Preboard-math.docx

REGISTERED ELECTRICAL ENGINEERS PRE-BOARD EXAMINATION MARCH 2017 MATHEMATICS

1.

The rectangular coordinate system in space is divided into eight compartments, which are known as: A. quadrants B. octants C. axis D. coordinate

2.

What is the value of x in Arctan 3x + Arctan 2x = 45 degrees? A. -1/6 and 1 B. 1/6 and -1 C. 1/6 D. -1

3.

In delivery of 14 transformers, 4 of which are defective, how many ways those in 5 transformers at least 2 are defective? A. 940 B. 920 C. 900 D. 910

4.

Sand is pouring to form a conical pile such that its altitude is always twice its radius. If the volume of a conical pile is increasing at a rate of 25 pi cu. ft./min, how fast is the radius is increasing when the radius is 5 feet? A. 0.5 ft/min B. 0.5pi ft/min C. 5 ft/min D. 5pi ft/min

5.

Evaluate lim A. 1

𝑥+4

as x approaches to infinity. B. 0 C. 2

𝑥−4

D. infinite

6.

Describe the locus represented by the equation |𝑧 − 1| = 2> A. circle B. ellipse C. parabola D. hyperbola

7.

An air balloon flying vertically upward at constant speed is situated 150 m horizontally from an observer. After one minute, it is found that the angle of elevation from the observer is 28 deg 59 min. What will be then the angle of elevation after 3 minutes from its initial position? A. 63 deg 24 min B. 58 deg 58 min C. 28 deg 54 min D. 14 deg 07 min

8.

In how many ways can you pick 3 dogs from a pack of 7 dogs? A. 32 B. 35 C. 30 D. 36

9.

Find the volume (in cubic units) generated by rotating a circle X2 + y2 + 6x + 4y + 12 = 0 about the y-axis. A. 47.23 B. 59.22 C. 62.11 D. 39.48

10. Peter can paint a room in 2 hrs and John can paint the same room in 1.5 hrs. How long can they do it together in minutes? A. 0.8571 B. 51.43 C. 1.1667 D. 70 11. Solve the differential equation 7yy’ = 5x. A. 7x2 + 5y2 = C B. 5x2 + 7y2 = C C. 7x2 - 5y2 = C

D. 5x2 - 7y2 = C

12. A cylindrical container open at the top with minimum surface area at a given volume. What is the relationship of its radius to height? A. radius = height B. radius = 2height

REGISTERED ELECTRICAL ENGINEERS PRE-BOARD EXAMINATION MARCH 2017 MATHEMATICS

C. radius = height/2

D. radius = 3height

13. A water tank is shaped in such a way that the volume of water in the tank is V = 2y3/2cu. in. when its depth is y inches. If water flows out through a hole at the bottom of the tank at the rate of 3(sqrt. Of y) cu. in/min. At what rate does the water level in the tank fall? A. 11 in/min B. 1 in/min C. 0.11 in/min D. 1/11 in/min 14. A family’s electricity bill averages $80 a month for seven months of the year and $20 a month for the rest of the year. If the family’s bill were averaged over the entire year, what would the monthly bill be? A. $45 B. $50 C. $55 D. $60 15. When a baby born he weighs 8 lbs and 12 oz. After two weeks during his check-up he gains 6 oz. What is his weight now in lbs and oz? A. 8 lbs and 10 oz B. 9 lbs and 4 oz C. 9lbs and 2 oz D. 10 lbs and 4 oz 16. A given function f(t) can be represented by a Fourier series if it A. is periodic B. is singled valued C. is periodic, single valued and has a finite number of maxima and minima in any one period D. has a finite number of maxima and minima in any one period 17. A periodic waveform possessing half-wave symmetry has no A. even harmonics B. odd harmonic C. sine terms D. cosine terms 18. N engineers an N nurses. If two engineers are replaced by nurses, 51 percent of the engineers and nurses are nurses. Find N, A. 102 B. 100 C. 55 D. 110 19. If f(x) = 10^x + 1, then f(x + 1) – f(x) is equal to A. 10(10^ + 1) B. 9(10^x) C. 1

D. 9(10^x + 1)

20. There is a vector v = 7j, another vector u starts from the origin with a magnitude of 5 rotates in the xy plane. Find the maximum magnitude of u x v. A. 24 B. 70 C. 12 D. 35 21. Find the coordinates of the centroid of the plane area bounded by the parabola y = 4 + x2 and the x-axis A. (0, 1.5) B. (0, 1) C. (0, 2) D. (0, 1.6) 22. A long piece of galvanized iron 60 cm wide is to be made into a trough by bending up two sides. Find the width of the base if the carrying capacity is a maximum. A. 30 B. 20 C. 40 D. 50

REGISTERED ELECTRICAL ENGINEERS PRE-BOARD EXAMINATION MARCH 2017 MATHEMATICS

23. The price of gas increased by 10 percent. A consumer reacts by decreasing his consumption by 10 percent. How does his total spending change? A. increase 1 percent B. decrease 1 percent C. no change D. decrease 1.5 percent 24. An audience of 450 persons is seated in rows having the same number of persons in each row. If 3 more persons seat in each row, it would require 5 rows less to seat the audience. How many rows? A. 27 B. 32 C. 24 D. 30 25. The volume of a cube becomes three times when its edge is increased by 1 inch. What is the edge of a cube? A. 2.62 B. 2.26 C. 3.26 D. 3.62 26. What is the angle of the sun above the horizon, when the building 150 ft high cast a shadow of 405 ft? A. 21.74 B. 68.26 deg C. 20.32 deg D. 69.68 deg 27. Water ir running out of a conical tunnel at the rate of 1 cu. in/sec. If the radius of the base of the tunnel is 4 in and the altitude is 8 in, find the rate at which the water level is dropping when it is 2 in from the top. A. -1/9pi in/sec B. -1/2pi in/sec C. 1/2pi in/sec D. 1/9pi in/sec 28. A statistic department is contacting alumni by telephone asking for donations to help fund a new computer laboratory. Past history shows that 80% of the alumni contacted in this manner will make a contribution of at least P50.00. A random sample of 20 alumni is selected. What is the probability that between 14 to 18 alumni will make a contribution of at least P50.00? A. 0.421 B. 0.589 C. 0.844 D. 0.301 29. Jun rows has banca a river at 4 km/hr. What is the width of the river if he goes at a point 1/3 km. A. 5.33 km B. 2.25 km C. 34.25 km D. 2.44 30. Find the volume generated by revolving about the x-axis, the area bounded by the curve y = cosh x from x = 0 to x = 1. A. 5.34 B. 3.54 C. 4.42 D. 2.44 31. Evaluate the integral of xsinxcosxdx 1 1 1 A. - 4 xcos2x + C C. - 4 xsin2x + 8 xcos2x + C B.

1

xsin2x + C 8

𝟏

𝟏

D. - 𝟒 xcos2x +𝟖 sin2x + C

32. A cross-section of a trough is a semi-ellipse with width at the top 18 cm and depth 12 cm. The trough is filled with water to a depth of 8 cm. Find the width at a surface of the water. A. 5√2 cm B. 𝟏𝟐√𝟐 cm C. 7√2 cm D. 6√2 cm

REGISTERED ELECTRICAL ENGINEERS PRE-BOARD EXAMINATION MARCH 2017 MATHEMATICS

33. Simplify cos2x + sin2x + tan2x A. cos2x B. sin2x

C. sec2x

D. csc2x

34. What is the general solution of (D2 + 2)y(t) = 0? A. y = C1cos2t + C2sin2t C. C1cos√𝟐t + C2sin√𝟐t B. y = C1sin2t + C2cos2t D. C1sin√2t + C2cos√2t 35. What is the distance between the lines. 𝑥 1 A. √6

90

C. √ 7

B. 5

D.

90 7

36. What is a so that the points (-2, -1, -3), (-1, 0, -1) and (a, b, 3) are in straight line? A. 2 B. 4 C. 3 D. 1 37. Find the volume generated when the area bounded by y = 2 x – x and y = (x – 1)2 is revolved about the x-axis A. 2.34 B. 3.34 C. 4.43 D. 1.34 38. Find the centroid of a semi-ellipse given the area of semi-ellipse as A = ab 4

and volume of the ellipsed as V = 3 𝜋ab2 A. 2b/3𝜋 B. b/2𝜋 C. 4b/3𝝅

D. 3b/4𝜋

39. How many 5 poker hands are there in a standard deck of cards? A. 2,595,960 B. 2,959,960 C. 2,429,956 D. 2,942,955 40. A biker is 30 km away from his home, he travel 10 km and rest for 30 mins. He travel the rest of the distance 2kph faster. What is his original speed? A. 7 kph B. 10 kph C. 8 kph D. 12 kph 5

5

11

41. Cup A = full, cup B = full, cup C = full, cup D = 9 6 12 to fill the three cups, what is left in the cup? A. 1/2 B. 3/4 C. 1/4 42. What percent of 500 is 750% A. B. 175

C. 57

17

full. If the 4th cup is used D. 19/36

D. 125

43. Using power series expansion about 0, find cosx by differentiating from sinx A. 1- (x^2/2!)+(x^4/4!)-(x^6/6!)+ B. x-(x^2/2!)+(x^4/4!)-(x^5/5!)+ C. 1- (x^3/3!)+(x^5/5!)-(x^7/7!)+ D. x-(x^3/3!)+(x^5/5!)-(x^7/7!)+ 44. Find the area bounded by y = √4𝑥in the first quadrant and the lines x = and x =3

REGISTERED ELECTRICAL ENGINEERS PRE-BOARD EXAMINATION MARCH 2017 MATHEMATICS

A. 7.8

B 6.7

C. 5.5

45. Express 2,400,000 in scientific notation A. 2.4 x 10 B. 2.4 x 10 C. 24 x 10

D. 6.5 D. 2.4 x 105

46. An interior designer has to design two offices, each office containing 1 table, 1 chair, 1 mirror, 2 cabinets. A supplier gives him options between 4 tables, 5 chairs, 5 mirrors and 10 cabinets. In how many ways can he design the offices assuming there is no repetition? A. 14100 B. 2400 C. 21600 D. 1740 47. What is the equation of a circle that passes through the vertex and the points of latus rectum of y2 = x A. x2 + y2 + 4x + 2y = 0 C. x2 + y2 + 4y + 2x = 0 2 2 B. x + y + 10x = 0 D. x2 + y2 - 10x = 0 48. Find the power series expansion of ln (1 – x) A. 1 + x + (x^2)/2 + (x^3)/3 + C. x + (x^2)/2 + (x^3)/3 + (x^4)/4 + B. -1 – x – (x^2)/2 – (x^3)/3 D. –x –(x^2)/2 – (x^3)/3 – (x^4)/4 – 49. Evaluate 10(-20j) + 4(-4j) A. 20 B. 20j

C. -20

D. -20j

50. Evaluate 1=1/(1+1/1+7) A. 15/7 B.13/15

C.4/7

D.7/4

51. The value of all the quarters and dimes in a parking meter is $18. There are twice as many quarters as dimes. What is the total number of dimes in the parking meter? A. 40 B. 20 C. 60 D. 80 52. A ball is dropped from height of 12 m and it rebounds ½ of the distance it falls. If it continues to fall and rebound in this way, how far will it travel before coming to rest? A. 36 m B. 30 m C. 48 m D. 60 m 53. At t = o, a particle starts at rest and moves along a line in such a way that at time t its acceleration is 24t2 feet per second per second. Through how many feet does the particle move during the first 2 seconds? A. 32 B. 48 C. 64 D. 96 54. If a trip takes 4 hours at an average speed of 55 miles per hour, which of the following is closest to the time the same trip would take at an average speed of 65 miles per hour? A. 3.0 hours B. 3.4 hours C. 3.8 hours D. 4.1 hours

REGISTERED ELECTRICAL ENGINEERS PRE-BOARD EXAMINATION MARCH 2017 MATHEMATICS

55. A laboratory has a 75-gram sample of radioactive materials. The half-life of the material. The half life on the material is 10 days. What is the mass of the laboratory’s sample remaining after 30 days? A. 9,375 grams B. 11.25 grams C. 12.5 grams D. 22.5 grams 56. The unit normal to the plane 2x + y + 2z = 6 can be expressed in the vector form as A. i3 + j2 +k2 B. i2/3 + j1/3 + k2/3 C. i1/3 + j1/2 + k1/2 D. i2/3 + j1/3 + k1/3 57.

𝑑 𝑑𝑥

(ln e2x) is 1

A. 𝑒 2𝑥

2

B. 𝑒 2𝑥

C. 2x

D. 2

58. Determine where, if anywhere, the tangent line to f(x) = x3 – 5x2 + x is parallel to the line y = 4x + 23 A. x = 3.61 B. x = 3.23 C. x = 3 D. x = 3.43

59. Which of the following is equivalent to the expression below? (x2 – 3x + 1) – (4x – 2) A. x2 – 7x – 1 B. x2 – 7x + 3 2 C. -3x – 7x + 3 D. x2 + 12x + 2 60. For what value of k will x + A. -4 B. -2

𝑘 𝑥

have a relative maximum at x = -2? C. 2 D. 4

61. When the area in sq. units of an expanding circle is increasing twice as fast as its radius in linear units, the radius is 1 1 𝟏 A. 4𝜋 B. 4 C. 𝝅 D. 1 62. If the function f is defined by f(x0 = x5 – 1, then f-1, the inverse function of f, is defined by f-1(x) = 1 1 𝟓 5 A. 5 B. 5 C. √𝑥 − 1 D. √𝒙 − 𝟏 𝑥 −1 √

√𝑥+1

63. A school has 5 divisions in a class IX having 60, 50, 55, 62, and 58 students. Mean marks obtained in a History test were 56, 64, 72, 63 and 50 by each division respectively. What is overall average of the marks per student? A. 56.8 B. 58.2 C. 62.4 D. 60.8 64. The number n of ways that an organization consisting of twenty-six members can elect a president, treasury, and secretary (assuming no reason is elected to more tha one position) is A. 15600 B. 15400 C. 15200 D. 15000

REGISTERED ELECTRICAL ENGINEERS PRE-BOARD EXAMINATION MARCH 2017 MATHEMATICS

65. Find the equation of the line that passes through (3, -8) and is parallel to 2x + 3y = 2 A. 2x + 3y = -18 B. 2x + 3y = 30 C. 2x + 3y = -30 D. 2x + 3y = 18 66. Find the center of the circle x2 + y2 + 16x + 20y + 155 = 0. A. (-8, -10) B. (8, 10) C. (8, -10)

D. (-8, 10)

67. In how many ways can 5 red and 4 white balls be drawn from a bag containing 10 red and 8 white balls? A. 11760 B. 17640 C. 48620D. none of these 68. The area of a right triangle is 50. One of its angles is 45°. Find the hypothenuse of the triangle A. 10 B. 5√2 C. 10√𝟐 D. 10 69. Each side of the square pyramid is 10inches. The slant height, H, of this pyramid measures 12 in. What is the area in square inches, of the base of the pyramid? A. 100 B. 144 C. 120 D. 240 70. Find the exact value of A. 1.732

tan 25°+tan 50° 1−tan 25° tan 50°

B. 3.732

C. 2.732

D. 0.732

71. Which term of the arithmetic sequence 2, 5, 8, … is equal to 227? A. 74 B. 75 C. 76 D. 77 72. Name the type of graph represented by x2 – 4y2 – 10x – 8y + = 0 A. circle B. parabola C. ellipse D. hyperbola 73. If logx 3 = ¼, then x = A. 81 B.1/81

C. 3

74. If f(x0 = -x2, then f(x + 1) = A. –x2 + 1 B. –x2

C. –x2 – 2x

D. 9 D. –x2 – 2x – 2

75. If this graph of y = (x – 2)2 – 3 is translated 5 units up and 2 units to the right, then the equation of the graph obtained is given by A. y = x2 + 2 B. y = (x-2)2 + 5 C. y = (x + 2)2 + 2 D. y = (x – 4)2 + 2 76. Which one is not a root of the fourth root of unity? A. I B. 1 C. i/√𝟐

D. –i

REGISTERED ELECTRICAL ENGINEERS PRE-BOARD EXAMINATION MARCH 2017 MATHEMATICS

77. Find the area of the largest circle which can be cut from a square of edge 4 in. A. 12.57 B. 3.43 C. 50.27 D. 16 78. If I = (-1)1/2, find the value of i36 A. 0 B. I

C. –I

D. 1

79. If cot B = 5/2, find sin B A. √29/5 B. 5/√29

C. √29/2

D. 2/√𝟐𝟗

80. A man 1.60 m tall casts a shadow 4 m long. Nearby, a flagpole casts a shadow 18 m long. How high is the flagpole? A. 6.4 m B. 7.2 m C. 4.5 m D. 11.25 m 81. If Z1= 1-I, Z2= -2 + 4i, Z3- √3 – 2i, Evaluate Z12+2z1-3. A. B. 7.2 m C. 4.5 m

D.11.25 m

82. A box contains 20 balls, 10 white, 7 blue, 3 red. What is the probability that a ball drawn at random is red? A. 3/20 B. 10/20 C. 7/20 D. 13/20 83. What is the probability of a three with a single die exactly 4 times out of 5 trials? A. 25/776 B. 125/3888 C. 625/3888 D. 1/7776 84. A man is on a wharf 4 m above the water surface. He pulls in a rope to which is attached a coat at the rate of 2 m/sec. How fast is the angle between the rope and the water surface changing when there are 20 m of rope out? A. 0.804 rad/sec B. 0.0408 rad/sec C. 0.0402 rad/sec D. 0.0204 rad/sec 85. Find the area of the largest rectangle that can be inscribed in the ellipse 25x^2 + 16x^2 = 400 A. 30 B. 40 C. 10 D. 20

REGISTERED ELECTRICAL ENGINEERS PRE-BOARD EXAMINATION AUGUST 2017 MATHEMATICS

1. What is the value of x in Arctan 3x + Arctan 2x = 45 degrees? A.1 B.-1 C.1/6 D. 1/6 2. Find the volume (in cubic units) generated by rotating circle 𝑥 2 + 𝑦 2 + 6𝑥 + 4𝑦 + 12 = 0 about the y axis. A. 47.23 B. 59.22 C.62.11 D. 39.48 3. If i= (-1)^1/2 find the value i^30 A.1 B.-1

C.-I

4. Solve the equation cos^2, A=1-cos^2 A A. 45֯,315 B. 45֯,225 C. 454֯,315

D.i

D.

45֯,225

5. Find the change in volume of a sphere if you increase the radius from 2 to 2.05 units. A.2.51 B.1.52 C.1.25 D.2.15 6. What is the general solution of (D^4 – 1)y(t) = 0? A. 𝐲 = 𝐂𝟏𝐞𝐭 + 𝐂𝟐𝐞−𝐭 + 𝐂𝟑 𝐜𝐨𝐬 𝐭 + 𝐂𝟒 𝐬𝐢𝐧 𝐭 C. y = C1et + C2e−t B. y = C1et + C2e−t + C3tet + C4te−t D. y = C1et + C2e−t 7. What percentage of the volume of a cone is the maximum right circular cylinder that can be inscribed in it? A.24 percent B.34 percent C.44 percent D.54 percent 8. if e^2x-3e^x + 2 = 0 , find x. A. ln2 B. ln4

C.ln3

D.

9. On a cortain day the nurses at a hospital worked the following number of hours; nurse howard worked 8 hrs, nurse pease worked 10hrs, nurse campbell worked 9 hrs, nurse grace worked 8 hrs, nurse mccarthy worked 7 hrs, and nurse murphy worked 12 hrs. What is the average number of hrs per nurse on this day? A.7 B.8 C. 9 D. 10 10. Joy is 10 percent taller than joseph and joseph is 10 percent taller than tom. How many percent is joy taller than tom? A. 18 percent B. 20 percent C. 21 percent D. 23 percent 11. An army food supply truck can carry 3 tons. A breakfast ration weights 12 ounces, and the other two daily meals weigh 18 ounces each assuming each soldier gets 3 meals per day, on a ten day trip how many soldiers can be supplied by one truck? A. 100 soldiers B. 150 soldiers C. 200 soldiers D. 320 soldiers 12. Find the area enclose in the second and third quadrants by the curve x=t -1, y= 5t^3(t^2-1)

REGISTERED ELECTRICAL ENGINEERS PRE-BOARD EXAMINATION AUGUST 2017 MATHEMATICS

A.

8/5

13. csc520֯=? A. cos20֯

B.

8/7

B.

C.

8/3

csc20֯

C.

D.18/5

sin20֯

D. sec20֯

14. From past experience it is known 90 percent of one year old children can distinguish their mothers voice of a similar sounding female. A random sample of one years old are given this voice recognize test. Find the probability that atleast 3 children did not recognize their mothers voice. A. 0.677 B. 0.323 C. 0.729 D.0.271

15. ln y = mx + b what is m? A. slope B. x-intercept

C.

y-intercept

D. asymptote

16.Find the area bounded by the parabola sqrt of x + sqrt of a and the line x + y = a A. a^2 B. a^2/2 C. a^2/4 D. a^2/3 17. What is the integral of cosxe ^sinx dx A. 𝑒 𝑐𝑜𝑠𝑥 + 𝐶 B. 𝒆𝒔𝒊𝒏𝒙 + 𝑪 C. 𝑒 −𝑐𝑜𝑠𝑥 + 𝐶

D. 𝑒 −𝑠𝑖𝑛𝑥 + 𝐶

18. The geometric mean and the arithmetic mean of number is 0 and 10 respectively what is the harmonic mean? A. 7.5 B. 5.7 C. 6.4 D. 4.6 19. In how many ways can four coins be tossed once? A. 4 B. 16 C. 32

D.

8

20. A statue 3 m high is standing on a base of 4m high. If an observers eye is 1.5 m above the ground how far should he stand from the base in order that the angle subtended by the statue is a maximum? A. 3.41 B. 3.51 C. 3.71 D. 4.41 21. What is the number in the series below? 3, 16, 6, 12, 12, 6, A. 4 B. 16

C.

20

D.

24

22. A man who is on diet losses 24 lb in 3 months 16 lb in the next 3 months and so on for a long time. What is the maximum total weight loss? A. 72 B. 64 C. 54 D. 81 23. What is the slope of the linear equation 3y-x=9? A. 1/3 B. -3 C. 3

D.

9

24. Each of the following figures has exactly two pairs of parallel sides except a A. parallelogram B.rhombus C. trapezoid D. square

REGISTERED ELECTRICAL ENGINEERS PRE-BOARD EXAMINATION AUGUST 2017 MATHEMATICS

25. A points A and B are 100 m apart and are of the same elevation as the foot of the building. The angles of elevation of the top of the building from points A and B are 21 degrees and 32 respectively. How far is A from the building? A. 259.28 B. 265.42 C. 271.62 D. 277.92 26. What is the area in sq.m. of the zone of a spherical segment having a volume of 1470.265 cu.m if the diameter of the sphere is 30m. A. 655.487 B. 565.487 C. 756.847 D. 465.748 27. Which of the following numbers can be divided evenly by 19? A. 54 B. 63 C. 76 D.

82

28. Where is the center of the circle x^2 + y^2 -10x + 4y – 196 = 0 A. (2,-5) B. (-2,5) C. (-5,2) D. (5,-2) 29. Two ships leave from a port. Ship A sails west for 300 miles and ship B sails north 400 miles. How far apart are the ships after their trips? A. 300 miles B. 400 miles C. 500 miles D. 900 miles

30. if the radius of a sphere is increasing at the constant rate of 3m per second how fast is the volume changing when the surface area is 10 sq.mm? A. 16 cu mm. per sec. B. 20 cu. mm. per sec. C. 30 cu.mm per sec. D. 40 cu. mm per sec. 31. The sum of the base and altitude of an isosceles triangle is 36cm. Find the altitude of the ttriangle if its area is to be a maximum. A. 16cm B. 17cm C. 18cm D. 19cm 32. An insurance policy pays 80 percent of the first P20,000 of a certain patients medical expenses, 60 percent of the next P40,000 and 40 percent of the P40,000 after that. If the patients total medical bill is P92,000 how much will the policy pay? A. 36,800 B. 49,600 C. 52,800 D. 73,600 33. A scientist found 12mg of radioactive isotope is a soil sample. After 2 hours, only 8.2 mg of the isotope remained. Determine the half life of the isotope? A. 2.64hr B. 4.64hr C. 3.64hr D. 5.64hr 34. find the area bounded the curves r = 2cosѲ and r = 4cosѲ. A. 6.28 B. 9.42 C. 12.57 D. 15.72 35. Give the degree measure of angke 3pi/5 A. 150 degrees B. 106 degrees C. 160 degrees D. 108 degrees 36. What is the median of the following group numbers? 1412 20 22 14 16 A. 12 B. 14 C. 15 D. 16

REGISTERED ELECTRICAL ENGINEERS PRE-BOARD EXAMINATION AUGUST 2017 MATHEMATICS

37. For what value of k will the line kx + 5y = 2k hace slope 3? A.

5

B.

-5

C.

15

D. -15

38. The cross product of vector A=4i + 2j with vector B=0. The dot product A·B=30, Find B. A.

6i+3j

B. 6i-3j

C.

3i+6j

C.

36

D.

3i-6j

39. Find the length of the curve r = (1 – cos Ѳ). A.

30

B.

28

D.

32

40. Find the equation of the curve that passes through (4,-2) and cuts at right angles every curve of the family 𝑦 2 = 𝐶𝑥 3 . A. 2𝑥 2 − 3𝑦 2 = 44 B. 3𝑥 2 − 2𝑦 2 = 44 𝟐 𝟐 C. 𝟐𝒙 + 𝟑𝒚 = 𝟒𝟒 D. 3𝑥 2 + 2𝑦 2 = 44 41.Find the area of circle with center at (1,3) and tangent to the line 5x – 12y – 8 = 0. A. 27.28 B. 28.27 C. 29.36 D. 26.39 42. If a flat circular plate of radius r = 2 m is submerged horizontally in water so that the top surface is at a depth of 3m, then the force on the top surface of the plate is A. 369,829.15N B. 184,914.57N C.739,658.3N D.1,479,316.6N 43. A hemispherical tank with a diameter of 8 ft is full of water find the work done in ft-lb in pumping all the liquid out of the top of the tank. A. 15,246 B. 12,546 C. 10,628 D. 16,210 𝑑2 𝑦

44. If 𝑥 = 3𝑡 − 1 , 𝑦 = 1 − 3𝑡 , 𝑓𝑖𝑛𝑑 𝑑𝑥 2 A. -1/3 B. -2/3 45. if sin3A = cos 6B then: A. A+B = 180 deg C. A-2B = 30 deg

C. -1

D.

-4/3

B. A+2B = 30 deg D. A+B = 30 deg

46. It takes a typing student 0.75 seconds to type one word. At this rate, how many words can the student type in 60 seconds? A. 8 B. 45 C. 75 D. 80 47. A chord, 6 inches long from the center of a circle. Find the length of the radius of the circle. A. 8 in B. 9 in C. 7 in D. 10 in

REGISTERED ELECTRICAL ENGINEERS PRE-BOARD EXAMINATION AUGUST 2017 MATHEMATICS

48. A train is moving at the rate of 8 mph along a piece of circular track of radius 2500 ft. Through what angle does it turn in 1 min? A. 16 deg 8 min B. 15 deg 6 min C. 18 deg 9 min D.17 deg 10 min 49. The diagonal of a face of a cube is 10 ft. The total area of the cube is A. 100 sq.ft B. 150 sq.ft C. 200 sq.ft D. 300 sq.ft 50. The volume of the sphere is 36 pi cu. m. The surface area of this sphere in sq.m. is: A. 24pi B. 36pi C. 12pi D. 16pi 51. Which of the following is an exact DE? A.(𝑋 2 + 1)𝑑𝑥 − 𝑥𝑦𝑑𝑦 = 0 B. 𝑥𝑑𝑦 + (3𝑥 − 2𝑦)𝑑𝑥 = 0 C. 𝟐𝒙𝒚𝒅𝒙 + (𝟐 + 𝒙𝟐 )𝒅𝒚 = 𝟎 D. 𝑥 2 𝑦𝑑𝑦 − 𝑦𝑑𝑥 = 0 52. Find the value of 4sinh(pi i/3) A. -2i(sqrt. of 3) B. 2i(sqrt. of 3) C. -4i(sqrt of 3) D. 4i(sqrt. of 3) 53. Find the coordinates of an object that has been displaced from the point (-4, 9) by the vector 4i-5j). A. (0,4) B. (0,-4) C. (4,0) D. (-4,0) 54. Find the work done in moving an object along a vector r= 3i + 2j - 5k if the applied force F = 2i – j – k. A. 9 B. 15 C. 10 D. 16 55. Find the value of k for which the line 2x + ky = 6 is parallel to the y-axis. A. k=0 B. k=1 C. k=2 D. k=3 56. Find the area inside one petal of the four leaved rose r = sin2theta. A. pi/2 B. pi/4 C. pi/6 D. pi/8 57. Which of the following is a vector? A. kinetic energy B. electric field intensity C. entropy D. work 58. In how many ways can 6 people be lined up to get on a bus if certain 3 persons refuse to follow each other? A.144 B. 120 C. 72 D. 480 59. The bases of a frustum of a pyramid are 18cm by 18cm and 10cm by 10cm. Its lateral area is 448 sq. cm. what is the altitude of the frustum? A. 26.39cm B. 6.93cm C. 5.96cm D. 5.69cm 60. A store advertises a 20 percent off sale. If an article marked for sale at $24.48, what is the regular price? A. $34.80 B. $28.65 C. $30.60 D. $36.55

REGISTERED ELECTRICAL ENGINEERS PRE-BOARD EXAMINATION AUGUST 2017 MATHEMATICS

61. IF the area of the equilateral triangle is 4 (sqrt. of 3), find the perimeter. A. 16 B. 12 C. 18 D. 14 62. Dave is 46 yrs old. Twice as old as rave. How old is rave? A. 30 yrs B. 28 yrs C. 23 yrs D. 18 yrs 63. The angles of elevation of the top of a tower at two points 30 m and 80 m from the foot of the tower, on a horizontal line are complementary. What is the height of the tower? A. 46m B. 47m C. 49m D. 48m 64. A large tank filled with 500 gallons of pure water. Brine containing 2 pounds of salt per gallon is pumped into the tank at a rate of 5 gal/min. The well-mixed solution is pumped out at the same rate. What is the concentration of the solution in the tank at t = 5 min? A. 0.0895 lb/ gal B. 0.0985 lb/ gal C. 0.0795 lb/ gal D. 0.0975 lb/ gal 65. The intensity I of light at a depth of x meters below the surface of a lake satisfies the differential dldx = (-1/4)I. At what depth will the intensity be 1 percent of thtat at the surface? A. 2.45m B. 2.29m C. 2.28m D. 2.87m 66. What is the discriminant of the equation 4𝑥 2 = 8𝑥 − 5? A. 8 B. -16 C. 16

D. -8

67. Find the percentage error in the area of a square of side s caused by increasing the side by 1 percent. A. 1 percent B. 2 percent C. 3 percent D. 4 percent 68. What is the height of a right circular cone having a slant height of 3.162 m and base diameter of 2 m? A. 1 B. 2 C. 3 D. 4 69. In how many orders can 7 different pictures be hung in a row so that 1 specified picture is at the center? A. 360 B. 2880 C. 1440 D. 720 70. What is the x-intercept of the line passing through (1,4) and (4,1)? A. 4.5 B. 5 C. 4 D. 6 71. One ball is drawn at random from a box containing 3 red balls, 2 white balls, and 4 blue balls. Determine the probability that is not red. A. 1/3 B. 2/3 C. 2/9 D. 7/9 72. An airplane flying with the wind took 2 hours to travel 1000 km and 2.5 hours flying back. What was the wind velocity in kph? A. 50 B. 60 C. 70 D. 40

REGISTERED ELECTRICAL ENGINEERS PRE-BOARD EXAMINATION AUGUST 2017 MATHEMATICS

73. In how many ways can a person choose 1 or more of 4 electrical appliances? A. 15 B. 16 C. 12 D. 17 74. What are the third proportional to y/x and 1/x? A. y B. xy C. 1/xy

D. y/x^2

75. If 7 coins are tossed together, in how many ways can they fall with most three heads? A. 63 B. 64 C. 65 D. 66 76. If y = ln (sec x tan x). find dy/dx. A. cot x B. cos x

C. csc x

D. sec x

77. A rubber ball is made to all from height of 50 ft and is observed to rebound 2/3 of the distance it falls. How far will the ball travel before coming to rest if the ball continues to fall in this manner? A. 250 ft B. 200 ft C. 300 ft D. 350 ft 78. In a class of 40 students, 27 like calculus and 25 like Chemistry. How many like calculus only? A. 12 B. 15 C. 13 D. 27 79. Simplify (cos θ / sin θ + 1 ) + tan θ A. sec θ B. csc θ

C. sin θ

D. cos θ

80. What kind of graph is r = 2 sec θ? A. straight line B. parabola

C. ellipse

D. hypebola

81. Find the inclination of the line passing through (5,3) and (10,7) A.14.73֯ B. 14.93֯ C.14.83֯ D.14.63֯ 82. An ellipse has an eccentricity of 1/3. Find the distance between the two directrix if the distance between the foci us 4. A.36 B. 18 C. 24 D. 32 83. Find the value of sin (arc cos 15/17). A. 8/9 B. 8/21

C. 17/9

D. 8/17

84. Find the area of the triangle having vertices at -4 -I, 1 +2i, 4-3i. A.15 B. 16 C. 17 D. 18 85. Find the location of the focus of the parabola 𝑥 2 + 4𝑦 − 4𝑥 − 8 = 0. A. (2.5,-2) B. (3,1) C. (2,2) D.(-2,-2) 86. What conic section is 2𝑥 2 − 8𝑥𝑦 + 4𝑥 = 12? A. hyperbola B. ellipse C. parabola

D. circle

REGISTERED ELECTRICAL ENGINEERS PRE-BOARD EXAMINATION AUGUST 2017 MATHEMATICS

87. A man bought 5 tickets in a lottery for aprize of P 2,000.00. If there are total 400 tickets, what is his mathematical expectation? A. P25.00 B. 20.00 C. P30.00 D. P35.00 88. In what quadrants will Ѳ be terminated if cos Ѳis negative? A. 1,4 B. 2,3 C.1,3

D.2,4

89. For what value of the constant k is the lie x + y = k normal to the curve 𝑦 = 𝑥 2 A. 3/4 B. 1/2 C. 2/3 D. 3/5 90. Any number divided by infinity is equal to: A. 1 B. infinity C. zero

D. indeterminate

91. The points Z1,Z2,Z3,Z4 in the complex plane are vertices of parallelogram taken in order if and only if A. Z1+ Z4 = Z2 + Z3 B. Z1+ Z2 = Z3 + Z4 C. Z1+ Z3 = Z2 + Z4 D. none of these 92. If the points (-1,-1,2),(2,m,5) and (3,11,6) are collinear, find the value of m. A. 8 B. 2 C. 10 D. 6 93. Infinity minus infinity is: A. infinity B. zero

C. indeterminate

D. none of these

94. If in the fourier series of a periodic function, the coefficient aჿ = 0 and aⁿ = 0, then it must be having ____________ symmetry. A. odd B. odd quarter wave C. even D. either A or B 95. Tickets number 1 to 20 are mixed up then and then a ticket is drawn has a number which is a multiple of 3 or 5? A. 1/2 B. 2/5 C. 8/15 D. 9/20 96. A car travels 90 kph. What is its speed in meter per second? A. 2 B. 30 C. 25 D. 50 97. The line y = 3x = b passes through the point (2,4) Find b. A. 2 B. 10 C. -2 D. -10 98.If y = tanh x, find dy/dx: A. 𝐬𝐞𝐜 𝟐 𝒙 B. csc 2 𝑥

C. sin2 𝑥

D. tan2 𝑥

99.From the given values A and B, find the vector cross product of A and B, if: A=2i – 5k, B=j A. 5i + 2k B. 4i - 2k C. 3i – 4j + 2k D. 3i – 2j 100. If a place on the earth is 12 degrees south of the equator, find its distance in nautical miles from the north pole. A. 6,021 B. 6,102 C. 6,210 D. 6,120

REGISTERED ELECTRICAL ENGINEERS PRE-BOARD EXAMINATION MARCH 2016 MATHEMATICS

1. Given a conic section, if B2-4AC=0, it is called? A. circle B. parabola C. hyperbola

D. ellipse

2. Give a conic section, if B2-4AC >0 it is called? A. Circle B. parabola C. hyperbola D. ellipse 3. A conic section whose eccentricity is equal to one is known as A. A parabola B. an ellipse C. a circle D. a hyperbola 4. A length of the latus rectum of the parabola y2 = 4px is A. 4p B. 2p C. p D. -4p 5. Two engineers facing each other with a distance of 5km from each other, the angles of elevation of the balloon from the two engineers are 56 degrees and 58 degrees, respectively. What is the distance of the balloon from the two engineers? A. 4.45km,4.54km C.4.64km,4.54km B. 4.54km,4.45km D. 4.46km,4.45km 6. Joy is 10% taller than joseph is 10% taller than Tom. How many percent is Joy taller than Tom? A. 18% B. 20% C. 21% D. 23% 7. In a hotel it is known than 20% of the total reservation will be cancelled in the last minute. What is the probability that these will be fewer than 2 reservations cancelled out of 4 reservations? A. 0.6498 B. 0.5629 C. 0.3928 D. 0.8192 8. Find the area of the region inside the triangle with vertices (1,1),(3,2), and (2,4) A. 5/2 B. 3/2 C. ½ D. 7/2 9. The cost per hour of running a boat is proportional to the cube of the speed of the boat. At what speed will the boat run against a current of 8kph in order to go a given distance most economically? A. 15kph B. 14kph C. 13kph D. 12kph 10. What is the unit vector which is orthogonal both to 9i+9j and 9i+9k? A.

B.

C.

D.

11. In polar coordinate system the distance from a point to the pole is known as A. Polar angle C. x-coordinate B. radius vector D. y-coordinate 12. N engineers and N nurses. If two engineers are replaced by nurses, 51% of the engineers and nurses are nurses. Find N. A. 100 B. 110 C. 50 D. 200

REGISTERED ELECTRICAL ENGINEERS PRE-BOARD EXAMINATION MARCH 2016 MATHEMATICS

13. If sinA= and cotB= 4, both in Quadrant III, the value of sin(A+B) is A. -0.844 B. 0.844 C. -0.922 D. 0.922 14. Two stores are 1 mile apart and are of the same level as the foot of the hill. The angles of depression of the two stores viewed from the top of the hill are 5 degrees and 15 degrees respectively. Find the height of the hill A. 109.01m B. 209.01m C. 409.01m D. 309.01m 15. A fair coin is tossed three times and it appeared always exactly three heads. Find the probability in a single toss it will appear head. A. ½ B. ¼ C. 1/6 D. 1/16 16. The product of the slopes of any two straight lines is negative 1, one of these lines are said to be A. Perpendicular B. parallel C. non intersecting D. skew 17. When two lines are perpendicular, the slope of one is A. Equal to the negative of the other B. equal to the other C. equal to the negative reciprocal of the other D. equal to the reciprocal of the other 18. A stalistic department is contacting alumni by telephone asking for donations to help fund a new computer laboratory. Past history shows that 80% of the alumni contacted in this manner will make a contribution of at least P50, 000. A random sample of 20 alumni is selected. What is the probability that more than 15 alumni will make a contribution of at least P50.00? A. 0.4214 B. 0.5890 C. 0.6296 D. 0.3018 19. If z1 =1-i , z2= -2+4i, z3= sqrt of 3-2i, evaluate Re(2z13+3z22-5z32) A. 35 B. 35i C. -35 D. -35i 20. Simplify (1-tan theta)/(1+tan theta) A. (cos theta+ sind theta)/(cos theta- sin theta) B. Cos theta/(cos theta-sin theta) C. (cos theta-sin theta)/(cos theta+sin theta) D. Sin theta/ (cos theta+sin theta) 21. A sinking ship makes a distance signal seen by three observers all 20m inland from the shore. First observer is perpendicular to the ship, second observer 100m to the right of the first observer and the third observer is 125m to the right of the first observer. How far is the ship from the shore? A. 60m B. 80m C. 100m D. 136.2m 22. A die and a coin are tossed. What is the probability that a three and a head will appear?

REGISTERED ELECTRICAL ENGINEERS PRE-BOARD EXAMINATION MARCH 2016 MATHEMATICS

A. ¼

B. ½

C. 2/3

D. 1/12

23. A tangent to a conic is a line A. Which is parallel to the normal B. Which touches the conic at only one point C. Which passes inside the conic D. All of the above 24. If tanA=1/3 and cotB=4 find tan(A+B) A. 11/7 B. 7/11 C. 7/12

D. 12/7

25. What would happen to the volume of a sphere if the radius is tripled? A. Multiplied by 3 C. multiply by 27 B. multiply by 9 D. multiply by 6 26. A container is in the form of a right circular cylinder with an altitude of 6in and a radius of 2in. If an asbestos of 1in thick is inserted inside the container along its lateral surface, find the volume capacity of the container. A. 12.57 cu. in B. 12.75 cu. in C. 18.58 cu. in D. 18.85 cu. In 27. Is it convergent or divergent? If convergent, what is the limit? A. Convergent, pi/2 C. convergent, pi B. divergent D. convergent, pi/4 28. If the sides of a right triangle is in arithmetic progression, what is the ratio of its sides? A. 1,2,3 B. 4,5,6 C. 3,4,5 D. 2,3,4 29. What is the area bounded by the parabola x2 = 8y and its latus rectum? A. 54/3 s.u. B. 8/3 s.u. C. 16/3 s.u. D. 31/3 s.u. 30. Find the general solution if y’’+10y=0 A. y = 𝐶1 cos(𝑠𝑞𝑟𝑡. 𝑜𝑓 10) 𝑥 + 𝐶2 sin(𝑠𝑞𝑟𝑡. 𝑜𝑓 10) 𝑥 B. y = 𝐶1 cos(𝑠𝑞𝑟𝑡. 𝑜𝑓 5) 𝑥 + 𝐶2 sin(𝑠𝑞𝑟𝑡. 𝑜𝑓 5) 𝑥 C. y = 𝐶 cos(𝑠𝑞𝑟𝑡. 𝑜𝑓 10) 𝑥 D. y = 𝐶 sin(𝑠𝑞𝑟𝑡. 𝑜𝑓 10) 𝑥 31. The volume of a cube becomes three times when its edge is increased by 1inch. What is the edge of a cube? A. 2.62 B. 2.26 C. 3.26 D. 3.62 32. The areas if a regular pentagon and a regular hexagon are equal to 12 sq.cm. What is the difference between their perimeters? A. 0.02 B. 0.03 C. 0.2 D. 0.3 33. Evaluate limxA. 4 B. 6

C. 8

D. 16

REGISTERED ELECTRICAL ENGINEERS PRE-BOARD EXAMINATION MARCH 2016 MATHEMATICS

34. The length of a rectangle is seven times of its width. If its perimeter is 72cm, find its width A. 3 B. 3.5 C. 4 D.15 35. A family’s electricity bill averages $80 a month for seven months of the year and $20 a month for the rest of the year. If the family’s bill were averaged over the entire year, what would the monthly bill be? A. $45 B. $50 C. $55 D. $60 36. In order to pass a certain exam, candidates must answer 70% of the last questions correctly. If there are 70 questions on the exam, how many questions be answered correctly in order to pass A. 46 B. 52 C. 56 D. 60 37. A firefighter determines that the length of hose needed to reach a particular building is 131m. If the available hoses are 47m long, how many sections of hose when connected together will it takes to reach the building? A. 3 B. 4 C. 5 D. 6 38. If the average person throws away 38.6 pounds of trash every day, how much trash would the average person throw away in one week? A. 270.2 pounds B. 207.2 pounds C. 290.6 pounds D. 209.6 pounds 39. If the csc2∅= 1+x, find cot2∅ A. X B. 1 + x

C. 1 – x

D. 𝑥2

40. A runner runs a circular track and a set of data is recorded: Time Distance 68 sec ----------------400m 114 sec ---------------600m 168 sec ---------------800m 209 sec ---------------1000m 256 sec ---------------1200m 322 sec ---------------1400m What is the average velocity from 68 sec to 168 sec? A. 3 𝑚/𝑠2 B. 4 𝑚/𝑠2 C. 8 𝑚/𝑠2 D. 𝟔 𝒎/𝒔𝟐 ? A. ½

B. ¼

C. 2/5

D. 5/2

42. Water is flowing into a conical vessel 10ft high and 2ft radius at the rate of 50 cu. Ft per minute. If the deep of the wateris 6ft, how fast is the radius increasing? A. 2.12 ft/min B. 12 ft/min C. 2.21 ft/min D. 11 ft/min

REGISTERED ELECTRICAL ENGINEERS PRE-BOARD EXAMINATION MARCH 2016 MATHEMATICS

43. A steel grinder 8m long is moved on rollers along a passageway 4m wide and into a corridor at right angles with the passageway. Neglecting the width of the girder, how wide must the corridor be? A. 3.6 m B. 1.4 m C. 1.8 m D. 2.8 m 44. If in the Fourier series of a periodic function, the coefficient a0 is zero, it means that the function has A. Odd symmetry C. odd-quarter wave symmetry B. Even quarter-wave symmetry D. any of the above 45. What is the general solution of (D4-1) y (t) = 0? A.𝑦 = 𝐶1𝑒𝑡 + 𝐶2𝑒−𝑡 + 𝐶3𝑐𝑜𝑠𝑡 + 𝐶4𝑠𝑖𝑛𝑡 C. 𝑦 = 𝐶1𝑒𝑡 + 𝐶2𝑒−𝑡 B. 𝑦 = 𝐶1𝑒𝑡 + 𝐶2𝑒−𝑡 + 𝐶3𝑡𝑒𝑡 + 𝐶4𝑡𝑒−𝑡 D. 𝑦 = 𝐶1𝑒𝑡 + 𝐶2𝑡𝑒−𝑡 46. Remy earns P10 an hour for walking the neighbor’s dog. Today she can only walk the dog for 45. How much will Remy make today? A. P10.00 B. P7.25 C. P7.60 D. P6.75 47. When a baby born the weighs 8 lbs. and 12 oz. After two weeks during his checkup he gains 8 oz. What is his weight now in lbs. and oz.? A. 8 lbs. and 10 oz. B. 9 lbs. and 4 oz. C. 9 lbs. and 2 oz. D.10 lbs. and 4 oz. 48. An equation of the form is A. An inequality B. an equality

C. a proportion

D. a ratio

49. Michael’s favorite cake recipe calls for 0.75 pounds of flour, he has a 5 pound bag. He wants to make several cakes for the school bake sale. How many cakes can he make? A. 5 B. 6 C. 7 D. 8 Solution: 5/0.75 = 6.67. the answer is 6 since .67 is equal only to 50.25 pound and not enough to make a single piece of cake. 50. Simplify (1+tan2x)/(1-tan2x) A. Sin 2x B. Cos 2x

C. Csc 2x

D. Sec 2x

51. 52. 53. Find the general solution of y’’+10y’+41y=0 A.𝑦 = 𝑒−5(𝐶1𝑐𝑜𝑠4𝑥 + 𝐶2𝑠𝑖𝑛4𝑥) C. 𝑦 = 𝑒−4(𝐶1𝑐𝑜𝑠5𝑥 +𝐶2𝑠𝑖𝑛5𝑥) B.𝑦 = 𝑒5(𝐶1𝑐𝑜𝑠4𝑥 + 𝐶2𝑠𝑖𝑛4𝑥) 54. Find the general solution of y’+ A. 𝑥2 + 2𝑦2 = 𝐶 B. 𝑥2 + 𝑦2 = 𝐶

D.𝑦 = 𝑒4𝑥(𝐶1𝑐𝑜𝑠5𝑥 +𝐶2𝑠𝑖𝑛5𝑥) C. 𝑥2 − 2𝑦2 = 𝐶 D. 𝑥2 − 𝑦2 = 𝐶

REGISTERED ELECTRICAL ENGINEERS PRE-BOARD EXAMINATION MARCH 2016 MATHEMATICS

55. Find the general solution of y’’-4y’+10y=sin x A. B. C. D. 56. Find the equation of the line that passes through (1,3) and tangent to the curve y= A. 4x+y-7=0 C. 4x-y+7=0

B. 24x+y-27=0 D. 24x-y+27=0

57. The ceiling in a hallway 10m wide is in the shape of a semi-ellipse and is 9m high in the center and 5m high at the side walls. Find the height of the ceiling 2m from either wall. A. 11.7 m B. 8.4 m C. 6.4 m D. 17.5 m 58. If in the Fourier series of a periodic function, the coefficient a 0=0 and a=0, then it must be having _____ symmetry. A. Odd B. Odd-quarter wave C. Even D. Either A or B 59. If the Fourier coefficient b0 of a periodic function is zero then it must possess ______ symmetry. A. Even B. Even-quarter-wave C. Odd D. Either A or B 60. Find the area of the region between the x-axis and y=(x-1)2 from x=0 to x=2 A. 1/3 B. 2/3 C. ½ D. ¼ 61. Find the slope of the line through the points (-2,5) and (7,1) A. 4/9 B. -4/9 C. 9/4 D. ¼ 62. A train is moving at the rate of 8mi/h along a piece of circular track of radius 2500 ft. Through what angle does it turn in 1min? A. 16 deg. 8 min. B. 15 deg. 6 min. C. 18 deg. 9 min. D. 17 deg. 10 min. 63. An artist wishes to make a sign in the shape of an isosceles triangle with a 42 degrees vertex angle and a base of 18m. What is the area of the sign? A. 109 sq. m B. 209 sq. m C. 112 sq. m D. 211 sq. m 64. If x2-y2=1 find y’’’ A. −2𝑥/𝑦5 B. 2𝑥/𝑦5

C. −𝑥/𝑦4

D. 𝑥/𝑦4

REGISTERED ELECTRICAL ENGINEERS PRE-BOARD EXAMINATION MARCH 2016 MATHEMATICS

65. A second hand scientific calculator was sold to Michael for P600. The original price of the item was P800. How many percent discount was given to him? A. 25 B. 35 C. 40 D. 20 66. Find the volume of a cube if its total surface area is 54 sq. cm. A. 21 cu. m B. 30 cu. m C. 27 cu. m D. 54 cu. M 67. A girl is flying a kite which is at a height of 120ft. The wind is carrying the kite horizontally away from the girl at a speed of 10ft/sec. How fast must be kite sizing be let out when the sizing is 150 feet long? A. 4 ft./s B. 5 ft./s C. 8 ft./s D. 6 ft./s 68. What is the solution set [2(x-1)-15] =7? A. {5} B. {12} C. {5,12} 69. If x:y:z= 2:-5:4 and x-3y+z=83, find x A. 6 B. 12 C. 3

D. {-5,12}

D. 4

70. Robert has 50 coins all in nickels and dimes amounting to $3.50. How many nickels does he have? A. 20 B. 30 C. 15 D. 35 71. The equation of the folium of Descartes is x2+y2=34xy. Find the area enclosed by the loop A.

B.

C.

D.

72. Find the acute angle of intersection of the curves x2+y2=5 and x2-y26x=15 A. 53.14 B. 52.13 C. 36.86 D. 37.87 73. For what value of k will the line kx+5y=2k have y-intercept 4? A. -10 B. 10 C. 9

D. -9

74. Find the volume formed by revolving the triangle whose vertices are (1,1),(2,4) and (3,1) about the line 2x-5y=10 A. 49 B. 94 C. 65 D. 56 75. A tank contains 760 liters of fresh water. Brine containing 2.5N/liter of salt enters the tank at 15 liter/min, and the mixture kept uniform by stirring runs out at 10liters/min. Find the amount of salt in the tank after 30 minutes? A. 1028.32 N B. 649.52 N C. 949.75 N D. 864.88 N 76. Find the volume of the solid generated when the region bounded by y=x24x+6 and y=x+2 is revolved about the x-axis A. 100.89 B. 104.60 C. 103.04 D. 101.79 77. The rate at which a body cools is proportional to the difference in temperature between it and the surrounding atmosphere. If in air at 60 deg. C a body

REGISTERED ELECTRICAL ENGINEERS PRE-BOARD EXAMINATION MARCH 2016 MATHEMATICS

cools from 90 deg. C to 80 deg. C in 10min, find its temperature 10 minutes later? A. 80 deg. C B. 73.3 deg. C C. 90 deg. C D. 64.4 deg. C 78. A sector of a circle has a central angle of 80 degrees and radius of 5m. What is the area of the sector? A. 16.5 sq. m B. 17.5 sq. m C. 15.8 sq. m D. 18.8 sq. m 79. A grocer bought a number of cans of corn for $14.40. Later the price increased 2 cents a can and as a result she received 24 fewer cans for the same amount of money. How many cans were in his first purchase? A. 142 B. 140 C. 144 D. 143 80. Find the area inside the cardiod r=1+costheta and outside the circle r=1. A. 2.79 B. 2.97 C. 3.98 D. 3.89 81. If 2log4x-log49=2, find the value of x A. 10 B. 12

C. 11

D. 9

82. If 7 coins are tossed together in how many ways can they fall with at most 3 heads? A. 63 B. 64 C. 65 D. 62 83. The eccentricity if the hyperbola having the rectangular equation 3x24y2-24x+16y+20=0 A. 1.12 B. 1.22 C. 1.32 D. 1.42 84. Find the slope of the tangent line to the parabola y2=4x+1 at the point (2,3) A. 1/3 B. 2/3 C. ¼ D. ¾ 85. If x=3t-1, y=1-3t^2, find d^2y/dx^2 A. -1/3 B. -2/3

C. -1

D. -4/3

86. Find the equation of the line through the point (3,4) which cuts from the first quadrant a triangle of maximum are A.4x+3y-24=0 C. 3x+4y-25=0 B.4x-3y+24=0 D. 3x-4y+25=0 87. Find the moment of inertia with respect to the y-axis of the plane area between the parabola y=2-x^2 and the x-axis A. 243/5 B. 234/5 C. 342/5 D. 324/5 88. A man drives 500ft along a road which is inclined 20 degrees to the horizontal. How high above the starting point is he? A. 171 ft. B. 182 ft. C. 470 ft. D. 162 ft. 89. An angle is 30 degrees more than one-half its complement. Find the angle A.20 degrees C. 60 degrees

REGISTERED ELECTRICAL ENGINEERS PRE-BOARD EXAMINATION MARCH 2016 MATHEMATICS

B.50 degrees

D. 75 degrees

90. How many ways can 5 keys be placed on a key ring? A. 8 B. 12 C. 20

D. 24

91. What is the diameter of a sphere for which its volume is equal to its surface area? A. 4 B. 6 C. 5 D. 7 92. Find the area of the triangle whose vertices are A(4,2,3) B(7,-1,4) and (3,-4,6) A. sqrt of 156 B. sqrt of 155 C. 13.5 D. 15.5 93. If the second term of a geometric progression is 6 and the fourth term is 64. How many terms must be taken for their sum to equal 242? A. 4 B. 6 C. 5 D. 7 94. Convert the point (r, , Φ) = (10, pi/2, 0) from spherical to Cartesian coordinates A. (10, 0, 1) B. (10, 1, 1) C. (10, 1, 0) D. (10, 0, 0) 95. The probability that A can solve a given problem is 4/5 that B can solve it is 2/3 and that C can solve it is 3/7. If all three try, compute the probability that the problem will be solved. A. 101/305 B. 101/105 C. 102/305 D. 102/105 96. A club of 40 executives, 33 like to smoke Marlboro, and 20 like to smoke Philip Morris. How many like to smoke Philip Morris only? A. 33 B. 13 C. 20 D. 7 97. Find the value of 4 sinh (pi i/3) A. -2i (sqrt of 3) C. -4i (sqrt of 3) B. 2i (sqrt of 3) D. 4i (sqrt of 3) 98. An equilateral triangle has an altitude of 5(sqrt of 3) cm long. Find the area in sq. m. A. 5(sqrt of 3) C. 100(sqrt of 3) B. 25(sqrt of 3) D. 50(sqrt of 3) 99. The line y = 3x + b passes through the point (2, 4). Find b. A. 2 B. 10 C. -2 D. 10 100. If f(x) = sinx and f(pi) = 3 then f(x) =

REGISTERED ELECTRICAL ENGINEERS PRE-BOARD EXAMINATION AUGUST 2016 MATHEMATICS

1. What is the area of the largest rectangle that can be inscribed in an ellipse with equation 4x˄2+y˄2=4? A. 3 B. 4 C. 2 D. 1 2. Sand is pouring to form a conical pile such that its altitude is always twice its radius. If the volume of a conical pile is increasing at rate of 25pi cu. Ft/min, how fast is the radius is increasing when the radius is 5 feet? A. 0.5 ft./min B. 0.5pi ft./min C. 5ft./min D. 5pi ft./min 3. An air balloon flying vertically upward at constant speed is suited 150m horizontally from an observer. After one minute, it is found that the angle of elevation from the observer is 28 deg 59 min. what will be then the angle of elevation after 3 minutes from its initial position? A. 63 deg 24 min B. 58 deg 58 min C. 28 deg 54 min D.14 deg 07 min 4. A machine only accepts quarters. A bar of candy cost 25ȼ, a pack of peanuts cost 50ȼ and a bottle of a coke cost 75ȼ. If Marie bought 2 candy bars, a pack of peanuts and a bottle of coke, how many quarters did she pay? A. 5 B. 6 C. 7 D. 8 5. A ball is dropped from a height of 18 m. On each rebound it rises 2/3 of the height from which it last fell. What is the total distance it travels in coming to rest? A. 80m B. 90m C. 72 m D. 86 m 6. Evaluate lim (𝑥 + 4 sin 𝑥) 𝑥→13𝑝𝑖

A. 2

B. 1

C. -1

D. 0

7. Find the length of the arc of the parabola x˄2=4y from x= ˗2 to x= 2. A. 4.2 B. 4.6 C. 4.9 D. 5.2 8. Find the coordinates of the centroid of the plane area bounded by the parabola y=4 - x˄2 and the x-axis. A. (0,1.5) B. (0,1) C. (0,2) D. (0, 1.6) 9. In how many ways can you pick 3 dogs from a pack of 7 dogs? A. 32 B. 35 C. 30 D. 36 10. In how many ways can 4 coins be tossed? A. 8 B. 12 C. 16

D. 20

11. Which of the following is not multiple of 11? A. 957 B. 221 C. 122

D. 1111

12. A certain rope is divided into 8 m, 7 m, 5 m. What is the percentage of 5 m with the original length?

REGISTERED ELECTRICAL ENGINEERS PRE-BOARD EXAMINATION AUGUST 2016 MATHEMATICS

A. 20

B. 15

C. 10

D. 25

13. Nannette has a ribbon with a length of 13.4 m and divided it by 4. What is the length of each part? A. 3.35 m B. 3.25 m C. 3.15 m D. 3.45 m 14. The area in the second quadrant of the circle x˄2 + y˄2 = 36 is revolved about the line y+ 10 = 0. What is the volume generated? A. 2208.53 B. 2218.33 C. 2228.83 D. 2233.48 15. It represents the distance of a point from the y-axis. A. Abscissa B. Ordinate C. Coordinate D. Polar distance 16. In polar coordinate system, the polar angle is negative when; A. Measured counterclockwise C. measured at the terminal side of ϴ B. Measured clockwise D. none of these 17. A coin is tossed in times. If it is expected that 7 heads will occur, how many times the coin is tossed? A. 12 B. 14 C. 16 D. 10 18. A long piece of galvanized iron 60 cm wide is to be made into a trough by bending up two sides. Find the width of the sides of the base if the carrying capacity is maximum? A. 30 B. 20 C. 40 D. 50 19. Totoy is 5 ft. 11 in. Nancy is 6 ft. 5 in. What is the difference in their height? A. 5 in B. 6 in C. 7 in D. 8 in 20. 5 years-old Tomas can tie his shoelace in 1.5 min and his right shoelace in 1.6 min. How long will it take him to tie both shoe lace? A. 2.9 min B. 3 min C. 3.1 min D. 3.2 min 21. The area enclosed by the ellipse 4x˄2+9y˄2 = 36 is revolved about the line x = 3, what is the volume generated? A. 370.3 B. 360.1 C. 355.3 D. 365.1 22. The equation y² = cx is the general solution of A. y’= 2y/x B. y’= 2x/y C. y’= y/2x

D. y’= x/2y

23. Solve the differential equation y’=y/2x. A. y= cx B. y˄2= cx

D. y˄3= cx

C. y= cx˄2

24. In a school, 30 percent of students are involved in athletics. 15 percent of these play football. What percent of the student in the school play football? A. 4.5 B. 15 C. 5.4 D. 30

REGISTERED ELECTRICAL ENGINEERS PRE-BOARD EXAMINATION AUGUST 2016 MATHEMATICS

25. Find the point along the line x = y = z that is equidistant from (3, 0, 5) and (1, 1, 4). A. (1, 1, 1) B. (2, 2, 2) C. (3, 3, 3) D. (4, 4, 4) 26. Which of the following is divisible by 6? A. 792 B. 794

C. 790

D. 796

27. The cost of operating a vehicle is given by C(x) = 0.25x + 1600, where x is in miles. If Jam just bought a vehicle and plan to spend between P5350 to P5600. Find the range of distance she can travel. A.14000 to 15000 B. 15000 to 16000 C. 16000 to 17000 D. 13000 to 14000 28. A 20-ft lamp casts a 25 ft. shadow. At the same time, a nearby building casts a 50 ft. shadow. How tall is the building? A. 20 ft. B. 40 ft. C. 60 ft. D. 80 ft. 29. Three circle of radii 3, 4, and 5 inches, respectively, are tangent to each other externally. Find the largest angle of a triangle found by joining the centers of the circle. A. 72.6 degrees B. 75.1 degrees C. 73.4 degrees D. 73.5 degrees 30. Simplify the expression cos²ϴ-sin²ϴ A. cos 2ϴ B. sin 2ϴ

C. sin 2ϴ

D. sec 2ϴ

31. csc 520º =? A. Cos 20º

C. sin 20º

D. sec 20º

B. csc 20º

32. Simplify x/(x – y) + y/(y –x). A. -1 B. 1 cos 𝐴 33. Simplify 1−sin 𝐴 − tan 𝐴. A. csc A B. sec A

C. x C. sin A

D. y D. cos A\

34. Find the minimum distance from the point (4, 2) to the parabola y² = 8x. A. 3 sqrt. of 3 B. 2 sqrt. of 3 C. 3 sqrt. of 2 D. 2 sqrt. of 2 35. From the past experience, it is known 90 percent of one year old children can distinguish their mother’s voice of a similar sounding female. A random sample of one year’s old are given this voice recognize test. Find the standard deviation that all 20 children recognize their mother’s voice? A. 0.12 B. 1.34 C. 0.88 D. 1.43 36. An equilateral triangle is inscribed in the parabola x² = 8y such that one of its vertices is at the origin. Find the length of the side of the triangle. A. 22.51 B. 24.25 C. 25.98 D. 27.71

REGISTERED ELECTRICAL ENGINEERS PRE-BOARD EXAMINATION AUGUST 2016 MATHEMATICS

37. Mary’s father is four time as old as Mary. Five years ago he was seven times as old. How old is Mary now? A. 8 B. 9 C. 11 D.10 38. The lateral area of a right circular cylinder is 77 sq. cm. and its volume is 231 cu. cm. Find its radius. A. 4 cm B. 5 cm C. 6 cm D. 7 cm 39. A weight of 60 pounds rest on the end of an 8-foot lever and is 3 feet from the fulcrum. What weight must be placed on the other end of the lever to balanced 60 pound weight? A. 36 pounds B. 32 pounds C. 40 pounds D. 42 pounds 40. The average of six scores is 83. If the highest score is removed, the average of the remaining scores is 81.2. Find the highest score. A. 91 B. 92 C. 93 D. 94 41. A point moves on the hyperbola x²- 4y² = 36 in such a way that the x-coordinate increase at a constant rate of 20 unit per second. How fast is the y-coordinate changing at a point (10, 4)? A. 30 units/sec C. 30 units/sec B. 30 units/sec D. 30 units/sec 42. If the tangent of angle A is equal to the square root of 3, angle A in the 3rd quadrant, find the square of the tangent A/2. A. 2 B. 3 C. 4 D. 5 43. A stone, projected vertically upward with initial velocity 112 ft./sec, moves according to s = 112t – 16t², where s is the distance from the starting point. Compute the greatest height reached. A. 196 ft. B. 100 ft. C. 96 ft. D. 216 ft. 44.) A cylinder of radius 3 is cut through the center of the base by a plane making an angle of 45 degrees with the base. Find the volume cut off. A. 15 B. 16 C. 17 D. 18 45.) Find the diameter of a circle with the center at (2, 3) and passing through the point (-1, 5). A. 3.6 B. 7.2 C.13 D. 16 46.) Find the value of x for which the tangent to y = 4x-x² is parallel to the x-axis. A. 2 B. -1 C. 1 D. -2 47. Find the surface area generated by rotating the parabolic arc about the x-axis from x = 0 to x = 1. A. 5.33 B. 4.98 C. 5.73 D. 4.73

REGISTERED ELECTRICAL ENGINEERS PRE-BOARD EXAMINATION AUGUST 2016 MATHEMATICS

48. A group of students plan to pay equal amount in hiring a vehicle for an excursion trip at a cost of P 6, 000. However, by adding 2 more students to the original group, the cost of each student will be reduced by P 150. Find the number of each students in the original group. A. 10 B. 9 C. 8 D. 7 49. What is the allowable error in measuring the edge of the cube that is intended to hold 8 cu. m., if the error of the computed volume is not to exceed 0.03 cu.m. A. 0.002 B. 0.003 C. 0.0025 D. 0.001 50. Find the value of x for which y = 2x³- 9x² + 12x – 2 has a maximum value. A. 1 B. 2 C. -1 D. -2 51. At a height of 23,240 ft., a pilot of an airplane measures the angle of depression of a light at an airport as 28 deg 45 min. How far is he from the light? A. 20,330 ft. B. 26,510 ft. C. 11, 180 ft. D. 48, 330 ft. 52. A substance decreases at a rate which is inversely proportional to the amount present. If 12 units of the substance are present initially and 8 units are present after 2 days, how long will it take the substance to disappear? A. 1.6 days B. 2.6 days C. 3.6 days D.4.6 days 53. A tower 150m high is situated at the top of a hill. At a point 650m down the hill, the angle between the surface of the hill and the line of sight to the top of the tower is 12 deg 30 min. Find the inclination of the hill to a horizontal plane. A. 7 deg 50 min B. 20 deg 20 min C. 77 deg 30 min D. 12 deg 55 min 54. A telephone company has a profit of $80 per telephone when the number of telephones in exchange is not over 10,000. The profit per telephone decreases by $0.40 for each telephone over 10, 000. Find the numbers of telephone that will yield the largest possible profit. A. 13,000 B. 14,000 C. 15,000 D. 16,000 55. Find the work done in moving an object along the vector a = 3i + 4j if the force applied is b = 2i +j. A. 11.2 B. 10 C. 12.6 D. 9 56. A man is paid P 1, 800 for each day he works and forfeits P 300 for each day he is idle. If at the end of 40 days, he nets P 53, 100, how many days was he idle? A. 6 B. 7 C. 8 D. 9 57. By stringing together 9 differently color beads, how many different bracelets can be made? A. 362,880 B. 20,160 C. 40,320 D. 181,440 58. In a circle of diameter 26 cm, a chord 10 cm in length is drawn. How far is the chord from the center of the circle?

REGISTERED ELECTRICAL ENGINEERS PRE-BOARD EXAMINATION AUGUST 2016 MATHEMATICS

A. 5 cm

B. 12 cm

C. 13 cm

D. 24 cm

59. Find the slope of the line passing through the pair of points (-2, 0) and (3, 1). A. 1/3 B. 1/4 C. 1/6 D. 1/5 60. Find the inverse of the function f(x) = sqrt. of (2x – 3). A.sqrt. of (2y-3) B. 1/ sqrt. Of (2x-3) C. ½(x2+3) D. ½ (y2+3) 61. If f (3) =7, f’ (3) = -2, g (3) =6 and g’ (3) = -10, find the (g/f)’ (3). A. -82/49 B. -49/82 C. -49/58 D. -58/49 62. The length of the median drawn the hypotenuse of a right triangle is 12 inches. Find the length of the hypotenuse. A. 24 in B. 20 in C. 23 in D. 25 in 63. Find the derivative of the function y = 3/(x²+ 1). A. 6x/(x2+1)2 B.6x(x2+1)2 C. -6x/(x2+1)2

D.-6x(x2+1)2

64. A passenger in a helicopter shines a light on a car stranded 45 ft from a point just below the helicopter is hovering at 85 ft, what is the angle of depression from the light source to the car? A. 82 degrees B. 80 degrees C. 60 degrees D.62 degrees 65. Find the area bounded by the curve r = 8 cos ѳ. A. 50.27 B.12.57 C. 8

D. 67.02

66. If 2log4x – log49 = 2, find the value of x. A. 10 B. 12

C. 11

D. 9

67. Find the value of 2 cos (pii/4). A. 1.41 B. 1.41i

C. 2.65

D. 265i

68. A pole is on top of a building. At a point 240 meters from the base of the building, the angle of elevation of the base and top of the pole are 42 degrees and 44 degrees respectively. Find the height of the pole. A. 15.8m B. 18.5m C. 16.9m D. 19.6m 69. The volume of a hemisphere of radius 2 m is A.14.67 cu.m B.67.04cu.m C.16.76cu.m

D.33.53cu.m

70. Five scores and 4 years is equivalent to how many years? A. 49 B. 29 C. 54

D. 104

71. Find the equation of one of the asymptotes of the hyperbola 𝑥 2 − 4𝑦 2 − 6𝑥 − 8𝑦 + 1 = 0. A. x – 2y – 5 = 0 B. x – 2y + 5 = 0 C. x – 2y – 1 = 0 D. x – 2y + 1 = 0

REGISTERED ELECTRICAL ENGINEERS PRE-BOARD EXAMINATION AUGUST 2016 MATHEMATICS

72. The wheel of a truck is turning at 6 rps. The wheel s 4 ft in diameter. Find the linear velocity iin fps point on the rim of the wheel. A.75.4 B.57.4 C.150.8 D.105.8 73. Solve the inequality 3 – 2x < 4x -5. A. x < 4/3 B. x > 4/3

C. x < ¾

D. x > ¾

74. The polynomial 𝑥 2 + 4𝑥 + 4 is the area of a square floor. What is the length of its side? A. x + 2 B. x – 2 C. x + 1 D. x – 1 75. If there are 2 computers for every 4 students, how many computers are needed .For 60 students? A.24 B.26 C.30 D.32 76. From Pagasa island in the Spratlys, two helicopters travel to two different islands.One helicopter travels 185 km N 65 deg E to island A and the other travels at S 25 deg E for 120 km to island B. What is the distance between the two islands? A. 198.5 km B. 187.3 C. 235.2 D. 202.5 77. If x = y + 2, what is the value of (𝑥 − 𝑦)4 ? A. 10 B. 16 C. 18

D. 24

78. An equilateral triangle has sides of 8 inches. What us the height? A. 6.32 in B. 6.93 in C. 5.66 in D. 6.56 in 79. If in the Fourier series of a periodic function, the coefficient 𝑎0 = 0 and 𝑎𝑛 = 0, then It must be having ____________ symmetry. A. odd B. odd quarter-wave C. even D. either A or B 80. Find the area of the triangle whose vertices are (4,2,3), (7,-2,4) and (3,-4, 6). A. 15.3 B. 13.5 C. 12.54 D. 12.45 81. Find the moment of inertia of the area bounded by the curve 𝑥 2 = 8𝑦, the line x =4 and the x-axis on the first quadrant with respect to y-axis. A.25.6 B. 21.8 C. 31.6 D. 36.4 82. If 8 oranges cost Php 96, how much do 1 dozen at the same rate? A. Php 144 B. Php 124 C. Php 148 D. Php 168 83. A particle moves in simple harmonic in accordance with the equation s = 3sin 8pit + 4cos 8 pit, where s and t are expressed in feet and seconds, respectively. What is the amplitude of its motion? A. 3ft B. 4ft C. 5ft D. 8ft 84. If z1 = 1 – i and z2 = -2 +4i, evaluate z12 + 2z1 – 3. A. -1 +4i B. 1 – 4i C. 1 + 4i

D. -1 – 4i

REGISTERED ELECTRICAL ENGINEERS PRE-BOARD EXAMINATION AUGUST 2016 MATHEMATICS

85. Identify the property of real numbers being illustrated: x + (y + z) = (x + y) + z A. Commutative Property of Addition C. Associative Property of Addition B. Commutative Property of MultiplicationD. Associative Property of Multiplication 86. The distance between -9 and 19 on the number line is A. 28 B. -28 C. 10 𝑎

D. -10

𝑎

87. If the function f is odd and ∫0 𝑓(𝑥)𝑑𝑥 = 5m – 1, then ∫−𝑎 𝑓(𝑥)𝑑𝑥 = A. 0 B. 10m – 2 C. 10m – 1 D. 10m 88. Find the mass of a 1.5-m rod whose density varies linearly from 3.5 kg/m from end to end A. 3.5 kg B. 2.5kg C. 4.5kg D. 5.0kg 89. Find the area bounded by the parabola y = x2, the tangent line to the parabola at the point (2, 4) and the x axis. A. 9/2 B. 2/3 C. 8/5 D. 9/4 90. Find the coordinates of an object that has been displaced from the point (-4, 9) by the vector (4i – 5j) A. (0, 4) B. (0, -4) C. (4, 0) D. (-4, 0) 91. Find the major axis of the ellipse x2 +4y2 -2x – 8y + 1 = 0. A. 2 B. 10 C. 4

D. 6

92. A car travels 90kph. What is its speed in meter per second? A. 43 B. 30 C. 25

D. 50

93. The vertices of the base of the isosceles triangle are (1, -2) and (1, 4). If the third vertex lies on the line 4x + 3y = 12. Find the area of the triangle. A. 8 B. 15 C. 12 D. 10 94. Assume that f is a liner function. If f(4) = 10 and f(7) = 24, find f(100). A.98 B. 144 C. 576 D.458 95. The line y = 3x +b passes thru the point (2, 4). Find b. A. 2 B. 10 C. -2

D. -10

96. How far is the directrix of the parabola (x - 4)2 = -8(y - 2) from the x-axis? A. 2 B. 3 C. 4 D. 1 97. Find the second derivate of y = xlnx. A. x B. 1/x

C. 1

D. x2

98. Find the point where the normal to y = x + x1/2 at (4, 6) crosses the y-axis. A. 5.75 B. 9.2 C. 23 D. 11

REGISTERED ELECTRICAL ENGINEERS PRE-BOARD EXAMINATION AUGUST 2016 MATHEMATICS

99. There are four geometric mean between 3 and 729. Find the sum of the geometric progression. A. 1092 B. 1094 C. 1082 D. 1084 100. Find the area of a circle inscribed in a rhombus whose perimeter is 100 inches and whose longer diagonal is 40 inches. A. 364. 43 sq. in C. 452. 39 sq. in. B.590. 62 sq. in. D. 389. 56 sq. in.

REGISTERED ELECTRICAL ENGINEERS PRE-BOARD EXAMINATION MARCH 2015 MATHEMATICS

1. Sand is pouring to from a conical pile such that its radius is always twice its height. If the volume of a conical pile is increasing at the rate of 2 cu. m/sec. how fast is the height is increasing when the height is 4m? A. 1/16pi m/s B. 1/32 pi m/s C. 1/64 pi m/s D. 1/8 pi m/s 2. A triangular corner lot has perpendicular sides of lengths 90 m and 60 m. find the dimension of the largest rectangular building that can be constructed on the lot with sides parallel to the streets. A. 30 m x 30 m B. 24 m x 24 m C. 25 m x 40 m D. 45m x 30 m 3. Joy is 10% taller than Joseph and Joseph is 10% taller than Tom. How many percent is Joy taller than Tom? A. 18% B. 20% C. 21% D. 23% 4. What is the length of the shortest line segment in the first quadrant drawn tangent to the ellipse b2 x2 + a2 y2 = a2 b2 and meeting to the coordinate axes? A. a/b B. a + b C. ab D. b/a 5. What is the area of largest rectangle that can be inscribed in an ellipse with equation 4x^2+y^2=4? A. 3 B. 4 C. 2 D. 1 6. A company hires 30 new employees today. It increases their workforce by 5%. How many workers now? A. 610 B. 600 C. 630 D. 620 7. Find the radius of the circle inscribed in the triangle determined by the lines y=x+4, y=-x-4 and y=7x-2. A.5/sqrt of 2 B. 5(2sqrt of 2) C. 3/R D. 3/(2sqrt of 2) 8. What is the ratio of the surface area of a sphere to its volume? A. 5/R B. 4/R C. 3/R D. 2/R 9. Using original diameter, d, what is the new diameter when the volume of the sphere is increased 8 times? A. 2d B.3d C.4d D. 5d 10. In a hotel it is known that 20% of the total reservation will be cancelled in the last minute. What is the probability that there will be less than 2 reservations cancelled out of 4 reservations? A. 0.6498 B. 0.5629 C. 0.3928 D. 0.4096 11. Find the area of the region inside the triangle with vertices (1,1), (3,2) and (2,4) A. 5/2 B. 3/2 C. ½ D. 7/2 12. The three sides of trapezoid are each 10m long. How long must the fourth side be to make the area a maximum?

REGISTERED ELECTRICAL ENGINEERS PRE-BOARD EXAMINATION MARCH 2015 MATHEMATICS

A. 20m 13. Simplify i^39 A.1

B. 50m

C. 52m

D. 45m

B. -1

C. i

D. -i

14. What is the value of x in Arc tan 3x+Arc tan2x= 45deg? A. -1/6 and 1 B. 1/6 and -1 C. 1/6

D. -1

15. Find the moment of inertia of the area bounded by the parabola y^2=4x and the line x=1 with respect to the x-axis A. 2.133 B. 1.333 C. 3.333 D. -1 16. The cost per hour of running a boat is proportional to the cub of the speed of the boat. At what speed will the boat run against a current of 8 kph in order to go a given distance most economically? A. 15kph B. 14kph C. 13kph D. 12kph 17. What is the unit vector which is orthogonal both to 9i+9j and 9i+9k? A. i/sqrt3+i/sqrt3+k/sqrt3 B. i/sqrt3+jsqrt3+k/3 C. i/sqrt3-jsqrt3- ksqrt3 18. A train running at 60 kph decelerated at 2.5m/min 2 for 12 minutes. Find the distance traveled in km within the period. A. 1.182 B. 11.82 C. 1.812 D. 2.282 19. A conic section whose eccentricity is less than one (1) is known as: A. A parabola B. an ellipse C. a circle D. a hyperbola 20. A transmitter with a height of 15m is located on top of a mountain whis is 3.0 km high. What is the farthest distance on the surface of the earth that can be seen from the top of the mountain? Take the radius if the earth to be 6400 km. A. 225km B.152km C.196km D. 205km 21. A political scientist asked a group of people how they felt about two political policy statements. Each person was to respond A (agree) (N) neutral or (D) disagree to each NN, NA, DD, DN, DA, AA, AD and AN. Assuming each response combination is equally likely, what is the probability that the person being interviewed agrees with exactly one of the political policy statements? A. 1/9 B. 2/5 C. 2/9 C. 4/9 22. Evaluate Laplace transform of t^n A. n!/s^n B. n!/s^(n+1)

C. n!/s^(n-1)

D. n! s^(n+2)

23. Find the area of a quadrilateral having vertices at (2,-1), (4.3), (-1,2) and (-3,2) A. 16 B. 18 C. 17 D. 14 24. In a 15 multiple choice test questions with five possible choices of which only one is correct, what is the standard deviation of getting a correct answer?

REGISTERED ELECTRICAL ENGINEERS PRE-BOARD EXAMINATION MARCH 2015 MATHEMATICS

A. 1.55

B. 1.07

C. 1.50

D. 1.65

25. In polar coordinate system the distance from a point to the pole is known as: A. Polar angle B. radius vector

C. x- coordinate

D. y-coordinate

26. Evaluate Laplace transform of cos2kt. A. s/s(s2 -2k2 ) B. s/(s2+2k2)

C. s/(s2-4k2)

27. Find the power series of tan-1 (t2) A. T2+t6/2 +t12/6 +t24/12+… B. T2 - t6/2 + t12/6 – t24 /12+…

C. t2+t6/3+t10/5+t14/7+… D. t2-t6/3+t10/5-t14/7+…

28. Simplify (1+tanx)/(1-tanx) A. Sec x + tan x B. cos x + tan x

C. cos 2x+ tan 2x

D. s/(s2+4k2)

D. sec 2x+tan 2x

29. Evaluate lim x+4/x-4 as x approaches to infinity A. 1 B. 0 C. 2

D. infinite

30. It represents the distance of a point from the y-axis A. Ordinate B. coordinate C. abscissa

D.polar distance

31. A and B can do piece of work is 5 days, B and C in 4 days while A and C in 2.5days in how many days can all of them do the work together? A. 40/11 B. 30//11 C. 30/17 D. 40/17 32. Chona the golden retriever gained 5.1 pounds is one month. She weights 65.1 pounds now. What is the percent weight gain of Chona in one month? A. 7.3% B. 8.2% D. 7.8% D. 8.5% 33. What is the center and radius of a circle with an equation x2+y2-1/4x-1/4y=1/64? A. C (1,1/2) R=4 B. C(1,1), R=sqrt5/9 C. C(1/2-1/2 R=sqrt2/5 D. C (1/8, 1/8) R=sqrt 3 34. A machine only accepts quarters. A bar of candy cost 25c a pack of peanuts cost 50c and the bottle of coke cost 75c. If Marie bought 2 candy bars a pack of peanut and a bottle of coke how many quarters did she pay? A. 5 B. 6 C.7 D. 8 35. Solve for x and y in xy +8+j (x2y+y)=4x+4+j(xy2+x) A. 2, 2 B. 2,3 C. 3,1

D. 3,4

36. There are a set of triplets. If there are 11 generations how many ancestors do they have if duplication is not allowed? A. 4095

B. 4065

C.59,049

D. 265,719

REGISTERED ELECTRICAL ENGINEERS PRE-BOARD EXAMINATION MARCH 2015 MATHEMATICS

37. Carmela and Marian were hired on a summer job. Each of them work 15 hours a week. Carmela was absent for one week and Marian has to take her shift. If they work for 8 weeks, what is the total number of hours did Marian works? A. 120 B. 135 C. 67.5 D. 60 38. From the top of a building the angle of depression of the floor of a pole is 48 deg 10min. from the foot of a building the angle of elevation of the top is 18 deg 50 min, both building and pole are on a level ground. If the height of a pole is 4m, how high is the building? A. 13.10m B. 12.10 C. 10.90 D. 11.60 39. The towers of a parabolic suspension brindge 300m long are 60 m high and the lowest point of a cable is 20m above the roadway. Find the vertical distance from the roadway to the cable at 100m from the center A. 17.78 B.37.78 C.12.86 D. 32.86 40. Find the centroid of the plane area bounded by the parabola y=4-x^2 and the x-axis A. (0 3/2) B. (0,1) C. (0 , 12/5) D. (0,8/5) 41. Evaluate the double integral 1/(x-y) dxdy with inner bounds of 2y to 3y and outer bounds of 0.2. A. Ln3 B. ln4 C. ln2 D ln8 42. Write the equation of a line with x-intercepts a=8 and y intercept b=-1 A. 8x+y-8=0 B. 8x-y+8=0 C. 8x+y+8=0 D. 8x-y-8=0 43. Solver for x; 125x-5=5x-4 A. 21/2 B. 15/2

C. 17/2

D. 19/2

44. Find the ration of the surface area of a cube to its volume if the side is s. A. 21/2 B. 15/2 C. 17/2 D.5/s 45. Solve the equation y” = y/2x A. Y^2=cx^3 B. y=cx^2

C. y^2=cx

D. y=cx

46. The sum of the first 7 terms of an A.P is 98 and the sum of the first 12 terms is 288. Find the sum of the first 20 terms A. 980 B. 800 C. 880 D. 980 47. When the sun is 20 degrees above the horizon, how long is the shadow cast by a building 150 ft high? A. 550 ft B. 580ft C. 405ft D. 450ft 48. A central angel of a circle of radius 30 in intercepts an arc of 6 in is how many radian? A. 1/3 B. 1/5 C. ¼ D. ½

REGISTERED ELECTRICAL ENGINEERS PRE-BOARD EXAMINATION MARCH 2015 MATHEMATICS

49. A, B and C work independently on a problem. If the respective probabilities that they will solve it are ½, 1/3, 2/5 find the probability that the problem will be solved. A. 1/5 B. 2/5 C. 3/5 D. 4/5 50. A car goes 14kph faster than a truck and requires 2 hours and 20 minutes less time to travel 300km. Find the rate of the car. A. 40kph B. 50kph C. 60kph D. 70kph

REGISTERED ELECTRICAL ENGINEERS PRE-BOARD EXAMINATION AUGUST 2015 MATHEMATICS

1. Given a conic section, if B2 - 4AC = 0, it is called? A. Circle B. Parabola C. Hyperbola

D. Ellipse

2. Given a conic section, if B2 - 4AC > 0, it is called? A. Circle B. Parabola C. Hyperbola

D. Ellipse

3. Describe and graph the locus represented by lm{z2} = 4. A. Circle B. Parabola C. Hyperbola

D. Ellipse

4. A tangent to conic is a line A. which is parallel to the normal B. which touches the conic at only one point C. which passes inside the conic D. all of the above 5. All circle having the same center but with unequal radii are called A. encircle B. tangent circles C. concyclic D. concentric circles 6. If z = 6eiπ/3, evaluate |eiz|, A. e-3(sqrt. of 3) B. e3(sqrt. of 3)

C. e-2(sqrt. of 2)

D. e2(sqrt. of 2)

7. Simply (cosβ - 1)(cosβ + 1) A. -1/sin2 β B. -1/cos2 β

C. -1/csc2 β

D. -1/sec2 β

8. Find the height of a right circular cylinder of maximum volume which can be inscribed in a sphere of radius 10 cm. A. 11.55 cm B. 14.55 cm C. 12.55 cm D. 18.55 cm 9. A bus leaves Manila at 12 NN for Baguio 250 km away, traveling an average of 55 kph. At the same time, another bus leaves Baguio for Manila traveling 65 kph. At what distance from manila they will meet? A. 135.42 km B. 114.58 km C. 129.24 km D. 120.76 km 10. A waiter earned tips for a total of $17 for 4 consecutive days. How much he earned per day? A. $4.25 B. $4.50 C. $3.25 D. $3.50 11. What is the value of x in Arctan 2x + Arctan x = pi/4 ? A. 0.28 and -1.78 B. -0.28 and 1.78 C. 0.28

D. -1.78

12. The length of the latus rectum of the parabola y2 = 4px is: A. 4p B. 2p C. p

D.-4p

REGISTERED ELECTRICAL ENGINEERS PRE-BOARD EXAMINATION AUGUST 2015 MATHEMATICS

13. A post office can accept for mailing only if the sum of its length and its girth (the circumference of its cross section) is at most 100 in. What is the maximum volume of a rectangular box with square cross section that can be mailed? A. 5432.32in3 B. 1845.24in3 C. 2592.25in3 D. 9259.26in3 14. Water is running out of a conical funnel at the rate of 1 cu. In/sec. If the radius of the base of the funnel is 4 in. and the altitude is 8 in, find the rate at which the water level is dropping when it is 2 in. from the top. A. -1/9pi in/sec B. -1/2pi in/sec C. 1/2pi in/sec D. 1/9pi in/sec 15. A ball is dropped from a height of 18m. On each rebound it rises 2/3 of the height from which it last fell. What distance has it traveled at the instant it strikes the ground for the 5th time? A. 37.89 m B. 73.89 m C. 75.78m D. 57.78 m 16. 3 randomly chosen senior high school students was administered a drug test. Each student was evaluated as positive to the drug test (P) or negative (N). Assume the possible combinations of the three student’s drug test evaluation as PPP, PNP, NPN, NNP, NNN. Assuming each possible combination is equally likely, what is the probability that all 3 students get positive results? A. 1/8 B. 3/4 C. 1/4 D. 1/2 17. The cost per hour of the running the boat is proportional to the cube of the speed of the boat. At what speed will the boat run against a current of 4 kph in order to go a given distance most economically? A. 6 kph B. 12 kph C. 20 kph D. 24 kph 18. Ben is two years away from being twice Ellen’s age. The sum of Ben’s age and thrice Ellen’s age is 66. Find Ben’s age now. A. 19 B. 20 C. 18 D. 21 19. The cable of suspension bridge hangs in the form of a parabola when the load is uniformly distributed horizontally. The distance between towers is 150 m, the points of the cable on the towers are 22m above the roadway, and the lowest point on the cable is7 m above the roadway. Find the vertical distance to the cable form a point in the roadways 15m from the foot of a tower. A. 16.6 m B. 9.6 m C. 12.8 m D.18.8 m 20. If z is directly proportional to x and inversely proportional to the square of y and that y= 2 when z=4 and x= 2. Find the value of z when x= 3 and y=4. A. 2/3 B. 3/2 C.3/4 D.4/3 21. Find a∙b if lal = 26 and lbl =17 and the angle between them is pi/3. A. 221 B. 212 C. 383 D.338 22. The side of a square is 5 cm less than the side of the other square. If the difference of their areas is 55cm2, what is the side of the smaller square? A. 3 B. 4 C. 5 D. 6

REGISTERED ELECTRICAL ENGINEERS PRE-BOARD EXAMINATION AUGUST 2015 MATHEMATICS

23. The area bounded by the curve y2= 12x and the line x= 3 is revolved about the line x= 3. What is the volume generated? A. 186 B. 179 C. 181 D. 184 24. Evaluate the integral of (sinx) raised to the 6th power and the limits from 0 to pi/2. A. 0.49087 B. 0.48907 C. 0.96402 D. 0.94624 25. How many ounces will she make to serve 25 half-cup? A. 25 B. 50 C. 12.5

D. 75

26. Two engineers facing each other with a distance of 5km from each other, the angles of elevation of the balloon from the two engineers are 56 degrees and 58 degrees, respectively. What is the distance of the balloon from the two engineers? A. 4.46 km, 4.54km B. 4.64, 4.45km C. 4.64km, 4.54km D.4.46km, 4.45km 27. Evaluate the line integral from (0,0) to (1,1) .∫[√𝑦𝑑𝑥 + (𝑥 − 𝑦)𝑑𝑦] A. 5/3 B.4/3 C. 2/3

D. 1/3

28. Find the area of the triangle having vertices at -4-I, 1+2i, 4-3i. A. 15 B. 16 C. 17

D. 18

29. How many even numbers of three digits each can be made with the digits 0,2,3,5,7,8,9 if no digit is repeated? A. 102 B. 126 C. 80 D. 90 30. What is the angle subtended in mils of arc length of 10 yards in a circle of radius 5000 yards? A. 1.02 B. 2.40 C. 4.02 D. 2.04 31. How many 5 poker hands are there in a standard deck of cards? A. 2,598,960 B. 2,958,960 C. 2,429,955 D. 2,942,955 32. In delivery of 14 transformers, 4 of which are defective, how many ways those in 5 transformers at least 2 are defective? A. 940 B. 920 C. 900 D. 910 33. A point is chosen at random inside the circle of diameter 8 in. What is the probability that it is at least 1.5 in away from the center of the circle? A. 53/64 B. 55/64 C. 52/64 D. 56/64 34. A student did not study for his upcoming examination on which is 15 multiple choice test questions, with five possible choices of which only one is correct, what is the expected number of correct answers he can get? A. 2 B. 3 C. 4 D. 5

REGISTERED ELECTRICAL ENGINEERS PRE-BOARD EXAMINATION AUGUST 2015 MATHEMATICS

35. Evaluate (1+i) raised to (1-i). A. 2.82+i1.32 B. 2.82-i1.32

C. -2.82-j1.32

D. -2.82+i1.32

36. A boy, 1.20m tall, is walking directly away from the lamp post at the rate of 0.90 m/sec. If the lamp is 6m above the ground, find the rate at which his shadow is lengthening. A. 2.25 m/sec B. 0.225 m/sec C. 1.125 m/sec D. 0.235 m/sec 37. A painter needs to find the area of the gable end of the house. What is the area of the gable if it is a triangle with two sides of 42.0 ft. that meet at a 105 degrees angle? A. 852 sq. ft. B. 825 sq. ft. C. 892 sq. ft. D. 829 sq. ft. 38. A sector of a circle has a central angle of 50 degrees and an area of 605 sq. cm. Find the radius of the circle A. 34.6 cm B. 36.4 cm C. 37.2 cm D. 32.7 cm 39. If f(x) = sin x and f(𝜋) = 3, then f(x) = A. 4+cos x B. 3+cos x

C. 2-cos x

D. 4-cos x

40. If f(x) = 32x, then f(x) = A. 2(32x) B. 62x

C. 9(ln6)

D. 9(ln9)

41. Find the slope of the line tangent to 3y2 - 2x2 = 5xy at the point (1,2). A. -1 B.-2 C. 1 D.2 42. The volume V in3 of unmelted ice remaining from the melting ice cube after t seconds is given by V(t)=2000-40t+0.2t2. How fast is the volume changing when t= 40 seconds? A.-26 in3 /sec B. -24in3 /sec C. -20in3 /sec D. -8in3 /sec 43. The radius of a circle is measured to be 3 cm correct to within 0.02 cm. Estimate the propagated error in the area of the circle. A. 0.183 cm B. 0.213 cm C. 0.285 cm D. 0.377 cm 44. What is the area within the curve r2 = 16cos𝜃. A. 26 B. 28 C. 30

D. 32

45. A solid is formed by revolving about the axis, the area bounded by the curve x3 = y, the y-axis and the line y = 8. Find its centroid. A. (0, 4.75) B. (0, 4) C. (0, 5.25) D. (0, 5) 46. Find the area in the first quadrant that is enclosed by y = sin 3x and the x-axis from x = 0 the first x-intercept on the positive x-axis. A. -1/4 B. 2/3 C. 1 D.2 47. Let f(x) = x3 + x + 4 and let g(x) = f-1 (x). Find g’(6)

REGISTERED ELECTRICAL ENGINEERS PRE-BOARD EXAMINATION AUGUST 2015 MATHEMATICS

A. -1/4

B. -4

48. 2 gallons is how many quartz? A. 2 B. 4

C. 1/4

D. 4

C. 6

D. 8

49. A recipe calls for 1 cup of milk for every 2-1/2 cups of flour to make a cake that would feed 6 people. How many cups of both flour and milk need to be measured to make a similar cake for 8 people? A. 1-1/3 B. 2-1/3 C. 1-1/2 D.2-1/2 50. Find the vertex of the parabola y2 - 8x + 6y + 1 = 0 A. (3, -1) B. (-3, 1) C. (3, 1)

D. (-3,-1)

51. Find the volume of a cone to be constructed from a sector having a diameter of 72 cm and a central angle of 150 degrees. A. 7711.82 B. 5533.32 C. 6622.44 D. 8866.44 52. A and B are points on the opposite sides of a certain body of water. Another point C is located such that AC= 200 meters, BC= 160 meters and angle BAC= 50 degrees. Find the length of AB. A. 164.67 m B. 174.67 m C. 184.67 m D.194.67 m 2 2 53. Find the area of the ellipse 4x + 9y = 36. A. 15.71 B. 18.85 C. 12.57 D. 21.99 54. A couple plans to have 7 children. Find the probability of having at least one boy. A. 0.1429 B. 0.1667 C. 0.9922 D. 0.8571 55. A person has 2 parents, 4 grandparents, 8 great grandparents and soon. How many ancestors during the 15 generations preceding his own, assuming no duplication? A. 131070 B. 65534 C. 32766 D. 16383 56. A vendor buys an apple for Php 10 and sells it for Php 15. What percent of the selling price of apple is the vendor’s profit? A. 50 B. 33.33 C. 25 D. 66.67 57. What is the numerical coefficient of the term next to 240x2y2? A. 220 B. 240 C. 320

D. 340

58. Determine the sum of the first 12 terms of the arithmetic sequence: 3, 8, 13,.. A. 366 B. 363 C. 379 D. 397 59. In how many ways can 5 letters be mailed if there are 3 mailboxes available? A. 60 B. 80 C. 243 D. 326 60. James is 20 years old and john is 5 years old. In how many years will James be twice as old as john?

REGISTERED ELECTRICAL ENGINEERS PRE-BOARD EXAMINATION AUGUST 2015 MATHEMATICS

A. 15

B. 10

C. 12

61. The diagonal of square is 6 cm. Find its area. A. 18 B. 24 C. 28

D. 8

D. 16

62. If cos A = 4/5 and angle A is not in Quadrant I, what is the value of sin A? A. 0.6 B. -0.6 C. 0.75 D. -.75 63. Find the area of a circle inscribed in a rhombus whose perimeter is 100 in. and whose longer diagonal is 40 in. A. 116 pi in2 B. 128 pi in2 C. 144 pi in2 D. 188 pi in2 64. A ranger’s tower is located 44 m from a tall tree. From the top of the tower, the angle of elevation to the top of the tree is 28 degrees, and the angle of depression to the base of the tree is 36 degrees. How tall is the tree? A. 48 m B. 62 m C. 55 m D. 99 m 65. In an ellipse, a chord which contains a focus and is in line perpendicular to the major axis is a: A. latus rectum B. minor C. focal width D. Conjugate axis 66. Find the force on one end of a parabolic trough full of water, if depth is 2ft, and with across the top is 2 ft. Use 𝜔 = 62.5 lb/ft3 A. 125 lbs B. 133.33 lbs C. 200 lbs D. 208.33 lbs 67. Find the Laplace transform of f(t)= e raised to (3t+1). A. e/(s+3) B. e/(s-3) C. e/(s2 + 3)

D. e/(s2 - 3)

68. If the half-life of a substance is 1,200 years, find the percentage that remains after 240 years. A. 76% B. 77% C. 87% D. 97% 69. Robin flies to San Francisco from Santa Barbara in 3 hours. He flies back in 2 hours. If wind was blowing from north at velocity of 40 mph going, but changed to 20 mph from the north returning, what was the airspeed of the plane? A. 140 mph B. 150 mph C. 160 mph D. 170 mph 70. A tree is broken over by a windstorm. The tree was 90 feet high and the top of the tree is 25 feet from the foot of the tree. What is the height of the standing part of the tree? A. 48.47 ft. B. 41.53 ft. C. 45.69 ft. D. 44.31 ft. 71. In a frustum of cone of revolution the radius of the lower base is 11 in, the radius of the upper base is 5 in, and the altitude is 8 in. Find the total area in square inches.

REGISTERED ELECTRICAL ENGINEERS PRE-BOARD EXAMINATION AUGUST 2015 MATHEMATICS

A. 80pi

B. 160pi

C. 226pi

D. 306pi

72. A cask containing 20 gallons of wine emptied on one-fifth of its content and then is filled with water, if this is done 6 times, how many gallons of wine remain in the cask? A. 5.242 B. 5.010 C. 5.343 D. 5.121 73. Goods cost a merchant $ 72. At what price should he mark them so that he may sell them at a discount of 10% from his mark price and still make a profit of 20% on the selling price? A. $ 150 B. $ 200 C. $ 100 D. $ 250 74. Determine the length of the latus rectum of the curve r= 4(1-sin theta). A. 6 B. 9 C. 8 D. 7 75. Find the radius of the curvature of r= tan theta at theta= 3pi/4. A. sqrt. of 3 B. sqrt. of 5 C. sqrt. of 6

D. sqrt. of 2

76. Given A= 5i+3j and B=2i+kj where k is a scalar, find k such that A and B are parallel. A. 3/5 B. 3 C. 6/5 D. 6 77. What is the x-intercept of the line whose parametric equations are x= 2t -1 and y= 6t+11? A. -2/3 B. -5/3 C. -7/3 D. -14/3 78. What is the coefficient of the (X-1)3 term in the Taylor series expansion of f(x)= lnx expanded about x= 1? A. 1/6 B. 1/4 C. 1/3 D. 1/2 79. The position of a particle moving along the x-axis at any time t is given by x(t)= 2t3 - 4t2 + 2t - 1. What is the slowest velocity achieved by the particle? A. 17/4 B. 3 C. -2/3 D. -3/2 80. For what value of k will the line kx +5y= 2k have y-intercept 4? A. 8 B. 9 C. 10 D. 11 81. Find the circumference of the circle x2+y2-12x+10y+15=0 A. 75.40 B. 57.40 C. 96.12

D. 42.61

82. Find the slope of the curve x=t2+et, y=t+et. At the point (1,1). A. 1 B. 2 C. 3

D. 4

83. Which of the following is true? A. sin(-θ)=sin θ B. tan(-θ)=tan θ

D. csc(-θ)=csc θ

C. cos(-θ)=cos θ

84. The hypotenuse of a right triangle is 34 cm. Find the length of the two legs, if one leg is 14 cm longer than the other.

REGISTERED ELECTRICAL ENGINEERS PRE-BOARD EXAMINATION AUGUST 2015 MATHEMATICS

A. 15 and 29

B. 16 and 30

C. 18 and 32

D. 17 and 31

85. John’s factory has 60 workers. If 4 out of 5 workers are married, how many workers are not married? A. 12 workers B. 24 workers C. 48 workers D. 60 workers 86. Find the equation of the line whose slope is-3 and the x-intercept is 5. A. y= -3x+5 B. 3x-y=5 C. 3x+y=15 D. y=3x+15 87. The positive value of k which will make 4x2-4kx+4k+5 a perfect square trinomial is A. 6 B. 5 C. 4 D. 3 88. If ln x=2 and ln y= 3, find ln(x3/y1/2). A. 3.5 B. 4.5

C. 2.5

D. 1.5

89. If 3x3y= 27 and 2x + y=5, find x. A. 3 B. 4

C. 2

D. 1

90. The area of a circle is six time its circumference. What is the radius of the circle? A. 10 B. 11 C. 12 D. 13 91. Twelve round holes are bored through a piece of steel plate. Their centers are equally spaced on the circumference of a circle 18 cm in diameter. What is the difference between the centers of two consecutive holes? A. 4.71 cm B. 4.66 cm C. 4.32 cm D. 4.55 cm 92. What is the minimum possible perimeter for a rectangle whose area is 100 sq. in? A. 50 in. B. 60 in. C. 30 in. D. 40 in. 93. Find the work done by the force of F= 3i + 10j newton’s in moving an object 10 meters north. A. 104.40J B. 100J C. 106J D. 108.60J 94. Find the abscissa of a point having an ordinate of 4 of a line that has a yintercept of 8 and slope of 2. A. -2 B. +2 C. -3 D. +3 95. Find arch of an underpass semi-ellipse 60ft wide and 20ft high. Find the clearance at the edge of a lane if the edge is 20 ft. from the middle. A. 18.2 ft. B. 12.8 ft. C. 14.9 ft. D. 16.8 ft. 96. Find the moment of inertia with respect to the y-axis of the first-quadrant area bounded by the parabola x2= 4y and the line y=x. A. 34/5 B. 24/5 C. 54/5 D. 65/5 97. What is the length of the transverse axis of the hyperbola whose equation is 9y2-16x2=144?

REGISTERED ELECTRICAL ENGINEERS PRE-BOARD EXAMINATION AUGUST 2015 MATHEMATICS

A. 6

B. 9

C. 8

D. 7

98. Find the mass of lamina in the given region and density function: pi D[(x, y)], 0 ≤ x ≤ , o ≤ y ≤ cosx and ρ = 7x 2 A. 2 B. 3 C. 4 D. 5 99. How many cubic inches of lumber does a stick contain if it is 4 in. by 4 in. at one end, 2 in. by 2 in. at the other end, and 16ft long? A. 1729 B. 1927 C. 1972 D. 1792 100. A goat is tied to a corner of 30ft by 35ft building. If the rope is 40ft and the goat can reach 1ft farther than the rope length, what is the maximum area the goat can cover? A. 4840.07 B. 4084.07 C. 4804.07 D. 4408.07

REGISTERED ELECTRICAL ENGINEERS PRE-BOARD EXAMINATION MARCH 2014 MATHEMATICS

1. What is the differential equation of the family of parabolas having their vertices at the origin and their foci on the x-axis? A. 2xdy – ydx = 0 C. 2ydx –xdy = 0 B. ydx + ydx = 0 D. dy/dx – x = 0 2. Find the rthogonal trajectories of the family of parabolas y^2 = 2x + C. A. y = Ce^x B. y = Ce^(-x) C. y = Ce^(2x) D. y = Ce^(-2x) 3. A reflecting telescope has a parabolic mirror for which the distance from the vertex to the focus is 30 ft. If the distance across the top of the mirror is 64 in., how deep is the mirror of the center? A. 32/45 in. B. 30/43 in. C. 32/47 in. D. 35/46 in. 4. Simplify (1 – tan2x) / (1 + tan2x) A. sin 2x B. cos 2x

C. sin x

D. cos x

5. Evaluate L { t^n }. A. n!/s^n

C. n!/s^(n-1)

D. n!/s^(n+2)

B. n!/s^(n+1)

6. Simplify 12 cis 45 deg + 3 cis 15 deg. A. 2 + j B. sqrt. of 3 + j2 arcsin 9𝑥

7. Evaluate lim ( 𝑥→0

A. 9/2

2𝑥

C. 2 sqrt. Of 3 + j2 D. 1 + j2

) B. π

C. ∞

8. Find the area of the lemniscate r2 = a2cos2θ A. a2 B. a C. 2a

D. -∞ D. a3

9. Find the area bounded by the parabola sqrt. of x + sqrt. of y = sqrt. of a and the line x + y = a. A. a2 B. a2/2 C. a2/4 D. a2/3 10. Ben is two years away from being twice Ellen’s age. The sum of twice Ben’s age and thrice Ellen’s age is 66. Find Ben’s age now. A. 19 B. 20 C. 16 D. 21 11. What percentage of the volume of a cone is the maximum volume right circular cylinder that can be inscribed in it? A. 24% B. 34% C. 44% D. 54% 12. A balloon rising vertically, 150 m from an observer. At exactly 1 min, the angle of elevation is 29 deg 28 min. How fast is the balloon using at that instant? A. 104m/min B. 102m/min C. 106m/min D. 108m/min 13. A conic section whose eccentricity is less than one (1) is known as: A. a parabola B. an ellipse C. a circle D. a hyperbola

REGISTERED ELECTRICAL ENGINEERS PRE-BOARD EXAMINATION MARCH 2014 MATHEMATICS

14. A tangent to a conic is a line A. which is parallel to the normal B. which touches the conic at only one point C. which passes inside the conic D. all of the above 15. A die and a coin are tossed. What is the probability that a three and a head will appear? A. 1/4 B. 1/2 C. 2/3 D.1/12 16. Find the integral of 12sin5xcos5xdx if lower limit = 0 and upper limit = pi/2. A. 0.8 B.0.6 C.0.2 D.0.4 17. 12 oz of chocolate is added to 10 oz of flavoring is equivalent to A.1 lb and 8 oz B. 1 lb and 6 oz C.1 lb and 4 oz D.1 lb and 10 oz 18. The Ford company increased its assets price from 22 to 29 pesos. What is the percentage of increase? A.24.14% B.31.82% C.41.24% D.28.31% 19. Find the area bounded by outside the first curve and inside the second curve, r = 5, r = 10sinθ A. 47.83 B.34.68 C.73.68 D.54.25 20. In two intersecting lines, the angles opposite to each other are termed as: A. opposite angles C. horizontal angles B. vertical angles D. inscribed angles 21. The area in the second quadrant of the circle x^2 + y^2 = 36 is revolved about the line y + 10 = 0. What is the volume generated? A. 2932 c.u. B. 2392 c.u. C. 2229 c.u. D. 2292 c.u. 22. A cardboard 20 in x 20 in is to be formed into a box by cutting four equal squares and folding the edges. Find the volume of the largest box. A.592 cu.in. B.529 cu.in. C.696 cu.in. D.689 cu.in. 23. A retailer bought a number of ball pens for P90 and sold all but 3 at a profit P2 per ball pen. With the total amount received she could buy 15 more ball pens than before. Find the cost per ball pen. A. P2 24. What is –i^i? A.4.81

B. P3

C.P4

D.P5

B.-4.81

C.0.21

D.-0.21

25. A balloon travel upwards 6m, North and 8m, East. What is the distance traveled from the starting point? A. 7 B. 10 C.14 D. 20

REGISTERED ELECTRICAL ENGINEERS PRE-BOARD EXAMINATION MARCH 2014 MATHEMATICS

26. What do you call the integral divided by the difference of the abscissa? A. average value C. abscissa value B. mean value D. integral value 27. Water is running out of a conical funnel at the rate of 1 cubic inch per sec. If the radius of the base of the funnel is 4 in. and the altitude is 8 in., find the rate at which the water level is dropping when it is 2 in. from the top. ` A. -1/pi in./sec B. -2/pi in./sec C. -1/9pi in./sec D.-2/9pi in./sec 28. How many inches is 4 feet? A. 36 B. 48

C. 12

D. 56

29. A rectangular trough is 8 ft. long, 2 ft. across the top, and 4 ft. deep. If water flows in at a rate of 2 cu. ft./min., how fast is the surface rising when the water is 1 ft. deep? A. 1/5 ft./min B. 1/8 ft./min C. 1/6 ft./min D. 1/16 ft./min 30. Five tables and eight chairs cost $115; three tables and five chairs cost $70. Determine the total cost of each table. A. $15 B. $30 C. $25 D. $20 31. Find the 16th term of the arithmetic sequence; 4, 7, 10,…….. A. 47 B. 46 C. 49

D. 48

32. Find the slope of the line through the points (-2, 5) and (7, 1). A. 9/4 B. -9/4 C. 4/9

D. -4/9

33. For what value of k will the line kx +5y = 2k have a y-intercept 4? A. 8 B. 7 C. 9 D.10 34. If a bug moves a distance of 3pi cm along a circular arc and if this arc subtends a central angle of 45 degrees, what is the radius of the circle? A. 8 B. 12 C. 14 D. 16 35. Two vertices of a rectangle are on the positive x-axis. The other two vertices are on the lines y = 4x and y = -5x + 6. What is the maximum possible area of the rectangle? A.2/5 B.5/2 C.5/4 D. 4/5 36. Find the length of the arc of 6xy = x^4 + 3 from x = 1 to x = 2. A.12/17 B.17/12 C.10/17

D.17/10

37. A certain radioactive substance has half-life of 3 years. If 10 grams are present initially, how much of the substance remain after 9 years? A.2.50g B.5.20g C. 1.25g D.10.20g

REGISTERED ELECTRICAL ENGINEERS PRE-BOARD EXAMINATION MARCH 2014 MATHEMATICS

38. A cubical box is to built so that it holds 125 cu. cm. How precisely should the edge be made so that the volume will be correct to within 3 cu. cm.? A.0.02 B.0.03 C.0.01 D.0.04 39. Find the eccentricity of the ellipse when the length of its latus rectum is 2/3 of the length of its major axis. A.0.62 B. 0.64 C.0.58 D.0.56 40. Find k so that A = <3, -2> and B =<1, k> are perpendicular. A. 2/3 B.3/2 C.5/3 D.3/5 B. 41. Find the moment of inertia of the area bounded by the curve x^2 = 8y, the line x = 4 and the x-axis on the first quadrant with respect to y-axis. A.25.6 B. 21.8 C.31.6 D.36.4 42. Find the force on one face of a right triangle of sides 4m and altitude of 3m. The altitude is submerged vertically with the 4m side in the surface. A.62.64 kN B.58.86 kN C.66.27 kN D.53.22 Kn 43. In how many ways can 6 people be seated in a row of 9 seats? A. 30,240 B. 30,420 C.60,840 D. 60,480 44. The arc of a sector is 9 units and its radius is 3 units. What is the area of the sector? A.12.5 B.13.5 C.14.5 D.15.5 45. The sides of a triangle are 195, 157, and 210, respectively. What is the area of the triangle? A.73,250 B.10,250 C.14,586 D.11,260 46. A box contains 9 red balls and 6 blue balls. If two balls are drawn in succession, what is the probability that one of them is red and the other is blue? A.18/35 B.18/37 C.16/35 D.16/37 47. A car goes 14 kph faster than a truck and requires 2 hours and 20 minutes less time to travel 300 km. Find the rate of the car. A.40 kph B.50 kph C.60 kph D.70 kph 48. Find the slope of the line defined by y – x = 5. A.1 B.1/4 C.-1/2

D.5

49. The probability of John’s winning whenever he plays a certain game is 1/3. If he plays 4 times, find the probability that he wins just twice. A.0.2963 B.0.2936 C.0.2693 D.0.2639 50. A man row upstream and back in 12 hours. If the rate of the current is 1.5 kph and that of the man in still water is 4 kph, what was the time spent downstream? A.1.75 hr B.2.75 hr C.3.75 hr D. 4.75 hr

REGISTERED ELECTRICAL ENGINEERS PRE-BOARD EXAMINATION MARCH 2014 MATHEMATICS

51. If cot A = -24/7 and A is in the 2nd quadrant, find sin 2A. A.336/625 B.-336/625 C.363/625

D. -363/625

52. The volume of a square pyramid is 384 cu. cm. Its altitude is 8 cm. How long is an edge of the base? A.11 B.12 C.13 D.14 53. The radius of the circle x^2 + y^2 – 6x + 4y – 3 = 0 is A.3 B.4 C.5

D.6

54. If the planes 5x – 6y - 7z = 0 and 3nx + 2y – mz +1 = 0 A.-2/3 B. -4/3 C.-5/3

D.-7/3

55. If the equation of the directrix of the parabola is x – 5 = 0 and its focus is at (1, 0), find the length of its latus rectum. A.6 B.8 C.10 D.12 56. If tan A = 1/3 and cot B = 4, find tan (A + B). A. 11/7 B. 7/11 C. 7/12

D. 12/7

57. A club of 40 executives, 33 like to smoke Marlboro, and 20 like to smoke Philip Morris. How many like both? A. 13 B. 10 C. 11 D. 12 58. The area of the rhombus is 264 sq. cm. If one of the diagonals is 24 cm long, find the length of the other diagonal. A. 22 B. 20 C. 26 D. 28 59. How many sides have a polygon if the sum of the interior angles is 1080 degrees? A. 5 B. 6 C. 7 D. 8 60. The line segment connecting (x, 6) and (9, y) is bisected by the point (7, 3). Find the value of x and y. A. 5, 0 B. 4, 0 C. 5, 2 D. 4, 1 61. What is the height of the parabolic arch which has span of 48 ft. and having a height of 20 ft. at a distance of 16 ft. from the center of the span? A. 30 ft. B. 40 ft. C. 36 ft. D. 34 ft. 62. Determine B such that 3x + 2y – 7 = 0 is perpendicular to 2x –By + 2 =0. A. 2 B. 3 C. 4 D. 5 63. The value of x + y in the expression 3 + xi = y + 2i is; A. 5 B. 1 C. 2 64. If sin3A = cos6B then: A. A + B = 180 deg B. A + 2B = 30 deg

C. A - 2B = 30 deg D. A + B = 30 deg

D. 3

REGISTERED ELECTRICAL ENGINEERS PRE-BOARD EXAMINATION MARCH 2014 MATHEMATICS

65. What is the area between y = 0, y = 3x^2, and x = 2? A. 8 B. 12 C. 24

D. 6

66. The volume of the sphere is 36pi cu. m. The surface area of this sphere in sq. m is: A. 36pi B. 24pi C. 18pi D. 12pi 67. The vertex of the parabola y^2 – 2x + 6y + 3 = 0 is at: A. (-3, 3) B. (3, 3) C. (3, -3)

D. (-3, -3)

68. Add the following and express in meters: 3 m + 2 cm + 70 mm A. 2.90 m B. 3.14 m C. 3.12 m D. 3.09 m 69. A store advertised on sale at 20 percent off. The sale price was $76. What was the original price? A. $95 B. $96 C. $97 D. $98 70. Find the equation of the straight line which passes through the point (6, -3) and with an angle of inclination of 45 degrees. A. x + y = 8 B. x – y = 8 C. x + y = 9 D. x – y = 9 71. A freight train starts from Los Angeles and heads for Chicago at 40 mph. Two hours later a passenger train leaves the same station for Chicago traveling at 60 mph. How long will it be before the passenger train overtakes the freight train? A. 3 hrs. B. 5 hrs. C. 4 hrs. D. 6 hrs. 72. The number of board feet in a plank 3 inches thick, 1 ft. wide, and 20 ft. long is: A. 30 B. 60 C. 120 D. 90 73. Boyles’s law states that when a gas is compressed at constant temperature, the product of its pressure and volume remains constant. If the pressure gas is 80 lb/sq.in. when the volume is 40 cu.in., find the rate of change of pressure with respect to volume when the volume is 20 cu.in. A. -8 B. -10 C. -6 D. -9 74. Find the average rate of change of the area of a square with respect to its side x as x changes from 4 to 7. A. 8 B. 11 C. 6 D. 21 75. How many cubic feet is equivalent to 100 gallons of water? A. 74.80 B. 1.337 C. 13.37

D. 133.7

76. A merchant purchased two lots of shoes. One lot he purchased for $32 per pair and the second lot he purchased for $40 per pair. There were 50 pairs in the first lot. How many pairs in the second lot if he sold them all at $60 per pair and made a gain of $2800 on the entire transaction?

REGISTERED ELECTRICAL ENGINEERS PRE-BOARD EXAMINATION MARCH 2014 MATHEMATICS

A. 50

B. 40

C. 70

D. 60

77. The diagonal of a face of a cube is 10 ft. The total area of the cube is A. 300 sq. ft. B. 150 sq. ft. C. 100 sq. ft. D. 200 sq. ft. 78. A ship is sailing due east when a light is observed bearing N 62 deg 10 min E. After the ship has traveled 2250 m, the light bears N 48 deg 25 min E. If the course is continued, how close will the ship approach the light? A. 2394 m B. 2934 m C. 2863 m D. 1683 m 79. If f(x) = 1/(x – 2), (f g)’(1) = 6 and g’(1) = -1, then g(1) = A.-7 B. -5 C. 5

D. 7

80. Find the work done by the force F = 3i + 10j newtons in moving an object 10 meters north. A.104 40 J B. 100 J C.106 J D. 108.60 J 81. The volume of a frustum of a cone is 1176pi cu.m. If the radius of the lower base is 10m and the altitude is 18m, compute the lateral area of the frustum of a cone A.295pi sq. m. B. 691pi sq. m. C.194pi sq. m. D. 209pi sq. m. 82. In an ellipse, a chord which contains a focus and is in a line perpendicular to the major axis is a: A.latus rectum B. minor axis C. focal width D. major axis 83. With 17 consonant and 5 vowels, how many words of four letters can be four letters can be formed having 2 different vowels in the middle and 1 consonant (repeated or different) at each end? A.5780 B. 5785 C. 5790 D. 5795 84. Evaluate tan2(j0.78). A.0.653

B.-0.653

C.0.426

D. -0.426

85. A particle moves along a line with velocity v = 3t^2 – 6t. The total distance traveled from t = 0 to t = 3 equals A.8 B. 4 C. 2 D. 16 86. An observer at sea is 30 ft. above the surface of the water. How much of the ocean can he sea? A.124.60 sq. mi. C. 154.90 sq. mi. B.142.80 sq. mi. D. 132.70 sq. mi. 87. There are three consecutive integers. The sum of the smallest and the largest is 36. Find the largest number. A.17 B. 18 C.19 D. 20

REGISTERED ELECTRICAL ENGINEERS PRE-BOARD EXAMINATION MARCH 2014 MATHEMATICS

88. If y = sqrt. of (3 – 2x), find y. A.1/sqrt. of (3 – 2x) B. -1/sqrt. of (3 – 2x)

C. 2/sqrt. of (3 – 2x) D. -2/sqrt. of (3 – 2x)

89. The logarithm of MN is 6 and the logarithm of N/M is 2, find the value of logarithm of N. A.3 B. 4 C. 5 D.6 90. A woman is paid $20 for each day she works and forfeits $5 for each day she is idle. At the end of 25 days she nets $450. How many days did she work? A.21 days B. 22 days C. 23 days D.24 days 91. Francis runs 600 yards in one minute. What is his rate in feet per second? A.25 B. 30 C.35 D.40 92. For a complex number z = 3 + j4 the modulus is: A.3 B. 4 C. 5 93. Which of the following is an exact DE? A. (x^2 + 1)dx – xydy = 0 B. xdy + (3x – 2y)dy = 0

D. 6

C. 2xydx + (2 + x^2)dy = 0 D. x^2 ydy – ydx = 0

94. There are 8 different colors, 3 of which are red, blue and green. In how many ways can 5 colors be selected out of the 8 colors if red and blue are always included but green is excluded? A.12 B.11 C. 10 D.9 95. Five cards are drawn from a pack of 52 well – shuffled cards. Find the probability that 3 are 10’s and 2 are queens. A. 1/32 B. 1/108,290 C. 1/54,350 D.1/649,740 7

7

7

96. If ∫1 𝑓(𝑥)𝑑𝑥 = 4 and ∫1 𝑔(𝑥)𝑑𝑥 = 2, find ∫1 [3𝑓(𝑥) + 2𝑔(𝑥) + 1]𝑑𝑥. A. 23 B. 22 C. 25 D. 24 97. When the ellipse is rotated about its longer axis, the ellipsoid is A. spheroid B. oblate C. prolate D. paraboloid 98. If the distance between points A(2, 10, 4) and B(8, 3, z) is 9.434, what is the value of z? A. 4 B. 3 C. 6 D. 5 99. A line with equation y = mx + b passes through (-1/3, -6) and (2, 1). Find the value of m. A. 1 B. 3 C. 4 D. 2 100. For the formula R = E/C, find the maximum error if C = 20 with possible error 0.1 and E = 120 with a possible error of 0.05.

REGISTERED ELECTRICAL ENGINEERS PRE-BOARD EXAMINATION MARCH 2014 MATHEMATICS

A. 0.0325

B. 0.0275

C. 0.0235

D. 0.0572

REGISTERED ELECTRICAL ENGINEERS PRE-BOARD EXAMINATION AUGUST 2014 MATHEMATICS

1. What percentage of the volume of a cone is the maximum right circular cylinder that can be inscribed in it? A. 24% B. 34% C. 44% D. 54% 2. A railroad curve is to be laid out on a circle. What radius should be used if the track is to change direction by 30 degrees in a distance of 300 m? A. 566 m B. 592 m C. 573 m D. 556 m 3. Express in polar form: -3-4i 𝟒

𝟒

A. 𝟓𝐞−𝐢(𝐩𝐢+𝐭𝐚𝐧−𝟏𝟑)

C. √𝟓𝐞−𝐢(𝐩𝐢+𝐭𝐚𝐧−𝟏𝟑)

𝟒

𝟒

B. 𝟓𝐞𝐢(𝐩𝐢+𝐭𝐚𝐧−𝟏𝟑)

D. √𝟓𝐞𝐢(𝐩𝐢+𝐭𝐚𝐧−𝟏𝟑)

4. Find the values of z for which 𝒆𝟒𝒛 = 𝒊. A. 1/6 pi i + ½ kpi i B. -1/6 pi i + ½ kpi i

C. 1/8 pi i + ½ kpi i D. -1/8 pi i + ½ kpi i

5. A ladder leans against the side of a building with its foot 12 ft. from the building. How long is the ladder if it makes of 70 degrees with the ground? A. 32 ft B. 33 ft C. 34 ft D. 35 ft 6. If the 5th term in arithmetic progression is 17 and the 3rd is 10, what is the 8th term? A. 27.5 B. 24.5 C. 36 D. 38 7. A balloon is released of eye level and rises at the rate of 5 ft/s. An observer 50 ft away watches the balloon rise. How fast is the angle of elevation measuring 6 seconds after the moment of release? A. 0.007 rad/s B. 0.07 rad/s C. 0.008 rad/s D. 0.08 rad/s 8. If cos z = 2, find cos 3z. A. 7 B. 17

C. 27

D. 37

9. Points (6,-2) and (a,6) are on a line with a slope of 4/3. What is the value of a? A. -2 B. 4.5 C. 9 D. 12 10. The foci of an ellipse are on the points (4,0) and (-4,0) and its eccentricity is 2/3. Find the equation of the ellipse. A. x^2/36 + y^2/20 = 1 C. x^2/20 + y^2/16 = 1 B. x^2/20 + y^2/36 = 1 D. x^2/16 + y^2/20 = 1 11. The plate number of a vehicle consists of 5 alphanumeric sequence is arranged such that the first 2 characters are alphabet and the remaining are 3 digits. How many arrangement are possible if the first character is a vowel and repetition is not allowed? A. 90 B. 900 C. 9,000 D. 90,000

REGISTERED ELECTRICAL ENGINEERS PRE-BOARD EXAMINATION AUGUST 2014 MATHEMATICS

12. One end of a 32-meter ladder resting on a horizontal plane leans on a vertical wall. Assume the foot of the ladder to pushed towards the wall at the rate of 2 meters per minute. When will be the top and bottom of the ladder move at the same rate? A. 30.4 m B. 22.6 m C. 17.75 m D. 26.6 m 13. A triangle is inscribed in a circle of radius 10. If two angles are 70 degrees and 50 degrees, find the length of the side opposite to the third angle. A. 15.32 B. 16.32 C. 17.32 D. 18.365 14. Find the volume generated by revolving the area cut off from the parabola y=4xx^2 by the axis about the line y=6. A. 295 B. 340 C. 286 D. 362 15. The axis of the hyperbola through its foci is known as: A. conjugate axis B. transverse axis C. major axis D. minor axis 16. From past experience it is known 90% of one year old children can distinguish their mother’s voice of similar sounding female. A random sample of 20 one year’s old given this voice recognize test. Find the probability that all children recognize mother’s voice. A. 0.122 B. 0.500 C. 1.200 D. 0.222 17. If the equation of the directrix of a parabola is x-5=0 and its focus is at (1,0), find the length of its latus rectum. A. 6 B. 8 C. 10 D. 12 18. Describe the locus represented by |𝒛 − 𝒊| = 𝟐. A. circle B. parabola C. ellipse 19. Evaluate lim (( z – 1 – I )/( z2 -2z+2)) z―›1+i A. ¼ B. -1/4

D. hyperbola

2

C. ½

D. -1/2

20. Nanette has a ribbon with a length of 13.4 m and divided it by 4. What is the length of each part? A. 3.35 m B. 3.25 m C. 3.15 m D. 3.45 m 21. Simplify 1 (csc x + cot x) 1(csc x – cot x). A. 2 cos x B. 2 sec x

C. 2 csc x

D. 2 sin x

22. If the area of a sector of a circle is 248 sq. m and the central angle is 135 degrees. Find the diameter of the circle. A. 29 m B. 26 m C. 32 m D. 39 m 23. In how many ways can two lines intersect from given 6 lines? A. 14 B. 15 C. 16

D. 17

REGISTERED ELECTRICAL ENGINEERS PRE-BOARD EXAMINATION AUGUST 2014 MATHEMATICS

24. Find the half line of a radioactive substance if 20 percent of it disappears in 40 years. A. 123.25 yrs. B. 124.25 yrs. C. 125.25 yrs. D. 126.25 yrs 25. Find the area of curvature of 𝐲 = 𝐞𝐱 − 𝟐𝐱 at the point (0,1). A. 2.91 B. 2.83 C. 2.72 D. 2.63 26. 3 randomly chose high school students were administered a drug test. Each student was evaluate as positive to the drug test (P) or negative to the drug test (N). Assume the possible combination of the 3 students drug test evaluation as PPP, PPN, PNP, NPN, NNP, NNN. Assume the possible combination is equally likely and knowing that 1 student get a negative results, what is the probability that all 3 students get a negative result? A. 1/8 B. 1/7 C. 7/8 D. ¼ 27. A bridge is 1.4 kilometers long. A bus 10 meters long is crossing the bridge at 30 kph. How many minutes will it take the bus to completely cross the bridge? A. 1.82 min B. 2.82 min C. 3.82 min D. 4.82 min 28. Find the fifth term of the sequence 16, 4, 1, -1/4,… A. 4 B. 16 C. ¼

D. 1/16

29. Find the area of the three-leaved rose r = 2 sin 2 theta. A. pi B. 2 pi C. 3 pi

D. 4 pi

30. Evaluate lim (x-6) tan (pix/12) x―›6 A. -3.82 B. 0

C. -1.91

D. -2.64

31. What is the area of an isosceles triangle whose base is 10 and its base angle is 60 degrees? A. 25 (sqrt of 3) B. 50 (sqrt of 3) C. 25 D. 50 32. If y = 2x + sin 2x, what is the value of x so that y' =0? A. 3 pi/2 B. pi/2 C. pi/3

D. 2 pi/3

33. What is the vector length 2 and direction 150 degrees in the form ai + bj. A. 1.73i + j B. -1.73i – j C.1.73i - j D. -1.73i + j 34. If a man works at an average speed of 4 kph, what is the time consume to reach 250 m. A. 0.25 min B. 2.50 min C. 3.75 min D. 4.25 min 35. N engineers and N nurses, if two engineers are replaced by nurses, 51% of the engineers and nurses are nurses. Find N. A. 100 B. 110 C.50 D.200

REGISTERED ELECTRICAL ENGINEERS PRE-BOARD EXAMINATION AUGUST 2014 MATHEMATICS

36. A house has assessed value of P 720,000.00 worth which is 60% of the market value. If the tax is P 3.00 for P 1,000.00 market value, how much is the tax? A. P 3, 200.00 B. P 3,800.00 C. P 3,600.00 D. 3,400.00 37. 1/6 is what percent of ¾? A. 37.5 B. 66.67

C. 50

D.75

38. In a hotel it is known that 20% of the total reservation will be cancelled in the last minute. What is the probability that out of 15 reservatons there will be more than 8 but less than 12 cancelled? A. 0.00784 B. 0.0784 C. 0.000784 D. 0.784 39. If 16 is more than 4x, find x. A. 1.4 B. 3

C. 12

D. 5

40. Locate the midpoint of the line segment joining point 1 (2,15,4) and point 2 (6,3,-12) A. (4,9,4) B. (4,-9,4) C. (4,94) D. (-4,9,4) 41. A conic section whose eccentricity is greater than one (1) is known as? A. A parabola B. an ellipse C. a circle D. a hyperbola 42. Find the distance travelled by the tip of a pendulum if the distance of the first swing is 8 cm and the distance of each succeeding is 0.75 of the distance of the previous swing. A. 32 cm B. 28 cm C. 27 cm D. 30 cm 43. Describe the locus represented by the curve |𝒛 + 𝟐𝒊| + |𝒛 − 𝟐𝒊| = 𝟔. A. circle B. parabola C. ellipse D. hyperbola 44. Find the area bounded by the curve 𝒚𝟐 = 𝟑𝒙 − 𝟑 and the line x = 4. A. 10 B. 16 C. 15 D. 12 45. Helium is escaping a spherical balloon at the rate of 2 cm3 /min. When the surface area is shrinking at the rate of 1/3 cm2 /min, find the radius of the spherical balloon. A. 14 cm B. 12 cm C. 16 cm D. 8 cm 46. What is the maximum area of the rectangle whose base is on the z-axis and whose upper two vertices lie on the parabola 𝒚𝟐 = 𝟏𝟐 − 𝒙𝟐 . A. 30 B. 32 C. 36 D. 40 47. A car racer covers 225 km in 2.5 hrs. How far can he go in 1.75 hrs? A. 267.5 km B.168.75 km C. 394 km D. 157.5 km 48. Find the area of the triangle with vertices A (0,1), B (5,3), and C (-2,-2)

REGISTERED ELECTRICAL ENGINEERS PRE-BOARD EXAMINATION AUGUST 2014 MATHEMATICS

A. 19

B. 19/2

C. 15

D. 15/2

49. What is the sum of coefficients of the expansion of (𝟐𝒙 − 𝟏)𝟐𝟎 A. 0 B. 1 C. 2

D. 3

50. The parabola defined by the equation 𝟑𝒚𝟐 + 𝟒𝒙 = 𝟎 opens ____________. A. upward B. downward C. to the left D. to the right 51. How many tiles 10 cm on a side are needed to cover a rectangular wall 3 m by 4 m? A. 1500 B. 1000 C. 1200 D. 1600 52. Find the equation of the line whose slope is -3 and the x-intercept is 5. A. 𝒚 = −𝟑𝒙 + 𝟓 B. 𝟑𝒙 − 𝒚 = 𝟓 B. C. 𝒚 = 𝟑𝒙 + 𝟏𝟓 D. 𝟑𝒙 + 𝒚 = 𝟏𝟓 53. In how many ways can the letters of the word “CHACHA” be arranged by taking the letters all at a time? A. 120 B. 720 C. 85 D. 90 54. Find the equation of the horizontal line though (-4,3). A. x = 4 B. x = -4 C. y = 3 55. If g(x) = 9f(x) and f(-6), find g’(-6) A. -54 B. -40

D. y = -3

C. -36

D. -28

56. Determine k so that the points A (7,3), B (-1,0), and C (k,-2) are the vertices of a right triangle with right angle at B. A. -1 B. 1 C. -1/4 D. ¼ 57. The radius of the circle 𝒙𝟐 + 𝒚𝟐 + 𝟒𝒙 − 𝟔𝒚 − 𝟑 = 𝟎 is _______ A. 2 B. 3 C. 4

D. 5

58. If the logarithm of MN is 6 and the logarithm N/M is 2, find the logarithm of N. A. 3 B. 4 C. 5 D. 6 =𝟒 59. If 4 electricians earn x pesos in 7 days, how much can 14 carpenters paid of the same rate, earn in12 days? A. 3x B. 4x C. 5x D. 6X 60. Write the differential equation of the family of circle with center at the origin. A. 𝐱𝐝𝐲 + 𝐲𝐝𝐱 = 𝟎 B. 𝐱𝐝𝐲 − 𝐲𝐝𝐱 = 𝟎 C. 𝐱𝐝𝐱 + 𝐲𝐝𝐲 = 𝟎 D. 𝐱𝐝𝐲 − 𝐲𝐝𝐱 = 𝟎 61. Find the volume of a spherical segment, the radii of whose bases are 4 m and 5 m respectively with an altitude of 6 m. A. 159 pi B. 165 pi C. 150 pi D. 145 pi

REGISTERED ELECTRICAL ENGINEERS PRE-BOARD EXAMINATION AUGUST 2014 MATHEMATICS

62. A taxpayer’s state and the federal income taxes plus an inheritance tax totaled $ 14,270. His California state income tax was $ 5,780 less than his federal tax. His inheritance tax was $ 2, 750. How much did he pay in state tax? A. $ 8,560 B. $ 2,870 C. $ 8,650 D. $ 2,780 63. The first term of a geometric sequence is 160 and the common ratio is 3/2. How many consecutive terms must be taken to give a sum of 2110? A. 3 B. 4 C. 5 D. 6 64. The total area of a cube is 150 sq. in. A diagonal of the cube is ______ in. A. 5(sqrt of 2) B. 4(sqrt of 3) C. 5(sqrt of 3) D. 4(sqrt of 2) 65. In triangle ABC, sin (A+B) = 3/5. What is the value of sin C? A. 2/5 B. 2/3 C. 3/5

D. ½

66. Find the slope of the curve whose parametric equations are x = -1 +t and y=2t. A. 2 B. 3 C. 1 D. 4 67. Find the length of the latus rectum of the ellipse 25x^2 + 9^2 – 300x – 144y + 1251 = 0. A. 3.4 B. 3.2 C. 3.6 D. 3.0 68. A triangular trough whose the edges are 5, 5, and 8 m long is place vertically in water with its longest edege uppermost, horizontal, and 3 m below the water level. Calculate the force on a side of the plate. A. 235.2 kN B. 470.4 kN C. 940.8 kN D. 1,881.6 Kn 69. Find the area of the ellipse whose eccentricity is 4/5 and whose major axis is 10. A. 12 pi B. 13 pi C. 14 pi D. 15 pi 70. Find the average rate of change of the area of a square with respect to its side x as x changes from 4 to 7. A. 14 B. 11 C. 12 D. 13 71. Find the moment of inertia with respect to the y-axis of the area bounded by y = x^2 and y = 2x. A. 11/5 B. 9/5 C. 7/3 D. 8/5 72. Find the length of the arc of r = 4 sin u from u = 0 to u = pi/2. A. pi B. 2 pi C. 3 pi

D. 4 pi

73. What is the angle between -2.5 + j4.33 and 4.33 – j2.5? A. 0 deg B. 30 deg C. 120 deg D. 150 deg 74. If A = (2, 4) and B = (4,3), find |𝟕𝑨 − 𝑩|. A. sq. rt. of 21 B. sq. rt. of 1061 B. C. sq. rt. of 41 D. sq. rt. of 949

REGISTERED ELECTRICAL ENGINEERS PRE-BOARD EXAMINATION AUGUST 2014 MATHEMATICS

75. Find the initial poin of v = -3i + j +2k if the terminal point is (5, 0, -1). A. (8,1, -3) B. (8, -1, 3) C. (8,-1,-3) D. (8,1,3) 76. What is the laplace transform of 1/sqrt of t? A. (sqrt of pi)/s^2 B. (sqrt of pi)/s C. pi/sqrt of s D. sqrt of (pi/s) 77. A pair of dice is tossed. Find the probability of getting at most a total of 5. A. 5/9 B. 5/16 C. 5/18 D. 5/36 78. On a day when the temperature is 30 deg C. a cool drink is taken from a refrigerator whose temperature is 5 deg. C. If the temperature of the drink is 20 deg C after 10 minutes, what will its temperature be after 20 minutes? A. 21 deg C B. 24 deg C C. 28 deg C D. 26 deg C 79. The positive value of k which will make 4x^2 – 4kx + 4k +5 a perfect square trinomial is A. 6 B. 5 C. 4 D. 3 80. A stone advertises a 20 percent-off sale. If an article is marked for the sale at $24.48, what is the regular price? A. $30.60 B. $34.80 C. $36.55 D. $28.65 81. For a given arithmetic series the sum of the first 50 terms is 200, the sum of the next 50 terms is 2700. The first term of the series is: A. -12.2 B. -21.5 C. -20.5 D. -25.2 82. The total area of a cube is 150 sq. in. A diagonal of the cube is: A. 4 in B. 5 in C. 7.07 in D. 8.66 in 83. A tree is broken over by a windstorm. The tree was 90 feet high and the top of the tree is 25 feet from the foot of tree. What is the height of the standing part of the tree? A. 48.47 ft B. 41.53 ft C. 45.69 ft D. 44.31 ft 84. Goods cost a merchant & 72. At what price should he mark them so that he may sell them at a discount of 10% from his marked price and still make a profit of 20% on the selling price? A. $ 150 B. $ 200 C. $ 100 D. $ 250 85. An edge of the base of a regular hexagonal prism is 4 in. and a lateral edge is 9 in. Find the lateral area of the prism. A. 216 sq. in. B. 299 sq. in. C. 206 sq. in. D. 288 sq. in. 86. In a potato race, 8 potatoes are place 6 ft apart on a straight line, the first being 6 ft from the basket. A contestant starts from the basket and puts one potato at

REGISTERED ELECTRICAL ENGINEERS PRE-BOARD EXAMINATION AUGUST 2014 MATHEMATICS

a time into the basket. Find the total distance must run in order to finish the race. A. 423 ft B. 432 ft C. 428 ft D. 436 ft 87. Given that sin theta = 3/5 and theta is acute, find cos 2theta. A. -7/25 B. -4/5 C. 7/25 D. 4/25 88. A side and a diagonal of a parallelogram are 12 inches and 19 inches, respectively. The angle between the diagonals, opposite the given side is 124 degrees. Find the length of the other diagonal. A. 7.48 in B. 7.84 in C. 8.47 in D. 8.74 in 89. A window in Mr. Royce’s house is stuck. He takes an 8-inch screwdriver to pry open the window. If the screwdriver rests on the still (fulcrum) 3 inches from the window and Mr. Royce has to exert a force of 10 pounds on the other end to pry open the window, how much force was the window exerting? A. 12-2/3 B. 14-2/3 C. 18-2/3 D. 16-2/3 90. A boat, propelled to move at 25 mi/hr in still water, travels 4.2 mi against the river current in the same time that it can travel 5.8 mi with the current. Find the speed of the current in mi/hr. A. 4 B. 5 C. 3 D. 2 91. An open-top cylindrical tank is made of metal sheet having an area of 43.82 square meter. If the diameter is 2/3 the height, what is the height of the tank? A. 3.24 m B. 2.43 m C. 4.23 m D. 5.23 m 92. How much water must be added to 8 gallons of 80% boric solution to reduce it to a 50% solution? A. 4 gal B. 4-4/5 gal C. 5 gal D. 5-3/5 gal 93. The line y = 3x + b passes through the point (2, 4). Find the b. A. 2 B. 10 C. -2

D. -10

94. The simplest form of in (𝒆𝟑𝒙 ) is ______ A. 3 B. 𝒆𝒙

D.3x

C. e

95. Thirty degrees is how many radius? A. pi/3 B. pi/6 C. pi/4

D.

pi/2

96. If the measure of one angle of a regular polygon is 135 degrees, then the number of sides of that polygon is ______. A. 4 B. 6 C. 8 D. 9 97. What is the Laplace transform of 𝒆−𝟐𝒕 A. 1/s-2 B. 1/s+2 C. 1/s-1

D. 1/s+1

REGISTERED ELECTRICAL ENGINEERS PRE-BOARD EXAMINATION AUGUST 2014 MATHEMATICS

98. The area in the second quadrant of the circle 𝒙𝟐 + 𝒚𝟐 = 𝟑𝟔 is revolved about the line y+10=0. What is the volume? A. 228.63 B. 2228.83 C. 2233.43 D. 2208.53 99. The average of six scores is 83. If the highest score is removed, the average of the remaining scores is 81.2. Find the highest score. A. 91 B. 92 C. 93 D. 94 100. The sum of the base and altitude of an isosceles triangle is 36 cm. Find the altitude of the triangle if its area is to be a maximum. A. 18 cm B. 16 cm C. 9 cm D. 17 cm

REGISTERED ELECTRICAL ENGINEERS PRE-BOARD EXAMINATION MARCH 2013 MATHEMATICS

1. If the man sleeps from 6:48 PM up to 7:30 AM. The number of hours and minutes he sleeps is. A. 11 hrs and 42 min C. 13 hrs and 42 min B. 12 hrs and 42 min D. 10 hrs and 42 min 2. The price of a ballpen rises from Php 4.00 to Php 12.00. What is the percent increase in price? A. 100 percent C. 150 percent B. 120 percent D. 200 percent 𝜋𝑥

3. Evaluate lim(2 − 𝑥)^tan( 2 ). 𝑥→1

A. e^(2/pi)

B. e^(pi/2)

C. e^(2pi)

4. Thirty is 40 percent of what number? A. 60 B. 70 C. 75

D. 0

D. 80

5. Roll a pair of dice. What is the probability that the sum of two numbers is 11? A. 1/36 B. 1/9 C. 1/18 D. 1/20 6. If the logarithm of MN is 6 and the logarithm of N/M is 2, find the logarithm of M. A. 2 B. 3 C. 4 D. 6 7. The mean duration of television commercials on a given network is 75 seconds, with a standard deviation of 20 seconds. Assume that duration time are approximately normally distributed. What is the approximate probability that a commercial will last less than 35 seconds? A. 0.055 B. 0.025 C. 0.045 D. 0.035 8. In how many ways can 5 people be lined up if two particular people refuse to follow each other? A. 52 B. 62 C. 72 D. 82 9. Which of the following is not included? A. 0.60 B. 60% C. 0.06

D. 3/5

10. Which of the following is not included? A. 0.60 B. 60% C. 0.06

D. 3/5

11. The area of the circle is 89.42 sq. in. What is its circumference? A. 32.25 in B. 33.52 in C. 35.33 in D. 35.55 in 12. If a truck parks in at 1 PM in a parking lot and leaves at 4 PM. Find the number of hours it stayed at the parking lot. A. 1 B. 2 C. 3 D. 4

REGISTERED ELECTRICAL ENGINEERS PRE-BOARD EXAMINATION MARCH 2013 MATHEMATICS

13. If (x+3) : 10=(3x-2) : 8, find 2x-1. A. 1 B. 3

C. 4

D. 2

14. Evaluate the laplace transform of t^n. A. n!/s^n B. n!/s^(n+1) C. n!/2s^n D. n!/2s^(n+1) 15. Find the volume generated by rotating a circle x^2+y^2+6x+4y+12=0 about the y-axis. A. 58.24 B. 62.33 C. 78.62 D. 59.22 16. Determine all the values of 1^sqrt. of 2. A. sin (sqrt. of 2 kpi) + icos (sqrt. of 2 kpi) B. cos (sqrt. of 2 kpi) + isin (sqrt. of 2 kpi) C. sin (2sqrt. of 2 kpi) + icos (2sqrt. of 2 kpi) D. cos (2sqrt. of 2 kpi) + isin (2sqrt. of 2 kpi) 17. The slope of the curve y^2-xy-3x=1 at the point (0, -1) is A. -1 B. -2 C. 1 D. 2 18. Express Ten million forty three thousand seven hundred seventy one. A. 10,403,771 B. 10,433,771 C. 10,430,771 D. 10,043,771 19. Find the length of the curve r = 8 sin theta. A. 8 B. 4 C. 8 pi

D. 4 pi

20. A pole which leans 11 degrees from the vertical toward the sun cast a shadow 12 m long when the angle of elevation of the sun is 40 degrees. Find the length of the pole. A. 15.26 m B. 14.26 m C. 13.26 m D. 12.26 m 21. How long is the latus rectum of the elipse whose equation is 9x^2+16y^2576=0? A. 7 B. 9 C. 10 D. 15 22. If the initial and final temperatures of an object are 97.2 and 99 deg F respectively, find the change in temperature. A. 1.7 deg F B. 1.8 deg F C. 1.9 deg F D. 1.6 deg F 23. A rectangular plate 6 m by 8 m is submerge vertically in a water. Find the force on one face if the shroter side is uppermost and lies in the surface of the liquid. A. 941.76 kN B. 1,883.52 kN C. 3,767.04 kN D. 470.88 Kn

REGISTERED ELECTRICAL ENGINEERS PRE-BOARD EXAMINATION MARCH 2013 MATHEMATICS

24. Find the area enclosed by the loop y^2 = x(x-1)^2 A. 8/15 B. 8/17 C. 7/15

D. 7/17

25. The GCF of two numbers is 34, and their LCM is 4284. If one of the number is 204, the other number is A.714 B. 716 C. 2124 D. 3125 26. Jonas, star player of Adamson University has free throw shooting of 83%. The game is tied at 87-87. He is fouled and given 2 free throws. What is the probability that the game will go overtime? A. 0.3111 B. 0.6889 C. 0.0289 D. 0.9711 27. Find the work done in moving an object along a vector a = 31 + 4j if the force applied is b = 21 + j. A. 8 B. 9 C. 10 D. 12 28. If 3z + 5 = 7z-7. Find Z A. 3 B. 5

C. 7

D. 9

29. Where does the normal line of the curve y = x - x^2 at the point (1,0) intersect the curve a second time? A. (-3,-12) B. (0,0) C. (-2,-6) D. (-1,-2) 1+tan2 𝑥

30. Simplify 1+cot2 𝑥 A. sec2x B. tan2x

C. csc2x

D. cot2x

31. Jodi wishes to use 100 feet of fencing to enclose a rectangular garden. Determine the maximum possible area of her garden. A. 850 sq. ft. B. 1250 sq. ft. C. 625 sq. ft. D. 1650 sq. ft. 32. Simplify 1/(csc x + 1) + 1/(csc x – 1). A. 2 sec x tan x B. 2 csc x cot x C. 2 sec x D. 2 csc x 33. A certain chemical decomposes exponentially. Assume that 200 grams becomes 50 grams in 1 hour. How much will remain after 3 hours? A. 1.50 grams B. 6.25 grams C. 4.275 grams D. 3.125 grams 34. The locus of a point that moves so that the sum of its distances between two fixed points is constant called: A. a parabola B. a circle C. an elipse D. a hyperbola

REGISTERED ELECTRICAL ENGINEERS PRE-BOARD EXAMINATION MARCH 2013 MATHEMATICS

35. Michael’s age is seven-tenths of Richard’s age. In four years Michael’s age will be eight-elevenths of Richard’s age. How old is Michael? A. 26 yrs. B. 28 yrs. C. 40 yrs. D. 48 yrs. 36. A conic section whose eccentricity is equal to one (1) is known as: A. a parabola B. an elipse C. a circle D. a hyperbola 37. The angle of a sector is 30 degrees and the radius is 15 cm. What is the area of a sector? A. 59.8 sq. cm. B. 58.9 sq. cm. C. 89.5 sq. cm. D. 85.9 sq. cm. 38. In a conic section, if the eccentricity is greater than (1), the locus is: A. a parabola B. an elipse C. a circle D. a hyperbola 39. If f’(x) = sin x and f(pi) = 3, then f(x) = A. 4 + cos x B. 3 + cos x C. 2 – cos x D. 4 – cos x 40. Two stones are 1 mile apart and are of the same level as the foot of a hill. The angles of depression of the two stones viewed from the top of the hill are 5 degrees and 15 degrees respectively. Find the height of the hill. A. 109.1 m B. 209.1 m C. 409.1 m D. 309.1 m 41. What is the equation of the line, in the xy-plane, passing through the point (6, 4) and parallel to the line with parametric equations x = 5t + 4 and y = t – 7? A. 5y – x = 14 B. 5x – y = 26 C. 5y – 4x = -4 D. 5x – 4y = 14 42. Evaluate (8+7i)^2 A. 15 + 112i C. -15 + 112i

B. 15 – 112i D. -15 – 112i

43. How far is the directrix of the parabola (x-4)^2 = -8(y-2) from the x-axis? A. 2 B. 3 C. 4 D. 1 44. A weight W is attached to a rope 21 ft long which passes through a pulley at P, 12 ft above the ground. The other end of the rope is attached to a truck at a point A, 3 ft above the ground. If the truck moves off at the rate of 10ft/sec, how fast is the weight rising when it is 7 ft above the ground? A. 9.56 ft/sec B. 7.82 ft/sec C. 8.27 ft/sec D. 6.25 ft/sec

REGISTERED ELECTRICAL ENGINEERS PRE-BOARD EXAMINATION MARCH 2013 MATHEMATICS

45. The first farm of 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. 8 46. Steve earned a 96% on his first math test, a 74% his second test, and 85% on 3 tests average. What is his third test? A. 82% B. 91% C. 87% D. 85% 47. The base radius of a right circular cone is 4 m while its slant height is 10 m. What is the surface area? A. 124.8 sq. m. B. 128.6 sq. m. C. 226.8 sq. m. D.125.7 sq. m 48. Ian remodel a kitchen in 20 hrs and Jack in 15 hours. If they work together, how many hours to remodel the kitchen? A. 8.6 B. 7.5 C. 5.6 D. 12 49. If 15% of the bolts produced by a machine will be defective, determine the probability that out of 5 bolts chosen at random, at most 2 bolts will be defective. A. 0.9754 B. 0.9744 C. 0.9734 D. 0.9724 50. Find the average rate of the area of a square with respect to its side x as x changes from 4 to 7. A. 9 B. 3 C. 11 D. 18 51. The equations for two lines are 3y – 2x = 6 and 3x + ky = -7. For what value of k will the two lines be parallel? A. -9/2 B. 9/2 C. -7/3 D. 7/3 52. 5pi/18 rad is how many deg? A. 60 B. 50

C. 30

D. 90

53. Find the point of infection of the curve y = x^3 + 3x^2 – 1. A. (-1, 1) B. (-2, 3) C. (0, -10) D. (-3, -1)

54. A fair coin is tossed three times. Find the probability that there will appear three heads. A. 1/4 B. 1/2 C. 1/8 D. 1/6 55. A spherical balloon inflated with r = 3(cube root of t) as t is greater than zero and t is less than equal or equal to 10. Find the rate of change of volume in cubic cm at t = 8. A. 37.70 B. 150.80 C. 113.10 D. 75.40

REGISTERED ELECTRICAL ENGINEERS PRE-BOARD EXAMINATION MARCH 2013 MATHEMATICS

56. Joe and his dad are bricklayers. Joe can lay bricks for a well in 5 days. With his father’s help, he can build it in 2 days. How long would it take his father to build it alone? A. 3-1/4 days B.3-1/3 days C. 2-1/3 days D.2 -2/3 days 57. Find x so that the line containing (x, 5) and (3, -4) has a slope of 3. A. 3 B. 4 C. 5 D. 6 58. Find the length of the chord of a circle of radius 20 cm subtended by a central angle of 150 degrees. A. 49 cm B. 42 cm C. 39 cm D. 36 cm 59. Find the area of the ellipse 4x^2 + 9y^2 =36. A. 15.71 B. 18.85 C. 21.99

D. 25.13

60. Convert Cartesian coordinates (9, -9, 2) into cylindrical coordinates. A. (-9sqrt. of 2, pi/4, 2) B. (9sqrt. of 2, pi/4, 2) C. (-9sqrt. of 2, 7pi/4, 2) D. (9sqrt. of 2, 7pi/4, 2) 61. The area of a square is 32 square feet. Find the perimeter of the square. A. 27. 71 feet B. 55. 43 feet C. 45. 25 feet D. 22.63 feet 62. If cos theta = -3/4 and tan theta is negative, the value of sin theta is A. -4/5 B. – (sqrt. of 7)/4 C. (4 sqrt. of 7)/7 D. (sqrt. of 7)/4

63. What is the numerical coefficient of the term containing x^3y^2 in the expansion of (x+2) ^5? A. 10 B. 20 C. 40 D. 80 64. Find the area bounded by y = 6x – x^2 and y = x^2 -4x. A. 125/3 B. 125/2 C. 100/3

D. 100/9

65. Find the second derivative of y = x ln x. A. x B. 1/x C. 1

D. x squared

66. What is 30% of 293? A. 87.9 B. 89.7

D. 98.2

C.92.8

67. The height (in feet) at anytime t (in seconds) of a projectile thrown vertically is h(t) = -16t^2 + 256t. What is the projectile’s average velocity for the first 5 seconds of travel? A. 48 fps B. 96 fps C. 176 fps D. 192 fps 68. Find the general solution of y” + 6y’ + 9y = x+ 1. A. y = (C1x + C2x2) e-3x + 1/27 + x/9

REGISTERED ELECTRICAL ENGINEERS PRE-BOARD EXAMINATION MARCH 2013 MATHEMATICS

C. y = (C1x + C2x2) e3x + 1/27 + x/9 B. y = (C1 + C2x) e-3x + 1/27 + x/9 D. y = (C1 + C2x) e3x + 1/27 + x/9 69. For a complex number z = 3 + j4 the modulus is A. 3 B. 4 C. 5 70. Evaluate lim

x →3

A. 3

D. 6

sqrt.of (x2 −9) 2𝑥−6

B. 0

C. infinity

D. Undefined

71. The probability that a man, age 60, will survive to age 70 is 0.80 the probability that a woman of the same age will live up to age 70 is 0.90. What is the probability that only one of the survives? A. 0.72 B. 0.26 C. 0.28 D. 0.0 72. Simplify 1(sec theta -1) + 1/ (sec theta + 1). A. 2 sec theta tan theta C. 2 sec theta B. 2 csc theta cot theta D. 2 csc theta 73. Find the base of an isosceles triangle whose vertical angle is 65 degrees and whose equal sides are 415 cm. A. 530 cm B. 464 cm C. 350 cm D. 446 cm 74. Find the general solution of y” + 10y = 0. A. y = C1 cos (sqrt. of 10x) + C2 sin (sqrt. of 10x) B. y = C1 cos (sqrt. of 5x) + C2 sin (sqrt. of 5x) C. y = C cos (sqrt. of 10x) D. y = C sin (sqrt. of 10x) 75. Evaluate the inverse Laplace transform of 6 over (s^2 + 4). A. 3 sin 2t B. 3 cos 2t C. 3 sinh 2t D. 3 cosh 2t 76. Evaluate L {sin t cos t} A. 1/2 (s^2 + 4) C. 1/ (s^2 + 1)

B. 1/ (s^2 + 4) D. 1/2 (s^2 + 1)

77. Determine the moment of inertia of the area enclosed by the curved x^2 + y^2 = 36 with respect to the line y = 8. A. 8628 B. 8256 C. 7642 D. 7864 78. A man sleeps on Monday, Tuesday, Wednesday, Thursday and Friday for 8, 6, 7, 4, and 5 hours, respectively. Find the number of hours he slept for 5 days. A. 35 B. 31 C. 30 D. 25 79. Find A fir which y = Ae^x will satisfy y” - 2y’ = 4e^x.

REGISTERED ELECTRICAL ENGINEERS PRE-BOARD EXAMINATION MARCH 2013 MATHEMATICS

A. -1

B. -2

80. Simplify 1/csc2 theta. A. sin2 theta C. cot2 theta

C. -3

D. -4

B. cos2 theta D. tan2 theta

81. Timothy leaves home for Legaspi City 400 miles away. After 2 hours, he has to reduce his speed by 20 mph due to rain. If he takes 1 hour for lunch and gas and reaches Legaspi City 9 hours after left home, what was his initial speed? A. 63 mph B. 62 mph C. 65mph D. 64 mph 82. How many arrangements of the letters in the word “VOLTAGE” begin with a vowel and end with a consonant? A. 1490 B.1440 C.1460 D.1450 83. An airplane flying with the wind, took 2 hours to travel 1000 km and 2.5 hours in flying back. What was the wind velocity in kph? A. 50 B. 60 C. 70 D. 40 84. A woman is paid $ 20 for each day she works and the forfeits $ 5 for each day she is idle. At the end of 25 days she nets $ 450. How many days did she work? A. 21 B. 22 C.23 D.24 85. Find the centroid if the solid formed by revolving about x = 2 bounded by y = x^3, X = 2 and y = 0. A. (2, 10/30) B. (2, 10/7) C. (2, 10/9) D. (2, 10) 86. What is the lowest common factor of 10 and 32. A. 320 B. 2 C. 180

D. 90

87. The positive value of k which make 4x^2 – 4kx + 4k + 5 a perfect square trinomial is A. 6 B. 5 C. 4 D. 3 88. A tree is broken over by a windstorm. The tree was 90 feet high and the top of the tree is 25 feet from the foot of the tree. What is the height of the standing part of the tree? A. 48.47 ft B. 41.53 ft C. 45.69 ft D. 44.31 ft 89. The Rotary Club and the Jaycee Club had a joint party. 120 members of the Rotary Club and 100 members of the Jaycees Club also attended but 30 of those attended are members of both clubs. How many persons attended the party? A. 190 B. 220 C. 250 D. 150

REGISTERED ELECTRICAL ENGINEERS PRE-BOARD EXAMINATION MARCH 2013 MATHEMATICS

90. If sin 3A = cos 6B, then A. A + B = 90 deg B. A + 2B = 30 deg

C. A + B = 180 deg D. A +2B = 60 deg

91. MCM is equivalent to what number? A. 1000 B. 2000 C. 1800

D.1900

92. What is the discriminant of the equation 5x^2 – 6x + 1 = 0? A. 12 B. 20 C. 16 D. 18 93. The number of ways can 3 nurses and 4 engineers be seated in a bench with the nurses seated together is A. 144 B.258 C. 720 D. 450 94. Find the distance from the plane 2x + y – 2z + 8 = 0 to the point (-1, 2, 3). A. 1/3 B. 2/3 C. 4/3 D. 5/3 95. Find the value of x if log x base 12 = 2. A. 144 B. 414 C. 524

D. 425

96. If f(x) = x^3 – 2x – 1, then f (-2) = A. -17 B. -13

D. -1

C. -5

97. A particle moves along a line with acceleration 2 + 6t at time t. When t = 0, its velocity equals 3 and it is at position s = 2. When t =1, it is at position s = A. 2 B. 5 C. 6 D. 7 98. The edge of a cube has length 10 in., with a possible error of 1 %. The possible error, in cubic inches, in the volume of cube is A. 3 B. 1 C. 10 D. 30 99. What is the rate of change of the area if an equilateral triangle with respect to its side s when s = 2? A. 0.43 B. 0.50 C.10 D. 1.73 100.

If ∫ ˥ f(x)dx = 4 and ∫ ˥ g(x)dx = 2, find ∫ ˥ [3f(x) + 2g (x) + 1]dx. A. 22 B. 23 C. 24 D. 25

REGISTERED ELECTRICAL ENGINEERS PRE-BOARD EXAMINATION AUGUST 2013 MATHEMATICS

1. Simplify 1/(csc x + 1) ÷ 1/(csc – 1) A. 2 sec x tan x B. 2 csc x cot x

C. 2 sec x

D. 2 csc x

2. A bus leaves Manila at 12 NN for Baguio 250 km away, traveling an average of 55 kph. At the same time, another bus leaves Baguio for Manila traveling 65kph. At what distance from Manila they will meet? A. 135.42 km B. 114.56 km C. 129.24 km D. 181.35 km 3. Simplify (cos ß – 1)(cos ß + 1) A. -1/ sin2 ß B. -1/cos2 ß

C. -1/ csc2 ß

D. -1/sec2 ß

4. Simplify 1/(csc x + cot x) + 1/(csc x – cot x) A. 2 cos x B. 2 sec x C. 2 csc x

D. 2 sin x

5. From past experience, it is known 90% of one-year-old children can distinguish their mother’s voice from the voice of a similar sounding female. A random sample of 20 one year’s old are given this voice recognize test. Find the probability that all 20 children recognize their mother’s voice. A. 0.122 B. 0.500 C. 1.200 D. 1.22 6. Find the differential equations of the family of lines passing through the origin. A. xdx – ydy = 0 C. xdx + ydy = 0 B. xdy – ydx = 0 D. ydx + xdy = 0 7. A chord passing through the foci’s of the parabola y^2 = 8x has ones end at the point (8,8). Where is the other end of the chord? A. (1/2, 2) B. (-1/2, -2) C. (-1/2, 2) D. (1/2, -2) 8. Find the radius of the circle inscribed in the triangle determined by the line y = 2 x + 4, y = -x – 4, and y = 7 𝑥 + 2 A. 2.29

B. 0.24

C. 1.57

D. 0.35

9. What would happen to the volume of a sphere if the radius is tripled? A. Multiplied by 3 B. Multiplied by 9

C. Multiplied by 27 D. Multiplied by 6

10. Six non-parallel lines are drawn in a plane. What is the maximum number of point of intersection of these lines? A. 20 B.12 C. 8 D. 15 11. In a triangle ABC where AC=4 and angle ACB=90 degrees, an altitude t is drawn from C to the hypotenuse. If t = 1, what is the area of the triangle ABC? A. 1.82 B. 1.78 C. 2.07 D. 2.28

REGISTERED ELECTRICAL ENGINEERS PRE-BOARD EXAMINATION AUGUST 2013 MATHEMATICS

12. In a 15 multiple choice test questions, with five possible choices if which only on is correct, what is the standard deviation of getting a correct answer? A. 1.55 B. 1.65 C. 1.42 D. 1.72 13. What is the area bounded by the curve y = tan2 x and the y = 0 and x = pi/2? A. 0 B. infinity C. 1 D. Ɵ 𝑒𝑥

14. What is the power series of 1−𝑥 about x = 0? A. B.

1 − 2𝑥 + 𝟏 − 𝟐𝒙 +

𝟓 𝟐

5 2

8

𝑥2 − 3 𝑥3 + ⋯ 𝟖

𝒙𝟐 + 𝟑 𝒙𝟑 + ⋯

C. 2𝑥 − D. 2𝑥 +

5 2 5 2

8

𝑥2 + 3 𝑥3 + ⋯ 8

𝑥2 − 3 𝑥3 + ⋯

15. What is the vector which is orthogonal both to 9i + 9j and 9l + 9k? A. 81l + 81j – 81k C.81l - 81j + 81k B. 81l – 81j – 81k D.81l+81j – 81k 16. 34 is 76 percent of what number? A. 16 B. 40

C. 36

D. 32

C. 16

D. 8

17. Evaluate lim(𝑥 2 − 4)/(𝑥 − 4) 𝑥→4

A. 4

B. 2 4

18. If sin A = − 5 and cot B = 4, both in Quadrant III, the value of sin ( A + B) is A. -0.844 B. 0.844 C. -0.922 D. 0.922

19. A force of 100 m perimeter such that its width is 6m less than thrice its length. Find the width? A. 28 m B. 14 m C. 36 m D. 40 m 20. Evaluate log (2 – 5i) A. 0.7 – 0.5i B. -0.7 + 0.5i

C. 0.7 + 0.5i

D. -0.5 – 0.7i

21. An air balloon flying vertically upward at constant speed is situated 150m horizontally from an observer. After one minute, it is found that the angle of elevation from the observer is 28 deg 50 min. what will be then the angle of elevation after 3 minutes from its initial position? A. 48 deg B. 56 deg C. 61 deg D. 50 deg 22. If m is jointly proportional to G and x, where a,b,c and d are constant. Therefore. A. M = aG + bx C. m = aG B. m = aGz D. m = bG

REGISTERED ELECTRICAL ENGINEERS PRE-BOARD EXAMINATION AUGUST 2013 MATHEMATICS

23. In how many ways can a student going to abroad accompanied by 3 teachers selecting from 6 teachers? A. 16 B. 24 C. 20 D. 12 24. If a man travels 1 km north, 3 km west, 5 km south, and 7 km east, what is his resultant displacement vector? A. 5.667 km, 45 deg above + x-axis C. 5.667 km, 225 deg above + x-axis B. 5.667 km, 45 deg above – x-axis D. 5.667 km, 225 deg above – x-axis 25. What is the general solution of (D4 – 1) y(t) = 0? A. y = c1Ɵt + c2Ɵ-t +c3 cost + c4 sint B. y = c1Ɵt + c2Ɵt +c3 Ɵ-t + c4t Ɵ-t

C. y = c1Ɵt + c2Ɵ-t D. y = c1Ɵt + c2tƟt

26. Marsha is 10 years older than John, who is 16 years old. How old is Marsha? A. 24 yrs. B. 26 yrs. C. 6 yrs. D. 12 yrs.

27. Seven times a number x increased by 2 is expressed as A. 7(x + 20 B. 2x + 7 C. 7x + 2 D. 2(x + 7) 28. The plane rectangular coordinate system is divided into four parts which are known as: A. octants B. quadrants C. axis D. coordinates 29. A student already finished 70% of his homework in 42 minutes. How many minutes does she still have to work? A. 18 B. 15 C. 20 D. 24 30. In how many ways can 5 people be lined up to get on a bus, if a certain 2 persons refuse to follow each other? A. 36 B. 48 C. 96 D. 72 31. Water is being pumped into a conical tank at the rate of 12 cu.ft/mins. The height of the tank is 10 ft and its radius is _ ft. How fast is the water level rising when the water height is _ ft? A. 2/3 pi ft/min B. 3/2 pi ft/min C. 3/4 pi ft/min D. 4/3pi ft/min 32. Write the equation of a line with x intercept a = -1, and y intercept b = 5 A. 8x + y – 8 = 0 C. 8x + y + 8 = 0 B. 8x – y + 8 = 0 D. 8x – y – 8 = 0 33. In a single throw of a pair of dice, find the probability that the sum is 11 A. 1/12 B. 1/16 C. 1/36 D. 1/18 34. Find the area bounded by one arch of the companion to the cycloid x = a theta, y = a (1 – cos theta) and the y-axis A. 2pi a^2 B. 4pi a ^2 C. pi a ^2 D. 3pi a^2

REGISTERED ELECTRICAL ENGINEERS PRE-BOARD EXAMINATION AUGUST 2013 MATHEMATICS

35. A rectangular plate 6m by 8m is submerged vertically in a water. Find the force on one face if the shorter side is uppermost and lies in the surface of the liquid. A. 941.76 kN B. 1,883.52 kN C. 3,767.04 kN D. 470.88 kN 36. Michael is four times as old as his son Carlos. If Michael was 18 years old when Carlos was born, how old is Michael now? A. 36 yrs. B. 20 yrs. C. 24 yrs D. 32 yrs. 37. In polar coordinate system, the distance from a point to the pole is known as: A. polar angle C. x-coordinate B. radius vector D. y-coordinate 38. A certain man sold his balot at Php1.13 per piece. If there 100 balot sold all in all, how much is his total collection? A. Php 113.00 C. Php 112.00 B. Php 115.00 D. Php 116.00 39. A certain population of bacteria grows such that its rate of change is always proportional to the amount present. It doubles in 2 years, if in 3 years there are 20,000 of bacteria present, how much is present initially? A. 9,071 B. 10,071 C. 7,071 D. 8,071 40. In throwing a pair of dice, what is the probability of getting a total of 5? A. 1/36 B. 1/9 C. 1/16 D. 1/8 41. What is the distance between at any point P(x ,y) on the ellipse b 2x2 + a2y2 = a2b2 to its focus. A. by ±ax B. b ± ay C. ay ± bx D. a ± ex 42. Calculate the eccentricity of an ellipse whose major axis and latus rectum has length of 10 and 32/5, respectively. A. 0.4 B. 0.5 C. 0.8 D. 0.6 43. Evaluate (3 + j4)(3 – j4) A. 9 – j16 B. 9 + j16

C. 25

D. 36

44. What is the area bounded between y = 6x^2 and y = x^2 + 7? A. 9 B. 10 C. 11

D. 12

45. Two vertical poles are 10 m apart. The poles are 5 m and 8 m, respectively. They are to be stayed by guy wires fastened to a single stake on the ground and attached to the tops of the poles. Where should the stake be placed to use the least amount of wire? A. 6.15 m from 5 m pole C. 6.51 m from 5 m pole B. 6.15 m from 8 m pole D. 6.51 m from 8 m pole

REGISTERED ELECTRICAL ENGINEERS PRE-BOARD EXAMINATION AUGUST 2013 MATHEMATICS

46. A and B are points on circle Q such that triangle AQB is equilateral. If AB = 12, find the length of arc AB. A. 15.71 B. 9.42 C. 12.57 D. 18.85 47. The area under the portion of the curve y = cosx from x = 0 to x = pi/2 is revolved about the x-axis. Find the volume of the solid generated. A. 2.47 B. 2.74 C. 3.28 D. 3.82 48. Find the length of arc of r = 2/(1 +costheta) from theta = 0 to theta = pi/2. A. 2.64 B. 3.22 C. 2.88 D. 3.49 49. Find the equation of the straight line which passes through the point (6, -3) and with an angle of inclination of 45 degrees. A. x + y = 3 B. 4x – y =27 C. x- 2y = 12 D. x – y = 9 50. The equation of the directrix of the y^2 = 6x is A. 2x – 3 = 0 B. 2x + 3 = 0 C. 3x – 2 = 0

D. 3x + 2 = 0

51. Find the area bounded by r = 4(sq.rt. of cos 2 theta). A. 16 B. 8 C. 4

D. 12

52. In an arithmetic progression whose first term is 5, the sum of 8 terms is 208. Find the common difference. A. 3 B. 4 C. 5 D. 6 53. If 3x = 7y, then 3x2/7y2 = ? A. 1 B. 3/7

C. 7/3

D. 49/9

54. What is the area of the ellipse whose eccentricity is 0.60 and whose major axis has a length of 6? A. 40.21 B. 41.20 C. 42.10 D. 40.12 55. Tickets to the school play sold at $4 each for adults and $1.50 each for children. If there were four times as many adult’s tickets sold as children’s tickets, and the total were $3500. How many children’s tickets were sold? A. 160 B. 180 C. 200 D. 240 56. If the line kx + 3y + 8 = 0 has a slope of 2/3, determine k. A. -3 B. -2 C. 3 D. 2 57. The Rotary Club and the Jaycees Club had a joint party. 120 members of the Rotary Club attended and 100 members of the Jaycees Club also attended but 30 of those who attended are members of both parts. How many persons attended the party? 58. A. 190 B. 220 C. 250 D. 150

REGISTERED ELECTRICAL ENGINEERS PRE-BOARD EXAMINATION AUGUST 2013 MATHEMATICS

59. Find the value of k for which the graph of y = x^3 + kx^2 + 4 will have an inflection point at x = -1. A. 3 B. 4 C. 2 D. 1 60. Solve for x if log4x = 5. A. 2048 B. 256

C. 625

D. 1024

61. An observer wishes to determine the height of a tower. He takes sights at the top of the tower from A and B, which are 50 ft apart at the same elevation on a direct line with the tower. The vertical angle at point A is 30 degrees and at point B is 40 degrees. What is the height of the tower? A. 85.60 ft B. 143.97 ft C. 110.29 ft D.92.54 ft 62. If four babies are born per minute, how many babies are born in one hour? A. 230 B. 250 C. 240 D. 260 63. What was the marked price of a shirt that sells at P 225 after a discount of 25%? A. P 280 B. P 300 C. P 320 D. P 340 64. Which number is divisible by both 3 and 5? A. 275 B. 445 C. 870

D. 955

65. If s = t^2 – t^3, find the velocity when the acceleration is zero A. 1/4 B. 1/2 C. 1/3 D. 1/6 66. Find k so that A = (3, -2) and B = (1, k) are parallel A. 3/2 B. -3/2 C. 2/3

D. -2/3

67. A lady gives a dinner party for six guest. In how many may they be selected from among 10 friends? A. 110 B. 220 C. 105 D. 210 68. A wheel 4 ft in diameter is rotating at 80 rpm. Find the distance (in ft) traveled by a point on the rim in 1 s. A. 9.8 ft B. 19.6 ft C. 16.8 ft D. 18.6 ft 69. If f(x) = 6x – 2 and g(x) = 4x + 3, then f(g(2)) = ____? A. 52 B. 53 C. 50

D. 56

70. From the top of lighthouse, 120 ft above the sea, the angle of depression of a boat is 15 degrees. How far is the boat from the lighthouse? A. 444 ft B. 333 ft C. 222 ft D. 555 ft 71. If 8 men take 12 days to assemble 16 machines, how many days will it take 15 men to assemble 50 machines? A. 16 B. 24 C. 16 D. 20

REGISTERED ELECTRICAL ENGINEERS PRE-BOARD EXAMINATION AUGUST 2013 MATHEMATICS

72. Find the coordinate of the highest point of the curve x = 90t, y = 96t – 16t^2. A. (288, 144) B. (144, 288) C. (288, -144) D.(-144, 288) 73. The vertex of parabola y = (x – 1)^2 + 2 is _____. A. (-1, 2) B. (1, 2) C. (1, -2)

D. (-1, -2)

74. Two angles measuring p deg and q are complementary. If 3p – 2q = 40 deg, then the smaller angle measures A. 40 deg B. 44 deg C. 46 deg D. 60 deg 75. In an ellipse, a chord which contains a focus and is in a line perpendicular to the major axis is a: A. latus rectum C. focal width B. minor axis D. conjugate axis 76. Determine the rate of a woman rowing in still water and the rate of the river current, if it takes her 2 hours to row 9 miles with the current and 6 hours to return against the current. A. 1 mph B. 2 mph C. 3 mph D. 4 mph

77. If f(x) = sin x and f(pi) = 3, then f(x) = A. 4 + cos x B. 3 + cos x C. 2 – cos x

D. 4 – cos x

78. What is the value of the circumference of a circle at the instant when the radius is increasing at 1/6 the rate the area is increasing? A. 3 B. 3/pi C. 6 D. 6/pi 79. A ball is thrown from the top of a 1200-foot building. The position function expressing the height h of the ball above the ground at any time t is given as h(t) = -16t^2 – 10t + 1200. Find the average velocity for the first 6 seconds of travel. A. -202 ft/sec B. -106 ft/sec C. -96 ft/sec D. -74 ft/sec −1

80. ∫−2 |𝑥 3 |𝑑𝑥 = A. -7/8

B. 7/8

C. -15/4

D. 16/4

81. The distance covered by an object falling freely rest varies directly as the square of the time of falling. If an object falls 144 ft in 3 sec, how far will it fall in 10 sec? A. 1200 ft B. 1600 ft C. 1800 ft D. 1400 ft 82. For what values(s) of x will the tangent lines to f(x0 + ln x and g(x) = 2x^2 be parallel? A. 0 B. 1/4 C. 1/2 D. ±1/2

REGISTERED ELECTRICAL ENGINEERS PRE-BOARD EXAMINATION AUGUST 2013 MATHEMATICS

83. What kind of graph has r =2 sec theta? A. Straight line B. parabola C. ellipse

D. hyperbola

84. The probability of A’s winning a game chess against B is 1/3. What is the probability that A will win at least 1 of a total 3 games? A. 11/27 B. 6/27 C. 19/27 D. 16/27 85. If f(x) = 2^(x^3 + 1), then to the nearest thousandth f(1) = A. 2.000 B. 2.773 C. 4.000 D. 8.318 𝑎

𝑎

86. If line function f is even and ∫0 𝑓(𝑥)𝑑𝑥 = 5𝑚 − 1, then ∫−𝑎 𝑓(𝑥)𝑑𝑥 = A. 0 B. 10m – 2 C. 10m – 1 D. 10m

87. What is the slope of the line through (-1, 2) and (4, -3)? A. 1 B. -1 C. 2 D. -2 88. The axis of the hyperbola through its foci is known as: A. Conjugate axis B. major axis C. transverse axis D. minor axis 89. Determine a point of inflection for the graph of y = x^3 + 6x^2 A. (-2, 16) B. (0, 0) C. (-1, 5) D. (2, 32) 90. Clarify the graph of the equation x^2 + xy + y^2 – 6 = 0. A. circle B. parabola C. ellipse

D. hyperbola

91. What is the coefficient of the (x – 1)^3 term in the Taylor series expansion of f(x) = ln x expanded about x = 1? A. 1/6 B.1/4 C. 1/3 D. 1/2 92. If x varies directly as y and inversely as z, and x = 14, when y = 7 and z = 2, find x when y = 16 and z = 4. A. 4 B. 14 C. 8 D. 16 93. Solve the differential equation A. y = cx

1

B. y = 𝑥 + 𝑐

𝑑𝑦

𝑦

+𝑥 =2 𝑑𝑥 C. y = 3x + c

𝒄

D. y = x + 𝒙

94. In triangle ABC, AB = 40 m, BC = 60 m and AC = 80m. How far from a will the other end of the bisector angle B located along the line AC? A. 40 B. 32 C. 38 D. 35 95. What amount should an employee receive a bonus so that she would net $500 after deducting 30% from taxes? A. $ 714.29 B. $814.93 C. $ 624.89 D. $ 538.62

REGISTERED ELECTRICAL ENGINEERS PRE-BOARD EXAMINATION AUGUST 2013 MATHEMATICS

96. A rectangular trough us 8ft long, 2ft across the top, and 4 ft deep. If water flows in at a rate of 2 cu. Ft per min. how fast is the surface rising when the water is 1ft deep? A. 1/4 ft/min B. 1/6 ft/min C. 1/3 ft/min D. 1/5 ft/min 97. If the parabola y = x^2 + C is tangent to the line y = 4x + 3, find the value of C. A. 4 B. 7 C. 6 D. 5 98. A parabola having its axis along the x-axis passes through (-3, 6). Compute the length of latus rectum if the vertex is at the origin. A. 12 B. 8 C. 6 D. 10 99. If the average value of the function f(x) = 2x^2 on the interval (0, c) is 6, then c = A. 2 B. 3 C. 4 D. 5 100. Find the volume of the tetrahedron bounded by the coordinate planes and the plane z = 6 – 2x + 3y. A. 4 B. 5 C. 6 D. 3

REGISTERED ELECTRICAL ENGINEERS PRE-BOARD EXAMINATION AUGUST 2012 MATHEMATICS

1. The equation y^2 = cx is the general equation of: A.y’ = 2y/x B. y’ = 2x/y C. y’ = y/2x

D. y’ = x/2y

2. A line segment joining two points on a circle is called: A. arc B. tangent C. sector

D. chord

3. Sand is pouring to form a conical pile such that its altitude is always twice its radius. If the volume of a conical pile is increasing at the rate of 25 pi cu.ft/min, how fast is the radius is increasing when the radius is 5 feet? A. 0.5 ft/min B. 0.5 pi ft/min C. 5 ft/min D. 5 pi ft/min 4. Evaluate ʃ ʃ 2r²sin Ө dr dӨ, 0 > r >sin Ө, > Ө > pi/2 A. pi/2 B. pi/8 C. pi/24

D. pi/48

5. A shopkeeper offers a 25% discount on the marked price on an item. In order to now cost $ 48, what should the marked price be? A. $ 12 C. $ 60 B. $ 36 D. $ 64 6. An observer wishes to determine the height of a tower. He takes sights at the top of the tower from A to B, which are 50 ft. apart, at the same elevation on a direct line with the tower. The vertical angle at point A is 30 degrees and at point B is 40 degrees. What is the height of the tower? A.85.60 ft B. 143.97 ft C. 110.29 ft D. 92.54 ft 7. A tangent to a conic is a line A. which is parallel to the normal B. which touches the conic at only one point C. which passed inside the conic D. all of the above 8. Find the area of the triangle which the line 2x – 3y + 6 = 0 forms with the coordinate axes. A.3 B. 4 C. 5 D. 2 9. Find the general solution of (D² - D + 2)y = 0 A. y = e^x/2 (C1 sin sqrt. 7/2 x + C2 cos sqrt. 7/2 x) B. y = e^x/2 (C1 sin sqrt. 7/2 x - C2 cos sqrt. 7/2 x) C. y = e^x/2 (C1 cos sqrt. 7/2 x + C2 sin sqrt. 7/2 x) D. y = e^x/2 (C1 cos sqrt. 7/2 x - C2 sin sqrt. 7/2 x) 10. If 10 is subtracted from the opposite of a number, the difference is 5. What is the number? A.5 B.15 C.-5 D. -15 11. If y = 5 – x, find x when y = 7 A.12 B.-12

C. 2

D. -2

REGISTERED ELECTRICAL ENGINEERS PRE-BOARD EXAMINATION AUGUST 2012 MATHEMATICS

12. A ranch has a cattle and horses in a ratio of 9:5. If there are 80 more head of cattle than horses, how many animals are on the ranch? A.140 B. 168 C. 238 D. 280 13. Martin bought 3 pairs of shoes at P240 each pair and 3 pieces of t-shirts at P300 each. How much did he spent? A. P720 B. P900 C. P22,500 D. P 1,620 14. Find the standard equation of the circle with the center at (1,3) and tangent to the line 5x – 12y -8 =0. A. (x-1)2 + (y-3)2 = 8 C. (x-1)2 + (y-3)2 = 9 2 2 B. (x-1) + (y-3) = 12 D. (x-1)2 + (y-3)2 = 23 15. Find the volume of the solid formed by revolving the area bounded by the curve y2 = (x3)(1-x) in the first quadrant about x-axis. A.0.137 B. 0.147 C. 0.157 D.0.167 16. In the pile of logs, each layer contains one more log than the layer above and the top contains just one log. If there are 105 logs in the pile, how many layers are there? A. 11 B. 12 C. 13 D. 14 17. A wall 8 feet high is 3.375 feet from a house. Find the shortest ladder that will reach from the ground to the house when leaning over the wall. A. 16.526 ft B. 15.625 ft C. 14.625 ft D. 17.525 ft 18. If f(x) = 10x + 1, then f(x+1) is equal to A. 10(10x ) B. 9(10x)

C. 1

D. 9(10x+1)

19. A particle moves on a straight line with a velocity v = (4 – 2t)3 at time t. Find the distance traveled from t = 0 to t = 3. A. 32 B. 36 C. 34 D. 30 20. The area enclosed by the ellipse 4x2 + 9y2 = 36 is revolved about the line x = 3, what is the volume generated? A. 370.3 B. 360.1 C. 355.3 D. 365.10 21. If the vertex of y = 2x2 + 4x + 5 will be shifted 3 units to the left and 2 units downward, what will be the new location of the vertex? A. (-2, 1) B. (-5, -1) C. (-3,1) D. (-4,1) 22. A coat of paint of thickness 0.01 inch is applied to the faces of a cube whose edge is 10 inches, thereby producing a slightly larger cube. Estimate the number of cubic inches of paint used. A. 4 B. 6 C. 3 D. 5 23. Find the mass of lamina in the given region and density function: π D[(x, y)], 0 ≤ x ≤ 2 , 0 ≤ y ≤ cos x and ρ = 7x A. 2

B. 3

C. 4

D. 5

REGISTERED ELECTRICAL ENGINEERS PRE-BOARD EXAMINATION AUGUST 2012 MATHEMATICS

24. Find the area of the region bounded by the curves y = x2 – 4x and x + y = 0 A. 4.5 B. 5.5 C. 6 D. 5 25. A conic section whose eccentricity is less than one is known as: A. circle B. parabola C. hyperbola D. ellipse 26. The plate number of a vehicle consists of 5-alphanumeric sequence is arranged such that the first 2 characters are alphabet and the remaining 3 are digits. How many arrangements are possible if the first character is a vowel and repetitions are not allowed? A. 90 B. 900 C. 9,000 D. 90,000 27. The axis of the hyperbola, which is parallel to its directrices, is known as: A. conjugate axis B. transverse axis C. major axis D. minor axis 28. The minute hand of a clock is 8 units long. What is the distance traveled by the tip of the minute hand in 75 minutes. A. 10pi B. 20pi C. 25pi D. 40pi 29. Find k so that A = (3, -2) and B = (1, k) are perpendicular. A. 2 B. 3 C. 1/2

D. 3/2

30. The probability of a defect of a collection of bolts is 5%. If a man picks 2 bolts, what is the probability that does not pick 2 defective bolts? A. 0.950 B. 0.9975 C. 0.0025 D. 0.9025 1

31. If f(x) = x−2 ,(f·g)’*(1) = 6 and g’(1) = -1, then g(1) = A. -7 B. -5 C. 5

D. 7

32. 3 randomly chosen senior high school students were administered a drug test. Each student was evaluated as positive to the drug test (P) or negative to the drug test (N). Assume the possible combinations of the 3 students drug test evaluation as PPP, PPN, PNP, NPP, PNN, NPN, NNP, NNN. Assuming each possible combination is equally likely, what is the probability that at least 1 student gets a negative result? A. 1/8 B. 1/2 C. 7/8 D. ¼ 33. The tangent line to the function h(x) at (6, -1) intercepts the y-axis at y = 4. Find h’ (6). A. -1/6 B. -2/3 C. -4/5 D. -5/6 34. The cable of a suspension bridge hangs in the form if a parabola when the load is uniformly distributed horizontally. The distance between two towers is 150m, the points of the cable on the towers are 22 m above the roadway, and the lowest point on the cables is 7 m above the roadway. Find the vertical distance to the cable from a point in the roadway15 m from the foot of a tower. A. 16.6 m B. 9.6 m C. 12.8 m D. 18.8 m 35. In how many ways different orders may 5 persons be seated in a row?

REGISTERED ELECTRICAL ENGINEERS PRE-BOARD EXAMINATION AUGUST 2012 MATHEMATICS

A. 80

B. 100

36. The symbol “/” used in division is called. A. modulus B. minus

C. 120

D. 160

C. solidus

D. obelus

37. Find the area of one loop r2 = 16 sin 2theta. A. 16 B. 8 C. 4

D. 6

38. Find the centroid of the upper half of the circle x2 + y2 = 9. A. (0, 3/pi) B. (0, 4/𝐩𝐢) C. (0, 5/pi)

D.(0, 6/pi)

39. In polar coordinate system, the distance from a point to the pole is known as A. polar angle C. radius vector B. x-coordinate D.y-coordinate 40. The number that is subtracted in subtraction. A. minuend C. dividend B. subtrahend D. quotient 41. In how many ways can a person choose 1 or more of a 4 electrical appliances? A. 12 B. 13 C. 14 D. 15 42. The surface area of a spherical segment. A. lune B. Zone

C. Wedge

D. sector

43. A particle has a position vector (2cos2t, 1+3sint). What is the speed of the particle at time t = pi/4? A. 1.879 B. 4.5 C. 5.427 D. 7.245 44. If the equation is unchanged by the substitution of –x for x, its curve is symmetric with respect to the A. y-axis C. origin B. x-axis D. line 45 degrees with the axis 45. Find the number of sides of a regular polygon if each interior angle measures 108 degrees. A. 7 B. 8 C.5 D. 6 46. The integer part of common logarithm is called the________. A. radicand B. root C. characteristic mantissa 47. The constant “e” is named in honor of: A. Euler B. Eigen C. Euclid

D.

D. Einstein

48. A man rows upstream and back in 12 hours. If the rate of the current is 1.5 kph and that of the man in still water is 4 kph, what was time spent downstream? A. 1.75 hrs B. 2.75 hrs. C. 3.75 hrs D. 4.75 hrs

REGISTERED ELECTRICAL ENGINEERS PRE-BOARD EXAMINATION AUGUST 2012 MATHEMATICS

49. The probability that A can solve a given problem is 4/5, that B can solve it is 2/3, and that C can solve it is 3/7. If all three try, compute the probability that the problem will be solved. A. 101/105 B. 102/105 C. 103/105 D. 104/105 50. A steel ball at 110 deg C cools in 8 min to 90 deg c in a room at 30 deg C. Find the temperature of the ball after 20 minutes. A. 58.97 °C B. 68.97 °C C. 78.97 °C D. 88.97 °C 51. A freight train starts from Los Angeles and head for Chicago at 40 mph. Two hours later passenger train leaves the same station for Chicago traveling at 60 mph. How long will it be before the passenger train overtakes the freight train? A. 3 hrs B. 4 hrs C. 5 hrs D. 6 hrs 52. Given the triangle ABC in which A = 30 deg 30 min, b = 100 m and c = 200 m. Find the length of the side a. A. 124.64 m B. 142.24 m C. 130.50 m D. 103.00 53. Lines that intersect in a point are called______. A. Skew linesB. Intersecting lines C. Agonic lines D. Coincident lines 54. Find the average rate of change of the area of a square with respect to its side x as x changes from 4 to 7. A. 14 B.6 C. 17 D. 11 55. If the distance x from the point of departure at time t is defined by the equation x = -16t2 + 5000t + 5000, what is the initial velocity A. 20000 B. 5000 C. 0 D. 3000 56. What conic section is represented by 2x2 + y2 – 8x + 4y = 16? A. parabola B. ellipse C. hyperbola D. circle 57. If 9 ounces of cereal will feed 2 adults or 3 children, then 90 ounces of cereal, eaten at the same rate, will feed 8 adults and how many children? A. 8 B. 12 C.15 D. 18 58. Mary is twice as old as Helen. If 8 is subtracted from Helen’s age and 4 is added to Mary’s age, Mary will then be four times as old as Helen. How old is Helen now? A. 24 B. 36 C. 18 D. 16

REGISTERED ELECTRICAL ENGINEERS PRE-BOARD EXAMINATION AUGUST 2012 MATHEMATICS

59. A point on the curve where the second the derivative of a function is equal to zero is called. A. maxima B. minima C. point of inflection D. point of intersection 60. Find the area of the triangle whose sides are 25, 39, and 40. A. 46 B. 684 C. 486 D. 864 61. A/An_______triangle is a triangle having three unequal sides. A. oblique B. scalene C. equilateral D. isosceles 62. Find the length of the arc of 6xy = x4 + 3 from x = 1 to x = 2. A. 1.34 B. 1.63 C. 1.42 D. 1.78 63. Give the degree measure of angle 3pi/5 radians. A. 108 B. 120 C. 105

D. 136

64. What do you call a radical expressing an irrational number? A. surd B. radix C. complex number D. index 65. Find the derivative of the function f(x) = (2x – 3x)2. A. 2x - 4 B. 2x - 3 C. 6x - 8

D. 8x -12

66. What is the length of the line with a slope of 4/3 from a point (6, 4) to the yaxis? A. 10 B. 25 C. 50 D. 75 67. The inclination of the line determine by the points (4, 0) and (5√3) is A. 30 degrees B. 45 degrees C. 60 degrees D. 90 degrees 68. A sequence of numbers where the succeeding term is greater than the preceding term is called: A. dissonant resonance C. Isometric series B. convergent series

D.divergent series

69. Find the value of x for which y = 4 + 3x – 3x3 will have a maximum value. A. 0 B. -3 C. -2 D. 1 70. How many cubic meters is 500 gallons of liquid? A. 4.8927 B. 3.0927 C. 2.8927

D. 1.8927

REGISTERED ELECTRICAL ENGINEERS PRE-BOARD EXAMINATION AUGUST 2012 MATHEMATICS

71. A certain radioactive substance has a half-life of 3 years. If 10 grams are present initially, how much of the substance remains after 9 years? A. 1.50 grams B. 1.25 grams C. 2.50 grams D. 1.75 grams 72. A statement of the truth of which is admitted without proof is called: A. an axiom B. a postulate C. a theorem D. a corollary 73. A rectangular trough is 8 feet long, 2 feet across the top and 4 feet deep. If water flows in at a rate of 2 ft3/min, how fast is the surface rising when the water is 1 ft deep? A. ¼ ft/min B. ½ ft.min C. 1/8 ft/min D. 1/6 ft/min 74. Find the point(s) on the graph of y = x2 at which the tangent line is parallel to the line y = 6x -1. A. (3, 17) B. (3, 9) C. (1, 2) D. (2, 4) 75. How many petals are three in the rose curve r = 3 cos 5theta? A. 5 B. 10 C. 15

D. 6

76. Find the acute angle between the vectors z1 = 3 – 4i and z2 = -4 + 3i. A. 17 deg 17 min C. 15 deg 15 min B. 16 deg 16 min

D. 18 deg 18 min

77. If z1 =1 – i and z2 = -2 + 4i evaluate z12 + 2z1 – 3. A. -1 + 4i B. 1 - 4i C. -1 – 4i

D. 1 + 4i

78. A motorboat moves in the direction N 40 deg E for 3 hours at 20 mph. How far north does it travel? A. 58 mi B. 60 mi C. 46 mi D. 32 mi 79. Find the value of 4 sinh(pi i/3) A. 2i (sqrt. of 3) B. 4i (sqrt. of 3)

C. i (sqrt. of 3)

80. Find the upper quartile in the set (0, 1, 3, 4) A. 0.5 B. 0.25 C. 2

D. 3i (sqrt. of 3)

D. 3.5

81. In debate on two issues among 32 people, 16 agreed with the first issue, 10 agreed with the second issue and of these 7 agreed with both. What is the probability of selecting a person at random who did not agree with either issue? A. 1/32 B. 13/32 C. 3/8 D. 3/10 82. From the top of the lighthouse, 120 m above the sea, the angle of depression of a boat is 15 degrees. How far is the boat from the lighthouse? A. 448 m B. 428 m C. 458 m D. 498 m

REGISTERED ELECTRICAL ENGINEERS PRE-BOARD EXAMINATION AUGUST 2012 MATHEMATICS

83. The cross section of a certain trough are inverted isosceles triangles with height 6 ft and base 4 ft. Suppose the trough contains water to a depth of 3 ft. Find the total fluid force on one end. A. 187.2 lb B. 178.2 lb C. 192.4 lb D. 129.4 lb 84. Two lines are not coplanar. A. Parallel lines B. Skew lines C. Secant lines

D. Straight lines

2

85. Find the inverse Laplace transform of − s−3. A. 2 e-3t B. 2e3t C. 3e-2t

D. 3e2t

86. Find the length of the latus rectum of the curve rcos2 theta – 4cos theta = 16sin theta. A. 4 B. 16 C. 12 D. 18 87. A quadrilateral with no pair of parallel sides. A. Trapezoid B. Trapezium C. Rhombus

D. Rhomboid

88. Find the equation of the line tangent to the curve y = x3 – 6x2 + 5x + 2 at its point of inflection. A. 7x – y B. -7x + y = 0 C. 7x +y = 10 D. -7x – y = 10 89. Find the area of the polygon with vertices at 2 + 3i, 3 + i, -2 – 4i, -1 + 2i. A. 47/5 B. 47/2 C. 45/2 D.45/4 90. Find the radius of curvature of y = x3 at x =1. A. 5.27 B. 4.27 C. 6.27

D. 7.27

91. Determine the probability of throwing a total of 8 in a single throw with two dice, each of whose faces is numbered from 1 to 6. A. 1/3 B. 1/18 C. 5/36 D. 2/9 92. Find the distance between the point (3, 2, -1) and the plane 7x – 6y + 6z + 8 = 0. A. 1 B. 2 C. 3 D. 4 93. How many parallelograms are formed by a set of 4 parallel lines intersecting another set of 7 parallel lines? A. 123 B. 124 C. 125 D. 126 94. The graphical representation of the cumulative frequency distribution in a set of statistical data is called: A. Ogive B. Histogram C. Frequency polyhedron D. mass diagram 95. Find the area bounded by the curve defined by the equation x2 = 8y and its latus rectum. A. 11/3 B. 32/3 C. 16/3 D. 22/3

REGISTERED ELECTRICAL ENGINEERS PRE-BOARD EXAMINATION AUGUST 2012 MATHEMATICS

96. Evaluate lim (i z 4 + 3z² − 10i) z→2i

A. -12 +6i

B. 12 - 6i

97. Naperian logarithm have a base of A. 3.1416 B. 2.171828

C. 12 +6i

D. -12 – 6i

C. 10

D. 2.71828

98. If an aviator flies around the world at a distance 2km above the equator, how many more km will he travel than a person who travels along the equator? A. 12.6 km B. 16.2 km C. 15.8 km D. 18.5 km 99. Find the volume of a spherical whose central angle is pi/5 radians on a sphere of radius 6 cm. A. 90.48 cu. cmB. 86.40 cu. cm C. 78.46 cu. cm D. 62.48 cu. cm 100. What is the coefficient of the (x -1)3 term in the Taylor series expansion of f(x) = lnx expanded about x = 1? A. 1/6

B. 1/4

C. 1/3

D. 1/2