Mit-math-correl-1st-term-ay-2014-2015-draft.pdf

MOCK BOARD EXAMINATION: MATHEMATICS, SURVEYING AND TRANSPORTATION ENGINEERING

SET A

MAPUA INSTITUTE OF TECHNOLOGY DEPARTMENT OF CEGE INSTRUCTIONS: Select the best answer for each of the following questions. Mark only one answer for each item by shading the box corresponding to the letter of your choice on the answer sheet provided. If your answer is not among the choices provided shade the box corresponding to letter E.STRICTLY NO ERASURES ALLOWED. 1.

By how much does the arc intercepted by a central angle of 38ᵒ exceed the chord intercepted by the same angle on a circle of radius 12? A. 0.145 C. 0.231 B. 0.167 D. 0.124

2.

It is an angular unit and is the angle subtended at the center of the circle subtended by an arc that is 1/6400 of the circumference. A. Mils C. Radian B. Gradian D. Degree

3.

From a point A, the angle of elevation of the top of the pole is measured as 37.1˚, measured from the point B on the opposite side but along the same straight line, the angle of elevation of its top is 35.9˚. If the height of the pole is 45.86 m, how far are points A and B? A. 124 m C. 112 m B. 165 m D. 108 m

4.

A triangular piece of land has vertices A, B and C and is surveyed producing the following data. A=30˚, C = 50˚ and AC = 13 m. what is the longest median? A. 11.17 m C.12.31 m B.10.22 m D. 5.54 m

5.

Find the middle-sized angle in the triangle whose sides are 350, 210 and 320. A. 64.1ᵒ C. 61.4ᵒ B. 59.2ᵒ D. None in the list

6.

Which of the following could not be the length of the sides of a triangle? A. (1, 2, 3) C. (60, 11, 61) B. (13, 12, 11) D. (24, 13, 15)

7.

A corner lot is 30 m on the street and 20 m on the other street, the angle between the two lines on the street being 80ᵒ. The other two lines of the lot are perpendicular to the lines on the street. Determine the area of the lot. A. 495 sq m C. 467 sq m B. 513 sq m D. 501 sq m

8.

Compute the difference of the areas of a pentagon with perimeter equal to 500 cm and a circle that could be inscribed tangent to all the sides. A. 2326 C. 2645 B. 1236 D. 2148

9.

What is the slope of the line which is defined by the equation 4y+3x+16=0. A.-3/4 C.1/3 B.-1/4 D.-2/3

10. A certain polynomial P(x) is divided by a certain linear divisor D(x). If D(x) is a factor of P(x) and P(2)=0 and P(1)=2, which of the following could be the value D(1)? A.-1 C. 2 1

MOCK BOARD EXAMINATION: MATHEMATICS, SURVEYING AND TRANSPORTATION ENGINEERING

SET A

MAPUA INSTITUTE OF TECHNOLOGY DEPARTMENT OF CEGE B. -2

D. 3

11. A water tank is in the form of a sphere. It is filled with water to a depth of 30 cm. the inner diameter of the tank is 45 cm, what is the volume of air space in it in liters? A. 12.37 L B. 47.71 L C. 28.49 L D. 35.34 L 12. If x varies directly as y and inversely as z, and x=14 when y=7 and z=2. Find x when z=4 and y=2. A. 2 B. 4 C. 8 D. 6 13. Researchers are concern for many internet users. A survey showed that 51% of the users are somewhat concerned about confidentiality of their emails. Based on the given information, what is the probability that for a random sample of 15 internet users, more than 10 are concerned about privacy of their emails? A. 0.0689 B. 0.1699 C. 0.0478 D. 0.1010 14. A circle is drawn such that its center is 14 units from the center of another circle. The points on the circles closest to each other are 5 units apart. If the other circle is twice as big (in terms of dimension), what is the area of the smaller circle? A. 9pi B. 6pi C. 3pi D. 36pi 15. The fourth term of a geometric progression is 189 and the sixth term is 1701. Find the 8th term? A. 15309 B. 15209 C. 45927 D. 5103 16. It is mango harvesting season when Jim picked the ripe ones and put it in the basket. 1/3 of the number is given to his family, 1/5 is eaten by Jim and the remaining 35 is sold to the market. How many ripe mangos did Jim pick initially? A. 75 B. 70 C. 60 D. 55 17. George sold a calculator for P 3,500 at a loss of 30% on the cost price. Find the corresponding loss or gain if he sold it for P 5,050 A. 1% gain B. 10% gain C. 10% loss D. 15% loss 18. How many minutes after 3:00 pm will the hands of the clock be at 180o? A. 49.1 B. 45.6 C. 50.2 D. 46.7 19. Find the value of x if the 8th term of the expansion of (x3+1)12 is equal to 25952256. A. 2 B. 6 C. 3 D. 4 20. The weight of a body above the surface of the earth varies inversely as the square of the distance from the center of the earth. If a certain body weighs 55 pounds when it is 4000 miles from the center of the earth, how much will it weigh when it is 4400 miles from the center? A. 45.45 lb B. 51.45 lb C. 48.54 lb D. 53.55 lb 21. There are two consecutive odd integers whose product is 143. Find the sum of the numbers. A. 24, -24 B. -24 C. 24 D. None in the list

2

MOCK BOARD EXAMINATION: MATHEMATICS, SURVEYING AND TRANSPORTATION ENGINEERING

SET A

MAPUA INSTITUTE OF TECHNOLOGY DEPARTMENT OF CEGE 22. A box contains 6 white balls, 10 green balls, 8 black balls, 12 red balls and 14 yellow balls. How many balls must be drawn in order to ensure that there will be three balls of the same color? A. 11 B. 10 C. 7 D. 8 23. The sum of the 100 terms of an arithmetic progression is 20100. If the first term of the progression is 3, find the 50th term. A. 199 B. 195 C. 203 D. 207 24. A triangle has side lengths 7cm, 9 cm and 13 cm. Find the area of the circumcircle. A. 146.80 B. 29.95 C. 73.40 D. 293.60 25. Find the period of cos3x. A. 2π/3 B. π

C. π/3

D. None in the list

26. A bathroom tub will fill in 15 minutes with both faucets open and stopper in place. With both faucets closed and the stopper removed, the tub will empty in 20 minutes. How long will it take for the tub to fill if both faucets are open and the stopper removed? A. 60 mins B. 25 mins C. 9 mins D. 76 mins 27. A swimmer requires 3 hours to swim 15 miles downstream. The return trip upstream takes 5 hours. Find the average speed of the swimmer in still water? A. 4mph B. 2 mph C. 3 mph D. 1 mph 28. The sum of three numbers is 48. The sum of the two larger numbers is three times the smallest. The sum of the two smaller numbers is 6 more than the largest. Find the smallest number. A. 12 B. 8 C. 16 D. 10 29. Which of the following is a prime number? A. None in the list B. 357 C. 323

D. 231

30. A polynomial P(x) satisfies that P(0)=3, P(2)=2, P(1)=5. If the polynomial P(x) is divided by x, what is the remainder? A. 3 B. 2 C. 5 D. 0 31. Two stations A and B are 5000 ft apart. When an airplane D was directly above A, an observer at B found angle B to be 31.2o. Find the distance from the plane to station B. A. 5845 ft B. 5633 ft C. 5945 ft D. 6115 ft 32. What is the slope of x=2y+1. A. 1/2 B. 2

C. 1

D. -1/2

33. A triangle has two sides with length 3 and 4 cm. If the third side has an integer length and as high as possible, what is the angle included of 3 and 4-cm sides? A. 117 B. 180 C. 161 D. 104 34. The sum of the digits of a two digit number is 7. Their difference is 3. Which of the following is the number? A. 25 B. 46 C. 43 D. 16 3

MOCK BOARD EXAMINATION: MATHEMATICS, SURVEYING AND TRANSPORTATION ENGINEERING

SET A

MAPUA INSTITUTE OF TECHNOLOGY DEPARTMENT OF CEGE 35. Two observing stations were set up 850 m apart. A structural building in between them was observed to have an angle of elevation at the top equal to 12.53o and 10.2o respectively from each stations. Find the height of the building. A. 277 ft B. 84.5 ft C. 103.7 ft D. 195.2 ft 36. If a<0, b<0 and |a|>|b|. What is the value of b-a? A. greater than 0 B. less than 0 C. 0

D. none in list

37. Mark treated his girlfriend to a bus ride, but on account of his limited resources it was necessary that they should walk back. If the bus goes at the rate of 9 mph and they walk at the rate of 3 mph, how far should they ride so that they may be back in 8 hours? A. 18 mi B. 20 mi C. 24 mi D. 26 mi 38. Consider the sequence 9, -3, 1, …, what is the 8th term? A. -1/243 B. 1/81 C.1/729

D. -1/729

39. What is the area bounded by the line with x and y intercepts 3 and -4, and the coordinate axes? A. 6 B. 10 C. 12 D. 8 40. Mark bought a car for P 600,000 and sold it to Jose at a loss of 20%. At what price must Jose sell it in order to make a profit of 5%? A. 504,000 B. 456,000 C. 750,000 D. 420,000 41. Find the amplitude of y = 2sin (3x +1). A. 2 B. 1

C. 1/2

D. 4

42. Determine the equation of the line passing through (3, -4) and parallel to another line passing through (0, -5) and (4, -3) A. x - 2y = 11 B. 2x – y = 10 C. x - 4y + 13=0 D. x + 4y +11=0 43. The present ages of A and B are as 6:4. Five years ago their ages were in the ratio 5:3. How old is A now? A. 30 B. 40 C. 25 D. 20 44. Find the area bounded by y2 = 3x + 9 and y2 = 9-3x A. 24 B.48 C. 42

D. 84

45. If a steel ball is immersed in an 8 cm diameter cylinder, it displaces water to a depth of 2.25 cm. What is the diameter of the ball? A. 6 B. 3 C. 9 D. 12 46. An ellipse has an equation of 4x2 + 16y2 = 625. Along which axis lies the major axis? A. x-axis B. y-axis C. both axes D. None in the list 47. There are 11 points on a plane for which no three are collinear. If these points are connected to form line segments, what is the probability that the line segment chosen is a diagonal of an 11-sided polygon? A. 4/5 B. 1/5 C. 3/5 D. 2/5 48. A regular pentagon is inscribed in a circle having an area of 158 square cm. Find the area of the circle not covered by pentagon. 4

MOCK BOARD EXAMINATION: MATHEMATICS, SURVEYING AND TRANSPORTATION ENGINEERING

SET A

MAPUA INSTITUTE OF TECHNOLOGY DEPARTMENT OF CEGE A. 38.42

B. 32.34

C. 22.98

D. 45.63

49. A chord of a circle x2 + y2 -24x +80 = 0 is 10.6 m long. How far is this chord from the center of the circle? A. 6 B. 7 C. 5.5 D. 5 50. Find the equation of a line whose intercepts are twice that of the line 3x – 2y – 12 =0. A. 3x – 2y = 24 B. 2x – 3y =24 C. 2x - 3y =12 D. None of these 51. If a pair of dice is tossed, what is the probability of getting an even number sum? A. 1/2 B. 2/3 C. 1/4 D. 1/6 52. Evaluate the first derivative of the implicit function 4x2 + 2xy + y2. A. -(4x + y) / (x + y) B. (4x - y) / (x + y) C. (4x + y) / (x + y) D. -(4x - y) / (x + y) 53. Find the area in sq cm of the sector covered by hour hand, 7 cm long, after it has moved through three hours. A. 38.5 B. 77 C. 35 D. 70 54. If x varies directly as y and inversely as z, and x=14 when y=7 and z=2, find x^2 when z^2=4 and y^2=16. A. 64 B. 16 C. 8 D. 4 55. Find the area bounded by the lines 5x-6y-30=0, 2y+3x-6=0 and the y-axis. A. 13.71 B. 8.57 C. 18 D. 18.67 56. The vertices of the heptagon are as follows: (1, 4), (3, 2), (2, -2), (1, -5), (-3, -4), (-4, 1), and (-2, 2). Which of the following gives the distance of the centroid from origin? A. 0.404 B. 0.331 C. 0.389 D. 0.286 SITUATIONAL I. The number of diagonals of a polygon is 44. 57. Find the number of sides of the polygon. A. 11 B. 9 C. 10

D. 12

58. Find the area of the polygon if the polygon is inscribed in a circle whose radius is 12 cm. A. 428 B. 522 C. 325 D. 576 59. Find the perimeter of the inscribed polygon. A. 74 B. 64 C. 54

D. 85

II. A 600-ft radio tower is being supported by two cables running from the top of the tower to the ground. The cables make an angle of 58o and 44o with respect to the horizontal. 60. Find the length of the cable farther from the tower. A. 864 ft B. 921 ft C. 707 ft

D. 978 ft

61. Find the distance between the anchorages of the two cables on the ground. A. 246 ft B. 621 ft C. 375 ft D. 214 ft 62. Find the distance between the base of the tower and the anchorage of the nearer cable. 5

MOCK BOARD EXAMINATION: MATHEMATICS, SURVEYING AND TRANSPORTATION ENGINEERING

SET A

MAPUA INSTITUTE OF TECHNOLOGY DEPARTMENT OF CEGE A. 375 ft

B. 621 ft

III. A curve is defined by the equation 63. Where is the center of the curve? A. (3, -1) B. (-3, 1)

C. 214 ft

x  32   y  12 4

3

1

D. 246 ft

.

C. (3, 1)

D. None in list

64. What is the length of the major axis? A. 8 B. 4

C. 3

D. 2

65. What does this equation represent? A. Ellipse B. Parabola

C. Circle

D. Hyperbola

IV. Two trains are running in the same direction on two parallel tracks. The trains are 85 m and 65 m, respectively, and running at 120 kph and 240 kph. If the trail end of the first train is 210 m ahead of the front end of the second train. 66. Determine the time required for the front end of the second train to reach the tail end of the first train. A. 6.3 s B. 4. 6 s C. 5.7 s D. 7.8 s 67. Determine the total distance traveled by the second train from the initial position when it has completely overtaken the first train. A. 720 m B. 756 m C. 845 m D. 900 m 68. Determine the distance traveled by the first train from the initial position until both ends of the two trains abreast each other. A. 295 m B. 280 m C. 300 m D. 270 m V. Find the volume of the solid described. 69. Spherical wedge of central angle 1 radian and 1 unit radius. A. 2/3 B. ½ C. 1/3

D. 2/5

70. Sphere with great circle of 6 cm circumference. A. 3.65 B. 4.12 C. 3.35

D. 2.54

71. Regular hexagonal pyramid with slant height of 8 cm and base width of 6 cm. A. 190 B. 569 C. 380 D. 210 VI. On the banks of a 3-km-wide straight river, runner A and runner B are initially on the opposite banks. Runner A can run 3 kph while runner B can run 5 kph. 72. How far is B from A after 2 hours? A. 5 km B. 4 km C. 3 km D. 6 km 73. After 2 hours, what is the angle subtended by the initial and final positions of B from A? A. 116.56ᵒ B. 63.43ᵒ C. 53.13ᵒ D. 121.45ᵒ 74. If after 5 hours, B stops running. How many hours will A overtake B? A. 3.33 B. 4.80 C. 4.96 D. 5.33 VII. A region is bounded by the lines x=6, 5x=y, 3x+5y=28 and x-axis. 75. Calculate the area of the region. 6

MOCK BOARD EXAMINATION: MATHEMATICS, SURVEYING AND TRANSPORTATION ENGINEERING

SET A

MAPUA INSTITUTE OF TECHNOLOGY DEPARTMENT OF CEGE A. 20

B. 26

C. 17

76. What is the coordinates of the centroid of the area? A. (2.83, 1.83) B. (1.83, 2.83) C. ( -1.83, 2.83)

D. 31

D. (2.83, -1.83)

77. Compute the moment of inertia of the region with respect to x-axis. A. 95 B. 67 C. 81 D. 101 VIII. Determine the quadrant for which the angle being describe terminates. 78. cotθ > 0 and cscθ >0 A. I B. II C. III D. IV 79. secθ < 0 and tanθ > 0 A. III B. I

C. II

D. IV

80. cscθ > 0 and cosθ < 0 A. II B. III

C. II

D. IV

IX. Given a circle of radius 5 cm. 81. Calculate the length of the arc subtend by and angle of 50°. A. 4.36 cm B. 3.56 cm C. 6.87 cm

D. 1.68 cm

82. Find the area of the minor segment whose chord length is 7 cm. A. 6.89 B. 7.91 C. 8.53 D. 8.55 83. Find the length of the arc of the minor segment whose chord length of 8 cm. A. 9.27 B. 10.21 C. 12.19 D. 8.76 X. What is the y-intercept of the following: 84. y = 2sinx A. 0 B. 2

C. 1

D. None in the list

85. y = cosx + 1. A. 2

B. 1

C. 0

D. None in the list

86. y = 2cotx + 1. A. 2

B. 1

C. 3

D. None in the list

XI. Given the trigonometric function: 2y=3cos(2x+1)+2. 87. What is the amplitude? A. 1.5 B. 3 C. 3.5

D. 2.5

88. What is the maximum value of y? A. 2.5 B. 1.5

C. 3

D. 3.5

89. What is the frequency? A. 2 B. 1

C. 1/2

D. 4 7

MOCK BOARD EXAMINATION: MATHEMATICS, SURVEYING AND TRANSPORTATION ENGINEERING

SET A

MAPUA INSTITUTE OF TECHNOLOGY DEPARTMENT OF CEGE XII. The distance “S” meters from a fixed point of a vehicle travelling in a straight line with constant acceleration “a” is given by the formula, S=ut+1/2 at^2, where “u” is the initial velocity in m/s and “t”, the time in seconds. Given that S=42 m when t=2 s and S=144 m when t=4 s. 90. What is the initial velocity? A. 6 m/s B. 5 m/s C. 4 m/s D. 3 m/s 91. What is the acceleration? A. 15 m/s2 B. 20 m/s2

C. -20 m/s2

D. -15 m/s2

92. Determine the distance travelled after 3 s. A. 85.5 m B. 55.5 m

C. 65.5 m

D. 70 m

XIII. In the next three problems, calculate the volume of the solid made by revolving the area bounded by the curves and revolved about as indicated. 93. y=x^2, x=2 and y=0, about the x-axis. A. 32pi/5 B. 128pi/5 C. 64pi/5 D. 16pi/5 94. y=x^2, x=2 and y=0, about y-axis. A. 8pi B. 6pi

C. 8pi/3

D. 13pi/5

95. The first quadrant region bounded by y=x^2, the y-axis and y=4 about the y-axis. A. 8pi B. 40pi/3 C. 10pi D. 67pi/5 XIV. The sides of triangle are 9cm, 11cm, and 15cm respectively. 96. Determine the radius of the inscribed circle. A. 2.81 B. 3.56 C. 1.86

D. 2.86

97. Find the radius of the circle which is escribed outside the triangle if it is tangent to the 9cm side. A. 5.78 B. 7.58 C. 8.57 D. 6.78 98. Determine the radius of the circumscribing circle. A. 7.55 B. 5.57 C. 5.78

D. 7.78

XV. Determine the number of tangent lines common to two circles of different radii given the following conditions: 99. The circles are non intersecting. A. 4 B. 3 C. 2 D. 1 100. The circles are concentric. A. 0 B. 1

C. 2

D. 3

8