Republic of the Philippines

Republic of the PhilippinesEDGE ECE REVIEW SPECIALISTBOARD OF ELECTRONICS ENGINEERINGELECTRONICS ENGINEER LICENSURE EXAMINATION

MATHEMATICS

INSTRUCTION: Do not write anything on this questionnaire. Select the correct answer for each of the following questions. Mark only one answer for each for each item by shading the box corresponding to the letter of your choice on the answer sheet provided.

1. An angle greater than /2 radians and less than radians.a. Acute Angleb. Obtuse Anglec. Straight Angle d. Reflex Angle

2. At 12:00 noon ship B is 100 miles east of ship A. If ship B sails west at 10 mi/hr and ship A sails south at 20 mi/hr, when will the ships be closest to each other?a. 1:00 PMb. 2:00 PMc. 3:00 PMd. 4:00 PM

3. The arithmetic mean of 80 numbers is 55. If two numbers namely 274 and 850 are removed what is the arithmetic mean of the remaining numbers?a. 42b. 28c. 30d. 32

4. Find the volume of the solid of revolution obtained by revolving the region bounded by y=x-x2 and the x axis about the x-axis.a. /10b. /20c. /30d. /40

5. Insert three geometric means between 2 and 162.a. 6, 18, 36b. 4, 18, 54c. 6, 20, 54d. 6, 18, 54

6. What is the equation of the circle with center at the origin and a radius of 5?a. x2 + y2 = 1b. x2 + y2 = 25c. x2 + y2 = 10 d. x2 + y2 = 5

7. A quadrilateral ABCD is inscribed in a circle, if AB = 90 cm, CD = 70 cm, AD = 50 cm, AC = 97.29 cm and BD = 101.76 cm. respectively. Find the distance BC.a. 72b. 68c. 74d. 77

8. Given the area in the first quadrant bounded by x2 = 8y, the line y 2 = 0 and the y-axis. What is the volume generated when this area is revolved about the line y 2 = 0?a. 53.31 cu. unitsb. 45.87 cu. unitsc. 26.81 cu. unitsd. 33.98 cu. Units

9. A statue 2 meters high stands on a column that is 3 meters high. An observer in level with the top of the statue observed that the column and the statue subtend the same angle. How far is the observer from the statue?

a. 5metersb. 20 meters

c. 20 metersd. 2meters

10. A police car is 30 ft away from a long straight wall. Its beacon, rotating 1 revolution per second, shines a beam of light on the wall. How fast is the beam moving when it is closest to the police car?a. 20b. 30c. 40d. 60

11. Find the area of the region bounded by y=x2-5x+6, the x-axis, and the vertical lines x=0 and x=4.a. 14/3b. 1/6c. 17/3d. 5/6

12. Transform the fraction by rationalizing the denominator

a.b.

c. d.

13. Simplify:

a. b.

c. d.

14. Ryan has 800 ft of fencing. He wishes to form a rectangular enclosure and then divide it into three sections by running two lengths of fence parallel to one side. What should the dimensions of the enclosure be in order to maximize the enclosure area?a. 100 ft, 150 ftb. 50 ft, 100 ftc. 150ft, 300 ftd. 100 ft, 200 ft

15. A trapezoid has an area of 360 m2 and an altitude of 20 m. Its two bases have ratio of 4:5. What are the lengths of the bases?a. 12,15b. 7,11c. 8,10d. 16,20

16. What is the equation of the line having a slope of 2 and passing through the point (-1, 1).a. 2x y + 3 = 0b. 3x +y 3 = 0c. 2x + y 3 = 0d. 2x + y 3 = 0

17. Find the limit: sin2x/sin3x as x approaches to 0.a.1/3b. 3/4c. 2/3d. 0

18. A baseball diamond has a shape of a square with sides 90 meters long. A player 30 m. from the third base and 60 m. from the 2nd base is running at a speed of 28 m / sec. At what rate is the players distance from the home plate changing?a. -8.85 m/sb. 8.85 m/sc. -4.40 m/sd. 17.9 m/s

19. How many sides has an equilateral polygon if each of its interior angles is 165 o?a. 24b. 12c. 18d. 10

20. Pedro can paint a fence 50% faster than Juan and 20% faster than Pilar, and together they can paint a given fence in 4 hours. How long will it take Pedro to paint the same fence if he had to work alone?a. 6b. 8c. 10d. 12

21. A rectangle is inscribed in a right triangle whose sides are 5, 12, and 13 inches. Two adjacent sides of the rectangle lie along the legs of the triangle. What is the maximum area of the rectangle?a. 15 sq. inb. 20 sq. inc. 25 sq. ind. 30 sq. in

22. A parabola has an equation of x2 = 20y. Locate the coordinates of the focus of the parabola.a. (5,0)b. (0,5)c. (4,5)d. (5,4)

23. From the top of tower A, the angle of elevation of the top of the tower B is 46 . From the foot of a tower B the angle of elevation of the top of tower A is 28. Both towers are on a level ground. If the height of tower B is 120 m., How far is A from the building? a. 42.3 mb. 40.7 m.c. 38.6 m.d. 44.1 m

In right triangle BAC:h = BC sin Bh = 86.718 sin 28h = 40.71 m

24. Simplify:

a.b.

c. d.

25. A truck travels from point M northward for 30 min. then eastward for one hour, then shifted N 30W. if the constant speed is 40kph, how far directly from M, in km. will be it after 2 hours?a. 37.3b. 47.9c. 45.2d. 41.6

MA=40(30 /60)=20KmAB=40(1) = 40 km

After 2 hours, tBC =30 minBC=40 (30 / 60) = 20 Km

In triangle MDC:MD = AB BC cos 30MD = 40 20 sin 30 = 30 kmCD = MA + BC cos 30CD = 20 + 20 cos 30 = 37.32 km

26. What is the minimum possible perimeter for a rectangle whose area is 100 in2?a. 20 inb. 30 inc. 40 ind. 60 in

27. A man sold a book by mistake at 120% of the marked price instead of discounting the market price by 20%. If he sold the book for P14.40, what was the price for which he has sold the book?a. P10.20b. P7.80c. P9.60d. P9.60

28. Two lines have an equation of 2x y + 2 = 0 and 2x + y 4 = 0. Find the smallest angle between the two lines.a. 36.87b. 42.80c. 53.13 d. 126.87

29. The square of a number increased by 16 is the same as 10 times the number. Find the numbers.a. 2,8b. 3,6c. 3,8d. 5/8,0

30. A particle moves along a path whose parametric equations are x = t3 and y = 2t2. What is the acceleration of the particle when t = 5 seconds?a. 30.26 m/s2b. 18.56 m/s2c. 20.62 m/s2d. 23.37 m/s2

31. Two triangles have equal bases. The altitude of one triangle is 3 units more than its base and the altitude of the other triangle is 3 units less than its base. Find the altitudes, if the areas of the triangle differ by 21 square units.a. 4 and 10b. 4 and 26c. 6 and 12d. 7 and 23

eq. 1

eq. 2

eq. 3 Substitute (1) and ( 2 ) to equation 3:

Thus:

32. A train travels 2.5 miles up on a straight track with a grade of 110. What is the vertical rise of the train in that distance?a. 0.716 miles b. 0.051 milesc. 0.279 milesd. 0.045 miles

33. Find the moment of inertia of the area bounded by the curve x2 = 4y, the line y = 1 and the y-axis on the first quadrant with respect to x-axis.a. 6/5b. 7/2c. 4/7d. 8/7

34. The polynomial x3 + 4x2 -3x + 8 is divided by x-5, then the remainder isa. 175b. 140c. 218d. 200

35. What is the largest possible volume a right circular cylinder can have if it is inscribed in a sphere of radius 5?a. 302 cu. unitsb. 261 cu. unitsc. 394 cu. unitsd. 211 cu. units

36. Find the real values of x and y in the equation

a. x=-1, y=2 b. x=1, y=-2c. x=-2, y=1d. x=2, y=-1

37. The axis of the hyperbola that passes through the foci, vertices, and center is calleda. minor axisb. conjugate axisc. major axisd. transverse axis

38. Sand is being dumped from a dump truck at the rate of 10 ft3/min and forms a pile in the shape of a cone whose height is always half its radius. How fast is its height rising when the pile is 5 ft high?a. 1/(5) ft/minb. 1/(10) ft/minc. 1/(15) ft/mind. 1/(20) ft/min

39. Find the distance between the points (2,5) and the line x 2y + 3 = 0.

a. b.

c. d.

40. The area of a triangle is 65 sq. cm. and its perimeter is 48 cm. compute the radius of the inscribed circle.a. 2.71 cm.b. 2.16 cm.c. 1.42 cmd. 2.49 cm

41. A plane, P, flies horizontally at an altitude of 2 miles with a speed of 480 miles/hour. At a certain moment it passes directly over a radar station, R. How fast is the distance between the plane and the radar station increasing 1 minute later?a. 287 mi/hrb. 318i/hrc. 466 mi/hrd. 524 mi/hr

42. A church window is in the shape of a rectangle surmounted by a semicircle. If the perimeter of the window is 20 ft, what is its maximum area?a. 28 ft2b. 49 ft2c. 36 ft2d. 52 ft2

43. How many diagonals can be drawn for a 12 sided polygon?a. 54b. 48c. 36d. 62

44. Find the equation of the axis of symmetry of the function y = 2x2 7x + 5.a. 7x + 4 = 0 b. 4x + 7 = 0c. 4x 7 = 0d. 4x 2 = 0

45. The two adjacent sides of a triangle are 5 and 8 meters respectively. If the included angle is changing at the rate of 2 rad/sec. at what rate is the area of the triangle changing if the included angle is 60 degrees?a. 23 sq.m/secb. 15 sq.m/secc. 20 sq.m/secd. 25 sq.m/sec

46. 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=8.a. 14b. 4c. 16d. 8

47. Find the surface area of the portion of the curve x2 =4y from y =1 to y =3 when it is revolved about the y-axis.a. 19.84b. 37.86c. 16.75d. 43.32

48. Find the area of the hexagon ABCDEF formed by joining the points A(1,4), B(0,-3), C(2,3), D(-1,2), E(-2,-1) and F(3,0).a. 24b. 20c. 22d. 15

49. Log of negative one to the base ten is written as log10 -1. Its rectangular form is: a. 0 j1.36b. zeroc. 0 + j1.36 d. infinity

50. The area of a hexagon inscribed in a circle is 158 cm2. Find the difference in area between the hexagon and a circle.a. 33.05 cm2b. 44.02 cm2c. 28.41 cm2d. 51.42 cm2

"Be the Best-Prepared ECE Examineeba20