FB Excel Review Math 1

Excel Review Center FB Math Exam 1

Cebu: JRT Bldg., Imus Avenue, Cebu City Tel. 2685989 – 90 | 09173239235 Manila: 3rd & 4th Fl. CMFFI Bldg. R. Papa St. Sampaloc Tel. 7365291

1. A storage battery discharge at a rate which is proportional to the charge. If the charge is reduced to 50% of its original value at the end of 2 days, how long will it take to reduce the charge to 25% of its original charge?

A. 2 days B. 3 days* C. 4 days D. 5 days

2. Solve the differential equation x(y –

1)dx + (x + 1)dy = 0 if y = 2 and x = 1. Determine y when x = 2.

A. 1.80 B. 1.48

C. 1.55 D. 1.63

3. Evaluate the expression (1 + i

2)10

where i is an imaginary number.

A. -1 B. 10 C. 0* D. 1

4. When two rows are interchanged in

position, the value of the determinants will be

A. Unchanged B. Become zero C. Multiplied by -1

D. Unpredictable

5. Twice the larger of two numbers is three more than five times the smaller and the sum of four times the larger and three times the smaller is 71. What are the numbers?

A. 13, 6 B. 14, 5 * C. 15, 5 D. 13, 3

6. The product of two consecutive

negative even integers is 24. Find the numbers.

A. - 5, - 3

B. - 8, - 2 C. - 6, - 4 * D. - 9, - 7

7. In three more years, Miguel's

grandfather will be six times as old as Miguel was last year. When Miguel's present age is added to his grandfather's present age, the total is 68. How old is each one now?

A. 57, 11 * B. 60, 8 C. 45, 23 D. 49, 12

8. One-half of Heather's age two years

from now plus one-third of her age

three years ago is twenty years. How old is she now?

A. 30 B. 20 C. 32 D. 24 *

9. Suppose you bought something that

was priced at $6.95, and the total bill was $7.61. What is the sales tax rate in this city? A. 8.5% B. 10.0%

C. 2.5% D. 9.5% *

10. A picture has a height that is 4/3 its

width. It is to be enlarged to have an area of 192 square inches. What will be the dimensions of the enlargement?

A. 12 inches x 16 inches * B. 10 inches x 15 inches C. 12 inches x 14 inches D. 10 inches x 14 inches

11. A collection of 33 coins, consisting of

nickels, dimes, and quarters, has a value of $3.30. If there are three times as many nickels as quarters, and one-half as many dimes as nickels, how

many dimes are there?

A. 6 B. 9 * C. 10 D. 18

12. A wallet contains the same number of

pennies, nickels, and dimes. The coins total $1.44. How many of each type of coin does the wallet contain?

A. 10 B. 12 C. 7 D. 9 *

13. A 555-mile, 5-hour plane trip was flown

at two speeds. For the first part of the trip, the average speed was 105 mph. Then the tailwind picked up, and the remainder of the trip was flown at an average speed of 115 mph. For how long did the plane fly at 155 mph speed?

A. 2 hours B. 3 hours * C. 4 hours D. 5 hours

14. Ivan gathered twice more chestnuts

than Peter and Boris gathered 2 kilograms more than Peter. Together they gathered 26 kilograms chestnuts. How many kilograms gathered by

Boris?

A. 6 kg B. 12 kg C. 8 kg * D. 10 kg

15. Simplify the expression i

1997 + i

1999,

where i is an imaginary number.

A. 1 + i B. – i C. 0 * D. 1 – i

16. A piece of paper is 0.05 inches thick.

Each time the paper is folded into half, the thickness is doubled. If the paper

was folded 12 times, how thick in feet the folded paper be?

A. 17.10 * B. 12.34 C. 11.25 D. 10.24

17. A speed boat can make a trip of 100

miles in one hour and 30 minutes if it travels upstream. If it travels downstream, it will take an hour and 15 minutes to travel the same distance. What is the speed of the boat in calm water?

A. 293.33 mph B. 108.45 mph C. 73.33 mph * D. 28.99 mph

18. A company sells 80 units and makes

P80 profit. It sells 110 units and makes P140 profit. If the profit is a linear function of the number of units sold, what is the average profit per unit if the company sells 250 units?

A. P1.68 * B. P1.50 C. P1.78 D. P2.05

19. Solve for x in the equation: arctan(2x)

+ arctan(x) = π/4

A. 0.821 B. 0.654 C. 0.182 D. 0.281 *

20. Three times the sine of a certain angle

is twice of the square of the cosine of the same angle. Find the angle.

A. 45

o

B. 30o *

C. 10o

D. 50o

21. Find the height of the tree if the angle

of elevation of its top changes from 20

degrees to 40 degrees as the observer advances 23 meters toward the base.

A. 13.78 m B. 15.88 m C. 14.78 m * D. 10.89 m

22. A transmitter with a height of 15 m is

located on top of a mountain, which is 3.0 km high. What is the furthest distance on the surface of the Earth that can be seen from the top of the mountain? Take the radius of the Earth to be 6400 km.

A. 196 km * B. 205 km

C. 255 km D. D156 km

23. A railroad curve is to be laid in a

circular path. What should be the radius if the track is to change direction by 30 degrees at a distance of 300 m?

A. 300 m B. 655 m C. 421 m D. 573 m *

24. Two triangles have equal bases. The

altitude of one triangle is 3 units more than its base and the altitude of the other is 3 units less than its base. Find the altitudes, if the areas of the

triangles differ by 21 sq.units.

A. 4 and 10 * B. 6 and 15 C. 10 and 11 D. 5 and 11

25. A metal washer 1-inch in diameter is

pierced by ½-inch hole. What is the

volume of the washer if it is 1/8 inch thick?

A. 0.074 * B. 0.085 C. 0.054



D. 0.082

26. Find the increase in volume of a spherical balloon when its radius is increased from 2 to 3 inches.

A. 74.12 cu.inch B. 89.05 cu.inch C. 75.99 cu.inch D. 79.59 cu.inch *

27. The volume of two spheres is in the

ratio 27:343 and the sum of their radii is 10. Find the radius of the smaller sphere.

A. 5 B. 4

C. 3 * D. 9

28. A wire with a length of 52 inches is cut

into two unequal lengths. Each part is bent to form a square. If the sum of the area for the two squares is 97 square inch, what is the area of the smaller square?

A. 34 B. 16 * C. 23 D. 10

29. The segment from (-1,4) to (2,-2) is

extended three times its own length. The terminal point is

A. (11,20) B. (11,-20) * C. (12,20) D. (12,-25)

30. The diameter of a circle described by

9x2 + 9y

2 = 16 is

A. 4/3 B. ½ C. 2 D. 8/3 *

31. Find the equation of the axis of

symmetry of the function y = 2x2 – 7x +

5.

A. 7x + 4 = 0 B. 4x + 7 = 0 * C. 4x – 7 = 0 D. 4x – 2 = 0

32. 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. 24 B. 12 C. 20 * D. 15

33. If the lines 4x – y + 2 = 0 and x + 2ky +

1 = 0 are perpendicular to each other, determine the value of k.

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

34. Find the volume of the pyramid formed

in the first octant of the plane 6x + 10y + 5z – 30 = 0 and the coordinate axes.

A. 15 * B. 13 C. 14 D. 16

35. The depth of the water in a cylindrical tank 4 m in diameter is increasing at the rate of 0.7 m/min. Find the rate at which the water flowing into the tank.

A. 2.5 B. 3.8 C. 9.0 D. 8.8 *

36. If ln(lny) + lny = lnx, find y’.

A. x/(x + y) B. x/(x – y) C. y/(x + y) * D. y/(x – y)

37. If y = 2x + sin2x, find x if y’ = 0.

A. π/4 B. π/2 * C. 2 π/3 D. 2 π/7

38. Find the change in y = 2x – 3 if x

changes from 3.3 to 3.5.

A. 0.5 B. 0.4 * C. 0.3 D. 0.2

39. A statue 3.2 m high stands on a

pedestal such that its foot is 0.4 m above an observer’s eye level. How far from the statue must the observer

stand in order that the angle subtended by the statue will be maximum?

A. 1.1 m B. 1.6 m C. 1.5 m D. 1.2 m *

40. What is the slope of the curve y = 1 +

x2 at the point where y = 10?

A. 6 * B. 9 C. 7 D. 8

41. Determine the area bounded by the

curve y = 1/(x^2), the y-axis and the lines y = 1 and y = 5.

A. 2.47 * B. 3.50 C. 1.90 D. 3.3

42. A condominium is to be constructed in

a rectangular lot with a perimeter of 800 m. What is the largest area that can be enclosed by fencing the perimeter?

A. 3.5 hectares B. 1.23 hectares C. 4 hectares * D. 5 hectares

43. A person draws 3 balls in succession

from a box containing 5 red balls, 6 yellow balls and 7 green balls. Find the probability of drawing the balls in the order red, yellow and green.

A. 0.3894

B. 0.03489 C. 0.5439 D. 0.04289 *

44. How many triangles are formed by 10 distinct points no three of which are collinear?

A. 56 B. 42 C. 120 * D. 150

45. How many four digit zip codes are

there if no digit is repeated?

A. 151.030 B. 5,040 * C. 32,090 D. 1,450

46. If the probability that a basketball

player sinks the basket at 3-point range is 2/5, determine the probability of shooting 5 out of 8 attempts.

A. 12.4% * B. 15.67% C. 25% D. 28.4%

47. Three forces 20N, 30N and 40N are in

equilibrium. Find the angle between the 30N and 40N forces.

A. 28.96

o *

B. 45.89o

C. 25.97o

D. 30.98o

48. How far does an automobile move while its speed increases uniformly from 15 kph to 45 kph in 20 sec?

A. 165 m B. 167 m * C. 134 m D. 205 m

49. Determine the sum of the first 4 terms

of the sequence whose general term is given by 3

n – 2.

A. 100 B. 89 C. 98 D. 112 *

50. If f(x – 1) = 1 + x2, then what is f(x)?

A. x

2 + 2x + 1

B. x2 + 2x + 2 *

C. x2 – 2x – 1

D. x2 – 2x – 2

51. 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 B. 110 C. 55 D. 100 *

52. Find the length of the chord of a circle of radius 20 cm subtended by a central angle of 150 degrees.

A. 29.7 cm B. 25.4 cm C. 38.6 cm * D. 18.8 cm

53. Two straight roads intersect to form an angle of 75 degrees. Find the shortest distance from one road to a gas station on the other road 1 km from the junction.



A. 3.732 km * B. 5.325 km C. 4.365 km D. 2.856 km

54. A television antenna 20 m high stands

on top of a house which is 12 m high. At what distance from the base of the house will the antenna and the house subtend equal angle?

A. 24 m * B. 15 m C. 31 m D. 28 m

55. The apothem of a regular pentagon is

10. Determine its area.

A. 227.43 B. 159.62 C. 363.30 * D. 315.23

56. Find the area of a trapezoid whose

median is 32 cm and whose altitude is 6 cm.

A. 150 cm

2

B. 164 cm2

C. 142 cm2

D. 192 cm2 *

57. 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 cm

3 *

B. 451.2 cm3

C. 281.6 cm3

D. 367.4 cm3

58. How many sides have a polygon if the

sum of the interior angles equals twice the sum of the exterior angles?

A. 7 B. 6 * C. 4 D. 5

59. The abscissa of a point is 3. If its

distance from a point (8,7) is 13, find

its ordinate.

A. -5 or 19 * B. 3 or 5 C. 5 or 19 D. -3 or 7

60. Compute the length of the latus rectum

of the parabola y2 – 4y – 12x – 32 = 0.

A. 10 B. 12 * C. 11 D. 16

61. Find the volume bounded by the plane

6x + 15y – 10z – 30 = 0 and the coordinate axes.

A. 5 cu.units * B. 4 cu.units C. 8 cu.units D. 9 cu.units

62. Find the point on the curve y = x

3 at

which the tangent line is perpendicular to the line 3x + 9y = 4.

A. (1,1) * B. (1,-1) C. (-1,2) D. (-2,-1)

63. If three sides of a trapezoid are each 10 cm long, how long must the fourth side be if the area is maximum?

A. 15 B. 10 C. 20 * D. 30

64. When two dice are thrown, what is the

probability that the sum of the two faces shown is 6?

A. 1/36 B. 1/6 C. 1/9 D. 5/36 *

65. In the quadratic equation ax2 + bx + c

= 0, if r1 and r2 represent the roots, then r1 times r2 is equal to:

A. b/a B. c/a* C. –b/a D. –c/a

66. A mechanical engineer bought 24

boxes of screws for P2200. There were three types of screws bought. Screw A cost P300 per box, screw B cost P150 per box and screw C cost P50 per box. How many boxes of screw A did he buy?

A. 2 boxes*

B. 3 boxes C. 4 boxes D. 5 boxes

67. If (x + 3): 10 = (3x – 2): 8, find 2x – 1.

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

68. Two years ago, a boy is 2/3 as old as

his sister. In two years, the boy will be ¾ as old as she. How old is the boy?

A. 8 B. 10* C. 12

D. 14

69. A tank can be filled in 48 minutes by two pipes running simultaneously. By the larger pipe, it can be filled in 5 minutes less time than by the smaller. Find the time required for the larger pipe to fill it.

A. 109.8 minutes B. 45.2 minutes C. 93.6 minutes* D. 90.65 minutes

70. A mixture of 40 kg of candy worth

P6/kg is to be made up by taking some worth P4.50/kg and some worth P8.50/kg. How many kilograms of each

should be taken?

A. 23 and 20 B. 25 and 12 C. 34 and 15 D. 25 and 15*

71. Find the bigger of two consecutive

positive odd integers such that the

difference of their squares is 40.

A. 11* B. 12 C. 10 D. 16

72. Find the fourth proportion to 3, 5 and 21.

A. 27 B. 56 C. 65 D. 35*

73. In the expansion of (x + 2y)

10, the

numerical coefficient of the 5th term is:

A. 5040 B. 210 C. 3340 D. 3360*

74. How many terms of the progression 3,

5, 7… must be taken in order that their

sum will be 2600.

A. 20 terms B. 30 terms C. 40 terms D. 50 terms*

75. Find the angle between the hour and

minute hands at 7:49.

A. 60° B. 59.5°* C. 58.5° D. 59°

76. How many three digit numbers may be

formed from the digits 0, 1, 2, 3, 4 and 5 if the digits may be repeated in a

given number?

A. 100 B. 180* C. 120 D. 130

77. A circle having a diameter of 8 cm is

inscribed in a sector of a circle whose central angle is 80°. Find the area of the sector.

A. 92.45 cm

2

B. 72.92 cm2*

C. 89.34 cm2

D. 45.23 cm2

78. The two legs of a triangle are 300 units

and 150 units each respectively. The angle opposite the 150 units side is 26°. What is the third leg?

A. 197.49 B. 218.61 C. 341.78* D. 282.15

79. A solid has a circular base of radius 20

cm. Find the volume of the solid if every plane section perpendicular to a particular fixed diameter is an equilateral triangle.

A. 12453.57 cm

3

B. 21342.56 cm3

C. 18475.21 cm3*

D. 15453.67 cm3

80. The area of an equilateral spherical

triangle is 10π sq.m, find the measure of each angle if its radius is 10.

A. 44° B. 88° C. 66°*

D. 77°



81. A solid formed by revolving the ellipse about its major axis is called a

A. Spheroid B. Oblate spheroid C. Prolate spheroid D. Ellipsoid

82. The face of a regular tetrahedron is a

A. Triangle* B. Square C. Pentagon D. Hexagon

83. Find the equation of the line passing

through the points (-8,1) and (8,-1).

A. 8 + xy = 0 B. y + 8x = 0 C. y + x = 0 D. x + 8y = 0*

84. 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

85. 4x

2 – 256 = 0 is the equation of

A. Parallel lines* B. Parabola

C. Circle D. Ellipse

86. Find the equation of the normal to x

2 +

y2 = 1 at the point (2,1).

A. y = 2x B. x = 2y* C. 2x + 3y = 3 D. x + y = 1

87. The parabola y = -x

2 – 6x – 9 opens

A. to the left B. to the right C. downward D. upward*

88. An ellipse with diameters 8 and 6 respectively has an area equal to _____ sq. units.

A. 48π B. 24π C. 12π* D. 6 π

89. A hyperbola with major axis 8 and

minor axis 6. Find the eccentricity.

A. 4/3 B. 5/4* C. 5/3 D. 7/5

90. It is a conic section whose eccentricity

is less than 1.

A. Ellipse* B. Hyperbola C. Circle D. Parabola

91. The equation r = a is the polar

equation of a

A. Line B. Circle* C. Hyperbola D. None

92. The derivative of lncosx is

A. secx B. –tanx* C. –secx D. tanx

93. If y = xlnx, find y’.

A. 1/x

2

B. 1/x* C. -1/x D. -1/x

2

94. Zero raise to any number is equals to

A. 0* B. Infinity

C. Indeterminate D. 1

95. The rectangular is to be fenced on its

entire perimeter. Find the ratio of length and width for minimum amount of fencing.

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

96. Find the slope of the curve defined by

the equation x2y – 8 = 0 at the point

(2,2).

A. 2

B. -1 C. -1/2 D. -2*

97. If the distance y from the origin at time

t is given by y = 16t2 + 3000t + 50000,

find the initial velocity when t = 0.

A. 3000* B. 53000 C. 0 D. 50000

98. The volume of solids of revolution is

governed by what theorem?

A. Pappus* B. Varignon’s

C. Newton D. Archimedes

99. Find the area bounded by the curve y

= x2 + 2, and the lines x = 0, y = 0 and

x = 4.

A. 88/3* B. 64/3 C. 54/4 D. 64/5

100. The integral of x

7(x

8 – 4x

6)5/7

evaluated with limits from -4 to +4 has a value which is

A. Below -4 B. Above -4 but less than 0

C. 0 * D. Above zero

Documents

FB Excel Review Math 1