DRY RUN EXAMINATION

ALGEBRA

Name: __________________________________________ Date: _____________________________

1. Which number has five significant digits?

a. 0.01410 b. 0.00101 c. 1.0140 d. 0.01414
2. The prefix of a no. 10 raise to the power minus 6 is:
a. tera b. deci c. centi d. micro
3. The length of a bar is one million of a meter is called:
a. omicron b. micron c. one bar d. one milli
4. 120 Giga Newton is how many Mega Newton?
a. 12,000 b. 120 c. 1,200 d. 120,000
5. Factor the expression (289 x3 – 204 x2 +36x)
a. 4x(17/2 x-3)(17/2 x -3)
b. 4x(17x-3)(17x-3)
c. 4x(4x-3)(4x+3)
d. 4x(17x-3)(17x+3)
6. Factor the expression as completely as possible: (2x3-7x2+6x)
a. x(x-2)(x-3) b. x(x-2)(x+3) c. x(x-2)(2x+3) d. x(x-2)(2x-3)
7. ( √ ) is equal to:
a. (xyz)1/n b. (xyz)n c. xyz d. (xyz)n-1
8. If x raise to the one half of one equals 4, x is equal to:
a. 24 b. 8 c. 12 d. 16
9. If the numbers one and above divided by zero the answer is:
a. zero b. infinity c. indeterminate d. absurd
10. Solve for x and y: 4x +3y =11 and 8x2 -9y = -7
a. x=5/3 and y=3/2 b. x=3/2 and y=3/2 c. x=3/5 and y=5/3 d. x=3/2 and y=5/3
11. If A can do the work in a days and B days in b days, how long it will take to do the job working together?
a. (a+b)/ab days b. (a+b)/2 days c. ab/(a+b) days d. a+b days
12. Five hundred kg of steel containing 8% nickel to be made by mixing a steel containing 14% nickel with another containing 6%
nickel. How much of each is needed?
a. 125 kg and 375 kg b. 150 kg and 350 kg c. 200 kg and 300 kg d. 250 kg and 250 kg
13. Logarithm of 10th root of, x raise to 10 equals to:
a. Log x b. (log x1/10)/10 c. 10 log x d. log x10
14. What is the natural logarithm of e to the plus b power?
a. ab b. log ab c. a+b d. 2.718(a+b)
15. What is the logarithm of negative one hundred?
a. no logarithm b. zero c. positive log d. negative log
16. The logarithm of 1 to base e is:
a. one b. 2.718 c. infinity d. zero
17. What is the value of (0.101)5/6?
a. antilog[log 0.101/5/6]
b. antilog[6/5 log 0.101]
c. 6/5 antilog[log 0.101
d. antilog[5/6 log 0.101]
18. A box contains 8 black and 12 white balls. What is the probability of getting 1 black and 1 white ball in two consecutive draws
from the box?
a. 0.53 b. 0.45 c. 0.50 d. 0.55
19. What is the sum of the following finite sequence of terms? 28, 35, 42, ……………….., 84.
a. 504 b. 525 c. 540 d. 580
20. Solve for the x that satisfy the equation, x2 + 36 = 9-2x2.
a. ±6i b. +9i c. ±3i d. -9i
21. Simplify √
√

a. √ b. ab c. √ d. √
22. Combine into a single fraction:

a. x-1 b. x+1 c. d.
23. Two cars start at the same time from two nearby towns 200 km apart and travel toward each other. One travels at 60 kph and
the other at 40 kph. After how many hours will they meet on the road?
a. 1 hour b. 2 hours c. 3 hours d. 2.5 hours
24. A single engine airplane has an airspeed of 125 kph. A west wind of 25 kph is blowing. The plane is to patrol due east and then
return to its base. How far east can it go if the round trip is to consume 4 hours.
a. 240 km b. 180 km c. 200 km d. 150
25. A car travels from A to B, a distance of 100 km at an average speed of 30 kph. At what average speed must it travel back from
B to A in order to average 45 kph for the round trip of 200 km?
a. 70 kph b. 110 kph c. 90 kph d. 50 kph
26. It takes Butch twice as long as it takes Dan to do a certain piece of work. Working together, they can do the work in 6 days. How
long would it take Dan to do it alone?
a. 12 days b. 10 days c. 11 days d. 9 days
27. A man leaving his office one afternoon noticed the clock at past two o’clock. Between two to three hours, he returned to his
office noticing the hands of the clock interchanged. At what time did he leave the office?
a. 2:26.01 b. 2:10.09 c. 2:30.05 d. 2:01.01
28. A company has a certain number of machines of equal capacity that produced a total of 180 pieces each working day. If two
machines breakdown, the work load of the remaining machines is increased by three pieces per day to maintain product. Find the
number of machines.
a. 12 b. 18 c. 15 d. 10
29. A rectangular field is surrounded by a fence 548 meters long. The diagonal distance from corner to corner is 194 meters.
Determine the area of the rectangular field.
a. 18,270 m2 b. 18,720 m2 c. 18,027 m2 d. 19,702 m2
30. Solve for x: √ √
a. x = 1 b. x = 3 c. x = 2 d. x = 4
31. Solve for x:
a. x = 1, x = -3 b. x = 3, x = 1 c. x = -1, x = 3 d. x = 2, x = 3
32. Solve for x: x2/3 + x-2/3 = 17/4
a. x = -4, x = -1/4 b. x = 8, x = -1/4 c. x = 4, x = 1/8 d. x = 8, x = 1/8
33. A rectangular lot has a perimeter of 120 meters and an area of 800 square meters. Find the length and the width of the lot.
a. 10m and 30m b. 30m and 20m c. 40m and 20m d. 50m and 10m
34. A 24-meter pole is help by three guy wires in its vertical position. Two of the guy wires are equal of length. The third wire is 5
meters longer than the other two and attached to the ground 11 meters farther from the foot of the pole than the other two equal
wires. Find the length of the wires.
a. 25m and 30m b. 15m and 40m c. 20m and 35m d. 50m and 10 m
35. In a racing contest, there are 240 cars which will have fuel provisions that will last for 15 hours. Assuming a constant hourly
consumption for each car, how long will the fuels provisions last if 8 cars withdraw from race every hour after the first?
a. 20 hours b. 10 hours c. 15 hours d. 25 hours
36. A pipe of boiler pipes contains 1275 pipes in layers so that the top layer contains one pipe and each lower layer has one more
pipe than the layer above. How many layers are there in the pile?
a. 50 b. 45 c. 40 d. 55
37. 35.2 to the x power = 7.5 to the x-2 power, solve for x using logarithms
a. -2.06 b. -2.10 c. -2.60 d. +2.60
38. Factor the expression 16 - 10x + x2
a. (x+8)(x-2) b. (x-8)(x+2) c. (x-8)(x-2) d. (x+8)(x+2)
39. If 1/x, 1/y, 1/z are in A.P., then y is equal to:
a. x-z b. ½(x+2z) c. (x+z)/2xz d. 2xz(x+z)
40. Determine the sum of the positive valued solution to the simultaneous equations: xy = 15, yz = 35, zx = 21
a. 15 b. 13 c. 17 d. 19
41. How many ways can 9 books be arranged on a shelf so that 5 of the books are always together?
a. 30,200 b. 25,400 c. 15,500 d. 14,400
42. If one third of the air in a tank is removed by each stroke of an air pump, what fractional part of the total air is removed in
strokes?
a. 0.7122 b. 0.6122 c. 0.8122 d. 0.9122
43. If 3X = 9Y and 27Y = 81Z, find x/z?
a. 3/5 b. 4/3 c. 3/8 d. 8/3
44. The seating section in a coliseum has 30 seats in the first row, 32 seats in the second row, 34 seats in the third row, and so on,
until the tenth row is reached, after which there ten rows each are containing 50 seats. Find the total number of seats in the section.
a. 900 b. 810 c. 890 d. 760
45. Equations relating x and y that cannot readily be solved explicitly for y as a function of x or for x as a function of y. Such
equations may nonetheless determine y as a function of x or vice versa, such a function is called ____________.
a. logarithmic function b. implicit function c. explicit function d. continuous function
46. If the sum is 220 and the first term is 10, find the common difference if the last term is 30.
a. 2 b. 5 c. 3 d. 2/3
47. Find the 1987th digit in the decimal equivalent to 1785/9999 starting from decimal point.
a. 8 b. 1 c. 7 d. 5
48. A club of 40 executives, 33 likes to smoke Marlboro, and 20 likes to smoke Philip Morris. How many like both?
a. 13 b. 10 c. 11 d. 12
49. Find the remainder if we divide 4y3+18y2+8y-4 by (2y+3)
a. 10 b. 11 c. 15 d. 13
50. What is the exponential form of the complex number 3 + 4i?
a. b. c. d. .
51. Simplify the complex numbers: (3 +4i) – (7-2i)
a. -4 +6i b. 10 + 2i c. 4 – 2i d. 5 – 4i
52. Simplify the following equation

a. b. c. d.

53. Simplify: { [ ( ) ] }

a. b. c. d.

54. Solve for x from the given equation: √ √ √

a. 4 b. 2 c. 3 d. 5
55. What is the lowest common factor of 10 and 32?
a. 320 b. 2 c. 180 d. 90
56. The numbers 12 and 16 has the greatest common divisor of:
a. 2 b. 4 c. 6 d. 192
57. Find the value of x which will satisfy the following expression: √ √
a. 3/2 b. 9/4 c. 18/6 d. None of these
58. If n is any positive integer, when (n-1)(n-2)(n-3)…..(3)(2)(1) = ______________.
a. e(n-1) b. (n-1)! c.n! d. (n-1)n
59. Given: f(x) = (x+3)(x-4)+4. When f(x) is divided by (x-k), the remainder is k. Find k.
a. 2 b. 4 c. 6 d. 8
60. The expression x4 + ax3 + 5x2 + bx+ 6 when divided by (x-2) leaves a remainder of 16 and when divided by (x+1) leaves a
remainder of 10. Find a and b.
a. a = 5, b= 7 b. a = -5, b= 7 c. a = -5, b= -7 d. a = 5, b= -7
61. If p – q =5 and pq = k/2, then p2 + q2 equals _________.
a. k b. 25k c. 25 + k d. k/25
62. What is the sum of the coefficients of the expansion of (2x-1)20 ?
a. 0 b. 1 c. 2 d. 3
63. Find the ratio of the infinite geometric series if the sum is 2 and the first term is.
a. 1/3 b. 1/2 c. 3/4 d. 1/4
64. Ten less than four times a certain number is 14. Determine the number.
a. 6 b. 7 c. 8 d. 9
65. Find the geometric mean of 64 and 4.
a. 16 b. 34 c. 32 d. 28
66. Find the value of x in the equations: [ ] [ ]

a. 50/9 b. 80/9 c. 70/9 d.60/9

67. Find the value of w in the following equations:
3x – 2y + w =11
x + 5y – 2w = -9
2x + y – 3w = -6
a. 3 b. 2 c. 4 d. -2
68. Solve the simultaneous equations:
x + y = -4
x+z–1=0
y+z+1=0
a. x = -1 ; y = -5 ; z = 3
b. x = 1 ; y = 2 ; z = -3
c. x = -1 ; y = -3 ; z = 2
d. x = -2 ; y = -3 ; z = -1
69. Give the factors of a2 – x2.
a. 2a – 2x b. (a + x)(a – x) c. (a + x)(a + x) d. 2x – 2a
70. Find the value of k so that 4x2 + 6x + k is a perfect square.
a. 36 b. 2.5 c. 9 d. 2.25
71. If f(x) = 2x2 + 2x + 4, what is f(2)?
a. 4x + 2 b. 16 c. x2 + x + 2 d. 8
72. Solve for x that satisfies the equation 6x2 – 7x -5 =0.
a. 5/3 or –1/2
b. 3/2 or 3/8
c. 7/5 or -7/15
d. 3/5 or ¾
73. What is the discriminant of the equation 4x2= 8x -5?
a. 8 b. -16 c. 16 d. -8
74. What is the sum of the coefficients in expansion of (x + y –z)8?
a. 0 b. 1 c. 2 d. 3
75. Evaluate the log6 845 = x.
a. 3.76 b. 5.84 c. 4.48 d. 2.98
76. What is the value of log to base 10 of 10003.3?
a. 10.9 b. 99.9 c. 9.9 d. 9.5
77. What is the value of (log 5 to the base 2) + (log 5 to the base 3)?
a. 7.39 b. 3.79 c. 3.97 d. 9.37
78. Given: log b y = 2x + log b x. Which of the following is true?
a. y = b2x b. y = 2xb c. y = 2x/b d. y =xb2x
79. Two planes leave Manila for a southern city, a distance of 900 km. Plane A travels at a ground speed of 90 kph faster than the
plane B. Plane A arrives in their destination 2 hours and 15 minutes ahead of plane B. What is the ground speed of plane A?
a. 205 kph b. 315 kph c. 240 kph d. 287 kph
80. Ten liters of 25% salt solution and 15 liters of 35% salt solution are poured into a drum originally containing 30 liters of 10% salt
solution. What is the per cent concentration of salt in the mixture?
a. 19.55% b. 22.15% c. 27.05% d. 25.72%
81. A geometric progression is 1+z+z2+z3+.....+zn where z<1. Determine the sum of the series as n approaches infinity.

a. 1/(1-2z) b. 1/(2-z) c. 1/(1-z) d. 2/(1-z)

82. Evaluate (1-i)-6

a. 0.300i b. 0.250i c. 0.125i d. 0.414i

83. Determine the solution of the inequality x2<9.

a. x<-3 b. -3<x c. x<3 d. -3 < x < 3

84. The sum of the cube of the consecutive numbers from 1 to 30 is.

a. 216,225 b. 215,325 c. 217,186 d. 216,961

85. Find the expression for the sum of the following series 12 + 22 + 32 + 42 +.....+n2

a. a. S = n(n+1)(n+2)/6
b. b. S = n(n+1)(n+2)(n+3)/7
c. S = n(n+2)(n+3)(n+4)/7
d. S = n(n+1)(2n+1)/6

86. The length of a room is 8 feet more than twice the width. If it takes 124 feet of molding to go around the perimeter of the room,
what are the room’s dimensions?

a. a. 15, 17 b. 18, 44 c. 100, 24 d. 80, 44

87. The perimeter of a triangular lawn is 42 yards. The first side is 5 yards less than the second, and third side is 2 yards less than
the first. What is the length of each side of the lawn?

a. 18, 14, 12 b. 16, 13, 11 c. 15, 12,10 d. 18, 13, 11

88. One side of a rectangular metal plate is five times as long as the other side. If the perimeter is 72 meters, what is the length of
the shorter side of the plate?

a. 6, 32 b. 5, 30 c. 6, 30 d. 5, 32

89. Numbers which allow us to count the objects or ideas in a given collection.

a. Cardinal b. Ordinal c. Arabic d. Irrational

90. Simplify bm/n

√
a. b. bm+n c. √ d.

91. The GCF of 25 and 135 is?

a. 5 b. 10 c. 15 d. 25

92. Which of the following is a root of this quadratic equation, 30 + 49x + 20 = 0?

a. 0.6 b. – 0.6 c. – 0.8 d. 0.75

93. Eight men can excavate 15 m3 of drainage open canal in 7 hours. Three men can backfill 10 m 3 in 4 hours. How long will it take
10 men to excavate and backfill 20 m3 in the project.

a. 9.87 hrs. b. 7.65 hrs. c. 8.76 hrs d. 10.98 hrs.

94. Find the value of m that will make 4x2 -4mx + 4m + 5 a perfect square trinomial.

a. 3 b. -2 c. 4 d. 5

95. Given 2 x 2 matrix [ ], find its determinant.

a. 31 b. 44 c. -20 d. 20

96. Find the remainder if we divide 4y3 + 18y2 + 8y -4 by (2y+3)

a. 10 b. 11 c. 15 d. 13
97. Find the value of x: ax –b = cx + d

a. x = (a-b)/(c+d) b. x = (b+d)/(a-c) c. x = (a-d)/(c-b) d. x = (c+d)/(a-c)

98. Simplify √ √

a. √ b. √ c. √ d. √

99. The sum of four positive integers is 32. Find the greatest possible product of these four numbers.

a. 5013 b. 645 c. 4096 d. 4913

100. Simplify 7 a+2 – 8(7)a+1 + 5(7)a + 49(7)a-2

a. -5a b. -3a c. -7a d. -4a