FB Excel Review Math 1

Excel Review Center 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. B. C. D.

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. B. C. D.

3.

57, 60, 45, 49,

11 * 8 23 12

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. B. C. D.

9.

- 5, - 3 - 8, - 2 - 6, - 4 * - 9, - 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. B. C. D.

8.

6 5* 5 3

The product of two consecutive negative even integers is 24. Find the numbers. A. B. C. D.

7.

Unchanged Become zero Multiplied by -1 Unpredictable

13, 14, 15, 13,

30 20 32 24 *

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. B.

C. D.

2.5% 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. B. C. D.

12 10 12 10

inches inches inches inches

x 16 inches * x 15 inches x 14 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 onehalf as many dimes as nickels, how many dimes are there? A. B. C. D.

6 9* 10 18

8.5% 10.0%

A. B. C. D.

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

6 kg 12 kg 8 kg * 10 kg

1+i –i 0* 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. B. C. D.

P1.68 * P1.50 P1.78 P2.05

19. Solve for x in the equation: arctan(2x) + arctan(x) = π/4 0.821 0.654 0.182 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. 45o 30o * 10o 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. B. C. D.

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

A. B. C. D.

196 km * 205 km 255 km D156 km

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?

300 m 655 m 421 m 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. B. C. D.

17.10 * 12.34 11.25 10.24

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A. B. C. D.

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?

15. Simplify the expression i1997 + i1999, where i is an imaginary number. A. B. C. D.

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

10 12 7 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. B. C. D.

A. B. C. D.

A. B. C. D.

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?

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. B. C. D.

6.

-1 10 0* 1

When two rows are interchanged in position, the value of the determinants will be A. B. C. D.

5.

1.80 1.48 1.55 1.63

Evaluate the expression (1 + i2)10 where i is an imaginary number. A. B. C. D.

4.

2 days 3 days* 4 days 5 days

FB Math Exam 1

4 and 10 * 6 and 15 10 and 11 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. B. C.

0.074 * 0.085 0.054

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0.082

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

74.12 cu.inch 89.05 cu.inch 75.99 cu.inch 79.59 cu.inch *

FB Math Exam 1 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. B. C. D.

A. B. C. D.

2.5 3.8 9.0 8.8 *

36. If ln(lny) + lny = lnx, find y’. 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. B. C. D.

5 4 3* 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. B. C. D.

34 16 * 23 10

29. The segment from (-1,4) to (2,-2) is extended three times its own length. The terminal point is A. B. C. D.

(11,20) (11,-20) * (12,20) (12,-25)

30. The diameter of a circle described by 9x2 + 9y2 = 16 is A. B. C. D.

4/3 ½ 2 8/3 *

31. Find the equation of the axis of symmetry of the function y = 2x2 – 7x + 5. A. B. C. D.

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

24 12 20 * 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. B. C. D.

1 3 4 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. B. C. D.

15 * 13 14 16

A. B. C. D.

x/(x + y) x/(x – y) y/(x + y) * y/(x – y)

π/4 π/2 * 2 π/3 2 π/7

38. Find the change in y = 2x – 3 if x changes from 3.3 to 3.5. A. B. C. D.

0.5 0.4 * 0.3 0.2

1.1 1.6 1.5 1.2

m m m m*

6* 9 7 8

probability of drawing the balls in the order red, yellow and green. 0.3894 0.03489 0.5439 0.04289 *

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12.4% * 15.67% 25% 28.4%

28.96o * 45.89o 25.97o 30.98o

48. How far does an automobile move while its speed increases uniformly from 15 kph to 45 kph in 20 sec? 165 m 167 m * 134 m 205 m

49. Determine the sum of the first 4 terms of the sequence whose general term is given by 3n – 2. 100 89 98 112 *

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

+ 2x + 1 + 2x + 2 * – 2x – 1 – 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. B. C. D.

3.5 hectares 1.23 hectares 4 hectares * 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

A. B. C. D.

A. B. C. D.

A. B. C. D.

2.47 * 3.50 1.90 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. B. C. D.

A. B. C. D.

A. B. C. D.

41. Determine the area bounded by the curve y = 1/(x^2), the y-axis and the lines y = 1 and y = 5. A. B. C. D.

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. B. C. D.

40. What is the slope of the curve y = 1 + x2 at the point where y = 10? A. B. C. D.

151.030 5,040 * 32,090 1,450

47. Three forces 20N, 30N and 40N are in equilibrium. Find the angle between the 30N and 40N forces.

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. B. C. D.

56 42 120 * 150

45. How many four digit zip codes are there if no digit is repeated? A. B. C. D.

37. If y = 2x + sin2x, find x if y’ = 0. A. B. C. D.

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

80 110 55 100 *

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

29.7 cm 25.4 cm 38.6 cm * 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.

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Excel Review Center A. B. C. D.

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

24 15 31 28

m* m m m

55. The apothem of a regular pentagon is 10. Determine its area. A. B. C. D.

227.43 159.62 363.30 * 315.23

56. Find the area of a trapezoid whose median is 32 cm and whose altitude is 6 cm. A. B. C. D.

150 cm2 164 cm2 142 cm2 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. B. C. D.

381.7 cm3 * 451.2 cm3 281.6 cm3 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. B. C. D.

7 6* 4 5

59. The abscissa of a point is 3. If its distance from a point (8,7) is 13, find its ordinate. A. B. C. D.

-5 or 19 * 3 or 5 5 or 19 -3 or 7

60. Compute the length of the latus rectum of the parabola y2 – 4y – 12x – 32 = 0. A. B. C. D.

10 12 * 11 16

61. Find the volume bounded by the plane 6x + 15y – 10z – 30 = 0 and the coordinate axes. A. B. C. D.

5 cu.units * 4 cu.units 8 cu.units 9 cu.units

62. Find the point on the curve y = x3 at which the tangent line is perpendicular to the line 3x + 9y = 4. A. B. C. D.

(1,1) * (1,-1) (-1,2) (-2,-1)

FB Math Exam 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. B. C. D.

A. B. C. D.

15 10 20 * 30

64. When two dice are thrown, what is the probability that the sum of the two faces shown is 6? A. B. C. D.

1/36 1/6 1/9 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. C. D.

b/a c/a* –b/a –c/a

2 boxes* 3 boxes 4 boxes 5 boxes

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

1 4 2 3*

8 10* 12 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. B. C. D.

109.8 minutes 45.2 minutes 93.6 minutes* 90.65 minutes

23 25 34 25

and and and and

20 12 15 15*

5040 210 3340 3360*

74. How many terms of the progression 3, 5, 7… must be taken in order that their sum will be 2600. A. B. C. D.

20 terms 30 terms 40 terms 50 terms*

A. B. C. D.

60° 59.5°* 58.5° 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. B. C. D.

100 180* 120 130

A. B. C. D.

92.45 cm2 72.92 cm2* 89.34 cm2 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. B. C. D.

197.49 218.61 341.78* 282.15

A. B. C. D.

12453.57 cm3 21342.56 cm3 18475.21 cm3* 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.

71. Find the bigger of two consecutive positive odd integers such that the difference of their squares is 40. A. B. C. D.

A. B. C. D.

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.

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. B. C. D.

73. In the expansion of (x + 2y) 10, the numerical coefficient of the 5th term is:

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.

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. B. C. D.

27 56 65 35*

75. Find the angle between the hour and minute hands at 7:49.

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. B. C. D.

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

A. B. C. D.

44° 88° 66°* 77°

11* 12 10 16

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Excel Review Center 81. A solid formed by revolving the ellipse about its major axis is called a A. B. C. D.

Spheroid Oblate spheroid Prolate spheroid Ellipsoid

FB Math Exam 1 92. The derivative of lncosx is A. B. C. D.

secx –tanx* –secx tanx

93. If y = xlnx, find y’. 82. The face of a regular tetrahedron is a A. B. C. D.

Triangle* Square Pentagon Hexagon

A. B. C. D.

1/x2 1/x* -1/x -1/x2

94. Zero raise to any number is equals to 83. Find the equation of the line passing through the points (-8,1) and (8,-1). A. B. C. D.

8 + xy = 0 y + 8x = 0 y+x=0 x + 8y = 0*

84. Find the area of the triangle which the line 2x – 3y + 6 = 0 forms with the coordinate axes. A. B. C. D.

3* 4 5 2

85. 4x2 – 256 = 0 is the equation of A. B. C. D.

Parallel lines* Parabola Circle Ellipse

86. Find the equation of the normal to x2 + y2 = 1 at the point (2,1). A. B. C. D.

y = 2x x = 2y* 2x + 3y = 3 x+y=1

87. The parabola y = -x2 – 6x – 9 opens A. B. C. D.

to the left to the right downward upward*

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

48π 24π 12π* 6π

89. A hyperbola with major axis 8 and minor axis 6. Find the eccentricity. A. B. C. D.

4/3 5/4* 5/3 7/5

90. It is a conic section whose eccentricity is less than 1. A. B. C. D.

A. B. C. D.

0* Infinity Indeterminate 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. B. C. D.

1* 3 2 4

96. Find the slope of the curve defined by the equation x2 y – 8 = 0 at the point (2,2). A. B. C. D.

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

3000* 53000 0 50000

98. The volume of solids of revolution is governed by what theorem? A. B. C. D.

Pappus* Varignon’s Newton Archimedes

99. Find the area bounded by the curve y = x2 + 2, and the lines x = 0, y = 0 and x = 4. A. B. C. D.

88/3* 64/3 54/4 64/5

100. The integral of x7(x8 – 4x6)5/7 evaluated with limits from -4 to +4 has a value which is A. B. C. D.

Below -4 Above -4 but less than 0 0* Above zero

Ellipse* Hyperbola Circle Parabola

91. The equation r = a is the polar equation of a A. B. C. D.

Line Circle* Hyperbola None

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