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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 + i2)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 i1997 + i1999, 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. 45o
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
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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 + 9y2 = 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. 28.96o* 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 3n – 2. A. 100 B. 89 C. 98 D. 112 * 50. If f(x – 1) = 1 + x2 , then what is f(x)? A. x2 + 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.
rd th
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 cm2 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 cm3*
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 = x3 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 cm2 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 cm3 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°*
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
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. 4x2 – 256 = 0 is the equation of A. Parallel lines* B. Parabola C. Circle D. Ellipse
86. Find the equation of the normal to x2 + 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 = -x2 – 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/x2 B. 1/x* C. -1/x D. -1/x2
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 x7(x8 – 4x6 )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 *
