Tolentino Pre Boards

7/24/2019 Tolentino Pre Boards

1/40


2/40


3/40


4/40


5/40


6/40

1

IF YOU CAN SOLVE THESE PROBLEMS IN 1 HR, THEN YOU ARE A CAL TECH EXPERT

PROBLEMS TAKEN FROM 1ST

MEETING REFRESHER AT TOLENTINO AND ASSOCIATES..

1. A deposit of P110, 000 was made for 31 days. The net interest after deducting 20% withholding tax is P890.36.

Find the rate of return annually.

2. P5, 000 is borrowed for 75 days at 16% per annum simple interest. How much will be due at the end of 75 days?S-1

Mr. J de la Cruz borrowed money from a bank. He received from the bank P1, 340.00 and promised to pay

P1, 500.00 at the end of 9 months. Determine the following

3. Simple interest rate.

4. The corresponding discount rate or often referred to as the Bankers Discount.

S-2

John borrowed P50, 000.00 from the bank at 25% compounded semi-annually.

5. What is the equivalent effective rate of interest?

6. How much must he pay if he pay after 5 years?

7. When will the money double ?

8. If he pay 10,000 after 1 year and 10,000 on the next year , how much must he pay on the 3rdyear to wipe out

his loan?

9. Convert the interest rate to compounded quarterly

10. Convert the interest rate to compounded monthly.

11. Convert the interest rate to compounded continuously .

12. Find the present worth of a future payment of P100, 000 to be made in 10 years with an interest of 12%

compounded quarterly.

13. If P5, 000.00 shall accumulate for 10 years at 8% compounded quarterly. Find the compounded interest at the

end of 10 years.

14. By the condition of a will, the sum of P2, 000 is left to a girl to be held in trust fund by her guardian until it

amounts to P50, 000, when will the girl received the money if the fund is invested at 8% compounded quarterly?15. A Mechanical Engineer wishes to accumulate a total of P10, 000 in a savings account at the end of 10 years. If

the bank pays only 4% compounded quarterly, what should be the initial deposit?

Mr X borrowed P 100,000 at en effective interest of 8% in a bank. He will pay the loan monthly for 5 years

16. Convert interest to compounded monthly

17. What should be the monthly payment?

18. If he decides to pay on a quarterly basis, convert the interest rate to compounded quarterly.

19. What must be the quarterly payment?

20. If he decides to pay on a semiannual basis, convert the interest rate to compounded seminannually.

21. What should be the semiannual payment?

22. Convert the interest rate to compounded continuously.

Mr Y deposited P 1,000 at the end of every month in an account that earns 12% effective interest.

23. What is the monthly interest rate?

24. What will be the amount of money after 5 years?

25. If Mr Y deposited P 1,000 at the beginning of each year, what will be the amount in 5 years. (There will be only

60 deposits )


7/40

2

S -5

Mr Z borrowed P 300,000 from a bank. The bank charges 16% effective interest.

26. What is the equivalent monthly interest rate?

27. What is the monthly amortization if he will pay at the end of each month for 5 years?

28. What will be the monthly amortization if he delays his payment by 6 months (his 1stpayment happened at the

end of 6 months ) .29. What is the monthly amortization if he pays at the beginning of each month for 5 years.

30. Which is the biggest interest rate?

a. 12% compounded quarterly

b. 11.88% compounded seminually

c. 11.99 % compounded monthly

d. 12.02% compounded continuously

S-6

Given the series of payments at the end of each year:

Year 1 2000Year 2 5000

Year 3 8000

and so on until year 20, If i = 12% per annum

31. The present worth of all payments. (year 0 )

32. The future worth of all payments ( year 20)

33. The equivalent equal annual worth of all the payments.

S7

Given the first cost of a machine FC = 500,000 Salvage Value is 150,000 Economic Life = 12 years

34. USING straight line method , the annual depreciation is

35. USING Straight line method, the book value after 5 years is

36. USING SOYD, the book value after 3 years is

37 USING SOYD, the maximum depreciation in any year is

38. USING SOYD, the total depreciation after 6 years is

39. USING MATHESONS METHOD, the Mathesons constant is

40. The sunk cost after 3 years using MATHESONS formula is

41. The total depreciation after 7 years is (MATHESONS FORMULA )

42. USING DOUBLE DECLINING BALANCE METHOD , the book value after 3 years is

43. USING SINKING FUND METHOD , with i = 8% , the annual depreciation is

44. The book value after 6 years is (SINKING FUND METHOD )

45. The total depreciation after 5 years is46. The depreciation on the 4thyear is

S-8

Find the present value of a perpetuity of P 15,000 payable semiannually if money is worth 8% compounded

quarterly

47. The interest rate every six months is

48. The present value of the given perpetuity is


8/40

3

49. A man invest in a medium scale business that cost him P 57,000.00. The net annual return is estimated at P

14,000 for each of the next 8 years. Find the benefit cost ratio if annual interest rate is 8%.

50. Compute the benefit cost ratio of the given project

Project Cost P 80,000

Gross Income 25,000 per yearOperating Cost P 6,000 per year

Salvage Value 0

Life of Project 10 years

Rate of Interest 12%

51. If the nominal interest rate is 3%, how much is P 5,000 worth in 10 years in a continuous compounded account?

52. P 6,000 is deposited each year into a savings account that pays 6% nominal interest compounded continuously.

How much will be the account at the end of 8 years?

53. A man borrows P 100,000 at a rate of 6% compounded continuously for 5 years. How much money must he

pay annually?

54. At 6% , find the capitalized cost of a bridge whose cost is 250 M and life is 20 years if the bridge must be

partially rebuilt at a cost of 100 M every 20 years.

S-9

A machine cost P 150,000 and will have a scrap value of P 10,000 when retired at the end of 15 years. If money is

worth 4%

55. Find the annual investment

56. The Capitalized Cost is

S-10

57. The cost of producing a certain commodity consist of P 45 per unit for labor and material cost and P 15 per unitfor other variable cost. The fixed cost per month is P 450,000. If the commodity is sold at P 250 per unit

57. What is the break even quantity ?

58. What is the profit/loss if the number of items sold is 3000?

59. A certain copier machine cost P 150,000 with a trade in value of P 1.50,000 after making 800,000 copies. Using

the declining balance method, what is the book value of the machine when it had made 300,000 copies?

60. What is the present worth of two P 100.00 payments at the end of the 3rdand the 4thyear is interest rate is 8%?

61. The nominal rate of interest is 4%. How much is P 10,000 worth in 10 years in a continuously compounded

account?

62. If P 500,000 is deposited at a rate of 11.25% compounded monthly, what will be the amount after 7 years and 9

months?

63. In year zero, you invest P 10,000 in a 15% security for 5 years. During the time, the average inflation is 6%. How

much in terms of year zero pesos will be the account at the maturity?


9/40

4

S11

A man inherited a regular endowment of P 100,000 every end of 3 months for 10 years. However he may elect to

get a single lump sum after 4 years.

64 . How much is the lump sum if the cost of money is 14% compounded quarterly?

65. What is the present worth of the endowment?66. A debt of x pesos with interest rate of 7% compounded annually will be retired at the end of 10 years through the

accumulation of deposit in a sinking fund invested at 6% compounded semiannually. The deposit in the sinking fund

every end of the six months is P 21,962.68. The value of x is

67. A man paid 10% downpayment of P 200,000 for a house and lot and agreed to pay the balance on a monthly

installments for 60 months at an interest rate of 15% compounded monthly. Determine the required monthly

payment.

S -12

Determine the break even point in terms of the number of units produced per month. Cost are in pesos per unit

Selling Price Per unit P 600

Labor Cost P 115

Cost of Materials P 76

Other Cost P 2.32

Total Monthly Overhead Cost 428,000

68. The break even point is

69. Determine the profit/loss if it sells 1000 units.

S -13

Given the bank deposits in an account that earns 3% per annum.

End of :

Year 1 5,000Year 2 6,000

Year 3 7,200

70. The deposit at year 20 is

71. The total deposits made without interest after 20 years.

72. The Present Worth of 20 deposits.

73. The Future worth of the 20 deposits

74. The equivalent equal annual deposits for the 20 deposits.

75. An amount of 1,000 becomes 3500 after 6 years. If money is x% compounded quarterly , x = ?

S14

A 3 deg simple curve is used to connect two highways whose bearings are S 110 W and S 470W . Use arc basis.

76. The radius of the curve is

77. The length of the curve is

78. The external distance is

79. The length of the middle ordinate is


10/40

5

80. The tangent distance is

S- 15

A simple curve has a degree of 6 deg and length of 140 m. What is the central angle of the curve. Use Chord

Basis.


82. The central angle is

S16

A 40simple curve have tangents with bearings of N 200E and N 600E. The stationing of PI is 3 + 980


84. The tangent distance is

85. The stationing of PC is


87. The stationing of the PT is

S -17

A reversed curve consists of two curves of equal radius has the following properties

D1 = 3 deg I1= 18 deg

D2 = 2 deg I2= 24 deg

Stationing Of PT is 32 + 121 Use Chord Basis

88. The radius of curve 1 is

89. The radius of the 2ndcurve is

90. The stationing of PC is

S18

A vertical sag parabolic curve is to connect a -2% grade to a 3% grade. The change in grade per meter station is

0.2%. The PT of of the curve is at station 25 + 325 and elevation 25.42.91. The length of the curve is

92. The stationing of the PC of the curve is

93. The stationing of the lowest point of the curve is

94. The elevation of the PC is at

95. The elevation of the lowest point of the curve is at

96. The elevation of PI is at

97. The stationing of the PI is at

98. The elevation at station 25 + 075 is

S19

Given the following cross section notes for a road in cut

x 0 7.8

+2.5 + c + y

S20


11/40

6

The road has a width of 10 m and have a slope of 2: 1 (horizontal: vertical ) . The area of the cross section is 47.4

m2

99. The value of x is

100. The value of y is

101. The value of c is

a. 4.23 m


12/40

1

PREBOARD EXAM

TOLENTINO AND ASSOCIATES

MATHEMATICS SURVEYING AND TRANSPORTATION ENGINEERING

1. The radius of the cone is increased by 2.7% and its height is reduced by 0.9%. Determine the

percentage change in its volume.

a. 4.52% b. 6.89% c. 7.90% d. 8.34%

Situation 1:

2. Where is the center of the circle 3x2+ 3y2+ 2x4y21 = 0

a. ( -1/8, 2/4) b.( -1/3, 2/3) c. ( -1/4, 3/3) d. ( -1/8, 1/3)

3. What is the radius

a. 7.60 b. 5.78 c. 4.76 d. 2.98

4. The 1stterm of a GP is 160 and the common ratio is 3/2. How many consecutive terms must be

taken to give a sum of 2110?

a. 5 b. 6 c. 7 d. 4

5. A company sells 80 units and makes P80 profit. It sells 110 units and makes P 140 profit. If the

profit is a linear function of the number of units sold, what is the average profit per unit if the

company sells 250 units?

a. P 1.76 b. P 1.68

c. P 1.66 d. P 1.866. Given

Station Elevation (m) Distance (km )

Alpha 680 m Alpha to Bravo = 12 km

Bravo 645 m Bravo to Charlie = 15 km

Charlie 620 m

Situation 2

6. Compute the elevation of the line of sight at station at station Bravo with the instrument placed

at station Alpha such that station Charlie would be visible from station Alpha considering the effect

of curvature and refraction correction.

a. 641.27 b. 758.33 c. 822.03 d. 856.66

7. Assuming that station Bravo will obstruct the line of sight from station Alpha while observing

station Charlie and a 4 meter tower is constructed on top of station Bravo, compute the height of

equal towers at station Alpha and station Charlie in order that both 3 stations will still be

intervisible.


13/40

2

a. 8.992 b. 7.727 c. 6.042 d. 5.673

Situation 3

From the closed traverse shown

Lines Bearings Distances

1-2 S 10000 E 485

2-3 N 56000 E 780

3-4 N 63000 W 975

4-5 ------------- -----

5-1 S 33000 W 890

8. The bearing of 4 -5 is closest to

a. N 60059 E b. N 68044 E c. N 71074 E d. N 73024 E

9. The distance 4 -5 is closest to

a. 812.45 m b. 711.90 m c. 691.55 m d. 534.77 m

10. The area of 34 4 -5 and 5 -1 is nearest to

a. 78160.28 m2 b. 67139.28 m2 c. 99169.28 m2 d. 88231.28 m2

11. A man leaves his house at 8:00 AM and traveling at an average speed of 2 kph, arrives at his

office 3 min ahead of the expected time. Had he left his house at 8:30 am and traveled at an

average speed of 3kph, he will arrive 6 min late of the expected time. Find the distance that he had

traveled.a. 2.4 km b. 1.8 km

c. 2.1 km d. 2.4 km

12. A ball is dropped from a height of 120ft and continuously rebounds to 2/3 of the distance it

falls. What is the total distance traversed by the ball when it comes to rest?

a. 1000ft b. 600 ft

c. 800ft d. 750 ft

13. A cask containing 20 liters of wine was emptied 1/5 of its contents and then filled with water. If

this is done 6 times, how many liters of wine will remain in the cask?

a. 5.242liters b. 5.811 liters

c. 6.242liters d. 6.134 liters

14. A train , one hour after starting, meets with an accident which detains it an hour , after which it

proceeds at 3/5 of its former rate and arrived 3 hrs after the time. Had the accident happened 50 km

farther on the line, it would have arrived 1.5hrs sooner. Find the length of the journey.


14/40

3

a. 87.91 km b. 92.23 km

c. 88.89 km d. 83.34 km

SITUATION 4

15. The length of a simple curve having a degree of 40is 210 m.

The middle ordinate of the curve is nearest to

a. 24.08 m b. 19.03 m c. 17.67 m d. 16.55 m

16 The external distance of the curve is nearest to

a. 20.38 m b. 21.44 m c. 22.48 d. 23.67 m

17. The area of the fillet of the curve is nearest to

a. 4532 m b. 3422 m c. 2931 m d. 1424 m

SITUATION 5

A compound curve has a common tangent of 84.5 m which makes an angle of 160and 200with the

tangents of the 1stand the 2ndcurve respectively. The length of the tangent to the 2ndcurve is 42 m.

18. The radius of the 1stcurve is closest to

a. 205.5 m b. 302.4 m c. 409.2 m d. 506. m

19. The radius of the 2ndcurve is nearest to

a. 238.19 m b. 334.11 m c. 445.28 m d. 522.12 m

20. The length of the curve from PC to PT is nearest toa. 167.59 m b. 233.67 m c. 332.67 m d. 483.12 m

SITUATION 6

A symmetrical parabolic summit curve connects two grades of 6% and -4%. It is to pass thru point

P on a curve at station 25 + 140 having an elevation of 98.134 m. If the elevation of the grade of

intersection is 100 with stationing of 25 + 160 ,


a. 120 m b. 140 m c. 160 m d. 112 m

21. The stationing of the highest point of the curve is closest to

a. 25 + 172 b. 25 + 140 c. 25 + 145 d. 25 + 156

22. The elevation at station 25 + 120 is closest to

a. 68.442 b. 79.872 c. 97.433 d. 102.546

SITUATION 7


15/40

4

The center height of the road at station 7 + 110 is 2 m fill while at station 7 + 160 is 1.2 m cut. From

station 7 + 110 to the other station , the ground makes a uniform slope of 4.8%.

23. The slope of the new road is

a. 0.016 b. 1.442 c. 2.641 d. 3.124

24. Distance in which the fill is extended is

a. 31.25 m b. 33.42 c. 35.26 d. 38.46

25. Stationing of the point where the fill is extended id

a. 71 + 112.25 b. 71 + 123.25 c. 71 + 141.25 d. 71 + 152.25

26. The resistance of a wire varies directly with its length and inversely with its area. If a certain

piece of wire 10 m long and 0.1 cm in diameter has a resistance of 100 ohms, what will be the

resistance if it is uniformly stretched so that its length becomes 12 m.

a. 120 b. 130 c. 140 d. 150

27. A stack of bricks has 61 in the bottom layer, 58 bricks in the second layer, 55 bricks in the 3 rd

layer and so on until there are 10 bricks in the last layer. How many bricks are there altogether

a. 510 b. 529 c. 639 d. 71

28. The base of a truncated prism is a rectangle with length twice its width. The corner edges have

heights of 12 m, 12 m , 16 m and 16 m respectively. If the volume of the prism is 8,200 cu m, find

the length of the base.

a.33.24 m b. 34.23 m c. 35.25 m d. 36.34 m

29. The perimeter of a triangle ABC is 400. If angle A is 300and angle B is 580, find the measure ofside AC.

a. 170.285 b. 180.214 c. 190.546 d. 193.472

30. A regular hexagon is inscribed in a circle having an area of 150 cm2. Find the area of the

circle not covered by the hexagon.

a. 27.326 cm2 b. 29.344 cm2 c. 31.253 cm2 d. 33.642 cm2

31. The sum of the digits of a 3 digit number is 14. The hundreds digit being 4 times the unit digit. If

594 is subtracted from the number, the order of the digits will be reversed. Find the tens digit of

the number.

a. 1 b. 2 c. 3 d. 4

32. An arch 18 m high has the form of a parabola with vertical axis. The length of a horizontal

beam placed across the arch 8 m from the top is 64 m. Find the width of the arch at the bottom.

a. 69.674 b. 72.442 c. 74.267 d. 76.987


16/40

5

33. How much of a 7% solution should be mixed with an appropriate amount of a 12% solution to

get 5 liters of a 10% solution?

a. 2 b. 3 c. 4 d. 5

34. Find the area bounded by = + and = a. 22 b. 24 c. 26 d. 28

35. If sin A = cos A < 0 , cos B = - 1/3 tan B > 0

sin( A + B ) = ?

a. 0.374 b. 1.892 c. 2.768 d. 3.452

36. What is the first period of y = 4 tan 4x ?

a. b. /2

c. /4 d. /8

37. What is the amplitude of 3 cos2 x + 5 sin 2x

a. 5.83 b. 8

c. -2 d. 15

38. Find the volume of the solid generated by rotating the curve

+ = along the line 4x + 3y = 20.a. 1184.34 u3 b. 3482.32 u3 c. 6713.37 u3 d. 8913.84 u3

39. Two cars begin a trip from the same point P. If car A travel north at 30 kph and car B travelwest at 40 mph, how fast is the distance changing 2 hrs later.

a. 45 mph b. 50 mph b 55 mph d. 60 mph

40. Determine the equation of the line passing ( -1, 3) and perpendicular to the line 4xy + 5 = 0.

a. x + 4y = 11 b. x + 4y = 14 c. x + 4y = 16 d. x + 4y = 18

41. If steel ball is immersed in an 8 cm diameter cylinder, it displaces water to a depth of 2.25 cm. What is

the radius of the ball?

a. 3.098 cm b. 4.762 c. 5.196 cm d. 6.462 cm

SITUATION 8

Studies show that 90% of married women claim that their husbands mother is the biggest bone of

contention in their marriages ( sex and money are lower rated areas of contention). Suppose that 6

women are having coffee together one morning.

42. What is the probability that no more than three of them dislike their mother in law?


17/40

6

Solution:

a. 0.01585 b. 2.01932 c. 3.12983 d. 4.98212

43. What is the probability that at least 3 of them dislike their mother in law?

a. 0.9987 b. 2.3427 c. 3.7844 d. 4.3477

SITUATION

iF. If = and =

,

44.x is

a. 1 b. 3 c. 5 d. 7

45. y isa. b. c. 1/3 d. 1/8

46. ( )a. /7 b. /5 c. /6 d. /8

47. A curve f(x) is concave upward at (-1,3) , concaves up and concave downward at ( 3, 7). Which of the

following is true?

a. f(5) > 0 , max point at x = 5

b. f(1) < 0, min points at x = 1

c. f(3) > 0, point of inflection is at x = 3.d. f(3) < 0, point of inflection is at x = 3.

48. A hemispherical tank having a top diameter of 40 ft is filled with oil having a density of 52.4 lb/ft3. Find

the work done in pumping all the water to the top of the tank.

a.. 7,234,668.2 ftlbs b. 6,584,778.2 ftlbs c. . 5,523,228.2 ftlbs d. .4,524,733.2 ftlbs

Solution:

SITUATION 9

Given triangle ABC, how many possible triangles can be formed from the following conditions?

Solution:

49. AB = 25 AC = 36 angle A = 280

a. 1 b. 2 c. 3 d. 4

50. AB = 18 AC = 25 and angle C = 420

a. 1 b. 2 c. 3 d. 4

51. AB = 40 AC = 35 and angle B = 650


18/40

7

a. 1 b. 2 c. 3 d. 4

SITUATION 10The following points are at the terminal sides of the angles in standard position. Determine the required

trigonometric function.

Solution:

52. Terminal point at (8,1). sin = ?

Solution:

a. 0.124 b. 2.342 c. 4.987 d. 6.239

53. Terminal point at ( 3, -8) cos = ?

Solution:

a. 0.3511 b. 3.209 c. 4.287 d. 2.439

54. Terminal Point at ( 3, -8) tan =?

Solution:

a. -8/3 b. -8/7 c. -7/2 d. 6/2

SITUATION 11

A tank has the form of a segment of a sphere of diameter 40 m. Its upper base is 8 m from the center and its

lower base is 14 meter from the center of the sphere. Determine the following.

55. The area of the upper base.

a. 1055.57 b. 1409.57 c. 1723.57 d. 2343.42

56. The curved surface of the tank.

a. 2,764.60 m2 b. 5,254.60 m2 c. 6,544.64 d. 7,982.21

57. The volume of the tank in cubic meters.a. 24,236.34 m3 b. 25,903.34 m2 c. 26,283.35 m2 d. 27,225.77 m2

SITUATION 12

58-60

Give the binomial +

.

Determine:

58. 3rdterm of the expansion.

a. b. c. d. 59. numerical coefficient of the 5thterm.

a. 12,223 b.16,106 c. 18, 103 d. 19,67460. The sum of exponents.

a. 105 b.-105 c. 109 d. -109

SITATIUON 13

One of the diameters of a frustum of a sphere is 9.8 cm while the other is 10.4 cm. If the thickness of the

frustum of a sphere is 4.2 cm, find the following:


19/40

8

61. volume of the frustum

a. 234.77 b. 301.18 c.375.59 d. 456.09

62. radius of the sphere

a. 5.483 b. 6.789 c. 7.549 d. 8.552

63. area of the zone formed

a. 78.23 b. 87.55 c. 98.275 d. 119.96

64. A particle is moving along the x axis with velocity of

= t> 0. What is the maximum acceleration over the interval [ 0, 2 ].a. b. c. d.

65.Two measurements for angle of elevations were made on the top of an inaccessible cliff, one from point A

and another from point B. Point B is 425 nearer to the cliff than A but 25.6 m lower in elevation. If the angles

of elevation from A and B are 18.650and 36.20respectively, find the elevation of the top of the cliff if A has an

elevation of 625.4m.

a. 674.355 m b. 785.322 m c. 842.566 m d. 913.506 m

66. A certain bacteria grows and multiplies exponentially and follows the formula =.where Ais the final number of bacteria after time t. is the initial number of bacteria and t is the time elapse. Ifthere were originally 4 bacteria , in how many hours will the bacteria increased to 2500?

a. 13.033 hrs b. 12.229 hrs c. 11.024 hrs d. 10.088

67. The height of a rectangular box is 10 cm. The length increase at the rate of 2 cm/s, its width decreases

at the rate of 4 cm/s. When the length is 8 cm and the width is 6 cm, the rate in cm3/s at which the volume is

changing is ?

a. -230 cm3/s. b. -220 cm3/s. c. -210 cm3/s .d. -200 cm3/s.

SITUATION 14Electrical Resistance of metal are dependent on temperature. For a certain given wire at t deg C, the

resistance R in ohms may be computed by

= (+ )whereis the resistance at 00C and a is the temperature coefficient of resistance in /degC.68. Solve the value ofin ohms if R = 30 ohms at 500C and R = 35 ohms at 1000C.a.19 b. 25 c. 33 d. 41

69. Find a. 0.004 b. 2.009 c. 3.002 d. 4.212


20/40

9

70. At what point on the graph = is its tangent line perpendicular to the line 2x + 3y = 6 ?

Solution:

a. ( 1/2, 1/4) b. ( 1/4,1/4) c. ( 3/5, 1/4). d. ( 4/4, 1/4).

71. Find the volume generated when the region bounded by = , the lines x = 1 and x = 4 isrevolved around the x axis.

a.

b.

c.

d.

72. A 4.2 cm by 4.2 cm square pyramid has sloping edges of 15 cm each.

Find the total surface area.

a. 452.2 cm2 b. 312.3 cm2 c. 255.3 cm2 d. 142.4 cm2

73. A certain physical characteristic of solid yields the following equation.

c = a + bt. When c = 52 , t = 100 and when c = 172, t= 400. Find

a. 8 b. 9 c. 11 d. 12

74. If the domain of y = 2x + 1 is [ -2, 3]

Which is not in the range.

a. -4 b. 0 c. -2 d. 7

75. Find the perimeter of r = 4 sin .

Perimeter

a. 3. b. 4. c. 5. d. 6.

Given the polar curve = ().76. Find the Cartesian form of the equation.

a. + = + b. + = +

c. + = + d. + = +

77. Find the slope of the curve when = 300.

a. 0 b. 1 c. 2 d. 3

SITUATION 15

LED lamps are packages in boxes of 200. If production is known to produce 1.5% defective lamps on the

average, determine the probability that a box chosen at random will contain

78.no defective lamps.a. 3.224 b. 2.235 c. 1.789 d. 0.0487

79. 2 defective led lamps.

a. 0.2246 b. 1.8923 c. 2.6753 d. 3.8672

80. more than 3 defective lamps.

a. 5.2219 b. 4.0921 c. 2.0912 d. 0.5785


21/40

10

SITUATION 16

Light bulbs having a mean life of 2400hrs and standard deviation of 62 hrs are used for a consignment of4000 bulbs.

81. Determine the number of bulbs likely to have a life in excess of 2500 lbs.

a. 5.2313 b. 4.2286 c. 2. 1233 d.0.05338

82. Determine the percentage of bulbs with a life between 2300 hrs to 2500 hrs.

a. 5.8841 b. 4.2217 c. 2.7632 d. 0.8923

83. In a certain triangle ABC, A = 950, B = 500 and C = 350. Which of the following expression correctly

defines the lengths of the sides of a triangle?

a. AB< BC < CA

b. AC< BC < AB

c. AB< AC < BC

d. BC< AC < AB

84. Find the angle between the curves + = and + = at the point of intersection ofwhich x and y are positive.

a. 23.76 deg. b. 30.76 deg. c. 32.76 deg. d. 37.76 deg.

85. If =

, give horizontalasymptotes

a. y = 1 b. y = 2 c.y = 3 d. y = 4

86. Ernie earned P 2,000 commission on a big deal raising his average commission by P100. Ernies new

average commission is 900. How many sales has he made so far?

a. 10 b. 12 c. 14 d. 16

87. The rate of population growth of a country is proportional to the number of inhabitants. If the

population of a certain country now is 40 million and 50 million in 10 years time,What will the population 20

years from now?

a. 53.2 m b. 62.5 m c. 65.2 m d. 66.5 m

88. A certain type of bacteria, given a favorable growth medium, doubles in population every6.5 hours.Given that there were approximately 100 bacteria to start with, how many bacteria will there be in a day anda half?a. 4647.74 b. 3155.32 c. 2756.12 d. 1266.23

89. A boat makes 25 mph in still water. It is headed N 450E. Find the direction of the course of the boat.

a. N 54.930E b. N 44.920E c. N 41.900E d. N 40.830E


22/40

11

90. A circle having a radius of 9 cm circumscribes a right triangle with area of 43.23 sq m. If one of the

side is 18 cm long, what is the length of the other side?

a. 16.03 b. 17.29 c. 23.11 d. 25.64

91. The distance S meters from a fixed point of a vehicle travels in a straight line with a constantacceleration a and is given by: = +

S is in m, u in m/s and t is in seconds.

Given S = 42 when t = 2 and S = 144 when t = 4s, Determine the acceleration.

a. 15 m/s2

b. 16 m/s2

c. 18 m/s2

d. 20 m/s2

92. Find the equation of the tangent line,normal line at P(-1,-4) and ordinate of the vertex of the curve = + ( )at P(-1,-4).

a. 3y + y + 8 = 0 b. 2 + y + 7 = 0 c. 3y + x + 6 = 2 d. 3x + y + 7 = 0

93. The ordinate of the vertex of the curve

a. -6.25 b. -5.31 c. 6.25 d. 5.31

SITUATION 18

Two towers A and B are placed at 100 m apart horizontally. The height of tower A is 40 m and that of B is 30

m.

90. At what distance above the ground will the intersection of the lines forming the angles of elevation of the

two

94. towers are observed from the bases of the towers A and B respectively.

a. 16.22 b. 17.14 c. 18.23 d. 19.15

95. At what distance horizontally is this point located from the tower A?

a. 57.14 b. 60.23 c. 62.73 d. 68.12

Consider the curve = + and the chord AB joining the points A( -4, 0) and B( 0,2).96. Find the coordinates of the point on the curve where the tangent line is parallel to the chord AB.

a. (4,-2) b. (3, -1) c. (2,-3 ) d. (1,-6)

SITUATION 19Consider the curve defined by + + = .

97. . Find the points on the curve where the lines tangent to the curve are vertical.

a. (6, -3) b. (5, -2) c. (4,-1) d. (3, 0)

98.The curve is

a. parabola b.circle

c.hyperbola d.elipse


23/40

12

99. The eccentricity is

a. 4.22 b. 3.05 c. 2.81 d. 1.41

Let R be the region enclosed by the graphs of y = ln(x2+1)

and y= cos x.

100. Find the area of R.a.0.23 b. 1.17 c. 2..55 d. 3.98


24/40

PREBOARD

DESIGN AND CONSTRUCTION

TOLENTINO AND ASSOCIATES

(Note There are few questions whose answers are not in the choices. Just Answer E. )

S -1

Given the figure shown.

1. Reaction at A is

a. 400N b. 445 N c. 457 N d. 479 N2. The Reaction at B is

a. 89 N b. 100 N c. 110 N d. 114 N

3. The tangential deviation of B with respect to a tangent drawn at A.

a. 1672/EI b. 1967/EI c. 2011/EI d. 2311/EI

4. The slope at B is

a. 89.58/EI b. 87.33/EI c. 85.23/EI d. 82.55/EI

S - 2

The beam shown weighs 30 N/m.

5. The vertical reaction at A

a. 422 N b. 322 N c. 201 N d. 246 N6. The tension at B

a. 308 N b. 352 N c. 442 N d. 588 N

7. The Horizontal Reaction at A.

a. 409.22 N b. 390.44 N c. 372.41 N d. 345.11 N

8. The Resultant reaction at A

a. 427.41 N b. 477.47 N c. 489.22 N d. 502.41 N

9. The angle that Reaction at A makes with the horizontal.


25/40

a. 31.010 b. 34.220 c. 37.410 d. 3.770

S - 3

Given the beam shown. The 100 kN load acts on the centroid of the cross section.

10. The flexular stress at A.

a. 64.95 Mpa b. 66.31 Mpa c. 68.22 Mpa d. 70.03 Mpa

11. The axial stress at Aa. 3 Mpa b. 5 Mpa c. 7 Mpa d. 9 Mpa

12. The total normal stress at A


13. The shearing stress at A

a. 9.743Mpa b. 11.412 Mpa c. 12.455 Mpa d. 13.111 Mpa

14. The principal stress at A


15. The angle that the principal stress makes with the horizontal

a. 5.67 deg b. 7.78 deg c. 8.91 deg d. 9.89 deg

S - 4

The 3 hinged arc shown is subjected to the two concentrated forces shown.

16. The vertical reaction at C is

a. 7.312kN b. 6.234 kN c. 5.231 kN d. 4.348 kN

17. The horizontal reaction at C is

a. 3 kN b. 4 kN c. 5 kN d. 6 kN

18. The reaction at B


26/40

a. 16.12 kN b. 18.33 kN c. 24.44 kN d. 27.11 kN

S - 5

A truck and a trailer combination crossing a 12 m span has axle loads as given.

19. The distance of the resultant load from the 10 Kn load is

a. 2 m b. 3 m c. 4 m d. 5 m

20. The maximum shear developed in the beam.

a. 30 kN b. 33 kN c. 39 kN d. 45 kN

21. The maximum moment in the beam isa. 78.22 kNm b. 82.36 kNm c. 96.12 kNm d. 104.17 kNm

S - 6

The 10 meter ladder weighing 35 kg is resting on a horizontal floor at A and on the wall at B making

an angle of 60 deg from the horizontal. The coefficient of friction between the ladder and the wall (

and the ground and the ladder ) is 0.25 .

A man of mass 72 kg climbs the ladder.

22. Determine the Normal reaction at the wall.

a. 25.176 kG b. 27.441 kG c. 29.417 kG d. 32.114 kG

23. Determine the resultant reaction at the wall.

a. 233.41 N b. 254.58 N c. 266.29 N d. 287.11 N

24. Determine the normal reaction at the ground.

a. 89.267 kG b. 100.706 kG c. 115.241 kG d. 132.221 kG

25. Determine the resultant reaction at the ground.

a. 1018.33 N b. 1233.75 N c. 1342.41 N d. 1661.22 N

26. Determine the distance x from the from the bottom of the ladder to which the man cal climb

without causing the ladder to slip at its lower end A.

a. 4.5 m b. 5.2 m c. 5.8 m d. 6 m

S - 7

A simply supported beam 10 m long has an overhang of 2 m at the left support. If a highway uniform

load of 9.35 kN/m and a concentrated load of 116 kN passes trough the beam, compute the followingbased on the influence line on the maximum shear at midspan.

27. The ordinate of the IL for max shear at midspan 4 m from A.


27/40

a. -0.2 b. -1.7 c. 2.4 d. 3.1

28. The length of the beam where uniform load can produce maximum positive shear in the beam at

the midspan.

a. 4 b. 7 c. 8 d. 11

29. The maximum positive shear at the midspan.

a. 71.56 kN b. 61.22 kN c. 58.21 kN d. 42.88 kN

30. The ordinate of the influence line for the maximum bending moment at the midspan 4 m from

A.

a. 6 b. 4 c. 3 d. 1

31. The value of the maximum positive bending moment at the midspan.

a. 389.212 kN m b. 406.875 kN m c. 412.441 kN m d. 422.412 kN m

S - 8

A 9 meter high retaining wall is laterally supported at the top and fixed at the base. The wall resists

active earth pressure increasing from 0 at the top to 52 kN/m at the base per meter length along the

longitudinal axis.

32. The design moment at the base isa. 455.5 kNm b. 423.1 kNm c. 301.2 kNm d. 280.8 kNm

33. The lateral support from the top

a. 46.8kN b. 49.2 kN c. 51.9 kN d. 58.1 kN

34. If the lateral support at the top is removed, the design moment is

a. 622 kNm b. 688 kNm c. 702 kNm d. 710 kNm

The entrance of a warehouse has a roof that supports a roof load of 8 kN/m. The supports B and C are

considered simply supported.

35. The vertical reaction at the column is

a. 37.5 kN b. 39.98 kN c. 41.26 kN d. 44.11 kN

36. The vertical reaction at C is

a. 19.4 kN b. 22.5 kN c. 25.1 kN d. 30.1 kN

37. Maximum negative moment at AC.

a. 7 kNm b. 9 kNm c. 11 kN m d. 13 kNm


28/40

38. Maximum positive moment at AC.

a. 25.58 kNm b. 31.64 kNm c. 33.01 kN m d. 36.22 kNm

39. Location of the point of inflection at AC from A.

a. 1.092 m b.1.567 m c. 1.872 m d. 1.987 m

S - 9

A water tank 3 meter in diameter and 6 meter high is made of steel having a thickeness of 12 mm.

40. When the tank is filled with water, determine the circumferential stress.


41. Determine the longitudinal stress when it is filled with water.


S- 10

A hollow circular pole 6 mm thick with a 300 mm ouside diameter and a height of 3 meter weighs

150 N/m. The pole is subjected to the following loads.

P = 3 kN and e = 100 mm from the centroid of the section. Lateral force of 0.45 kN acts at the top of

the pole.

42. The maximum compressive stress at the base due to the vertical load plus the weight of the pole.

a. 4.22 Mpa b. 3.66 Mpa c. 2.09 Mpa d.1.37 Mpa

43. The maximum tensile stress at the base due to lateral and vertical loads and the weight of the

pole.

a. 2.41Mpa b. 3.51 Mpa c. 4.89 Mpa d. 5.77 Mpa

44. BONUS-----If the hollow pole is replaced by a solid wood pole of 250 mm diameter, determine the

maximum shear stress in the pole.

a.3.091 Mpa b. 1.781 Mpa c. 0.012 Mpa d. 0.000

S -11

A barge shown diagramatically supports a load of W1 and W2 for every one meter strip along thelongitudinal section.


29/40

44.Bonus!--- Find total legth L so that the upward pressure is uniform and that the barge remains

horizontal

a. L = 8 m b. L = 3 m c. L = 15 m d. L = 17 m

45. The shear at 3 meter from the left end when upward pressure q = 72 kN/m.

a. 1.03 kN b. 1.67 kN c. 219 kN d. 241 kN

46. Distance from the left end where Shear = 0 when q = 87 kN/m

a. 3 m b. 4 m c. 5 m d. 6 m

S -12

The tensile member shown is 50 mm by 75 mm and subjected to a load of P = 200 kN. The plane AA

makes an angle of 150with the a axis.

47. The tensile stress at section AA.


48. The shear stress on Plane AA.


S - 13

A load W is to be lifted using the crane shown. x1 = 10 m, x2 = 8 m . Weight of the crane is 2 kN.


30/40

49. The force at cable AC is

a. 19.34 kN b. 24.91 kN c. 27.98 kN d. 29.12 kN

50. The reaction at B

a. 33.11 kN b. 43.35 kN c. 46.11 kN d. 48.21 kN

51. Largest force that can be lifted if maximum force AC= 50kN

a. 40.11kN b. 42.15 kN c. 45.12 kN d. 47.12 kN

S -14

A simply refinforced concrete beam reinforced for tension has a width of 300 mm and a total depth of

600 mm. It is subjected to external Moment Mu = 540kN m.

fc = 28 Mpafy = 280 MpaEs = 200 Gpa

52. The balanced steel ratio is

a. 3.981% b. 4.926% c. 6.011% d. 7.221%

53. The depth a in terms of d if = 1/2balance Use = 0.9

a. 22.11% b. 25.45% c. 28.11% d. 30.71%

54. The minimum effective depth is

a. 583.21 mm b.421.44 mm c. 341.22 mm d. 301.29 mmS -15

The beam is to be analyzed using moment distribution.

55. The Fixed End Moment at D for span CD is

a. 7.11kNm b. 8.23 kN m c. 9.28 kN m d. 11.21 kN m

56. The Distribution Factor at C for member BC is

a. 0.667 b. 2.031 c. 3.331 m d. 4.127 m


31/40

57. Using Three Moment Equations , the bending Moment Equations

the

for member CD if you consider span BCD is

a. 85.33kN m2

b. 80.12 kN m2 c. 78.44 kN m

2d. 73.11 m

2

58. The bending moment at B is


S -16

A W 420 x 85 steel beam is fully restrained with a uniformly distributed load of 25 Kn/m. The beam

has a span of 10 m.

Properties:

A = 10839 mm2

bf = 180 mm

tf = 18 m

tw = 11 mm

d = 420 mm

59. The actual uniform load carried by the beam ( include its weight )

a. 25.834kN/m b. 26.878 kN/m c. 27.451 kN/m d. 28.221 kN/m

60. The maximum moment carried by the beam.

a. 312.11 kN m b. 289.56 kN m c. 266.77 kN m d. 215. 28 kN m

61. The maximum bending stress


62. The maximum web shear stress fv = V/( d tw)


63.The maximum horizontal shear stress


S -17Given the figure shown.


32/40

64. The tensile stress in the body of the bolt.


65. The Tensile stress at the root of the threads

a.91.22Mpa b. 94.11 Mpa c. 99.47 Mpa d.106.22 Mpa

66. Find the compressive stress at the head as the bolt bears on the surface to resist the tensile load.


S -18

The pin jointed assembly supports a billboard 2 m high x 4 n wide on each end. The total weight of

the billboard is 24 kN. H = 1 m and

= 600.

Wind pressure q = 1.44 KpA

Wind pressure coefficient C = 1.2

67. The resultant wind load is

a. 13.824 kN b. 15.214 kN c. 17.226 kN c. 20.112 kN

68. The axial force at AB is

a. 12.41 kN b. 14.21 kN c. 16.02 kN d. 18.21 kN69. The axial force at BC is

a. 28.12 kN b. 31.98 kN c. 34.21 kN d. 37.77 kN

70. The vertical reaction at A is

a. 7.21 kN b. 8.01 kN c. 9.81 kN d. 11.31 kN

71. The horizontal reaction at C is

a. 27.7 kN b. 33.1 kN c. 37.2 kN d. 39.1 kN

72. If the strut AB is replaced by 16 mm diameter cable, determine the normal stress in the cable.


S-19

The figure shows a semicircular arc with the given load.


33/40

73. The shear at D is

a. 0.03 kN b. 0.84 kN c. 1.44 kN d. 2.42 kN

74. The moment at D is


75. The axial force at D is

a. 1.12 kN b. 2.44 kN c. 4.12 kN d. 4.98 kN

S-20

When the columns at E and H of the floor framing plan are deleted, girder BEHK becomes a one spanfixed ended beam supporting DEF and beam GHI at H. The following loads on girder BEHK are as

follows.

Concentrated load at E = 266 kN

Concentrated load at H = 266 Kn

Uniform load throughout its length = 5Kn/m

Hint: Consider BK as beam fixed at B and K with the given loads.

76. Compute the reactive moment at B.


77. Compute the reactive moment at K.

a. 378.48 kN m b. 466.67 kN m c. 522.11 kN m d. 531.88 kN m78. The maximum shear in the beam

a. 201.49kN b. 284.75 kN c. 304.88 kN d. 387.11 kN

79. The maximum positive bending moment in the beam.



34/40

S -21

P1 = 1.8 kN P2 = 0.9 kN P3 = 0.45 kN= 300 = 45

0

80. The magnitude of the resultant of the 3 forces.

a. 2.455 kN b. 3.412 kN c. 4.791 kN d. 5.012 kN

81. The angle that the resultant makes with the horizontala. 56.12

0 b. 59.65

0c. 67.11

0d. 71.41

0

82. The vertical reaction at B.

a. 1.06 kN b. 2.41 kN c. 3.01 kN d. 3.78 kN

83. The horizontal component of the reaction at B.

a. 5 b. 3 c. 1 d. 0

S-22

The suspended girder shown is supported by a series of hangers uniformly spaced along the parabolic

cable.

84. The minimum tension is

a. 160 kN b. 170 kN c. 180 kN d. 190 kN

85. The maximum tension isa. 101.412 kN b. 134.211 kN c. 178.885 kN d. 189.412 kN

86. The safe uniform load that the cable can support if maximum tension is 250kN.

a. 13.976kN/m b. 16.221 kN/m c. 18.412 kN/m d. 19.661 kN/m

87. The length of the cable is

a. 11.232 m b. 13.441 m c. 16.644 m d. 18.412 m


35/40

S-23

A concrete mixture has a ratio of 1:2:4 by mass. The water requirements is 24 liters per bag of

cement.

Weight of Cement = 40 kg/bag.

Materials SG

cement 3.33

sand 2.5

gravel 2.67

88. The volume of cement per bag

a. 0.012 m3

b. 1.441 m3

c. 2.455 m3

d. 3.011 m3

89. The volume of sand for 1 bag of cement

a. 3.451 m3 b. 2.411 m3 c. 1.442 m3 d. 0.032 m3

90. The volume of gravel for 1 bag of cement is

a. 2.44 m3 b. 2.04 m3 c. 1.44 m3 d. 0.06 m3

91. The total volume of concrete is

a. 0.128 m3 b. 1.331 m3 c. 2.412 m3 d. 3.331 m3

S -24

A 5 kg block is at rest at time t = 0 and is acted upon by a horizontal force P that varies with time as

shown.

92. The initial acceleration of the block is

a. 8.37 m/s2 b. 3.41 m/s2 c. 4.44 m/s2 d. 4.89 m/s2

93. The velocity of the block after 5 seconds

a. 22.441 m/s b. 34.917 m/s c. 36.428 m/s d. 41.221 m/s

94. The distance travelled after 5 sec is

a. 97.438 m b. 103.442 m c. 105.321 m d. 110.228 m

S-25

The rectangular reinforced concrete beam with a width of 200 mm and an effective depth of 500 mm

is subjected to a service moment of 120 kN m. The beam is reinforced with 4 25 mm diameter bars

with n= 8.

95. The distance from the neutral axis from the top of the beam.

a. 461.452 mm b. 342.123 mm c.301.411 mm d. 212.507 mm

96. The maximum stress in concrete is


36/40

a. 13.518 Mpa b.15.221 Mpa c. 21.412 Mpa d. 22.881 Mpa

97.The maximum stress in steel is


S -26

For the given set of system shown:

98. The magnitude of the resultant of the force system shown.

a. 77.14 N b. 81.21 N c. 84.22 N d. 87.55 N

99. The angle that the resultant makes with the + x axis is

a. 44.220 b. 48.420 c. 52.220 d. 54.770

100. The moment of all forces with respect to 0.

a.204.17 Nm b. 231.11 Nm c. 369.69 Nm d. 412.41 Nm

BONUS!----. The x intercept of the resultant force is

a. 4.221 m b. 5.092 m c. 6.063 m d. 7.551 m

BONUS!--The y intercept of the resultant force is

a. -7.823 m b. 7.829 m c. 6.612 m d.-6.421 m


37/40

S -26

A beam 100 mm by 200 mm has a simple span of 5 m. It carries a uniform load of

5 kN/m.

92. The shear force 1 m from the left support is

a. b. 7.5 kN

93. The shear stress at 30 mm from the top of the beam at a section 1 meter from the left support.

a. b. 0.287 Mpa

94. The shear force carried by the section from the top to 30 mm below the top at a section where

shear is maximum.

a. b. c. 0.7593 kN

S -27

The force acting per meter length of the dam are shown.

78. The bearing pressure at A is

a. 163.2716Kpa

79. The bearing pressure at B is

a. b. 108.025 kPa

80. The distance from B where the resultant applied forces intersect base AB.

a. 2.883 m

81. Factor of safety against sliding if the coefficient of friction at the base of the dam is 0.25.

a. b. 1.386

S -28

To prevent excessive deflection of a 3 m long cantilever beam subjected to a load of 2 Kn/M. Its free

end is attached to a tension rod.

Beam properties are as follows.

A = 1900 mm2 I = 5.12 x 106mm4 E = 200 Gpa

82. The maximum deflection before attaching the tension rod is


38/40

a. 19.78 mm

83. Maximum moment at the fixed end if the rod attached to the beam has a tension of 2 Kn.

a. b. 3 kN m

84. The maximum positive moment in the beam if the tension in the rod is 2.5kN.

a. b. 1.5625 kN m

S - 29

The bridge truss shown on the figure carries a concentrated load of 20 kN and a uniform load of 2

kN/m.

A unit load moves along the span AE .

85. The force at BG when the unit load is at B is

a. +0.3536 kN

86. The force at BG when the unit load is at C

a. b. -0.707

87. The maximum value of the tensile force at BG due the given applied loads is

a. 9.9kN

88. The maximum value of compressive force at BG due to the given applied loads.

a. b. 24.45 kN

S -30The beam shown in the figure carries a triangular load as shown.


39/40

89. The reaction at A is

a. 17.333kN

90. The reaction at B is

a. b. 38.667 kN

91. The location of the zero shear from A is

a. 1.6795 m

92. The maximum positive bending moment isa. b. 13.766 kN m

93. The location of the point of inflection from point A is

a. 3.615 m

94. The maximum negative moment is

a. b. 40 kN m

S -31

A rectangular footing 2.5 meter wide along the y axis, 3 m long along the x axis supports a circular

pedestal 0.45 m in diameter. The horizontal force acting at the top of the pedestal along the x axis of

the footing is 144 kN. The total axial load from the pedestal is 1200 kN. Thickness of the footing is 0.7

m, height of backfill on top of the footing is 1.5 m, depth from the top pedestal to the base of thefooting is 2.5 m. Concrete unit weight = 24 kN/m3 Unit weight of soil = 17 Kn/m3


40/40

95. The maximum soil pressure is

a. 256 kPa b. 276 kPa c. 298 kPa d. 321 kPa

96. The minimum soil pressure is

a. 61 kPa b. 64 kPa c. 67 kPa d. 71 kPa

97. The required soil bearing capacity is

a. 201.1 kPa b.244.1 kPa c. 298.3 kPa d. 308.4 kPa

S- 32

From the given frame shown using CANTILEVER method.

98. The location of the centroid from the leftmost column is

a. 6.667 m b. 7.411 m c. 8.761 m d. 9.231 m

99. The axial load at AD is

a. 1.044 kN b. 2.534 kN c. 3.142 kN d. 4.231 kN

100. The moment at D is

a. 4.41 kN b. 5.22 kN m c. 6.21 kN m d. 7.06 kN m

Tolentino Pre Boards

Text of Tolentino Pre Boards

San Nicola da Tolentino...san niCoLa da toLentino agostiniano N. 1 - Gennaio-Febbraio 2011 - Anno LXXXIII Direzione Santuario san Nicola 62029 TOLENTINO (MC) Tel. 0733.97.63.11 - C.C.P

Metodo Tolentino

Braian tolentino alva

Tolentino Vs

Islamic boards - CORE

Apuntes rw tolentino

28269217 San Nicolas de Tolentino

Coleção Grude Boards

Gypsum Boards Homework

Belleza Boards

POR : POR : FERNANDO TOLENTINO FERNANDO TOLENTINO ELISA CUADRADO ELISA CUADRADO EMILDA CRUZ

BOARDS - Starman

Cuento - Consuelo Tolentino

DanLoad 6000 Preset Controller - Emerson Electric...MicroController) boards, Any of the AC I/O boards, Any of the CE-specific DC I/O boards, Any of the CE-specific RTD/Analog boards

5 Tolentino Versus Comelec

Boards Test 2012

Tolentino slr programa ng pamahalaan

Boards Glycosides

PRD Presentation Boards

BREIZH BOARDS

6. Tolentino v COMELEC- Constitution

FPGA Boards

Acelga Tolentino

Leading Boards - présentation

Tolentino vs. Comelec 41scra702

Presentation renet. tolentino

Boards for crit

A4-Startup Boards

Lift Control Boards

RAMS Boards - performance

Documents

Tolentino Pre Boards

Text of Tolentino Pre Boards