Technological Institute of the Philippines

TECHNOLOGICAL INSTITUTE OF THE PHILIPPINES MANILA PRE BOARD EXAM DAY 3 STUDENT NUMBER_________________________________________ ______________DATE________________ DIRECTIONS: PROVIDE THE SOLUTION TO SELECT THE CORRECT ANSWER. 1. At what point in the Celsius and Fahrenheit scale will they be equal? a. – 30 b. – 55 c. – 40 d. – 25 2 Find the orthogonal family to the family of circles, x2 + y2 = C2 a. y = mx + b b. y = ln x c. y = mx d. NOTG 3. Simplify the following expression: a. 2i/(2)1/2 b. 4i/(2)1/2 c. (2)1/2 /4i d. none of the given 4. A 200 lb man hangs from the middle of a tightly stretched rope so that the angle between the rope and the horizontal 5 direction is . Calculate the tension of the rope? a. 1104 lb b. 1147 lb c. 1205 lb d. 1250 lb 5. The bottle sterilizing machine of a beverage company costs P1M when new. The service life is estimated to be 10 years and the scrap value is P100,000. Using the sum-of-the-years digit method, what is the asset value after the second year? a. P689,091 b. P852,727 c. P589,900 d. P736,364 6. If the straight line method is used, what is the asset value at the end of 3 years? a. 630000 b. P700000 c. P750000 d. P730000 7. Six draws are made from an ordinary deck of playing cards, the card drawn being replaced and the deck thoroughly shuffled before the next draw is made. What is the probability of obtaining exactly 4 spades? a. 135/4960 b. 153/4096 c 135/4690 d. 135/4096 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. The plate is acted on by 4 parallel forces. Three of which are shown. The fourth force P and its line of action are unknown. The resultant of this force system is the couple – vector CR = -1100i + 1500j KN-m. Determine P and its line of action (x,y) a. (3m, 4m) b. (4m, 3m) c. (3m,4003m) d. (4m, 2m)15 KN/m KN 300 KN

200 KN

10 KN/m

3m 4m

Figure 9

4m

6m

Figure 10

10. Determine the resultant of the line load acting on the beam shown in the figure. a. P = 105 KN b. P=75 KN c. P=90 KN d. P=45 KN 11. Tom’s retirement account 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 12. The equation of a circle on the y-axis and passes through the origin and the point (4,2) is 2 a. x + y2 - 10y = 0 c. x2 + y2 - 10x = 0 2 2 b. x + y - 10x + 10y = 0 d. x2 + y2 + 10y = 0 13. Find the largest area of a rectangle with vertices at the origin of a cartesian coordinates system, on the x – axis, on the y – axis, and on the parabola y = 4 – x2. a. 16/3 b. 16/3½ c. 4(3) - ½ d. NOTG 14. Find the centroid of a hemisphere of radius R revolving about the x-axis. a. 5/8 from center b. 2/5 from center c. 3/5 from center d. 3/8 from center 15. Any line through two points on a curve is called. a. tangent line b. secant line c. slope d. normal line 16. The solution for dy/dx = xe –x when y(0) = 0 a. y = - e–x (x+1) b. y = - e–x (x+1) + 2 –2x c. y = - e (x+1) + 1 d. NOTG 17. Given the force vectors; A = 8i + 4j -2k and the position vectors B = 2j + 6k m and C =3i – 2j + 4k m, the dot product of A and B is a. – 4N.m b. – 3.71 N.m c. – 4.5 N.m d. 7.3 N.m 18. You are saving up for a big investment in six years. You estimate it will take Php14,500 to secure this investment. How much do you need to put into a savings account at the end of each year if the savings account earns 4%? (A) Php2,185 (B) Php2,375 (C) Php2,415 (D) Php2,485 19. A man wants to fence a rectangular area as inexpensively as possible. If the fencing material cost Php 38 per meter and Php 1,520 is available for the project, how much area can be enclosed? a. 100 m2 b. 105 m2 2 c. 110 m d. NOTG 20. Find the smallest angle between the lines 2x + y = 0 and x + 3y + 4 = 0 a. 40° b. 60° c. 45° d. 30°

90 C 21. In preparing a tea, 600 g of water at

is poured into C

200 g china pot whose specific heat capacity is 840J/kg

20 C and temperature of water? 81 .6C a.

. What is the final temperature of 83 .6C

b. 85 .6C

87 .6C

c. d. 22. 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 23. Find the equation of the hyperbola with vertices at ( ±2,0) and asymptotes y = ±3x a. 4x2 – 36y2 = 144 b. 36x2 – 4y2 = 144 c. 9x2 – 4y2 = 36 d. 4x2 – 9y2 = 36 24. Certain manufactured articles are sold in boxes of 25 each. They are inspected by taking a random sample of 5 from each box and passing the box as satisfactory if no defective articles are found in the sample. Find the probability that a box will be passed if it contains 1 defective. a. 0.8 b. 0.76 c. 0.65 d. NOTG 25. Assume that a 20-mm-diameter rivet joins the plates that are each 110 mm wide. The allowable stresses are 120 MPa

for bearing in the plate material and 60 MPa for shearing of rivet. Determine (a) the minimum thickness of each plate; and (b) the largest average tensile stress in the plates. a. 8.9 mm, 30 MPa b. 7.9 mm, 26.7 MPa c. 4.2 mm, 28.5 MPa d. NOTG

Figure 26

A B

26. At each point (x,y) on a certain curve, the tangent line has slope 4x3 + 2. Find the equation of the curve if it contains the point (1,7) a. x4 + 2x + 3 b. x4 + 2x + 4 4 c. x + 2x + 6 d. NOTG 27. In an arithmetic sequence, t23 = 519 and t71 = 1503, what is t114? a. 3824.5 b. 2458.3 c. 2384.5 d. none of the given 28. Find an approximation for the sum of all the terms of {16, -8, 4, -2, 1, -1/2, ¼, …} a. 11 1/3 b. 10 2/3 c. 9 ¼ d. none of the given 29. A circle whose equation is X2 + Y2 + 4X+ 6Y- 23 = 0 has a radius of a. 3 b. 4 c. 5 d. 6 30. 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 31. Buildings are usually depreciated at an annual rate of about ____ of the initial cost. (A) 5% (B) 12% (C) 15% (D) 10% 32. 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 hours b. 10 hours c.12 hours d. 13 hours 33. A man 5.5 ft tall walks away from a lamppost 10 feet high at a rate of 8 feet per second. How fast does his shadow lengthen? c a. 88/9 fps . 9/88 fps d b. 160/9 fps . 9/160 fps 34. A rubber ball is dropped on a floor from a height of 5 m. If the coefficient of restitutions is 0.7, find the height of the which ball rebounds? a. 2.45 m b. 2.75 m c. 3.25 m d. 3.5 m 35. 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 36. The particular solution of d2y/dx2 + 4y = 0 a. y = c1 sin 2x + 3 cos 2x b. y = 3sin 2x + c1cos 2x c. y = c1 sin 2x + 6 cos 2x d. NOTG 37. A ball is thrown from a tower 30 m high above the ground with a velocity of 300 m/s directed at 20° from the horizontal. How long will the ball hit the ground? a. 21.2 s b. 22.2 s c. 23.2 s d.24.2s 38. Using a powerful air gun, a steel ball is shot vertically upward with a velocity of 80 meters per second, followed by another shot after 5 sec. Find the initial velocity of the second ball in order to meet the first ball 150 meters from the ground.

a.65.3 m/s b. 45.1 m/s

c. 56.2 m/s d. 61.3 m/s 0.5C 0.2C 39. Two charges, one of + and the other of , attract each other with a force of 100 N. How far apart are they? a. 3 mm b. 4 mm c. 30 mm d. 40 mm 40. A particular moon rock is analyzed and it is found to contain equal amounts of Potassium-19 and Argon-18, which are denoted as , respectively. is a radioactive isotope that can decay to

. Note that

potassium decay and that the yield of

for is about 11% (i.e.

about 1 out of every 9 atoms decays to ). Assuming that the initial amount of argon was zero and that all of the argon is the result of potassium decay, estimate the age of the moon rock. a. 2 billion years b. 4.3 billion years c. 5.3 billion years d. NOTG 41. In how many ways can 3 red balls, 4 black balls, and 2green balls be arranged adjacent to each other in a shelf if one does not distinguish between balls of the same color? a. 1260 b. 1344 c. 1458 d. NOTG 42. The act regulating the practice of chemical engineering in the Philippines is a. R.A. 9297 b. R.A. 9792 c. R.A. 813 d. R.A. 318 43. Find the particular solution of y''' = 0 given that: y(0) = 3, y'(1) = 4, y''(2) = 6 a. y = 2x2 − 3x + 3 b. y = 3x2 − 2x + 3 2 c. y = 2x − 2x + 2 d. NOTG 44. In how many ways can one make a selection of 4 black balls, 5 red balls, and 2 white balls from a box containing 8 black balls, 7 red balls and 5 white balls? a) 14700 b) 17400 c) 47100 d) 10740 45. A nominal rate of 9.5% has an equivalent effective rate of 9.84%. What is the compounding period? a) monthly b) bi-monthly c) quarterly d) semi- annually 46. The total surface of two cubes is 150 sq. m, The total length of their edges is 84 cm. Find the edge of the larger cube. a. 3.54 b. 3 c. 4 d. NOTG 47. What is the probability that 5 cards dealt from a well shuffled deck , 3 will be hearts and 2 spades? a. 0.00633 b. 0.00858 c. 0.011 d. 0.0153 20 C 48.. A total of 0.8 kg of water at is placed in 1 kW electric kettle. How long a time is needed to raise the 100 C temperature of water to . a. 3.5 min b. 4.5 min c. 5.5 min d. 6.5 min 49.. 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. 15.3 ksi b. 18.3 ksi c. 14.3 ksi d. NOTA 50. A flanged bolt coupling consists of 8 10 – mm diameter steel bolts on a bolt circle 400 mmm in diameter, and 6 10 mm diameter steel bolts on a concentric bolt circle 300 mm in diameter. What torque can be applied without exceeding a shearing stress of 60 Mpa in the bolts. a. T = 10.7 kN.m b. 15.7 kN.m c. 20.5 kN.m d. NOTA

Figure 55

51. The 36 m cable shown in Figure weigh 1.5 KN/m. determine the sag H and the maximum tension in the cable. a. T = 44.3 KN, H = 8.67 m b. T = 34.3 KN, H = 8.77 m c. T = 74.3 KN, H = 5.77 m d. T = 94.3 KN, H = 6.77 m 52. Miles is camping in Glacier National Park. In the midst of a glacier canyon, he makes a loud holler. He hears an echo 1.22 seconds later. The air temperature is 20 degrees C. How far away are the canyon walls? a. 310 m b. 209 m c. 107 m d. 236 m 53. 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% 54. What is the distance between the center of the circles X2 + Y2 + 2X + 4Y – 3 = 0 and X2 + Y2- 8X – 6Y + 7 = 0 a. 7.07 b. 7.77 c. 8.07 d. 8.77 55.. Calculate the distance when the moment is zero. a. 3.25 m b. 2.55 m c. 2.154 m d. 1.75 m 56. How many different value of X lies between 0 º and 180 º for the equation ( 2 sinX -1 ) (cosX + 1) = 0 a) 0 b) 1 c) 3 d) 2 57. In a triangle ABC, angle B = 45o and angle A= 60o. What is the ratio of the sides AB to AC? a. 1.37 b. 1.22 c. 1.48 d. 0.73 58. A thermometer reading 750F is taken out where the temperature is 200F. The thermometer reading is 300F after 4 minutes later. Find the thermometer reading in 0F, 7 minutes after the thermometer was brought outside. a. 21.8 b. 22.8 c. 23.8 d. 24.8 59. 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 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 c. 865.2 m e. 912.1 m60. 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 61. What part of 90% alcohol must be removed and replaced by an equal amount of pure alcohol to make 95% alcohol solution? a. 5% or less b. between 5% and 10% c. 5% d. 50% 62.The set of all possible outcomes in an experiment. a. sample space b. event c. sample point d. population 63. Future value less the present value a. discount b. rate discount c. discount rate d. profit 64. 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. 65. Find the asymptotes of the hyperbola 4x2 – 9y2 = 36. a. y = ±3 b. y = ±2/3 c. y = ±(13)1/2 d. y = ±1/3 66. What is the modulus of elasticity if the stress is 44,000 psi and a unit strain of 0.00105? a. 41.905 x 10+8 c. 41.202 x 10+6 +6 b. 42.300 x 10 d. 43.101 x 10+6 67. If the ultimate shear strength of a steel plate is 42,000 psi, what force is necessary to punch a 0.75-inch hole in a 0.625 inch thick plate? a. 63,000 c. 61,850 b. 68,080 d. 66,800 68. It is the stress caused by forces acting along or parallel to the area resisting the forces. a. shearing stress c. punching stress

b. bearing stress d. tensile stress 69. It refers to the highest ordinate in the stress-strain diagram. a. working stress c. ultimate stress b. allowable stress d. non eof the above Figure 51

70. A flywheel is 15 cm in diameter accelerates uniformly from rest to 500 rpm in 20 s. What is its angular acceleration? a.2.62 rad/s c. 3.95 rad/s b. 3.45 rad/s d. 4.42 rad/s 71.simplify secθ-(secθ)sin2θ a. cos2θ b. cosθ c.sin2θ d. sinθ 72. What is the number of permutations of the letters in the word BANANA? a. 36 b. 60 c. 52 d. 42 73. Environmental Impact Assessment Law A. PD 602 C. PD 1586 B. PD 1160 D. NOTG 74. Ecological Solid Waste Management

A. RA 6969 C. RA 9003 B. RA 9275 D. NOTG 75. When using net present worth calculations to compare two projects, which of the following could invalidate the calculation? a) difference in the magnitudes of the projects b) evaluating over the different time periods c) mutually exclusive projects d) nonconventional cash flows 76. What must two investments with the same present worth and unequal lives have? a) identical salvage values b) different salvage values c) identical equivalent uniform annual cash flows d) different equivalent uniform annual cash flows 77. Which of the following is true regarding the minimum attractive rate of return used in judging proposed investments? a) it is the same for every organization. b) it is frequently a policy decision made by an organization’s management. c) it is not relevant in engineering economy studies. d) both A and B 78. For an equipment purchased three years ago for $15,000 if it is depreciated using the sum of years digit method. The expected life is five years. The depreciation charge for year 2 is a) $4,000 b) $5,000 c) $6,000 d) $7,000 79. The total depreciation in year 3 is a) $12,000 b) $13,000 c) $14,000 d) $15,000 80. The book value is a) $3000 b) $4,000 c) $5,000 d) $6,000 81. 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 82. Find the particular solution of y''' = 0 given that: y(0) = 3, y'(1) = 4, y''(2) = 6 a. y = 2x2 − 3x + 3 b. y = 3x2 − 2x + 3 2 c. y = 2x − 2x + 2 d. NOTG 83. In an arithmetic sequence, t23 = 519 and t71 = 1503, what is t114? a. 3824.5 b. 2458.3 c. 2384.5 d. none of the given 84. 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)

85. If an ellipse and a parabola share a focus and corresponding vertex, which of these is true? a. The parabola has a shorter latus rectum b. The length LR of the conics are equal. c. The ellipse has a shorter latus rectum d. The length of LR cannot be compared.