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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