5

TECHNOLOGICAL INSTITUTE OF THE PHILIPPINES MANILA PRE BOARD EXAM DAY 3 STUDENT NUMBER_______________________________________________________DATE________________ DIRECTIONS: PROVIDE THE SOLUTION TO SELECT THE CORRECT ANSWER. 1. Patent law of the Philippines a. R.A. 105 b. 1 R.A. 145 c. R.A. 165 d. R.A. 166 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 e. NOTG

3. Find the integral of tan x. a. ln sin x + C b. - ln sin x + C

c. ln cos x + C

d. - ln cos x + C

The region of the stress-strain diagram extending from the proportionality limit to the point of rupture. a. Elastic Range b. Ultimate Rupture Stress. c. Yield Point d. d. Plastic Range 4.

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 ft2/sec b. 1.73 ft2/sec c. 3.0 ft2/sec d. 3.7 ft2/sec 6. The measure of spread or variation in a given data set.

a. measure of central tendency c. measure of occurrence

b. measure of relative standing d. measure of variability

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. For a particular experiment you need 5 liters of a 10% solution. You find 7% and 12% solution on the shelves. How much of the 7% solution should you mix with the appropriate amount of the 12% solution to get 5 liters of a 10% solution? a. 1.5 b. 2 c. 3 d. 2.5 9. At what point in the Celsius and Fahrenheit scale will they be equal?

a. – 30

b. – 55

c. – 40

10. In an arithmetic sequence, t23 = 519 and t71 = 1503, what is t114? a. 3824.5 b. 2458.3 c. 2384.5

d. – 25 d. none of the given

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. 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.. 13. An act to provide for the registration and protection of trademarks, tradenames, and service marks, defining unfair competition and false marking and providing remedies against the same a. R.A. 105 b. 1 R.A. 145 c. R.A. 165 d. R.A. 166 14. Thrice the sum number of the numbers is 30 and the sum of the squares of the numbers is 52. Find the product of the two numbers. a. 24 b. 30 c. 36 d. 48

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. 84,902 years

e. 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. The middle of a given data set. a. mean b. median

c. mode

18. The reciprocal of Bulk modulus of any liquid is called ________. a. Compressibility b. Volume strain c. volume stress

d. range d. shape elasticity

19. 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 20. Find the equation of the parabola whose focus is at the origin and whose directrix is the line y = -4. a. x2 = 4y+4 b. x2 = 4y-4 c. x2 = 8y +16 d. x2 = 8y + 8 21. Whenever a net force acts on a body, it produces acceleration in the direction of the resultant force, an acceleration that is directly proportional to the mass of the body. This theory is popularly known as A Newton’s Second Law of Motion C Hooke’s Law of Equilibrium B Newton’s First Law of Motion D Farday’s Law of Forces 22. _ is the condition wwhere a third person becomes a new debtor w/o the knowledge of or against the will of the debtor but always with the consent of the creditor. a. subrogation b. rescission

c. delegation

d. expromission

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. An equipment costs P10,000 with a salvage value of P500 at the end of 10 years. What is the depreciation charge by straight-line method? a. P1000 b. P850 c. P950 d. P1,200 25. 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 26. 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

27. When the corresponding elements of two rows of a determinant are proportional, then the value of the determinant is a. Unknown b. Zero c. Multiplied by the ratio d. One 28. At a certain interest rate compounded quarterly, P 1,000 will amount to P 4,500 in 15 years. What is the amount at the end of 10 years? a. P 2,725.17 b. P 2,303.33 c. P 2,425.63 d. P 2,375.93 29. A culture has No number of bacteria. At t=1 hour, the number of bacteria is measured to be (3/2) No. If the rate of growth is proportional to the no. of bacteria present, determine the time necessary for the no. of bacteria to triple. a. 2.71 hours b. 3.22 hours. c. 4.86 hours. d. 5.29 hours

30. What is the diameter of a circle with the following equation: x 2 + y2 – 6x + 4y – 12 = 0? a. 6 b. 8 c. 10 d. 12

31. The siren of a stationary fire engine has frequency of 50o 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. If P25,000 is invested at 8% interest compounded quarterly, how many years will it take for this amount to accumulate to P45,000? a. 7.5 years b. 30 years c. 15.5 years d. 31.5 years 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 hours b. 10 hours c.12 hours d. 13 hours 35. A tensile stress is to be applied along the long axis of a cylindrical brass rod that has a diameter of 10 mm. Determine the magnitude of the load required to produce a 2.5 x 10 – 3 mm change in diameter if the deformation is entirely elastic.. Poisson’s ratio for Brass is 0.34 and the modulus of elasticity for brass is 97 GPa a. 5600N b. 5400N c. 5000N d. 4800 N

36. The rate of change of stress with respect to strain. a. Tangent Modulus b. Modulus of Rigidity

c. Modulus of Elasticity

d. Stress Change

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. “TIDE ULTRA” is an example of a. trademark b. service mark

c. collective mark

d. tradename

39. 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. 4 b. 5.5 c. 6.4 d. 7.2 40. Three forces 20 N, 30 N and 40 N are in equilibrium. Find the angle between the 30 N and the 40 N forces.

a. 28.960

b. 400

c. 300 15’ 25”

d. 25.970

41. Two equal resistors are connected in series across a certain supply. If the resistances are now connected in

parallel across the same supply, then the power produced will be _________ that of the series connection. a. Two – times b. Four – times c. One – half d. One – fourth 42 The stress in the transverse section that resists the bursting force in

a. Hoop Stress

b. Circumferential Stress

the cylinder is called c. Longitudinal Stress d. Cylindrical Stress

43. 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 e. 3.375 44. A tensile testing apparatus is to be constructed that must withstand a maximum load of 220,000N. The design calss for two cylindrical support posts, each of which is to support half of the maximum load. Furthermore, plain carbon (1045) steel ground and polished shafting rounds are to be used: the minimum yield and tensile strengths of this alloy are 310 MPa and 565 MPa respectively. Specify a suitable diameter for these support points. Use a factor of safety of 5 and the formula a. 40.5 mm b. 47.5 mm

c. 54.2 mm

d. 58.3 mm

45. 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 46. A series of numbers that are perfect square such as the series (1, 4, 9, 16, 25…)

a. Fermat’s Numbers

b. Fibonacci Numbers

c. Euler’s Numbers

47. An agreement between or among two or more persons is a/an a. obligation b. charter c. writ

d. Fourier Series

d. contract

48. Gabriel made three investments totaling P22,000.00 with interest rates at 4%, 5%, and 8%. The total annual income from the three investments was P13,500.00. The income from the 8% investment was P2,500.00 more than the combined income from the other two investments. How much was invested at 5% rate? a. P50,000 b. P60,000 c. P70,000 d.NOTG 49. It is the amount which a willing buyer will pay to a willing seller for the property were each has equal advantage and is under no compulsion to buy or sell. a. Book value b Market value c. Use Value d. Fair value 50. 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 51. Find the distance between two lines represented by the linear equations: 4x – 3y – 12 = 0 and 4x – 3y + 8 = 0 a. 4 units b. 8 units c. 12 units d. 20 units 52. The new intellectual property code is a. R.A. 165

b. R.A. 8293

c. P.D. 1856

d. E.O. 192

53. Twelve persons are to sit a round table. Two particular people insist on sitting opposite each other. Find the number of ways the twelve can be seated. a. 2638800 b. 6238800 c. 3826800 d. 3628800 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 hours b. 3.6 hours c. 4.8 hours d. 5.5 hours e. 6.1 hours

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. A thermometer reading 750F is taken out where the temperature is 20 0F. 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 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. 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. When the two waves of the same frequency speed and amplitude traveling in opposite direction are superimposed. a. Phase difference is always zero b. Distractive waves are produced c. Standing waves are produced d. Constructive interference always results 61. At maximum point the value y” is a. zero b. infinite

c. positive

d. negative

62. The difference between an approximate value of a quantity and its exact value or true value is a. absolute error b. relative error c. one d. change 63. Find the area bounded by the parabola x2 = 16 (y-1) and its latus rectum a. 42.62 sq.u b. 46.27 sq.u. c. 52.67 sq.u. d. 56.27 sq.u. 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 e. 4.3 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. The altitude of the sides of a triangle intersect at the point known as a. incenter b. orthocenter c. circumcenter

d. centroid

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. 3.89 m/s

e. 4.104 m/s

68. The integral of a function between certain limits divided by the difference in abscissas between those limits gives the _________________ of the function. a. average b. domain c. intercept d. asymptote e. limits 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. The ASME BPV Code Sec VIII D.1 specifies a minimum of wall thickness of _____ not including Corrosion allowance, and regardless of vessel dimensions and material of construction. a. 1/16 in b. 2/16 in. c. 3/16 in. d. 1

73. Consider a cylindrical specimen of a steel alloy (Figure 6.21), 8.5 mm in diameter and 80 mm long that is pulled in tension. The modulus of elasticity value is nearest a. 100 GPa b. 150 GPa c. 200 GPa d. none of the given 74. The yield strength of the alloy is a. 1990 MPa b. 2000 Mpa

c. 1500 MPa

75. Determine its elongation when a load of 65,520 N is applied a. 0.33 mm b. 0.40 mm c. 0.43 mm

d. none of the given d. none of the given

mm 72. The present worth of process Q (PWQ) over 10 years is: (A) $2,640 (B) $3,040 (C) $3,440

D) $3,840

73. The present worth of process R (PWR) over 10 years is: (A) $2,630 (B) $3,030 (C) $3,430

D) $3,830

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.