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TECHNOLOGICAL INSTITUTE OF THE PHILIPPINES MANILA PRE BOARD EXAM DAY 3 NAME:_________________________DATE: 8/31/17 DIRECTIONS: PROVIDE THE SOLUTION TO SELECT THE CORRECT ANSWER.
1. Riu and Crizaldy worked as foreman in the field at $14 and $12 per hour respectively. In the month of November, Riu worked 10 hours more than Crizaldy. If their total income for the month of November was $3520, how many hours did each work during the month of November? a. 110, 120 b. 150, 170 c. 120, 150 d. 130, 140 2. A man wants to sell his scooter. There are two offers, one at Rs. 12,000 cash and the other a credit of Rs. 12,880 to be paid after 8 months, money being at 18% per annum. Which is the better offer? A. 12,000 in cash B. 12,880 at credit C. Both are equally good
3. A company’s marginal revenue function is given by dR/dx
= 1000/
x
–
1, where x>1 is the number of items manufactured. Find the total revenue R in terms of x, if R =$13,000 when x = 26 a. R = 1000/
x
–
1 + 3000 b. R = 1000/
x
–
1 + 3000 c. R= 2000/
x
–
1 + 3000 d. NOTG 4. The equation of motion of a particle starting from rest along a straight line is x = t
3
- 3t
2
+ 5. The ratio of the accelerations after 5 sec and 3 sec will be A. 2 B. 3 C. 4 D. 5 5. The diagonals of a rhombus measure 24 and 18 inches. What is the measure of the larger angle of the rhombus? a. 73.7° b. 53.1° c. 120° d. 106.3° 6. A water tank is three-fifth full. Pipe A can fill a tank in 12 minutes and pipe B can empty it in 6 minutes. If both the pipes are open, how long will it take to empty or fill the tank completely?
A. 4.8 min B. 5.2 min C. 6.8 min D. 7.2 min 7. Tickets numbered 1 to 20 are mixed up and then a ticket is drawn at random. What is the probability that the ticket drawn has a number which is a multiple of 3 or 5? A. ½ B. 2/5 C. 8/15 D. 9/20 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 the temperature of the bar after 10 minutes? a.32.1°F b. 44.3°F c. 70.5°F
d. 64.5°F 9. When equal and opposite forces applied to a body, tend to elongate it, the stress so produced, is called A. shear stress B. compressive stress C. tensile stress D. transverse stress. 10.
–
12 Determine the force in members AB, BD, and CD, of the cantilever truss shown If the loads were applied at C and E instead of at B, 10. AB a. 150 kN/T b. 180 kN/T c. 250 kN/T d. NOTG 11. BD a. 180kN/T b. 200 kN/C d. 250 kN/T d. 300kN/C 12. CD a. 180kN/T b. 200 kN/C d. 250 kN/T d. 300kN/C 12. What is the time required for one dollar to double when invested at the rate of 5% per annum? Assume that interest is compounded continuously. a.13.86 yrs b. 25.12 years c. 15.38 yrs d. 16.69 yrs 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. A spring will be stretched 1 ft. by a pull of 3 5/8 lb. A 5 lb weight is attached to the spring and it is arbitrarily set in motion. The coefficient of air resistance is 1/8. Find the frequency of the motion. a.11/4
b. 36/6
c. 12/5
d. 50/8
15.
Tom’s retirement acco
unt in a company currently totals Php416,384. What perpetual income can Tom and his heirs receive per year if he retires now and the money is invested in an annuity earning 6% interest? (A) Php20,980 (B) Php22,980 (C) Php24,980 (D) Php26,980 16. A rectangular lot is bounded at the back by a river. No fence is needed along the river and there is to be 24-ft opening in front. If the fence along the front costs $1.50 per foot, along the sides $1 per foot, find the dimensions of the largest lot which can be thus fenced in for $300. a. 82 ft x 144 ft. b. 84 ft × 112 ft c. 78 ft x 110 ft d. 81 ft x 124 ft.
17.
A ball kicked from ground level at an initial velocity of 60
m/s and an angle θ with ground reaches a horizontal distance
of 200 meters.
What is the size of angle θ?
a. 15.2° b. 16.5° c. 18.4° d. 20.8° . 18. A 2lb mass is dropped from a great height. Air resistance is proportional to kv
2
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 19. On a certain stretch of track, trains run at 96.56 kph. How far back of a stopped train should be a warning torpedo be placed to signal an oncoming train? Assume that the brakes are applied at once and retard the train at the uniform rate of 0.61 m/s
2
. a. 289m b. 345 m c. 486 m d. 589 m 20. The point ( 3,2) is the midpoint of the segment defined by the points ( h, 1) and ( 5, k) , h and k are respectively: a. 1 and 3 b. 3 and 1 c. -2 and 1 d. 2 and -1 21. Against the current in a river, a boat traveled 230 miles in 4 hours. With the same current, the boat traveled the same
distance in only 3 hours and 20 minutes. What is the boat’s
speed? a. 6.1 mi/h b. 9.8 mi/h c. 63.6 mi/h d. 75.6 mi/h 22. A nuclear breeder reactor produces waste that contains (amongst other things) the isotope 239Pu (Plutonium-239). After 15 years, the initial concentration of 239Pu in the waste has decreased by 0.043%. Find the half-life of the isotope. a. 4500 yrs. B. 4800 yrs c. 5200 yrs d. 5700 yrs 23. Five red books and 3 blue books are placed at random on a shelf. Find the probability that the blue books will be together. a. 2/13 b. 3/ 18 c. 3 / 28 d. 3/ 14 24. Find the equation of perpendicular bisector of the line passing through points (2,-5) and (-3,4). a. 5x -9y=2 b. 3x-4y=1 c. x+y=4 d. 3x+7y =3 25. The distance between the vertices of an ellipse is 10. The distance between the foci is 6. What is the distance between directrices. a. 0.60 b. 7.33 c. 16.7 d. 8.33 26. The beam shown in the figure is supported by a hinge at A and a roller at B. The reaction RA of the hinged support A of the beam, is A. 10.8 t B. 10.6 t C. 10.4 t D. 10.2 t. 27. A thermometer reading 75 degree Fahrenheit is taken out where the temperature is 20 degree Fahrenheit. The thermometer reading is 30 degree Fahrenheit 4 minutes later. Find the time (in minutes) taken for the reading to drop from 75 degree Fahrenheit to within half degree of the air temperature. a. 5.45 min b. 8.24 min c. 11.03 min d. 12.4 min
28. The vertical reaction at the support A of the structure shown in below figure, is A.1 t B.2 t C.3 t D.2.5 t. 29. In the figure, rectangle ABCD is inscribed in the circle, if the radius of the circle is 1 and AB=1, what is the area of the shaded region? a. 0.091 b.0.285 c. 0.614 d. 0.705 30. Find the angle in degrees between the asymptote of the hyperbola 9x
2
-25y
2
+ 50y
–
250 =0 and the x
–
axis. a. 30.96° b. 25.66° c. 11.76° d. 15.4° 31. Calculate the focus of the parabola x
2
+ 2 x y + y
2
- 4 x + 2 y - 6 = 0. a. 5x + 4y -8 = 0 b. -6 x + 6 y + -17 c. 3x -4y -12 = 0 d. -3x +2y +12 = 0 32. The present worth of Php 1404 due in two equal half-yearly installments at 8% per annum simple interest is: A. Php 1325 B. Php 1300 C. Php 1350 D. Php 1500 33. Calculate the axis of the parabola x
2
+ 2 x y + y
2
- 4 x + 2 y - 6 = 0. a. x + 2y -2 = 0 b. 3x -2y +5 = 0 c. 2 x + 2 y - 1 = 0 d. 4x + 2y +3 = 0 34. The masses of two balls are in the ratio of 2 : 1 and their respective velocities are in the ratio of 1 : 2 but in opposite direction before impact. If the coefficient of restitution is 1/2 , the velocities of separation of the balls will be equal to A. srcinal velocity in the same direction B. half the srcinal velocity in the same direction C. half the srcinal velocity in the opposite direction D. srcinal velocity in the opposite direction 35. During a chemical reaction, substance A is converted into substance B at a rate that is proportional to the square of the amount of A. When 60 grams of A are present, and after 1 hour only 10 grams of A remain unconverted. How much of A is present after 2 hours? a. 4.25 g b. 5.45 g c. 5.89 g d. 6.05g 36. Calculate the minimum wall thickness for a cylindrical vessel that is to carry a gas at a pressure of 1400 psi. The diameter of the vessel is 2 ft, and the stress is limited to 12 ksi. a. 0.8 in b. 1.4 in c. 1.9 in d. notg 37. A rectangular beam 20 cm wide is subjected to a maximum shearing force of 10, 000 kg, the corresponding maximum shearing stress being 30 kg/cm2. The depth of the beam is A. 15 cm B. 20 cm C. 25 cm D. 30 cm. 38. For a given material Young's modulus is 200 GN/m2 and modulus of rigidity is 80 GN/m2. The value of Poisson's ratio is A. 0.15 B. 0.20 C. 0.25 D. 0.40 39. The force in member
U
2
L
2
of the truss shown in the figure, A.10 T tension B.10 T compression C.zero D.15 T compression. 40. What are the intercepts of the circle given by the equation (x+3)
2
+(y-3)
2
=9? a. (-3,3) b.(0,+3),(+3,0) c.(0,-3),(3,0) d.(0,+3),(-3,0) 41. Radium decomposes at a rate proportional to the quantity of radium present. Suppose it is found that in 25 years approximately 1.1% of certain quantity of radium has decomposed. Determine how long (in years) it will take for one-half of the srcinal amount of radium to decompose. a. 1254 years b. 1567 yrs c. 2145 years d. 2800 yrs 42. From a point 96 ft above the ground, a stone is thrown in such a way that it is at the same point; 3 sec after it was thrown, as it was 2 sec after it was thrown. How long does it take the stone to reach the ground? a.3 sec b. 6 sec c. 9 sec d. 15 sec 43. Mr. Thomas invested an amount of Php 13,900 divided in two different schemes A and B at the simple interest rate of 14% p.a. and 11% p.a. respectively. If the total amount of simple interest earned in 2 years be Php 3508, what was the amount invested in Scheme B? A. Php 6400 B. Php 6500 C. Php 7200 D. Php 7500 44. A tank has for its boundary a curve given by the equation x
2
+y
2
+6x-12y+29=0 where the units are all in meters. Find the volume of water required to fill the tank to a depth of 3 meters. a. 46
m
3
b. 50
m
3
c. 48
m
3
d. 52
m
3
45. Which of the following could be a quadratic equation with integral coefficient having roots 3+i and 3 - i? a. x2+9x-10=0 b. x2-6x+10=0 c. x2-9x+8=0 d.x2+9x-8=0 46. The tensile force required to cause an elongation of 0.045 mm in a steel rod of 1000 mm length and 12 mm diameter, is (where E = 2 x 106 kg/cm2) A. 166 kg B. 102 kg C. 204 kg D. 74 kg 47. 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 48. The compound interest on Rs. 30,000 at 7% per annum is Rs. 4347. The period (in years) is: A. 2 B. 2 ½ C. 3 D. 4 49-50. A company is considering two alternatives for manufacturing a certain part. Method R will have a first cost of $40,000, an annual operating cost of $25,000, and a $10,000 salvage value after its five year life. Method S will have an initial cost of $100,000, an annual operating cost of $15,000, and a $12,000 salvage value after its 10 year life. At an interest rate of 12% per year, the present worth values of the two alternatives are closest to: Method R (A)$154567 (B) $195057 (C) $ 215054 (D) $245984 50. Method S (A)$425100 (B) $521,000 (C) $745210 (D) $ 810,889 51. If the shadow of a building increases by 10 meters
when the angle of elevation of the sun rays decreases from 70
o
to 60
o
, what is the height of the building? a.35.65 m b. 40.26 m c. 46.86 m d. 52.13 m 52. The second term of a geometric sequence is 6 and the 5th term is 81/4. What is the common ratio of the sequence? a. 3/2 b. 27/8 c. 19/4 d. 3(6/4)
1/2
53. If 8 persons are seated at random in a row, what is the probability that a certain couple will not be together? a) 1/4 b) 3/4 c) 2/5 d) 1/2
Figure 26 Figure 39 Figure 28 Figure 29
54. The shear stress at any section of a shaft is maximum A. at the centre of the section B. at a distance r/2 from the centre C. at the top of the surface D. at a distance 3/4 r from the centre 55. A cylinder is said to be thin if the ratio of its thickness and diameter, is less than A. 1/25 B. 1/20 C. 1/15 D. 1/10 56. A cylindrical pressure vessel is fabricated from steel plating that has a thickness of 20 mm. The diameter of the pressure vessel is 450 mm and its length is 2.0 m. Determine the maximum internal pressure that can be applied if the longitudinal stress is limited to 140 MPa, and the circumferential stress is limited to 60 MPa. a. 4.67 MPa b. 5.33MPa c. 6.75 MPa d. 8.24 MPa 57. Stress in members of statically determinate simple frames, can be determined by A. method of joints B. method of sections C. graphical solution D. all the above 58. You purchase 1,000 shares of stock at Php15.00 per share. The stock pays quarterly dividends of Php125 for two years at which time you sell the stock at the trading price of Php16.50 per share. The yearly return on your investment is most nearly: (A) 2% (B) 4% (C) 6% (D) 8% 59. Find the limit of the sequence a
n
= 3 (1 + n
-1
)/(2
–
n
–
2
), n =
1, 2 ….
a. 2 b. 1 c. 3 d. NOTG 60. Two forces of 6 Newtons and 8 Newtons which are acting at right angles to each other, will have a resultant of A. 5 Newtons B. 8 Newtons C. 10 Newtons D. 12 Newtons. 61. A company produces transmission gears used by several farm tractor manufacturers. The base cost of operation is Php596,700 per year. The cost of manufacturing is Php18.40 per gear. If the company sells the gears at an average price of Php37.90 each, how many gears must be sold each year to break even? (A) 15,740 (B) 18,400 (C) 30,600 (D) 32,430 62. A man draws 1 card from each of 2 separate decks. What is the probability that the card from the first deck is an ace and the one from the second deck a face card? a) 14/169 b) 2/169 c)16/169 d) 3/169 63. A corporation that pays 53% of its profit in income taxes invests $ 10,000 in an asset that will produce $ 3,000 annual revenue for eight years. If the annual expenses are $ 700, salvage after eight years is $ 500, and 9% interest is used, what is the after-tax present worth? Disregard depreciation. a. $ 3,766 b.$ 4255 c. $5342 d. $5892 64. The area of the ellipse is 62.83m
2
. The semi-minor axis is 0.8 times the semi-major axis. Find the perimeter of the ellipse. a. 19.97 b. 28.45 c. 4.53 d. 4 65. An archeologists discovered some ancient objects which had organic remains. He found that 60% of the srcinal amount of C
–
14 remains and the disappearance of C-14 obeys the first-order decay law, give an estimation for the age of the objects given the half life of C14 is approximately 5600 years, determine the age of the fossil. a. 4127. 01 yrs. b.4205.6 yrs. c. 4569.5 yrs. d. NOTG 66. When the top T of a mountain is viewed from point A, 2000 m from ground, the angle of depression a is equal to 15
o
and when it is viewed from point B on the ground the angle of elevation b is equal to 10
o
. 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 c. 865.2 m 67. It is a quantity that when applied to a member, tends to deform the member by causing a rotation of one part of the member relative to another. a. couple b. torque c. axial force d. reaction 68. 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 69. A square and a regular hexagon have the same perimeter. If the area of the square is 2.25, what is the area of the hexagon? a. 2.250 b. 2.598 c. 2.838 d. 3.464 70. How much should be put in an investment with a 10% effective annual rate today to have $10,000 in five years? a.$ 5891 b. $ 6,209 c.$7425 d.$8423 71. A spring scale in a stationary lift shows a reading of 60 kg for a man standing on it. If the lift starts descending at an acceleration of g/5, the scale reading would be A. 48 kg B. 60 kg C. 72 kg D. NOTG 72. A 50 kg boy climbs up a 8 m rope in gymnasiam in 10 sec. The average power developed by the boy is approximately A. 400 watts B. 500 watts C. 4000 watts D. none of these 73. Given part of an arithmetic sequence ( -312, ___, ___, -174) and t
50
= 1160, what is the value of the 26
th
term a. 48 b. 56 c. 67 d. 74 74. A wall 10 ft high is 8 ft from a house. Find the length of the shortest ladder that will reach the house when one end rests on the ground outside the wall. a. 22.2 ft b. 24.1 ft c. 25.4 ft
d. 28.3 ft 75. An airplane is approaching point A along a straight line and at a constant altitude h. At 10:00 am, the angle of elevation of the airplane is 20
o
and at 10:01 it is 60
o
. What is the altitude h of the airplane if the speed of the airplane is constant and equal to 600 miles/hour? (round answer to 2 decimal places). a. 4.1 miles b. 4.6 miles c. 5.2 miles d. 5.5 miles 76. Find the diameter of the minimum size of circular cloth that will cover a triangular table, 2.5 ft by 2.5ft by 2.5 ft. a. 2.82 b. 3.02 c. 3.22 d. 3.42 77. The angle of inclination of ascend of a road having 8.25% grade is ______ degrees. a. 4.72° b. 4.27° c. 5.12° d. 1.86° 78. Find the centroid of the triangle whose vertices are
A
(2,4),
B
(3
,−
1) and
C
(−
3,3). a.3, 4 b. ½, 3 c. 1/3, 4 d. 2/3, 2 79. Determine the equation of the directrix of the curve 3x=2y
2
-4y +7 a. x=30/20 b. x=30/24 c. x=31/20 d. x=31/24 80. The semi-major axis of an ellipse is 4 and its semi-minor axis is 3. The distance from the center to the directrix is: a. 6.222 b. 6.532 c. 6.047 d. 0.661 81.
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 82. Into how many equal parts should you divide 90 so that the continued product of those equal parts will be maximum. a. 45 b. 33 c. 60 d. 25 83. The three sides of a triangle are variable in lengths but the perimeter is constantly 75 cm. What is the maximum possible area of the triangle in sq. cm. a. 200.46 b. 270.6 c. 115.23 d. 114.5 84. How much should be put in an investment with a 10% effective annual rate today to have $10,000 in five years? a.$5249 b. $ 6,209 c. $ 7845 d. $8478 85. In a class of 25 students, 80% are passing the class with a grade of C or better. If two students are randomly selected from the class, what is the probability that neither student is passing with a grade of C or better? a. 0.03 b. 0.20 c. 0.08 d. 0.63 86. In a certain class there are 21 students in subject A, 17 in subject B and 10 in subject (C) Of these 12 attend subjects A and B, 5 attend subjects B and C, 6 attend subjects A and (C) These include 2 students who attend all the three subjects. Find the probability that a student studies one subject alone. (a) 16/37 (b) 15/39 (c) 5/33 (d) 8/27 87. A box is to be made of a piece of cardboard 9 inches square by cutting equal squares out of the corners and turning up the sides. Find the volume of the largest box that can be made in this way.
a. 49 in2 b. 54 in2 c. 58 in 2 d. 60.25in2 88. A line has a parametric equations x=4t+1 and y=-3+2t, given t is the parameter. What is the y intercept of the line? a. -3 b. 3 c. -7/2 d. -1/3 89. In how many ways can 12 people be divided into two groups if one group has 8 people and the other has 4? a. 40320 b. 11880 c. 1485 d. 495 90. A machine is purchased for $1000 and has a useful life of 12 years. At the end of 12 years, the salvage value is $130. By straight-line depreciation, what is the book value of the machine at the end of 8 years? a. $360 b. $420 c. $420 d. $510 91. The product of either force of couple with the arm of the couple is called a. resultant couple b. moment of the forces c. resulting couple d. moment of the couple 92. If the resultant of two equal forces has the same magnitude as either of the forces, then the angle between the two forces is a. 30 b. 60 c. 90 d. 120
93. A couple produces a. translatory motion b. rotational motion c. combined translatory and rotational motion d. none of the above 94. When the data are skewed to the right, the measure of Skewness will be (a) negative (b) zero (c) positive
(d) one 95. According to the law of moments, if a number of coplaner forces acting on a particle are in equilibrium, then a. their lines of action are at equal distances b. their algebraic sum is zero c. the algebraic sum of their moments about any point is equal to the moment of their resultant force about the same point. d. the algebraic sum of their moments about any point in their plane is zero 96
–
97 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 (96) no defective articles, 96. a. 0.854 b. 0.885 c. 0.904 d. 0.924 (97)exactly one defective article, a. 0.056 b. 0.064 c.0.092 d. 0.098 (98) exactly 2 defective articles. a. 0.00376 b. 0.0045 c. 0.0054 d. 0.0064
99.
A cylindrical drinking cup of circular cross section is to
contain 12Π sq. in. of material . What dimensions should the
cup have in order to hold as much liquid as possible.
a. L = 22”
b. L = 20”
c. L = 14”
d. L = 16”
100. A test paper containing 10 problems is given to three students A,B,(C) It is considered that student A can solve 60% problems, student B can solve 40% problems and student C can solve 30% problems. Find the probability that the problem chosen from the test paper will be solved by all the three students. (a) 0.132 (b) 0.027 (c) 0.153 (d) 0.072

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