. 3. 14. 85. 16.46 m B.171.28 m C.75 m D. 5.432. 4. what is the corrected length of the line? A. 387.8° 24. Find the radius of the inscribed circle. Density of steel is 8.18. 3. 82. A solid spherical steel ball has a volume of 1500cm³.3° C.9° D.1° B.2 B.834 m B. 42.4 meters. What is the radius of the curve? A.9° SITUATION 2.743 m 23.98 m Situation 1. 18.2° C.84 m 19. 4. 4. 46. 85. The vertical distance between the ends of the line is 0.78m. A.65°. What is the volume of steel in cubic centimetre? A.272 m C.A solid steel weighing 155 kg is remoulded into a wire of uniform diameter and length of 1500m. A Quonset hut 18 meters long has a parabolic cross. The sides of a triangle measures 59. 0.72 m B. 53. 2.338 m 25. and 64. 13. Find the thickness of hallow spherical steel ball of the same volume and with inside diameter equal to the diameter of the solid ball. 82.1° D. 15.61 21. A line was measured on a sloping ground to be 15.Two sides of a triangle measure 2.89 D.01 m B. What is the measure of the third side of the triangle? A. 53. 46. 0. 15. 18. A flat horizontal ceiling 12. What is the angle facing the 3. Its base is 16.2 square meter.53 grams per cubic centimetre. 15. 27. 417.34 m D.32 m D.563 m D.12 m 20.94 m long.54m side? A. 13. The outside perimeter of the lot is to be provided with a pathway of uniform width.54m and their included angle is 48. A rectangular lot is 12m long and 5m wide. 402.892 m C. what is its width? A. What is the angle facing the 2.3° B. 0.921 m D. 15.56m side? A.376 m 22.98 cm C. 2.2 meters wide is constructed inside the hut. How high is the ceiling above the base? A. A. If the area of the pathway is 11.673 m C.1° 26.3 meters wide and its height at the center is 12. A 20-m chord of a simple curve subtends an angle of 2. 2.56 m and 3. 2.456.87 B. 0.318 m B. 5.2 .

945.11 C.8 D. 15.84 . 12.24 D. What is the diameter of the wire in mm? A.5 28.93 C. 3. What is the cross-sectional area of the wire in square millimeters? A.68 29.41 B.834. 18.17 D. 17. 13.C. 4. 4.37 B. 4. 18.

1 KN B. in m³/S A.013.2x10⁹.112X10⁹ Pa C. 15. Determine the water hammer pressure assuming instantaneous closure.32 KN 2.291 X10⁹ Pa D. 21.34 B.2 meters wide and 1.2 square meter 9.76 D.24KN. 1.8m/s. 4.3 KN D. 1. 1. 15. 1. Modulus of elasticity of pipe material is 1.45 KN C. 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. 7. 1177 m/s C.678 X10⁹ Pa B. 25. 23. A.4x10¹¹ Pa. 1. 0. The velocity of flow is 1.45 cubic meter . What weight of lead (lead=110KN/m³) must be placed inside in order for the cylinder to float with 2. 17.6 KN B. 16. 16. 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. Bulk modulus of elasticity of water is 2.1 square meter C. 1876 kPa SITUATION 3.384 X10⁹ Pa 5. 600mm in diameter.3 KN SITUATION 2. Determine the celerity of pressure wave of water.76 KN B.3 KN D. 18.9 KN C. 1256 m/s D.24 C.Water flows on a straight 150m pipe.002 and roughness coefficient is 0.A rectangular canal is 6.5 meters below the water surface? A.2 meters depth. 0.02 KN D. A.HYDRAULICS & GEOTECHNICAL ENGINEERING SITUATION 1.4 KN C. 1m in diameter and 3m tall weighs 3.2 KN 3. 20. 1. 19. 2. 0. 1. Calculate the discharge on the canal. 1935 kPa B. 1421 m/s B.21 cubic meter B. 21. 23. 19. 1382 m/s 6. What weight of lead must be fastened to the outside bottom in order for the cylinder to float with 2. 19. What is the composite modulus of elasticity of water? A. 18.21 8.67 square meter B.5 meters below the water surface? A. The canal laid on a uniform slope of 0. What additional load can be placed on top of the cylinder for it to be submerged completely in water? A.A cylindrical tank.8 square meter D. 2365 kPa D. Pipe thickness is 16mm. 2118 kPa C.

62 16.98 D. the soil weighs 975 grams. 43. 108 B.67 cubic meter D. Determine the nearest value to the moisture content of the soil in percent.A sample of saturated soil taken from the field weighs 1.63 B. 95 15. Determine the dry unit weight of the soil in kn/m³ A.66 Void ratio at its densest state=0. Laboratory test shows the soil particles have specific gravity of 2. 18. A. 300 cubic meter C. 59 B. 51 D. 65 SITUATION 6. 16.2 B. 17. What is the void ratio of the soil in percent? A. 100 cubic meter D. Determine the minimum reservoir capacity in cubic meter. 500 B.7 C. 13.44 Void ratio at its loonsest state=0. 200 cubic meter B. 112 D.5 14. 400 cubic meter SITUATION 5. What is the minimum requirement from the reservoir in cubic meter? A. 0. what is the volume at 2000hrs? A. 400 12. What is the porosity of the soil in percent? A. 600 C.350 grams.67 . 700 D. 34 C.70.39 cubic meter SITUATION 4. 104 C. After oven drying for 24 hours.C. 600 11. The demand every 4 hour interval is as follows: Time` Demand 0400 200 0800 800 1200 1100 1600 700 2000 500 2400 300 10.34 C. 0. 40. 38. 500 C.Given the following soil properties of a road grading works Moist unit weight=1900kg/m³ Moisture content=12% Specific gravity of solids=2. A. 900 B.Water is pumped into a reservoir at 600m³ every 4 hours. 18.6 D. 800 D. If the volume of water in the tank at 0800hrs is 700m³. 32.

145. What is the approximate settlement of the foundation? A.5° B. 900 C. 1100 B. 157 mm . 32. 43.7 D.3% C. 55. 157.5 23. L=9m. A. A. 56. A.A triaxial test was conducted on a cohesionless soil.9 C.7Mm.33 B. What is the nearest value to the angle of internal friction of the soil? A. 59. What is the nearest value to the maximum principal stress in kPa? A. 0.7 D. 0.3% 18. 99 mm 130 mm C. 76. 22.17.28 24.8 SITUATION 7. 63. 68. What is the nearest value to the angle of failure plane? A. 65. that is the effective pressure at the midheight of the consolidating clay layer. Determine the relative density of the soil in percent.FS=3 22. 28. L2=1. 43. 0.2 B.1% D.2 C. Determine the in situ void ratio of the soil.A group of friction piles is shown in the figure. 1000 D. At failure plane. in kPa.9° 20.qu=180kPa. The total load on the pile less the soil displaced by the footing is 1600 Kn. L1=1. 62.2° C.7° D. 32.8% B. 36. 167.4° 21.5° B. 0. 39.8° D. A.23 D.8m.45 C. 123 mm D.9° C. 19. the normal stress is 400 kPa and the shearing stress is 300 kPa. 800 SITUATION 8.5 B. Compute for the compression inside of the clay. 131. B. Compute for the overburden pressure.

22. Compute for the value of the total stress at a depth of 10m from the ground surface. 167. 210. 3.4 kPa D. 19. 189. 17. in kPa.5 kPa 27. Calculate the hydraulic gradient.35 kn/m³ 26. Compute for the value of the effective stress at a depth of 10m from the ground surface.66 m³/day B. 0. 28. 115.A 5.SITUATION 9.29 m³/day D. 173. A. 4. H1=35m. The clay has moisture content of 42%.32 Kpa SITUATION 10.76 m³/day C. 18.32 kn/m³ C. The water table is 2. 3.5 D. Calculate the equivalent coefficient of permeability in horizontal direction A.82 kPa D. 0. The sand have void ratio of 52% and the degree of saturation above water table is 37%.L=2km. A.45 m/day 29.H2=30m. 26.0025 30. 25.25 C. A. in kPa.3 kPa C. GIVEN THE FOLLOWING: d1=52M.98 kPa B. K2=25m/day.2 kPa B.45 kn/m³ D.74 kPa C.025 B. 2. Assume specific gravity of solids for both sand and clay equal to 2. 0.5m below the ground (sand) surface. Compute for the value of the unit weight of sand above water table. 18. 104.97 kn/m³ B. D2=47m.12 m/day D. 27. Calculate the flow of water from one stream to another per meter width. A.93 m/day C.62 m/day B. 138.65 25.A confined aquifer underlies an unconfined aquifer as shown in the figure.21 m³/day STUCTURAL ENGINEERING & CONSTRUCTION .5 meter thick sand is overlying a very thick clay layer.K1=28m/day. 127. A. 2.

66 KN B.4° D. A. 67.12 KN C.5 kn//m along its circumferential length. 1.12 B.5° 3. 8.2° C. The tension in the wires are T1=3KN and T2=7.17 mm C. 4.The ring moulding shown in Figure 004 is 2m in diameter and supported by six steel cables spaced equally along its perimeter. 51. Minimum weight W to prevent uplift with a factor of safety of 1. 2. 5. What is the resultant of the forces in the wires.59 mm B.98 KN D.76 D. 4. 4 mm 6. in KN? A.5KN. The ring weighs 2. 5. 5.45 C.34 mm D.32 D. 0. 5 mm D. 1.87 2. 46. 4.3° B. 6 mm C. 5. 6. 2.56 5.78 KN SITUATION 2. 3.25 A. 0. 58. 1.78 C. Determine the force in each cable in KN. 6.SITUATION 1. At what angle will the resultant make with the horizontal? A. A. 7 mm B.Two tension wires are supported by a concrete block shown in Figure 002.23 B. What is the minimum diameter of cable if its allowable stress is 124 MPa? A. Determine the vertical displacement of moulding if the diameter of the cable wire is 10mm.98 mm .

42 KN-m 9. 1.37 MPa . 62 KN D.75 m SITUATION 4.5 m D.3m o. Determine the location of zero bending moment measured from the left end of the slab. 2. A.5 m C. 10. 1 m B. Determine the maximum moment in the slab. 36 KN-m D. 3. 48 KN 8.SITUATION 3.4 kPa.c. The superimposed load on the floor due to ceiling. 50 KN B. floor finish (including weight of joint) is 2. The joists to be used have lengths of 3m and 3. What is the maximum bending stress in the beam using 3-m long joist? A. 38 KN-m C. A. Determine the maximum shear in the slab. 58 KN C.45 MPa B.5 m. The girders are spaced 3 meters on centers.The concrete slab shown in Figure 005 is subjected to uniform loads 7. 3.The timber floor joist shown in the figure has dressed dimension of 40mm x 190mm and spaced 0. A. 5. 40 KN-m B.

0.78 MPa C. 0. The roof loads are as follows: Dead load pressure…………………. 3.. w=71N/m Allowable bending stress.1000 Pa Wind pressure……………………………….1400 Pa Wind pressure coefficients: Windward……………………………0.…. 1.67 MPa D.65 MPa D.21 MPa C.1200 Pa Live load pressure……………………. 4.32 MPa 11. 2.. 0. 6. 0.45 MPa B.2 Leeward…………………………….8x10³ mm³ Weight.8x10³ mm³ Sy=11.…. What is the maximum bending stress in the beam using 3. Fbx=Fby=138 MPa ..43 MPa 12..60 Channel properties: Sx=48.74 MPa D. 0.18 MPa B.32 MPa SITUATION 5. 5. What is the maximum shearing stress in the beam using 3-m long joist? A. The trusses are spaced 3 meters on centers.The channel shown in Figure 001 is used as a purlin on a roof truss with slope of 3H to 1V.C.5-m long joist? A..

A. 0.58 C.45 D. Determine the value of interaction equation due to dead load and live load. 0. 0. 532 18.94 C.71 SITUATION 6.28mm compression bars on top and 4. A.75(DL+LL+WL) A. 123 KN C. 387 B.86 D. Depth of compression block assuming both tension and compression steel yields. each located 70mm from the extreme concrete fiber.98 D.87 C. The properties of the column section are as follows: .56 B. 45 KN D.87 B.A 6 meter long simply supported reinforced concrete beam has a width of 350mm and an overall depth of 400mm. 83 C. 0. and steel yield strength fy=415 MPa. 0. 0. 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. A. 71 D.An 8-m long steel column is pinned at the top and fixed at the bottom. 0.28 mm tension bars at the bottom.02 14.72 15. Determine the value of interaction equation due to load combination 0. The column is provided with lateral support at midheight of its weak axis. 312 C. The beam is reinforced with 2.7 MPa. 132 17. A. 86 KN SITUATION 7. The Euler critical load is P=πEI/(Le)² where Le is the effective length of the column.32 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. 0. 453 D. Concrete strength f’c=20. What is the ultimate moment capacity of the beam in KN-m? A. 1. 98 B. 0. 73 KN B.13. 16. 1.

70 19..5 m C. 6. Allowable bearing strength of concrete is 0. Allowable compressive stress in the web at the toe of fillet is 0. A.75Fx Properties of beam: B=225mm t=12mm D=600mm k=36mm T=18mm 22.8x10⁶ mm⁴ Ix= 178. 3170 KN B. 430 KN C.0. 620 KN B. 118 20. 179 KN C. The steel are A-36 with Fy=248MPa.1x10⁶ mm⁴ A= 8129 mm² Effective length factors: Pin at both ends………………………………………………………1.The steel beam shown in Figure 006 is resting on a 200-mm thick concrete wall. 2750 KN D. 1980 KN C.…. 112 KN 24.5 Fixed and one end and pin on the other end………….0. 98 B. A. 9. Determine the mean reaction based on bending at a distance k from the X axis of the web. 153 KN D. 504 KN B. 2320 KN 21. Concrete strength Fx= 24 MPa. Determine the beam reaction based on web crippling at a distance N+25k A.6 m D.66Fy. 456 KN 23.3 m B. Iy= 18. 576 KN C. 11.8 m SITUATION 8. 198 KN B. 78 C.35 f’c. 510 KN D. 570 KN . The wall is provided with 300mmx200mmx25mm steel base plate. 7. 83 D. What is the critical load P that will cause an initial buckling? A. Determine the maximum length of the column if the proportional limit is 320 MPa. Determine the beam reaction based on bearing on concrete wall. Allowable bending stress of steel base plate is 0.. A. 372 KN D. What is the critical effective slenderness ration of the column? A.0 Fixed at both ends……………………………………………….

154. Determine the nominal balanced moment of the column in KN-m A.7 KN C. 1190 C. It is required to determine the moment in girder BEHK 28. 174. A. 198. f’c=21MPa. Concrete protective cover is 40mm.3 KN 30.3 KN C.SITUATION 9.6 KN B. What is the factored load included by beam BEF at E in girder BEHK? A. reinforced with 8. fy=415 MPa. 1850 D. 560 B. 194 . 4620 26. 211. 440 SITUATION 10. 234 B.Concrete column. 4415 D. Determine the nominal axial load capacity of the column. 450mm x 450mm. 4890 B.2 KN D. A.2 KN 29. 380 C.The slab shown in Figure 007 carries uniform factored load of 12. 1530 B. 25. What is the maximum positive moment in beam BEHK in KN/m? A. What is the factored load by beam GHI t H in girder BEHK? A.7 KN B.36 kPa including its own weight. 211. 176 C. stirrup used is 12mm in diameter.28mm bars spaced evenly on all sides. in KN. 1480 27. 270 D. 198. 4185 C. 154. 174.6 KN D. Determine the nominal balanced load of the column in KN. 146 D.