Figure 7
TECHNOLOGICAL INSTITUTE OF THE PHILIPPINES- MANILA
PRE BOARD EXAM DAY 3
NAME:_____________________SN_______________ DATE: OCTOBER 15, 2014
DIRECTIONS: PROVIDE THE SOLUTION TO SELECT THE CORRECT ANSWER.
1. On the television show “Kayang – kaya kaya?” each contestant was given P100.00 at the start. For each question answered correctly, he was given a bonus of P75.00 and for each one he missed, he was penalized by 15.00. If a contestant was asked a total of 20 questions and ended the game with P1330.00, how many questions were answered correctly?
a. 13 b. 15 c. 17 d. 19
2. Rain is falling into a cylindrical barrel at the rate of 20 cm3/min. If the radius of the base is 18 cm, how fast is the water rising?
a. 5.81cm/min b. 3.10cm/min c. 0.3cm/min d. 4.28cm/min
3. A ship leaves port at 1 pm traveling north at the speed of 30 miles/hour. At 3 pm, the ship adjusts its course 20 degrees eastward. How far is the ship from the port at 4pm?
a. 55 mib. 68 mi c.73 mi d. 89 mi
4. A pipe 10 cm in diameter contains steam at 100°C. It is covered with asbestos 5cm. thick, the thermal conductivity of which , k= 0.00060 cal/cm sec. The outside surface is at 30°C. Find the heat loss per hour from a meter length of pipe.
a. 11,840cal/hr b. 140,000 cal/hr c. 125,256 cal/hr d. 36,000 cal/hr 5. Find the volume of the largest circular cylinder that can be cut from a circular cone of radius 6cm and height 9cm. a. 36 cu.cm. b. 48cu.cm c. 54cu.cm d. 49cu.cm 6. The rigid platform in the figure has negligible mass and rests on two steel bars, each 250.00 mm long. The center bar is aluminum and 249.90 mm long. Compute the stress in the Al bar after the center load P=400 kN has been applied. For each steel bar, the area is 1200 mm2 and E = 200 Gpa. For the Al bar, the area is 2400 mm2 and E=70 GPa.
a. 22.5 MPa b. 25.4 MPa
c. 32.1 MPa d. 35.8 MPa
A structure costs P12,000 now. It is estimated to have a life of 5 years with a salvage value at the end of life of P1,000.
1. Determine the depreciation at the end of the second year.
a. P3666.67 b. P2933.33
c. P2200.00 d. NOTG
2. Determine the book value at the end of the third year.
a. P1733.33 b. P8800.00
c. P5666.67 d. P3200.00
8. A metal bar at a temperature of 100°F is placed in a room at a constant temperature of 0°F. If after 20
minutes the temperature of the bar is 50°F, find (a) the time it will take the bar to reach a temperature of 25°F? a.39.6 mins b. 43.1mins
c. 15.28mins d. 12.1 mins
9. Determine the area bounded by y =8 – x3, the x-axis and the y-axis.
a. 14 b. 10 c. 16 d. 12
10. In an arithmetic sequence, t23 = 519 and t71 = 1503, what is t114?
a. 3824.5 b. 2458.3 c. 2384.5 d. NOTG 11. A sequence of annual payments of $2000 each will start with the first payment at the end of 5 years, then will continue forever. Find the present value of the perpetuity when money is woth 5%?
a. $33,000 b. $ 35,000
c. $40,000 d. $ 54,000
12. What is the velocity of a projectile at an altitude of 8,000 feet after it was fired directly upward from the ground with a muzzle velocity of 1,000 feet per second? a. 130 ft/sec b. 616 ft/sec
c. 158ft/sec d. 700 ft/sec
13. The lines y = ±(5/12)x are asymptotes of a hyperbola whose foci are 26 units apart. Which CANNOT be a vertex of the hyperbola?
a. (-12, 0) b. (0, 5)c. (0, -12) d. (12, 0)
14. It is desired to give a spherical tank of diameter 20 feet ( 240 inches) a coat of point 0.1 inch thick. Estimate how many gallons of paint will be required, if 1 gallon is about 231 cubic inches.
a.9.44 gal b. 21gal c. 7.83 gal d. 32 gal
15. A fossilized bone is found to contain (1/1000) the original amount of radioactive carbon C-14. Given the half life of C14 is approximately 5600 years, determine the age of the fossil.
a. 187,00 years b. 157,320 years c. 103,583 years d. 55,800 years
16. A car is braked to a stop with constant acceleration.
The car stops 10 secs after the brakes are applied and travels 250 ft. during this time. Find the speed of the car when the brakes were applied.
a. 100 fps b. 75 fps c. 50 fps d. NOTG 17. A parallel force system acts on the lever shown in Fig. P-236. Determine the magnitude and position of the resultant.
a. 80 lb,4 ft. to the r of A b. 90 lb,6 ft. to the r of Ac. 100 lb, 5 ft. to the r of A d. 110 lb,6 ft. to the r of A
18. The reciprocal of Bulk modulus of any liquid is called ________.
a. Compressibility b. Volume strain
c. volume stress d. shape elasticity 19. A plant bought a calciner for P220,000 and used it for 10 years, the life span of the equipment. What is the book value of the calciner after five years of use. Assume a scrap value of P20,000 for the double declining method.
a. PP69,570.108 b. P72,089.60
20. Two vertices of triangle are (2,4) and (-2,3) and the area is 2 sq. units, the locus of the third vertex is
a. 4x-y =14 b. 4x+4y =14
c. x+4y =12 d. x-4y =-10
21. An aircraft tracking station determines the distance from a common point O to each aircraft and the angle between the aicrafts. If angle O between the two aircrafts is equal to 49 o and the distances from point O to the two aircrafts are 50 km and 72 km, find distance d between the two aircrafts.
a. 40.3 km b. 45.3 km c.54.4 km d. 58.9 km 22. A 5 kg rifle fires a 15 g bullet at a muzzle velocity of 600 m/s. Find the recoil velocity of the rifle.
a. –1.8 m/s b. –2.25 m/s
c. –2.5 m/s d. –3 m/s
23. In a certain culture the rate of growth of bacteria is proportional to the amount present. Initially, 1000 bacteria are present and the amount doubles in 12 minutes. Determine the time it takes for the bacteria to multiply to 10,000.
a. 20 min b. 40 min c. 60 min d. NOTG 24. A steel shaft 3 ft long that has a diameter of 4 in is subjected to a torque of 15 kip·ft. Determine the maximum shearing stress. Use G = 12 × 106 psi. a. 12.3 ksi b. 13.3 ksi c. 14.3 ksi d. 15.3 ksi 25. A developer of a new subdivision offers a prospective home buyer a choice of 4 designs, 3 different heating systems, a garage or carport, and a patio or screened porch. How many different plans are available to this buyer?
a. 48 b. 56 c. 36 d.24
26. A tank initially holds 100 gallons of a brine solution containing 20 lb of salt. At t =0 , fresh water is poured into the tank at the rate of 5 gal/min, while the well – stirred mixture leaves the tank at the same rate. Find the amount of salt in the tank at any time t.
a. S = 10e-t/5 b. S = 20e-t/20 c. S = 20e-t/5 d. S = 5e-t/10 27.
What weight W is necessary to start the system of blocks shown in Fig. P-510 moving to the right? The coefficient of friction is 0.10 and the pulleys are assumed to be frictionless.
a. 29.5 kN b. 32.4 kN c. 38.4 kN d. notg 28. What is the radius of a circle, if a central angle of 110º subtends a chord of length 84 inches.
a) 34.4 b) 48.4 c) 51.1 d) 68.8 29. Find the distance of the centroid from the y-axis, bounded by x=10, y=x and y=-x
a. 6.67 b. 6.06 c. 5.51 d. 7.33
30. If the distance between an endpoint of the latus rectum to the vertex of a parabola is 80, than what is the length of the latus rectum?
a. 45(5)1/2 b. 62(2)1/2 c.62(5)1/2 d.64(5)1/2
31. The siren of a stationary fire engine has frequency of 500 Hz. If a car drives away from it at 20m/s, what frequency does a person in the car hear?
a. 471 Hz b. 500 Hz c. 531 Hz d. 565 Hz 32. An investment of P60,000 can be made in
depreciable assets that will produce revenues of P29,000 per year for 5 years Annual cost for operations and maintenance will be P12,000 per year. Taxes and insurance will be 2% of the first cost. If the company expects capital to earn not less than 15% before tax, is this a desirable investment. Use sinking fund method to calculate for annual depreciation. What is the % rate of return ?
4. 10% b. 11.5% c. 13.5% d. 17%
33. Find the distance between center and directrix of an ellipse x2/36 + y2/16 =1
a.5 b. 6 c. 7 d. 8
34. An inlet pipe can fill up the tank in 6 hours while an outlet pipe can empty the tank in 9 hours. One day, the tank was being filled. When it was 1/3 full, a boy opened the outlet pipe. How long did it take to fill the rest of the tank?
a.8 h b. 10 h c.12 h d. 13 h
35. Farmer Johnson hitches his tractor to a sled loaded
with firewood and pulls it a distance of 20 m along level frozen ground. The total weight of sled and load is 14700 N. The tractor exerts a constant 5000 N force at an angle of 36.9* above the horizontal as shown. There is a 3500N. Friction force opposing the motion. Find the work done by each force acting on the sled and the total work done by all the forces.
a. 10 kJ b. 20 kJ c. 30 kJ d. 40 kJ 36. Determine the coordinates of the point which is three-fifths of the way from the point (2,-5) to the point (-3,5)
a.(-1,1) b. (-1,-2) c. (-2,-1) d. (1,-1)
37. Given : dy1/dx = (2/13) (1+ 5/2 x - 3/2 – ¾ k), What is the value of k such that y1 is perpendicular to the curve y2 = 2x at (1,1)
a. 3 b. 6 c. 7 d. 10
38. A plane cuts through a cube in such a way that the plane passes through three of the cube’s vertices, no two of which lie on the same edge. If the edge of the cube has a length of 1, what is the surface area of the smaller fragments of the cube?
a. 2.4 b. 2.7 c. 3.1 d. 3.7
39. Determine the reactions R1 and R2 of the beam in Fig. P-333 loaded with a concentrated load of 1600 lb and a load varying from zero to an intensity of 400 lb per ft.
a. 1400 b. 1900 c. 2100 d. notg
40. A passenger weighing 60 kg rides a ferris wheel with
a radius of 8.0 m. The wheel makes one revolution in 10 s. Calculate the force the seat exerts on the passenger at the top of the circle.
41. A hotel swimming pool has for its boundary a curve given by the equation:x2 +y2 =2x-4y+20 where the units are all in meters. Find the volume of water required to fill the pool to a depth of 1.5m.
a. 117.8m3 b. 168.7m3 c. 121.5m3 d. 171.5m3
42. At 7:00 AM, Mr. Castro left home for work driving at a rate of 40kph. 15 minutes later, his wife discovered that Mr. Castro left his wallet at home so Mrs. Castro pursue him on her car at a rate of 50 kph. At what time did Mrs. Castro catch up with her husband?
a. 8:00 AM b. 8:15 AM c. 8:30 AM d. 8:45 AM 43. Determine the reaction R1 of the beam in Fig. P-333 loaded with a concentrated load of 1600 lb and a load varying from zero to an intensity of 400 lb per ft. a.1900 b.2100 c.2500 d. 1400
44. A fisher man 10 km from the shore desires to reach a point on the shore 20 km. from his present position. If he can walk 4km per hr and rows 2km per hr, in what direction Ѳ should he row in order to reach his destination in the shortest possible time?
a.25° b. 30° c. 53° d. 45°
45. A student taking a true-false test consisting of 15 questions guesses at the answers. Assuming that he is equally likely to make a correct or an incorrect guess on each question, find the probability that 8 of his answers will be right and the rest wrong.
a) 6435 / 32768 b) 6543 / 32768 c) 6435 / 37268 d) 6435 / 32876
46. The lower edge of a picture frame is 4ft. while its upper edge is 9ft. above the eyes of the observer who is 6 ft. tall. How far horizontally from the picture should the observer stand such that the angle subtended by the picture at the observers eyes would be maximum?
a.5ft b. 6ft c. 4ft d. 3ft
47. A 2lb mass is dropped from a great height. Air resistance is proportional to kv2 where k = 1/20,000. Find the velocity when the mass has fallen 1000ft.
a. 162.3 b. 158.7 c. 178.6 d. 175.4
48. Find the annual payments to extinguish a debt of P10,000 payable for five years at 12% interest.
a. P1985.90 b. P2774.10
c. P3,012.35 d. P3550.67
49. Find the moment of inertia about the indicated x-axis for the shaded area shown in Fig. P-821.
a. 606.19 in4 b. 756.19 in4 c. 865.19 in4 d. 906.19 in4
50. Ten coins are tossed. What is the probability that at least six of them will be tail? a) 512 /193 b) 391 / 152
c) 193 / 512 d) 512 / 391
51. A train moving with constant acceleration travels 24 ft (7.32 m) during the 10th sec of its motion and 18 ft (5.49 m) during the 12th sec of its motion. Find its its constant acceleration.
a. 1.47 m/s2 b. -0.915 m/s2 c. - 0.47 m/s2 d. 2.47 m/s2
52. Vector A has magnitude 6 units and is in the direction of the +x-axis. Vector B has a magnitude 4 units and lies in the xy-plane, making an angle of 30˚ with the + x-axis. Find the vector product A x B.
a. 9 b. 10 c. 11 d. 12
53. The distance between points ( 4,7,z) and ( 5,1,6) is 7.28. Find z.
a.2 b. 6 c. 4 d. 8
54. A hemispherical tank of radius 2 ft. is initially filled with water. At the bottom of the tank, there is a hole of radius 1 in. through which the water drains under the influence of gravity. Determine how long it will take the tank to drain completely.
a. 2.3 h b. 3.6 h c. 4.8 h d. 5.5 h 55. A particle moves according to the following function of time: x(t) = 3sint and y(t) = 4 cost, what is the
resultant velocity at t= pi?
a. 3 b. 4 c. 9 d. 25
56. A Ferris wheel has a radius of 10m. Its center is 12m above the ground. When a passenger is 17m above the ground he is moving vertically at the rate of 1.81 m/s. What is the speed of rotation of the wheel in rpm?
a. 0.209 b. 10.5 c. 1.81 d. 2
57. Water is pouring into a swimming pool. After t hours, there are t+ t1/2 gallons in the pool. At what rate is the water pouring into the pool when t = 9 hours? a. 7/6 gph b. 1 gph c. ½ gph d. 1/6 gph 58. A man agrees to make $5,000 payments at the ends of the first five years, $4000 at the ends of the next five years, and $3,000 at the ends of the next five years. If money is worth 4%, find the present value of this agreement.
a. $46,000 b. $50,000
c. $ 65,000 d. $69,000
59. What is the standard equation of the locus of points in the Cartesian plane, the absolute difference of whose distances from the points (±4,0) is 4?
a. (x2/9)-(y2/16) =1 b. (x2/4)-(y2/12) =1
c. (x2/12)-(y2/16) =1 d. (x2/12)-(y2/9) =1.
60. The truss pinned to the floor at D, and supported by a roller at point A is loaded as shown in Fig. T-06. Determine the force in member CG.
a. 8.01 KN b.9.48 KN c. 10.98 KN d. NOTG
61. A debtor agrees to pay $500 at the beginning of each 3 months for 6 years. If money is worth 6.5% compounded quarterly, find the present value of his debt before he makes his payment.
a. $4655 b. $ 4155
c. $6703 d. $10,032
15.His outstanding liability just before his 15th payment
a. $4655 b. $ 4155
c. $6703 d. $10,032
62. A conic has the lines y = -3 and y = 5 as directrices and the point (1, 26) as a focus. What are the coordinates of the vertex closest to the given focus?
a. (1,11) b. (2, 11) c. (3, 8) d. NOTG 63. The cost of producing a small transistor radio set consists of P23 for labor and P37 for materials. The fixed charges in operating the plant are P100,000 per
month. Other variable cost is P1/set. The radio set can be sold for P75 each. Determine how many sets must be produced per month to break even.
a. 5000 b 7200 c. 8400 d. 10000 64. A plane cuts through a cube in such a way that the plane passes through three of the cube’s vertices, no two of which lie on the same edge. If the edge of the cube has a length of 1, what is the surface area of the smaller fragments of the cube?
a. 2.4 b. 2.7 c. 3.1 d. 3.7
65. A circular cylinder is circumscribed about a right prism having a square base one-meter on an edge. The volume of the cylinder is 6.283m3. Find its altitude in m.
a. 3 b.4m c. 4.2 m d. 5.2 m
66. Find the area of the triangle which the line 2x-3y+6=0 forms with the coordinate axes.
a. 3 b. 4 c. 5 d. 2
67. A balloon leaving the ground 60 ft from an observer, rises 10 ft per sec. How fast is the angle of elevation of the line of sight decreasing after 8 sec?
a.0.03 rad/sec b. 0.09 rad/sec c. 0.011 rad/sec d. 0.06 rad/sec
68. A shell is fired at an angle above the horizontal
at a velocity of 300 m/s. What is the time of flight? a. 39 s b. 41 s c. 43 s d. 45 s 69. Future value less the present value
a. discount b. rate discount c. discount rate d. profit
70. It is the worth of the property as recorded in the books of account of the company.
a. book value b. fair value c. market value d. goodwill value.
71. A 200 g of water is mixed to 300 g of alcohol whose density is 790kg/ m3. Calculate the specific gravity of the total mixture.
a. 0.675 b. 0.862 c. 0.912 d. 1.0 72. A firm bought an equipment for P56,000, other expenses including installations amounted to P4,000. The equipment is expected to have a life of 16 years with a salvage value of 10% of the original cost. Determine the book value at the end of 12 years by the straight line method.
5. a. P19,500 b. P25,500
c. P29,500 d. P34,500
6. Determine the book value using the sinking fund method at 12% interest.
a. P19,500 b. P25,500
c. P29,500 d. P34,500
74. The set of all possible outcomes in an experiment. a. sample space b. event
c. sample point d. population
75. It is the worth of the property as recorded in the books of account of the company.
a. book value b. fair value c. market value d. goodwill value.
76. Plastic deformation means __________ deformation
a. elastic b. temporary
c. permanent d. reversible
77. In Fig. P-512, the homogeneous block weighs 300 kg and the coefficient of friction is 0.45. If h = 50 cm, determine the force P to cause motion to impend. a. 45 kg b. 65 kg
c. 72 kg d. NOTG
78. Find the number of different arrangements that can be made of the letters to the word COLLEGE. a) 2160 b) 6210 c) 2016 d) 1260
79.Locate the centroid of the shaded area in Fig. P-723. a. x= 49.40 mm, y = 10.29 mm
b. x= 38.27 mm, y = 20.39 mm c. x= 39.71 mm, y = 30.39 mm d. x= 29.14 mm, y = 10.9 mm
80. How many different kinds of bouquets of 3 kinds of flowers each can be made from 8 varieties of flowers? a) 363 b) 65 c) 56 d) 336 81) At the end of each year for 8 years, a corporation will deposit $12,500 in a depreciation fund to provide for replacement of machinery at the end of 8 years. If the fund accumulates at 8% effective, how much is in it just after the last deposit.
a. $120,453 b. $126,980
c. $132,958 d. NOTG
20. How much is it after the fifth deposit?
a. $58,980 b. $67,777
c. $73,333 d. $83,333
82. Find the altitude of a rectangular close box with volume 100 with length twice the width so that surface area is minimum; Note this is also the wet economical.
a.5.681 b. 4.463 c. 1.566 d. 4.672
83. The perimeter of a triangle is 84m. while its area is 102 sq.m. Determine the diameter of the circle that maybe inscribed in this triangle.
a. 2.48m b. 4.86m c. 8.43m d. 1.23m 84. Compute the volume generated if we revolve the area about the line x-y =0
a. 53.95 b. 77.12 c. 62.1 d. 12.4
85. The area of a circle circumscribed about an equilateral triangle is 254.47 sq. m. What is the area of the triangle in sq. m.?
a.105.22 b. 85. 612 c. 125.34 d. 184.52
86. The formula for lateral strain is ε a.
¿
δ
L
o b.¿
−
δ
L
O c.¿
−
δ
W
o d. notg87. A cable has a length of 10 meters and is hung between two poles set 7 meters apart. How much does the cable sag?
a. 2.8 m b. 3.2 m c. 3.8 m d. 4.1 m 88. There are 8 baseball teams in a league. How many games will be played if each team plays each of the other teams 40 times?
a) 280 b) 560 c) 320 d) 1120 89. A water tank, 22 ft in diameter, is made from steel plates that are 1/2 in. thick. Find the maximum height to which the tank may be filled if the circumferential stress
Figure 7 is limited to 6000 psi. The specific weight of water is
62.4 lb/ft3.
a. 38.7 ft b. 42.6 ft. c. 52.5 ft. d. 68.9 ft
TECHNOLOGICAL INSTITUTE OF THE
PHILIPPINES- MANILA
PRE BOARD EXAM DAY 3
NAME:_________________SN_______________
DATE: OCTOBER 15, 2014
DIRECTIONS: PROVIDE THE SOLUTION
TO SELECT THE CORRECT ANSWER.
1. On the television show “Kayang – kaya kaya?”
each contestant was given P100.00 at the start. For
each question answered correctly, he was given a
bonus of P75.00 and for each one he missed, he was
penalized by 15.00. If a contestant was asked a total
of 20 questions and ended the game with P1330.00,
how many questions were answered correctly?
a. 13
b. 15
c. 17
d. 19
2
A tank is initially filled with 100 gal of salt solution containing 1 lb of salt per gallon. Fresh brine containing 2 lb of salt per gallon runs into the tank at the rate of 5 gal/min, and the mixture , assumed to be kept uniform by stirring runs out at the same rate. Determine how long it will take for this amount to reach 150 lb.a. 10.2 min b. 12.6 min c. 13.9 min d. 14.5 min
3. A ship leaves port at 1 pm traveling north at the
speed of 30 miles/hour. At 3 pm, the ship adjusts its
course 20 degrees eastward. How far is the ship
from the port at 4pm?
a. 55 mi
b. 68 mi
c.73 mi
d. 89 mi
4.
A 200 lb man hangs from the middle of a tightly stretched rope so that the angle between the rope and the horizontal direction is . Calculate the tension of the rope?a. 1104 lb b. 1147 lb c. 1205 lb d. 1250 lb
5. A spherical balloon is being filled with air at the
rate of 1 cfs. Compute the time rate of change of the
surface area of the balloon at the instant when its
volume is 113.1 cubic feet.
a. 0.67 ft
2/sec
b. 1.73 ft
2/sec
c. 3.0 ft
2/sec
d. 3.7 ft
2/sec
6. The rigid
platform in the
figure has
negligible mass
and rests on two
steel bars, each
250.00 mm long.
The center bar is
aluminum and
249.90 mm long. Compute the stress in the Al bar
after the center load P=400 kN has been applied.
For each steel bar, the area is 1200 mm2 and E =
200 Gpa. For the Al bar, the area is 2400 mm2 and
E=70 GPa.
a. 22.5 MPa
b. 25.4 MPa
c. 32.1 MPa
d. 35.8 MPa
7. In a certain manufacturing process, it is found
that, on the average, 2 articles out of 100 are
defective. What is the probability that a random
sample of 5 articles will contain exactly one
defective article.
a. 09039
b. 0.0922
c. 0.00376
d. 0.0725
8. Suppose that a corpse was discovered in a motel
room at midnight and its temperature was 80
F. The
temperature of the room is kept constant at 60
F.
Two hours later the temperature of the corpse
dropped to75
F. Find the time of death. Note: The
temperature of a live person is 98.6
F.
a. 8:30 PM
b. 7:30 PM
c.9:00 PM d. NOTG
9. Determine the area bounded by y =8 – x3, the x-axis and the y-axis.
a. 14 b. 10 c. 16 d. 12
10. In an arithmetic sequence, t
23= 519 and t
71=
1503, what is t
114?a. 3824.5
b. 2458.3
c. 2384.5
d. NOTG
11. An ore mine will yield an annual operating
profit of $150,000 starting with a return at the end
of five 95) years, and ending with profit at the end
of 20 years, when the mine becomes worthless.
What is the value of this mine to an investor to
whom money is worth 5%?
a.$1,220,000
b. $1,340,000
c. $1,430,000
d. NOTG
12.
A 300-lb box is
held at rest on a
smooth plane by a
force P inclined at an
angle θ with the plane
as shown in Fig.
P-310. If θ = 45°,
determine the value of
P
a. 212.31 lb
b. 325.36 lb c. 409.81 lb d. notg
13. The lines y = ±(5/12)x are asymptotes of a
hyperbola whose foci are 26 units apart. Which
CANNOT be a vertex of the hyperbola?
a. (-12, 0)
b. (0, 5)
c. (0, -12)
d. (12, 0)
14. The cost C, of a product is a function of the
quantity x, of the product: C(x) = x
2– 4000x + 50.
Find the quantity for which the cost is minimum.
a. 1000
b. 1500
c. 2000
d. 3000
15.
A fossilized bone is found to contain (1/1000) the original amount of radioactive carbon C-14. Given the half life of C14 is approximately 5600 years, determine the age of the fossil.a. 187,00 years b. 157,320 years c. 103,583 years d. 55,800 years
16. A car is braked to a stop with constant
acceleration. The car stops 10 secs after the brakes
are applied and travels 250 ft. during this time.
Find the speed of the car when the brakes were
applied.
a. 100 fps
b. 75 fps
c. 50 fps
d. NOTG
17. A parallel force system acts on the lever shown
in Fig. P-236. Determine the magnitude and
position of the resultant.
a. 80 lb,4 ft. to the r of A b. 90 lb,6 ft. to the r of Ac.
100 lb, 5 ft. to the r of A
d. 110 lb,6 ft. to the r of A
18. The reciprocal of Bulk modulus of any liquid is
called ________.
a. Compressibility
b. Volume strain
c. volume stress
d. shape elasticity
19. A plant bought a calciner for P220,000 and used
it for 10 years, the life span of the equipment. What
is the book value of the calciner after five years of
use. Assume a scrap value of P20,000 for the double
declining method.
a. PP69,570.108
b. P72,089.60
c. P120,000.00
d. NOTG
20. Two vertices of triangle are (2,4) and (-2,3) and
the area is 2 sq. units, the locus of the third vertex is
a. 4x-y =14
b. 4x+4y =14
c. x+4y =12
d. x-4y =-10
21. An aircraft tracking station determines the
distance from a common point O to each aircraft
and the angle between the aicrafts. If angle O
between the two aircrafts is equal to 49
oand the
distances from point O to the two aircrafts are 50
km and 72 km, find distance d between the two
aircrafts.
a. 40.3 km
b. 45.3 km
c
.54.4 km
d. 58.9
km
22.
A 5 kg rifle fires a 15 g bullet at a muzzle velocity of 600 m/s. Find the recoil velocity of the rifle.a. –1.8 m/s b. –2.25 m/s
c. –2.5 m/s d. –3 m/s
23. In a certain culture the rate of growth of bacteria
is proportional to the amount present. Initially, 1000
bacteria are present and the amount doubles in 12
minutes. Determine the time it takes for the bacteria
to multiply to 10,000.
a. 20 min
b. 40 min
c. 60 min d. NOTG
24.
A steel shaft 3 ft long that has a diameter of 4 in
is subjected to a torque of 15 kip·ft. Determine the
maximum shearing stress. Use G = 12 × 10
6psi.
a. 12.3 ksi
b. 13.3 ksi
c. 14.3 ksi
d. 15.3 ksi
25. A developer of a new subdivision offers a
prospective home buyer a choice of 4 designs, 3
different heating systems, a garage or carport, and a
patio or screened porch. How many different plans
are available to this buyer?
a. 48
b. 56
c. 36
d.24
26. Two lines tangent to a circle at points M and N
have a point of intersection A. The size of angle
MAN is equal to x degrees and the length of the
radius of the circle is equal to r. Find the distance
from point A to the center of the circle in terms of x
and r.
a.
r[ 1 + 1 / tan(x/2)
2]
1/2b. r[ 1 / tan(x/2)
2]
1/2c. r[ 1 + 2 / tan(x/2)
2]
1/2d. NOTG
27.
A 7/8 inch diameter bolt
having a diameter at the
root of the threads of 0.731
inch is used to fasten two
timbers together as shown.
The nut is tightened to
cause a tensile strength of
18,000 psi in the bolt.
Determine the outside
diameter of the washers if
their inside diameter is 9/8
inches and the bearing
stress is limited to 800 psi.
a. 3.18 in. b. 3.65 in c. 4.1 in d. 4.3 in.
28. What is the radius of a circle, if a central angle
of 110º subtends a chord of length 84 inches.
a) 34.4 b) 48.4
c) 51.1
d) 68.8
29. Find the distance of the centroid from the
y-axis, bounded by x=10, y=x and y=-x
a. 6.67
b. 6.06 c. 5.51
d. 7.33
30. If the distance between an endpoint of the latus
rectum to the vertex of a parabola is 80, than what is
the length of the latus rectum?
a. 45(5)
1/2b. 62(2)
1/2c.62(5)
1/2d.64(5)
1/231.
The siren of a stationary fire engine has frequency of 500 Hz. If a car drives away from it at 20m/s, what frequency does a person in the car hear?a. 471 Hz b. 500 Hz c. 531 Hz d. 565 Hz
32. An investment of P60,000 can be made in
depreciable assets that will produce revenues of
P29,000 per year for 5 years Annual cost for
operations and maintenance will be P12,000 per
year. Taxes and insurance will be 2% of the first
cost. If the company expects capital to earn not less
than 15% before tax, is this a desirable investment.
Use sinking fund method to calculate for annual
depreciation. What is the % rate of return ?
4. 10%
b. 11.5%
c. 13.5%
d. 17%
33. Find a point in the parabola y
2=4x at which the
rates of change of the ordinate and abscissa are
equal.
a. (4,4)
b. (1,2)
c. (0,0)
d. (3,2)
34. An inlet pipe can fill up the tank in 6 hours
while an outlet pipe can empty the tank in 9 hours.
One day, the tank was being filled. When it was 1/3
full, a boy opened the outlet pipe. How long did it
take to fill the rest of the tank?
a.8 h
b. 10 h
c.12 h
d. 13 h
35.
Farmer Johnson hitches his tractor to a sled loaded with firewood and pulls it a distance of 20 m along level frozen ground. The total weight of sled and load is 14700 N. The tractor exerts a constant 5000 N force at an angle of 36.9* above the horizontal as shown. There is a 3500N. Friction force opposing the motion. Find the work done by each force acting on the sled and the total work done by all the forces.a. 10 kJ b. 20 kJ c. 30 kJ d. 40 kJ
36. A revolving beacon is located 1000 ft. from a
straight sea wall and rotates at the constant rate of 2
rpm. How fast does the beam of light cast by the
beacon sweep along the sea wall at the nearest point
to the beacon?
a. 262 fps
b. 210 fps
c. 186 fps d. NOTG
37. Given : dy1/dx = (2/13) (1+ 5/2 x - 3/2 – ¾ k),
What is the value of k such that y1 is perpendicular
to the curve y2 = 2x at (1,1)
a. 3
b. 6
c. 7
d. 10
38. A plane cuts through a cube in such a way that
the plane passes through three of the cube’s
vertices, no two of which lie on the same edge. If
the edge of the cube has a length of 1, what is the
surface area of the smaller fragments of the cube?
a. 2.4
b. 2.7
c. 3.1
d. 3.7
39. Determine the reactions R1 and R2 of the beam
in Fig. P-333 loaded with a concentrated load of
1600 lb and a load varying from zero to an intensity
of 400 lb per ft.
a. 1400
b. 1900
c. 2100
d. notg
40.
A passenger weighing 60 kg rides a ferris wheel with a radius of 8.0 m. The wheel makes one revolution in 10 s. Calculate the force the seat exerts on the passenger at the top of the circle.a. 398 N b. 498 N c. 588 N d. 778 N 41. When the top T of a mountain is viewed from point A, 2000 m from ground, the angle of depression a is equal to 15o and when it is viewed from point B on the ground the angle of elevation b is equal to 10o. If points
A and B are on the same vertical line, find the height h of the mountain.
a. 756.3 m
b. 793.8 m
c. 821.4 m d. 865.2 m
42. At 7:00 AM, Mr. Castro left home for work
driving at a rate of 40kph. 15 minutes later, his
wife discovered that Mr. Castro left his wallet at
home so Mrs. Castro pursue him on her car at a
rate of 50 kph. At what time did Mrs. Castro catch
up with her husband?
a. 8:00 AM
b. 8:15 AM
c. 8:30 AM d. 8:45 AM
43.
Determine the reaction R1 of the beam in Fig.
P-333 loaded with a concentrated load of 1600 lb
and a load varying from zero to an intensity of 400
lb per ft.
a.1900
b.2100 c.2500
d. 1400
44.
Suppose a student carrying a flu virus returns to an isolated college campus of 1000 students. Determine the no. of infected students after 6 days if it is observed that 50 students are infected after 4 days. Assumed that nobody leaves the campus throughout the duration of the disease.a. 276 students b. 305 students c. 348 students d. 487 students
45. A student taking a true-false test consisting of 15
questions guesses at the answers. Assuming that he
is equally likely to make a correct or an incorrect
guess on each question, find the probability that 8
of his answers will be right and the rest wrong.
a) 6435 / 32768 b) 6543 / 32768
c) 6435 / 37268
d) 6435 / 32876
46. A fencing materials has a limited length of 60 ft.
What is the largest triangular area that can fenced
in?
a.190.53 sq.ft
b. 181.87sq. ft
c. 173.21 sq. ft
d. 164.74 sq.ft
47. You throw a 0.145 kg baseball straight up in the air, giving it an initial upward velocity of magnitude 20 m/ s. Use the conservation of energy to find how high it goes, ignoring air resistance.
a. 15.2 m b. 17.8 m c. 20.4 m d. 21.9 m
48. At the end of each year for 8 years, a
corporation will dposit $12,500 in a depreciation
fund to provide for replacement of machinery at the
end of 8 years. If the fund accumulates at 8%
effective, how much is in it just after the last
deposit.
a. $120,453
b. $126,980
c. $132,958
d. NOTG
49. Find the moment of
inertia about the indicated
x-axis for the shaded area
shown in Fig. P-821.
a. 606.19 in
4 b. 756.19 in
4 c.865.19 in
4 d.906.19 in
450. Ten coins are tossed. What is the probability that
at least six of them will be tail?
a) 512 /193 b) 391 / 152
c) 193 / 512
d) 512 / 391
51.
A train moving with constant acceleration
travels 24 ft (7.32 m) during the 10th sec of its
motion and 18 ft (5.49 m) during the 12th sec of its
motion. Find its its constant acceleration.
a. 1.47 m/s2
b. -0.915 m/s2
c. - 0.47 m/s2
d. 2.47 m/s2
52.
Vector A has magnitude 6 units and is in the direction of the +x-axis. Vector B has a magnitude 4 units and lies in the xy-plane, making an angle of 30˚ with the + x-axis. Find the vector product A x B.a. 9 b. 10 c. 11 d. 12
53. A funnel in the form of cone is 10 cm across the
top and 8 cm deep. Water is flowing into the funnel
at the rate of 12 cm
3/sec and out at the rate of
4cm
3/sec. How fast is the surface of the water rising
when it is 5 cm deep.
a. 0.26 cm/sec
b. 0.32 cm/sec
c. 0.14 cm/sec
d. 0.40 cm/sec
54. A hemispherical tank of radius 2 ft. is initially filled with water. At the bottom of the tank, there is a hole of radius 1 in. through which the water drains under the influence of gravity. Determine how long it will take the tank to drain completely.
a. 2.3 h b. 3.6 h c. 4.8 h d. 5.5 h
55. A particle moves according to the following
function of time: x(t) = 3sint and y(t) = 4 cost, what
is the resultant velocity at t= pi?
a. 3
b. 4
c. 9
d. 25
56. The length of a rectangle is 3 inches more than
twice the width. If the length is increased by 1 inch
and the width is increased by 2 inches, the area is
increased by 20.5 sq. inches. What is the perimeter
of the rectangle?
a. 21 in
b. 22 in.
c. 23 in. d. 24 in.
57. Water is pouring into a swimming pool. After t
hours, there are t+ t
1/2gallons in the pool. At what
rate is the water pouring into the pool when t = 9
hours?
a. 7/6 gph
b. 1 gph c. ½ gph d. 1/6 gph
58. A man agrees to make $5,000 payments at the
ends of the first five years, $4000 at the ends of the
next five years, and $3,000 at the ends of the next
five years. If money is worth 4%, find the present
value of this agreement.
a. $46,000
b. $50,000
c. $ 65,000
d. $69,000
59. What is the standard equation of the locus of
points in the Cartesian plane, the absolute
difference of whose distances from the points (±4,0)
is 4?
a. (x
2/9)-(y
2/16) =1
b. (x
2/4)-(y
2/12) =1
c. (x
2/12)-(y
2/16) =1 d. (x
2/12)-(y
2/9) =1.
60. Three bars, hinged at A and D and pinned at B
and C as shown in Fig. P-318, form a four-link
mechanism. Determine the value of P that will
prevent motion.
a. 30.48 KN
b. 25.48 KN
c. 46.98 KN
d. NOTG
61. If money is worth
8% compounded
quarterly, find the
present value of a
sequence of payments
of $200 each at the
end of each 3 months
forever.
a. $8620
b. $10,000
c. $10200
d. NOTG
62. A conic has the lines y = -3 and y = 5 as
directrices and the point (1, 26) as a focus. What are
the coordinates of the vertex closest to the given
focus?
a. (1,11)
b. (2, 11)
c. (3, 8) d. NOTG
63. The cost of producing a small transistor radio
set consists of P23 for labor and P37 for materials.
The fixed charges in operating the plant are
P100,000 per month. Other variable cost is P1/set.
The radio set can be sold for P75 each. Determine
how many sets must be produced per month to
break even.
a. 5000
b 7200
c. 8400
d. 10000
64. A plane cuts through a cube in such a way that
the plane passes through three of the cube’s
vertices, no two of which lie on the same edge. If
the edge of the cube has a length of 1, what is the
surface area of the smaller fragments of the cube?
a. 2.4
b. 2.7
c. 3.1
d. 3.7
65. The daily cost to a small firm of producing x
units of a product is C(x) = 2002 + 120 x – 5x2 +
1/3 x3 dollars. The market price of 1 unit is $264.
What should be the daily output x in order to
maximize the daily profit.
a. 10 units
b. 18 units
c. 36 units d. NOTG
66. An ellipse with major axis 16 and minor axis 8
is revolved about its minor axis. Find the volume of
the solid generated.
a.512/3(n)
b. 1125/3 (n)
c. 1024/3 (n)
d. 1058/3 (n)
67. The angle of elevation of a hot air balloon, climbing vertically, changes from 25 degrees at 10:00 am to 60 degrees at 10:02 am. The point of observation of the angle of elevation is situated 300 meters away from the take off point. What is the upward speed, assumed constant, of the balloon?
a. 2.25 m/s
b. 2.76 m/s
c. 3.16 m/s
d. 3.89m/s
68. A shell is fired at an angle
above the
horizontal at a velocity of 300 m/s. What is the time
of flight?
a. 39 s
b. 41 s
c. 43 s d. 45 s
69. Future value less the present value
a. discount
b. rate discount
c. discount rate
d. profit
70. It is the worth of the property as recorded in the
books of account of the company.
a. book value
b. fair value
c.
market value
d. goodwill value.
40
71.
A 200 g of water is mixed to 300 g of alcohol whose density is 790kg/ m3. Calculate the specific gravity of the total mixture.a. 0.675 b. 0.862 c. 0.912 d. 1.0
72. A structure costs P12,000 now. It is estimated to
have a life of 5 years with a salvage value at the end
of life of P1,000. Determine the depreciation at the
end of the second year.
a. P3666.67
b. P2933.33
c. P2200.00
d. NOTG
73. Determine the book value at the end of the third
year.
a. P1733.33
b. P8800.00
c. P5666.67
d. P3200.00
74. The set of all possible outcomes in an experiment.
a. sample space b. event c.
sample point d. population
75. It is the worth of the property as recorded in the books of account of the company.
a. book value b. fair value c. market value d. goodwill value.
76. There are 8 baseball teams in a league. How many games will be played if each team plays each of the other teams 40 times?
a) 280 b) 560 c) 320 d) 1120
77.
In Fig. P-512, the homogeneous block weighs
300 kg and the coefficient of friction is 0.45. If h =
50 cm, determine the force P to cause motion to
impend.
a. 45 kg b. 65 kg c. 72 kg d. NOTG
78. Find the number of different arrangements that can be made of the letters to the word COLLEGE.
a) 2160 b) 6210 c) 2016 d) 1260
79.Locate the centroid of the shaded area in Fig.
P-723.
a. x= 49.40 mm, y = 10.29 mm
b. x= 38.27 mm, y = 20.39 mm
c. x= 39.71 mm, y = 30.39 mm
d. x= 29.14 mm, y = 10.9 mm
80. How many different kinds of bouquets of 3 kinds of flowers each can be made from 8 varieties of flowers? a) 363 b) 65 c) 56 d) 336
