MATH 2017

31. If the edge of a cube is doubled, _________ statement in INCORRECT. a. The diagonal is doubled b. The weight is doubled c. The volume is increased 8 times d. The lateral area will be quadrupled

b. The weight is doubled

33. The equation ∫-π/4 0 tan^2 θ d θ is equal to __________. a. 1/3 b. π/4-1 c. π/4+1 d. 1-π/4

b. π/4-1

50. If y = tan u , u -v — l/v, and v = In x then the value of dy/dx at x = e is ________. a. 2/e b. 1

a. 2/e

61. _______ is (x^-y) (2x^y) (3y^x) if x=2 and y=2 a. 24 b. 6 c. 8 d. 12

a. 24

3. The area enclosed by the graph of r = 5 cos (40) is _________. a. 25π/4 b. 25π/2 c. 25π d. 10

a. 25π/4

44. One degree on the equator of the earth is equivalent to a. 4 minutes b. 1 minute c. 1 hour d. 30 minutes

a. 4 minutes

46. Given the equations below, ab is 10b -9a = 6 B — a = l a. b. 1 c. 12 d. -12

c. 12

36. The equation ∫1 0 xe^2 dx is equal to ___________. a. 2-e b. -1 c. 1 d. x-1

c. 1

12. _________ is an amount which a willing buyer will pay to a seller for the property where each has equal advantage and is used for compulsion to buy or sell a. Use value b. Market Value c. Book value d. Fair value

b. Market Value

1. A market situation where there is only one seller with many buyer is known as a. Monophony b. Monopoly c. Oligopoly d. Perfect competition

b. Monopoly

58. Given f(x) = x^2 + 2x= 4, _____ following statement is NOT true. a. The graph off has no x-intercept b. f(x) has a maximum value c. the graph off has a y-intercept d. The graph off is not a line

b. f(x) has a maximum value

14. ______ is the volume of the solid bounded by the region y = x^2 , y = 1 and x = 1 if revolved about the x-axis. a. 2π (e^2-1) b. π(e^2+1) c. π(e^2-1) d. 2π(e^2-2)

b. π(e^2+1)

32. _______ is a definite integral which is not equal to zero. a.∫π 0 cos x dx b. ∫x -π cos^3xdx c. ∫π -π x^2 sinxdx d. ∫x -π cos^3xdx

b. ∫x -π cos^3xdx

23.___________ is the vertex of the parabola whose equation is y = x +4 a. (0,-4) b. (-2,0) c. (0,4) d. (-4,0)

c. (0,4)

16. The suitable identity to find (x+3)(x+3) is_______. a. a^2-b^2 b. (ab)^2 c. (a+b)^2 d. (x+a)(x+b)

c. (a+b)^2

5. _________is used to evaluate (m+3) (m+2). a. a^2-b^2 = (a+b)(a-b) b. (x+a)(x+b) = x^2+ (a+b)x+ab c. (a+b)^2 = a^2 + 2ab + b^2 d. (a-b)^2 = a^2-2ab+b^2

c. (a+b)^2 = a^2 + 2ab + b^2

76. A man invested P 110,000 for 31 days. If the net interest after deducting 20% with holding tax is P890.36 then the rate of return annualy is _________ a. 12.32% b. 11.95% c. 11.75% d. 11.50%

c. 11.75%

68. __________ is the distance from the center of a sphere of a radius 10cm a plane should be passed so that the ratio of the areas of two zones is 3x7. a. 6cm b. 3cm c. 4cm d. 5cm

c. 4cm

15. The frustum of a rectangular triangular pyramid has equilateral triangles for its bases, and the lower and upper base edges are 9m and 3m, respectively. If the volume is 118.2 cu.m. then the bases are a. 10m b. 9m c. 7m d. 8m

c. 7m

69. __________ is the suitable identity to evaluate 99x a. 10201 b. 10199 c. 9801 d. 10901

c. 9801

62. The range of the function f (x) = x^2-4 is _________. a. All real numbers greater than or equal to 0 b. Alt real numbers excluding 2 and -2 c. All real numbers greater than or equal to -4 d. Atl real numbers excluding 0

c. All real numbers greater than or equal to -4

10. The Geodetic Engineers of the Phi*ippines Inc. (GEPI) in planning to put up its own building. Two proposal being considered are: A. The construction of the building now to cost P 400, 000 B. The construction of a smaller building now to cost P 300, 000 and at the end of 5years, an extension to be added to cost P200, 000. Proposal "B" is more economical than proposal A byif interest rate is 20% and depreciation to be neglected. a. P 19,423.69 b. P 19,518.03 c. P19,624.49 d. P19, 122.15

c. P19,624.49

74. ________ is the distance from the point ( 2,3) to the line 3x + 4y + 3=0 a. 6.2 b. 5.4 c. 5 d. 5.8

a. 6.2 or 4.2

66. The inverse of the function given below is __________. fx= 3√x/5-2 a. F^-1(x) = 5(x+2)^3 b. F^-1(x) = (5(x+2))^3 c. F^-1(x) = 5(x^3+2) d. F^-1(x) = 15(x+2)

a. F^-1(x) = 5(x+2)^3

77. If fg + 2f-g = 2 — (f + g), then the value of x-y is__________. a. (2-f)/f b. 4/f c. 1/f d. -1

a. (2-f)/f

42. The expression in one variable is _________. a. X+y b. X+x^2+1 c. X+9y d. Xyz

b. X+x^2+1

27. _________ is the equation of the parabola whose vertex is (5, 5). a. Y = x^4+5 b. Y = (x-5)^2 c. Y = (x+5)^2 d. Y= x^2-5

b. Y = (x-5)^2

11. The place where buyers and sellers come together is known as ______. a. Store b. Bargain center c. Port d. Market

d. Market

17. Subtracting 7X+Y from -X+Y gives ________. a. -8x b. 8X+2y c. 8x d. 6X+2y

a. -8x

72. A man standing at a point P is watching the top of the tower, which makes an angle of elevation of 30d with the man's eye. The man walks some distance towards the tower to watch its top and the angle of the elevation becomes 60d. The distance between the base of the tower and the point P would be ___. a. 8 units b. 12 units c. 42 units d. Data Inadequate

d. Data Inadequate

37. The center of gravity of a solid cone lies on the axis at the height ______. a. Three eight of the total height above the base b. One third of the total height above base c. One-half of the total height above base d. One fourth of the total height above base

d. One fourth of the total height above base

22. Find the phase shift of the function: The phase shift of the function y = cos (x — n/2) is __________. a. 1 b. -π/2 c. 2π d. π/2

d. π/2

47. If an amount of P 1,000 became P 1,409.41 after 4 years compounded bimonthly then the minimal interest is a. 12 % b. 12.08% c. 11.27% d. 12.32%

wala

52. If a function "f' is continuous for all "x" and if 'f' has a relative maximum at (-1,4) and relative minimum at (3,-2) then ______ statement must be true. a. The graph off has a horizontal tangent line of x = 3 b. The graph off has a horizontal asymptote c. F' (-1) = 0 d. The graph off intersect both axes

wala

59. In ((x-1)^2 ) = 2 In(x-l) for all x in the interval ________. a. (-∞, 1) u(1,+∞) b. (1, +∞) c. (-∞,+∞) d. (0, +∞)

wala

63. ________ is the centroid of a triangle whose vertices are (2,3) (-4, 6) (2, -6). a. (1,0) b. (0,1) c. (-1,0) d. (0,-1)

wala

70. If f(x) = 2x + 1 and g(x) = x^2 , then the value of f( g(-3)) is ______ a. 17 b. -7 c. 2 d. 9

wala

75. The expression in (x-2) < 0 is true if and only if ________. a. 2<x<3 b. X>2 c. X>3 d. X<3

wala

78. Given the equations below, then the value of x —y is (x+y)/3=8 2x-y=9 a. 1 b. -24 c. 0 d. -2

wala

79. _________ defines a function 'f' for which f(-x) = -f(x) a. F(x) = log x b. F(x) = cos x c. F(x) = x^2 d. F(x) = sin x

wala

The sum of interior angles of a polygon is

wala katuloy questions

21. If the displacement of a particle on a line given by ... then the number of of time the particle changes direction is __________. a. 3 b. 0 c. 1 d. 2

wala sagot

60. If a, b, c, d and e are real numbers and a not equal to O then the polynomial equation ax^2 + bx^2 + cx^2 + dx +e =O has ________. a. No positive real roots b. Only one real root c. At least one real root d. No real roots

c. At least one real root

55. ______ is the equation of the perpendicular bisector of the joining (5, 0) and (-7,3) a. 8x-y+11=0 b. 8x+2y+11=0 c. 8x+y+11=0 d. 8x-2y+11=0

d. 8x-2y+11=0

4. The graph of y = 5x^4-x^5 has a point of inflection at a. (3 , 162) only b. (4 , 256) only c. (0,0) and (2,162) d. (0,0) only

a. (3 , 162) only

40. The exact value of tan 165d using a half angle identity is __________. a. -2±√3 b. 2±√3 c. 2-√3 d. -2 - √3

a. -2±√3

57. Mr. Quirisit borrowed money from the bank. If he received from the bank Php 1842 and promised to repay Php 2000 at the end of 10 months then the rate of simple interest is ___________. a. 10.23% b. 12.03% c. 12.19% d. 11.54%

a. 10.23% or 10.29%

6. A ship on a certain day is at latitude 20d N and longitude 140d E sailing for 150 hours at a uniform speed along a great circle ... reaches a point at latitude IOd S and longitude 170d W. If the r... the earth is 3959 miles, find the speed in miles per hour. a. 16.4 b. 17.4 c. 15.4 d. 19.4

a. 16.4

26. The equation of d/dx(ln e)^2x is equal to ___________. a. 2 b. 2x c. 1 d. 1/e^2x

a. 2

39. A leading shoe manufacturer produces a pair of Lebron James signature shoes at a labor cost of P900.00 a pair and a material cost of P400.00 a pair. The fixed charges on the business are P 5,000,000 a month and the variable costs are P400.OO a pair. Royalty to Lebron James is P 1,000 per pair of shoes sold. If the shoes sell at P5,OOO a pair then there is a need to produce ___________ pairs each month for the manufacturer to break-even. a. 2,890 b. 2,590 c. 2,632 d. 2,712

c. 2,632

35. Two ships are sailing in the sea on the two sides of a lighthouse. The angle of elevation of the top of the lighthouse is observed from the ships are 30d and 45d respectively. If the lighthouse is 100m high, the distance between two ships is __________. a. 200 b. 273 c. 173 d. 300

b. 273

67. The value of expression a(a^2+n+1)+5 for a^1 =0 is ________. a. 1 b. 5 c. A+5 d. 6

b. 5

41. The length of a rectangle is four less than twice its width. If x is the width of the rectangle, then the perimeter of the rectangle would be ________. a. 6x-4 b. 6x-8 c. 6x+4 d. 3x-4

b. 6x-8

30. In a shower, 3cm of rain falls. The volume of water that falls on 1.5 hectares of ground is ______. a. 7500 cu.m. b. 750 cu.m. c. 75 cu.m. d. 75 cu.m.

b. 750 cu.m.

7. Given the right spherical triangle whose given parts are a - - 77d. . b = 62d and c = 90d. The value of the side opposite the right angle. a. 84d45m b. 86d15m c. 84d30m d. 85d15m

b. 86d15m

24._________ is the perimeter of a square with a diagonal measuring units a. 4x units b. 8x units c. 8x√2 units d. 2x units

b. 8x units

38. The domain of f(x) = In (2 —x) + In (3 —x) is given by a. (-infinity , 3) b. (-infinity , 2) c. (2,3) d. (-infinity, 7)

b. (-infinity , 2)

64. The equation lim n ->π cosx/x-π/2 is equal to ________. a. 0 b. -1 c. Infinity d. 1

b. -1

73. Using identity a^2-b^2 = (a+b) (a-b), 4^x-6^x is _______. a. 20 b. -20 c. 12 d. -12

b. -20

43. If the distance between the points (9, 7) and (3,y) is 13 then the value of y is __________. a. -19 b. 19 or -5 c. 5 d. 5 or -19

b. 19 or -5

56. If a cube has side 6 cm then the total surface area should _________. a. 216 sq. m. b. 226 sq. m. c. 214 sq. cm. d. 236 sq. cm.

b. 226 sq. m.

29. _________ is the distance of the line 3x + 4y + 15 = 0 from the origin. a. 3 b. 4 c. 2 d. 1

a. 3

51. If a cylindrical gasoline lying horizontally has 0.50 diameter and 3m long is filled to a depth of 0.60 m then it can stilt contain _________ gallons of gasoline. a. 360 b. 250 c. 270 d. 300

a. 360

49. If f(2x+3) = 2x-1 then f(3x + 4) is equal to __________. a. 3x b. 9x+15 c. 6x+11 d. 6x+7

a. 3x

9. ____________ is the distance in nautical miles between Manila and San Francisco given that Manila is located at 14d36m N latitude and 121d05m E longitude while San Francisco is situated at 37d48m N latitude and 122d24m W longitude. a. 6046.2 nautical miles b. 6326.2 nautical miles c. 5896.2 nautical miles d. 7856.2 nautical miles

a. 6046.2 nautical miles

13. A right circular cone with an altitude of 9 meters is divided into two segments; one is a smaller circular cone having the same vertex with an altitude of 6m. With there, the ratio of the volume of the two cones is _____. a. 8:27 b. 1:3, c. 19:27 d. 2:3

a. 8:27

53. ______ is an equation of a curve that intersects at right angles every curve of the family y = l/x + k (where k takes ail real values). a. y = x^3/3

a. y = x^3/3

34. The equation ∫ x/√9-x^2 dx is equal to _________. a. 2√9-x^2 +c b. 1/2ln √9-x^2+c c. -1/4 √9-x^2 +c d. -√9-x^2 +c

d. -√9-x^2 +c

65. If 1/2x + 6 = —x — 3, then the value of -2x is _________. a. -3 b. -12 c. -6 d. 12

d. 12

54. A college freshman borrowed Php 2000 from a bank for his tuition fee and promised to pay the amount for one year. If he received only the amount of Php1920 after the bank collected the advance interest of Php 80 then the rate of discount is ________. a. 4.15% b. 4.25% c. 3.67% d. 4.00%

d. 4.00%

71. The sum of the series 2-1 + 1/2 -1/4 + 1/8 -.... is __________ a. 3/4 b. 3/2 c. 5/4 d. 4/3

d. 4/3

8. If the edge of a cube is increased by 30% then _______.. surface area. a. 63 b. 65 C. 67 d. 69

d. 69

48. If a right spherical triangle has an angle C = 99d , a = 59d, and c = 43d then the value of side b is a. 78.66d b. 75.89d c. 45.73d d. 74.33d

d. 74.33d

2. If a cone was formed by rolling a thin sheet of metal in the form of a sector of a circle 72 cm in diameter with a central angle of 150d then the volume of the cone in cc is a. 7722 b. 7733 c. 7744 d. 7711

d. 7711

18. The equation of the line through (-3,-5) parallel to 7x + 2y -4 =0 is ______. a. 2x+7y+30=0 b. 7x-2y+30=0 c. 7x-2y-4=0 d. 7x+2y+31=0

d. 7x+2y+31=0

45. _______ is the rate of interest compounded annually which is the same as the rate of interest on 8% compounded quarterly. a. 8.12% b. 8.07% c. 8.16% d. 8.24%

d. 8.24%