A triaxial test was conducted on a cohesionless soil. At failure plane, the normal stress is 500kPa and the shearing stress is 300kPa.
1. What is the nearest value to the angle of internal friction of the soil?
A. 31°
B. 33°
C. 29°
D. 27°
2. What is the nearest value to the angle of failure plane?
A. 60.5°
B. 62.5°
C. 58.5°
D. 59.5°
3. What is the nearest value to the maximum principal stress in kPa?
A. 1280
B. 1240
C. 1030
D. 1150
Solution:
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Water flows on a straight 150m pipe, 600mm in diameter. The velocity of flow is 2.5m/s. Pipe thickness is 20mm. Bulk modulus of elasticity of water is 2.2 x 109 Pa. Modulus of elasticity of pipe material is 1.4 x 1011 Pa.
1. What is the composite modulus of elasticity of water?
A. 5.24 x 109 Pa
B. 4.67 x 109 Pa
C. 1.85 x 109 Pa
D. 1.49 x 109 Pa
2. Determine the celerity of pressure wave of water.
A. 1,365 m/s
B. 1,458 m/s
C. 1,056 m/s
D. 1,223 m/s
3. Determine the water hammer pressure assuming instantaneous closure.
A. 3,425 kPa
B. 3,057 kPa
C. 2,875 kPa
D. 3,254 kPa
Solution:
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A parallel pipe system is shown in the figure. The pressure head at A is 76m and the pressure head at B is 52m. Hazen Williams coefficient for all pipes C1 = 120.
1. Determine the nearest value to the flow in Line 1 in m3/s.
A. 0.103
B. 0.056
C. 0.214
D. 0.038
2. Determine the nearest value to the flow in Line 2 in m3/s.
A. 0.214
B. 0.038
C. 0.056
D. 0.103
3. Determine the nearest value to the total flow in m3/s.
A. 0.181
B. 0.164
C. 0.197
D. 0.214
Solution:
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Given the following road cross-section notes in cut:
Station 1000+100
2.75 1.00 0.50
9.45 0.00 4.50
Station 1000+220
2.50 1.25 0.80
8.50 0.00 6.00
Width of roadway is 8m.
1. Determine the area of cut at Station 1000+100 in square meter.
A. 13.475
B. 12.586
C. 15.663
D. 10.685
2. Determine the area of cut at Station 1000+220 square meter.
A. 12.586
B. 10.685
C. 13.475
D. 15.663
3. Determine the volume of cut using the end-area method in cubic meter.
A. 1,856.36
B. 1,748.25
C. 1,625.36
D. 1,997.58
Solution:
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A closed traverse ABCD has the following data:
| Line |
Length |
Bearing |
| AB |
122.00 |
N 30° E |
| BC |
149.00 |
N 60° E |
| CD |
241.00 |
S 10° E |
| DA |
159.00 |
N 70° W |
1. Determine the corrected bearing of side BC using compass rule.
A. N 59° 11’E
B. N 59° 11’E
C. N 60° 12’E
D. N 60° 49’E
2. Determine the corrected bearing of side CD using the compass rule.
A. 149.632 m
B. 148.368 m
C. 149.547 m
D. 148.453 m
3. Determine the corrected length of side BC using the compass rule.
A. 242.067 m
B. 241.852 m
C. 240.148 m
D. 239.933 m
Solution:
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A telephone company have a production capacity of 500,000 units per month. At its present capacity of 350,000 units per month, the company have a total monthly income of P350,000,000. The company has a fixed cost of P100,000,000 per month and a variable cost of P200 per unit.
1. What is the present profit or loss in millions of pesos?
A. 200
B. 210
C. 180
D. 190
2. What is the break-even quantity?
A. 135,000
B. 125,000
C. 155,000
D. 165,000
3. If the production is increased to 80% of its capacity, what is the profit or loss in millions of pesos?
A. 220
B. 250
C. 200
D. 190
Solution:
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The following data of road accident versus driver’s age form a quadratic equation:
Age of Driver Accident per year
20 250
40 150
60 200
1. Find the coefficient a of x2.
A. 0.1875
B. 0.1575
C. 0.2125
D. 0.1765
2. Find the coefficient b of x.
A. -14.75
B. -15.25
C. -17.75
D. -16.25
3. Find the number of accidents per year for an age of 30.
A. 154.75
B. 254.25
C. 189.65
D. 181.25
Solution:
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A 50-kg block is being pushed horizontally with a constant force F such that its acceleration is 1 m/s2. The coefficient of friction between the block and the surface is 0.40. The block has an initial velocity of 5 m/s.
1. What is the magnitude of the constant force F in Newtons?
A. 265.8
B. 246.2
C. 212.2
D. 302.7
2. What is the distance travelled by the block after 10 seconds?
A. 100m
B. 120m
C. 150m
D. 80m
3. What is the velocity by the block after 5 seconds?
A. 12 m/s
B. 15 m/s
C. 8 m/s
D. 10 m/s
Solution:
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Evaluate the following integrals:
Solution:
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Line A has a slope of 04 and passes through (-25, – 10). Line B has x-intercept of 10 and y-intercept of 25.
1. Determine the distance of line A to point (8, -3).
A. 35.85
B. 33.71
C. 30.21
D. 28.54
2. Determine the point of intersection of lines A and B.
A. (-90, 240)
B. (-90, 250)
C. (-80, 250)
D. (-80, 240)
3. Determine the equation of a line perpendicular to line B and passing through (-20, 10).
A. 2x – 5y – 90 = 0
B. 2x + 5y + 90 = 0
C. 2x + 5y – 90 = 0
D. 2x – 5y + 90 = 0
Solution:
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Answer the following problems:
1. Find the equation of the line parallel to 2x + y = 3 and normal to the curve y = x4
A. 8x + 4y + 9 = 0
B. 8x – 4y + 9 = 0
C. 32x + 16y – 17 = 0
D. 16x – 32y – 17 = 0
2. Find the angle of intersection of the curve x + xy = 1 and y3 = (x + 1)2.
A. 100m
B. 120m
C. 150m
D. 80m
3. Find the value of the second derivative of the curve y = x2 ex at x = -1.
A. -0.368
B. -0.421
C. -0.587
D. -0.699
Solution:
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The perimeter of a triangle is 102 cm and its area is 431.1554 square centimeters. Find the maximum diameter of a circle that can be inscribed in this triangle.
A. 7.63 cm
B. 12.45 cm
C. 9.54 cm
D. 8.45 cm
Solution:
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If a = 4 cos x + 6 sin x and b = 6 sin x – 4 cos x, what is the value of a2 + b2?
A. 32+40 sin2x
B. 16+2- sin2x
C. 40+32 sin2x
D. 20+16 sin2x
Solution:
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Two interior angles of a triangle measure 48° and 62°. If the perimeter of this triangle is 84cm, find the longest side of the triangle.
A. 28.91cm
B. 34.56cm
C. 30.76cm
D. 24.33cm
Solution:
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Salt is poured into a conical tank 100cm in diameter on top and 70cm high. If the volume of salt is 30,000 cm3, what is the depth of salt in the tank?
A. 45.21cm
B. 38.29cm
C. 31.25cm
D. 52.45cm
Solution:
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The lower and upper bases of a frustum of a pyramid measure 18cm x 18cm and 10cm x 10cm, respectively. If its lateral surface area is 448cm2, find the altitude of the pyramid.
A. 9.36cm
B. 8cm
C. 6.72cm
D. 6.93cm
Solution:
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What is the surface area of a sphere having a volume of 1904 cubic meters?
A. 856.3 m2
B. 742 m2
C. 624.7 m2
D. 1056.2 m2
Solution:
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Three sides of a triangle measure 16cm, 24cm, and 20cm, respectively. What is the median to the 20-cm side?
A. 17.78cm
B. 18.32cm
C. 16.92cm
D. 20.59cm
Solution:
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The upper base of a frustum of a rectangular pyramid is 2.5m x 4m and its altitude is 5m. If its volume is 116.67 m3 what is the area of the lower base?
A. 38m2
B. 40m2
C. 44m2
D. 64m2
Solution:
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Solve for y from the following complex equation:
2x + 5y + 3yi + 15 – 3i = 0.
A. 2
B. -5
C. -10
D. 1
Solution:
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When f(x) = x4 + ax3 + 7x2 + bx + 6 is divided by (x-2) the remainder is 16 and when divided by (x+1) the remainder is 10. What is the value of a?
A. -7
B. 11
C. -5
D. 3
Solution:
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What is the arithmetic mean of the following set of numbers?
-14, -4, -10, 5, -1, -12
A. -6
B. 6
C. 5
D. -5
Solution:
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The upper base diameter of the frustum of a right circular cone is 2m and the lower base diameter is 4m. if its altitude is 5m find its lateral area.
A. 55.21 m2
B. 43.98 m2
C. 48.06 m2
D. 32.87 m2
Solution:
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Two sides of a triangle are measuring 20cm and 28cm, respectively. If the area of the triangle is 227.125 cm2, what is the measure of the third sides in cm?
A. 22
B. 23
C. 24
D. 25
Solution:
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A polygon has twenty-four sides. How many are its diagonals?
A. 222
B. 212
C 232
D. 252
Solution:
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An examination has two types of questions as follows:
Type A: 10 points at 3 minutes each
Type B: 15 point at 6 minutes each
There are 16 questions in the exam for a total time of 60 minutes.
1. How many Type A questions are there in the examination?
A. 4
B. 12
C. 10
D. 6
2. How many Type B questions are there in the examination?
A. 12
B. 10
C. 4
D. 6
3. What is the maximum score of this exam?
A. 160 points
B. 180 points
C. 190 points
D. 170 points
Solution:
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An area is bounded by the curve y = sin x and the x-axis from x = 0 to x=π.
1. What is the area bounded by the curve?
A. 2.4
B. 4.1
C. 2.0
D. 3.2
2. How far above the x-axis is the centroid of the area?
A. 0.452
B. 0.276
C. 0.393
D. 0.321
3. Find the volume generated by revolving the area about the x-axis.
A. 5.446
B. 6.773
C. 4.453
D. 4.935
Solution:
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A 10-lb object A moving to the right with a velocity of 10 fps is in direct collision course with a 5-lb object B which is moving to the left at a speed of 5fps.
1. Find the velocity of A after collision if the coefficient of restitution is 0.
A. 5 fps
B. 4 fps
C. 0 fps
D. 1 fps
2. Find the velocity of A after collision if the coefficient of restitution is 0.8.
A. 4 fps
B. 0 fps
C. 1 fps
D. 5 fps
3. Find the velocity of A after collision if the coefficient of restitution is 1.
A. 1 fps
B. 0 fps
C. 5 fps
D. 4 fps
Solution:
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A vertical sag parabolic curve is to connect a -2% grade to a +3% grade. The change in grade per meter station must be 0.2%. The PT of the curve is at Station 25 + 325 and elevation 25.42m.
1. What is the elevation of the PC of the curve?
A. 21.12 m
B. 26.44 m
C. 23.45 m
D. 22.92 m
2. What is the length of the curve?
A. 450 m
B. 550 m
C. 500 m
D. 600 m
3. What is the stationing of the PC of curve?
A. 24+750
B. 24+865
C. 24+825
D. 24+625
Solution:
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A closed traverse has the following data:
| Line |
Latitude |
Departure |
| 1-2 |
75.54 |
44.35 |
| 2-3 |
-4.40 |
—- |
| 3-4 |
-50.85 |
23.93 |
| 4.5 |
-101.25 |
-18.89 |
| 5-6 |
-24.28 |
-48.49 |
| 6-1 |
— |
-33.00 |
1. What is the length of line 6-1?
A. 110.29 m
B. 112.43 m
C. 111.87 m
D. 113.98 m
2. What is the bearing of line 6-1?
A. N 17° 24’ 36” W
B. N 16° 45’ 12” W
C. N 18° 21’ 12” W
D. N 15° 54’ 22” W
3. What is the DMD of line 3-4?
A. 156.43 m
B. 176.83 m
C. 166.33 m
D. 189.22 m
Solution:
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Determine the slope of the following polar curves at the indicated angle:
1. γ2 = cos 2x at x = π/6.
A. 0
B. 1
C. 2
D. 3
2. γ = tan x at x = π/3.
A. 2.22
B. 6.33
C. 4.33
D. 8.66
3. γ = (sin x)2 at x = π/4
A. 2
B. 3
C. 1
D. 0
Solution:
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Answer the following probability problems:
1. In a family of five children, what is the chance that there are three boys and two girls?
A. 7/16
B. 3/8
C. 5/16
D. 3/16
2. A basketball player averages 65% in a free-throw line. What is the probability of missing one for two free throws?
A. 0.523
B. 0.455
C. 0.574
D. 0.486
3. A store has three kinds of toys given in every purchase. What is the probability of getting all three toys in five purchases?
A. 0.617
B. 0.542
C. 0.685
D. 0.752
Solution:
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Given the hyperbola x2 – 8x – 4y2 – 16y = 256:
1. What is the distance between foci?
A. 35.78
B. 43.23
C. 38.41
D. 40.22
2. Find the coordinate of the center.
A. (4, -2)
B. (-4, – 2)
C. (-4, 2)
D. (4, 2)
3. What is the distance between the vertices?
A. 33
B. 32
C. 30
D. 31
Solution:
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The logarithm of the product and quotient of two numbers are 1.47712125 and -07918125, respectively. What is the smaller number?
A. 3
B. 4
C. 6
D. 5
Solution:
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A conical buoy with vertex submerged and circular base exposed has a base diameter of 120cm and a height of 2m. It floats in water with a draft of 1.5m. What is the volume submerged in m3?
A. 0.523
B. 0.318
C. 0.432
D. 0.265
Solution:
