Republic of the PhilippinesProfessional Regulation Commission

Board of Electronics Engineering

EE Licensure Examination – Diagnostic Exam 8:00 am – 12:00 noon

MATHEMATICS SET No:

INSTRUCTION: Select the correct answer for each of the following questions. Mark only one answer for each item by shading the box corresponding to the letter of your choice on the answer sheet provided.STRICTLY NO ERASURES ALLOWED. Use pencil no. 1 only.

NOTE: Whenever you come across a caret (^) sign, it means exponentiation. Ex. X^2 means x2; (x+y)^(x-z) means

(x+y) raised to the (x-z). Pi=3.1416

MULTIPLE CHOICE:

1. The distance from Earth to the Sun is approximately 93 million miles. A scientist would write that number of miles asA. 9.3 x 10^6 C. 9.3 x 10^7*B. 93 x 10^7 D. 93 x 10^10

2. Find the area of a pentagon which is circumscribing a circle having an area of 420.60 sq. cm.A. 386.57 C. 450.54B. 486.35 * D. 260.24

3. For a class trip to a museum, 461 students and 20 teachers will be taking buses. Each bus can seat a maximum of 52 persons. What is the least number of buses needed for the trip?A. 8 C. 9B. 10* D. 11

4. What type of curve is generated by a point, which moves in uniform circular motion about an axis, while travelling with a constant speed parallel to the axis? A. cycloid C. spiral of Archimedes B. epicycloids D. Helix*

5. Which set is closed under subtraction?A. odd integers C. counting numbersB. integers* D. prime numbers

6. A satellite orbits the earth at a constant height above the surface of the earth equal to twice the radius of the earth. A man observes that the satellite appears above the horizon every two hours and passes directly overhead. For how long is the satellite above the horizon?A. 35.40 minutes C. 25.05 minutesB. 47.02 minutes* D. 30.74 minutes

7. The equation r = cos θ is a A. rosette * C. lemniscate B. limacon D. spiral

8. The probability that both stages of a 2-stage missile will function correctly is 0.95. The probability that the first stage will function correctly is 0.98. What is the probability that the second stage will function correctly given that the first does?A. 0.99 C. 0.97*B. 0.98 D. 0.96

9. Lim (x^2-1)/(x-1) as x approaches 1A. 2* C. 0B. infinity D. 1

10. If 10^k= 1/2, what is the value of 10^k+3?A. 125 C. 250B. 500* D. 1000

page 1 of 9

Republic of the PhilippinesProfessional Regulation Commission

Board of Electronics Engineering

EE Licensure Examination – Diagnostic Exam 8:00 am – 12:00 noon

MATHEMATICS SET No:

11. A cubical container that measures 2’ on a side is tightly packed with 8 marbles and is filled with water. All 8 marbles are in contact with the walls of the container and the adjacent marbles. All of the marbles are the same size. What is the volume of water in the container?A. 0.38 in3 C. 2.5 in3B. 3.8 in3* D. 4.2 in3

12. A transit set up 112.1 feet from the base of a vertical chimney reads 32° 30’ with the cross hairs set on the top of the chimney. With the telescope level, the vertical rod at the base of the chimney is 5.1 feet. How tall is the chimney?A. 66.3 ft. C. 76.5 ft.*B. 71.4 ft. D. 170.9 ft.

13. At approximately what time before the hours of 12:00 noon and 1:00 p.m. would the angle between the hour and the minute hand of a continuously driven clock be exactly 180°?A. 12:28 p.m. C. 12:33 p.m.*B. 12:30 p.m. D. 12:37 p.m.

14. Study the series of numbers to discover the “system” in which they are arranged.For the series 1 5 14 30 ___ 91 the fifth term is:A. 59 C. 61B. 53 D. 55 *

15. Rick’s recorded times in four 1-mile runs are 4.8 minutes, 5.3 minutes, 4.7 minutes, and 5.4 minutes. For Rick’s next run, which time will give him a mean of 5.0 minutes?A. 4.8 min* C. 5.3 minB. 5.7 min D. 6.0 min

16. The value of Tan (A + B), where Tan A = 1/3 and Tan B = 1/4 is (Note: A and B are acute angles)A.7/12 C.1/11 B.7/11* D.7/13

17. If log10 (to the base a) = 0.250, log a (to the base 10) equalsA. 4 * C. 0.50B. 0.25 D. 2

18. If the volume of a cube is increased by 30%, by how much is the surface area increased?A. 42.22% C. 69% * B. 19.11% D. 33%

19. Divide the number 60 into two parts so that the product of one part and square of the other is maximum. Find the smallest part.A. 15 C. 25B. 20* D. 10

20. A kite is flying 100 ft above the ground, moving in a strictly horizontal direction at a rate of 10 ft/s. How fast is the angle between the string and the horizontal changing when there is 300 ft of string out?A. 1/90 rad/s* C. 1/15 rad/sB. 1/30 rad/s D. 1/60 rad/s

21. Marcia paid $36 for a dress that was on sale for 25% of the original price. What was the original price of the dress?A. $48 C. $60B. $108 D. $144*

22. If 25% of a number is 6x, the number isA. 2.4x C. 24x*B. 1.5x D. 15x

23. Find the sum of all positive integers between 84 and 719 which are exactly divisible by 5.A. 23,780 C. 50,800*

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Republic of the PhilippinesProfessional Regulation Commission

Board of Electronics Engineering

EE Licensure Examination – Diagnostic Exam 8:00 am – 12:00 noon

MATHEMATICS SET No:

B. 45,680 D. 30,400

24. Find the sum of the first five terms of the geometric progression if the third term is 144 and the sixth term is 486.A. 844* C. 749B. 978 D. 540

25. A cube whose edge has a length of 6 has the same volume as a rectangular box whose length is 12 and whose width is 9. The height of the rectangular box isA. 6 C. 2*B. 3 D. 4

26. At exactly what time after 5 o’clock will the hour hand and the minute hand be perpendicular for the first time?A. 5:10 and 54 sec.* C. 5:05 and 34 sec.B. 5:20 and 14 sec. D. 5:15 and 25 sec.

27. The inequality 5<x-2 is equivalent toA. x<7 C. x>3B. x>7* D. x<-3

28. A group consists of n engineers and n nurses. If two of the engineers are replaced by two other nurses, then 51% of the group members will be nurses. Find the value of n.A. 80 C. 55B. 110 D. 100*

29. The graph of r = a + b cosθ is a A. Lemniscate C. Limacon *B. Lituus D. Cardioid

30. A surveyor wishes to find the width of a river. He set up his transit at C on one bank and sighted across to point A on the opposite bank, then turning through an angle of 90°, he walks 225 m from C to a point B and finally, setting his transit at B, he measured angle BCA as 48.33°. What is the width of the river?A. 238.5 m C. 328.6 mB. 252.8 m* D. 142.7 m

31. If n pencils cost c cents, what is the cost, in cents, of p pencils?A. pc/n* C. nc/pB. c/np D. c-(p/n)c

32. If the length of each side of a square is increased by 10%, by what percent does the area of the square increase?A. 20 C. 21*B. 40 D. 100

33. An isosceles spherical triangle has angle A=B=54O and side b=82O.Find the measure of the third angle.

A. C.

B. * D.

34. A semi - circle of radius 14 cm is bent to form a rectangle whose length is 1 cm more than its width. Find the area of the rectangle.A. 323.75 cm2* C. 233.57 cm2B. 322.32 cm2 D. 233.75 cm2

35. A conical vessel has a height of 24 cm. and a base diameter of 12 cm. It holds water to a depth of 18 cm above its vertex. Find the volume of its content.A. 381.7 cm2 * C. 281.6 cm2B. 451.2 cm2 D. 367.4 cm2

36. A sector is bent to form a cone. If the angle of the sector is 30 degrees and the radius is 6 cm. what is the altitude of the cone?A. 5.98 cm* C. 6.36 cmB. 10.12 cm D. 8.25 cm

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Republic of the PhilippinesProfessional Regulation Commission

Board of Electronics Engineering

EE Licensure Examination – Diagnostic Exam 8:00 am – 12:00 noon

MATHEMATICS SET No:

37. A solid has a circular base of radius 20 cm. Find the volume of the solid if every plane section perpendicular to a certain diameter is an equilateral triangle.A. 18445.50 cm3 C. 14231.50 cm3B. 18475.21 cm3* D. 17485.12 cm3

38. Let x, y and z represent positive integers greater than 1. If xy=35 and yz=21, which inequality must be true?A. x<y<z C. y<x<zB. z<y<x D. z<x<y*

39. A sphere of radius 5 cm and a right circular cone of base radius 5 cm and height 10 cm stand on the table. How far from the table should the two solids be cut in order to have equal circular sections?A.2 cm* C.4 cmB.5 cm D.7 cm

40. Line L contains points P and Q. The number of different points whose distance from point P is two times its (their) distance from point Q isA. 1 C. 2B. more than 4* D. 4

41. Find the equation of the perpendicular bisector of the segment joining the points (2,6) and (-4,3).A. 2x-4y+5=0 C. 4x+2Y-5=0*B. 4x-2y-5=0 D. 2X+4Y+5=0

42. An arc in the form of a parabolic curve is 40 m across the bottom. A flat horizontal beam 26 m long is placed 12 m above the base. Find the height of the arc.A. 20.78 m* C. 25.68 mB. 18.67 m D. 15.87 m

43. A fireplace arc is to be constructed in the shape of a semi-ellipse. The opening is to have a height of 2 ft at the center and a width of 6 ft along the base. Find the equation of the cross-section of the fireplace.A. 9X^2+4Y^2=36 C. 4X^2+9Y^2=36*B. 4X^2+36Y^2=144 D. 36^2+4Y^2=144

44. Find the volume of the solid of revolution formed by rotating the region bounded by the parabola y=x2 and the lines y=0 and x=2 about the x axis.A. 25.01 cu. units C. 20.11 cu. Units*B. 15.50 cu. Units D. 30.14 cu. units

45. Assuming that the earth is a perfect sphere, with radius 4000 miles. The volume of ice at the north and south poles is estimated to be 8,000,000 cubic miles. If this ice were melted and if the resulting water were distributed uniformly over the globe, approximately what would be the depth of the added water at any point on the earth?A. 120 ft. C. 210 ft.*B. 320 ft D. 230 ft.

46. If two isosceles triangles have congruent vertex angles, the two triangles must beA. congruent C. rightB. equiangular* D. equilateral

47. There are 3 copies each of 4 different books. In how many different ways can they be arranged on a shelf?A. 349,800 C. 549,600B. 469,500 D. 369,600 *

48. What is the sum of 4a^2-7a-5 and -6a^2-2a+7?A. -2a^2-9a+2* C. -10a^2+5a+12B. 2a^2-5a+2 D. 2a^4-9a^2+2

49. Solve for x in the following equation:

A. 1/4 C. 1*B. 1/2 D. 3/2

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Republic of the PhilippinesProfessional Regulation Commission

Board of Electronics Engineering

EE Licensure Examination – Diagnostic Exam 8:00 am – 12:00 noon

MATHEMATICS SET No:

50. Which product is a factored form of 2x^2-10x-12?A. 2(x+2)(x-2) C. 2(x+6)(x-1)B. 2(x+3)(x-2) D. 2(x+1)(x-6)*

51. If sin3x = cos6y then:A. x-2y=30 C. x+2y=30 *B. x+y=180 D. x+y=90

52. A car is traveling at an average rate of 45 miles per hour. How many feet per second is the car traveling?A. 48 C. 60B. 66* D. 88

53. Find the acute angles between the two planes 2x-y+z=8 and x+y+2z-11=0.A. 30° C. 45°B. 60°* D. 40°

54. A ship is sailing due east when a light is observed bearing N62°10’E. After the ship has travelled 2250 m, the light bears N48°25’E. If the course is continued, how close will the ship approach the light?A.2934 m* C. 3924 mB.2349 m D. 3249 m

55. Evaluate the determinant:

A. 22 C. -19B. 34 D. -39*

56. If the lengths of the diagonals of a rhombus are 6 and 8, the perimeter of the rhombus isA. 14 C. 20*B. 28 D. 40

57. The vertices of triangle ABC are A(-4,0), B(2,4), and C(4,0). What is the area, in square units, of triangle ABC?A. 8 C. 16*B. 32 D. 64

58. Two secants AC=80m and AE=100m are drawn from a point A outside a circle and intersecting the circle at B, C and E. The angle between the two secants is 25°. Find the area of the quadrilateral ECBD inscribed in a circle if AB=40m long.A. 1240 m2 C. 1420 m2*B. 1024 m2 D. 2140 m2

59. If the endpoints of a diameter of a circle are (2,-1) and (4,0), what are the coordinates of the center of the circle?A. (6,-1) C. (3,-1/2)*B. (3,1/2) D. (2,-1)

60. What is the slope of a line through points (-4,2) and (6,8)?A. -3/5 C. 3/5*B. 5/3 D. -5/3

61. What is an equation of a line that is parallel to the y-axis and contains point (-3,1)?A. x=-3* C. x=1B. y=-3 D. y=1

62. What is the solution set for the following system of equations? x=-y x+2y=6 A. (-2,2) C.(2,-2)B. (6,-6) D.(-6,6)*

page 5 of 9

Republic of the PhilippinesProfessional Regulation Commission

Board of Electronics Engineering

EE Licensure Examination – Diagnostic Exam 8:00 am – 12:00 noon

MATHEMATICS SET No:

63. Which could be an equation of a circle that touches the x-axis at one point and whose center is at (-6,8)?A. (x-6)^2+(y-8)^2=36 C. (x+6)^2+(y-8)^2=36B. (x-6)^2+(y+8)^2=64 D. (x+6)^2+(y-8)^2=64*

64. What is the area, in terms of pi, between the circles whose equations are x^2+y^2=25 and x^2+y^2=39?A. 8pi C. 64piB. 14pi* D. (√39-5)pi

65. What are the coordinates of the highest point on the parabola whose equation is y=x^2+2x-7?A. (-1,-10) C. (-1,6)C. (1,-6)* D. (1,10)

66. What is the minimum value of y in the equation y=x^2-6x+5?A. -14 C. -4*B. 3 D. 4

67. A bag has five green marbles and four blue marbles. If one marble is drawn at random, what is the probability that it is not green?A. 1/9 C. 4/9*B. 5/9 D. 5/20

68. For which set of numbers do the mean, median , and mode all have the same value?A. 1,3,3,3,5* C. 1,1,1,2,5B. 1,1,2,5,6 D. 1,1,3,5,10

69. On a quiz taken by the students in a mathematics class, a score of 78 is at the 25th percentile. If 8 students scored 78 or less on the test, how many students scored higher than 78?A. 12 C. 16B. 24* D. 32

70. Nine students scored 75 or less on a mathematics test. If 75 is the 25th percentile, what is the number of students who took this test?A. 12 C. 27B. 36* D. 45

71. How many different three-member teams can be formed from six students?A. 20* C. 120B. 216 D. 720

72. If xC10=xC2, what is the value of x?A. 5 C. 8B. 12* D. 20

73. A whole number from 1 to 12, inclusive, is picked at random. What is the probability that the number is less than 7 or its prime?A. 1/2 C. 7/12B. 2/3* D. 11/12

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