1. It Rita can run around the block 5 times in 20 minutes.

how many times can she run around the

block in one hour?
a. 10
b. 50
c. 15
d. 100
2. Determine if the sequence in sin (u/n) is convergent or divergent. Find its limit if it is
convergent
a. convergent, π/4
b. divergent
c. convergent, π/2
d. convergent, π
3. Evaluate the double integral dx dy / (x - y), with interior limits 2y to 3y and outer limits from
0 to 2.
a. In 4
b. In 2
c. In
d. In 3
4. A snack machine accepts only 5-centavo coins. Chocolate bars cost 25c each, packages of
peanuts cost of 75c and a can of cola costs 50c. How many 5-centavo coins are needed to buy 2
chocolate bars, one pack of peanuts and a can of soda?
a. 30
b. 32
c. 35
d. 6
5. Find the equation of the circle which passes through the vertex and the endpoints of the latus
rectum of the parabola y2 = 8x.
a. x2 + y2 + 10x = 0
b. x2 + y2 - 10x + 2y + 3 = 0
c. x2 + y2 - 10x = 0
d. x2 + y2 + 2x - 10y - 1 = 0
6. Express -3- 4i in polar form.
a. (square root of 5)^e-i arctan 2
b. square root of 2)^e -- i arctan square root of 5
c. (square root of 5) e - i^(π + arctan 4/3)
d. 5 ei^(π + arctan 4/3)
7. Find the equation of the normal line to x2 + y2 at the point (2, 1)
a. 4x - 3y = 0
b. x-2y = 0
c. x+y=0
d. x-y=0
8. Find the value of x for which f(x) = cot 2x is discontinuous.
a. x= 3/2
b. x=0
c. x = π/2
d. x = 0, π
9. What is the ratio of the sides of a triangle if the product of the sines of its angle is a
maximum?
a. 1:2:2
b. 1:3:3
c. 1:1:2
d. 1:1:1
10. A pendulum 1 m long oscillates through an angle of 100. Find the distance through which the
end of the pendulum swings in going from one extreme position to the other.
a. πm
b. 2π m
c. π/8 m
d. π/18 m
11. If y = arctan (In x), find y' when x = 1/e.
a. e/2
b. e/3
c. e
d. e/4
12. Hotels, like airlines, often overbook, relying on the fact that some people with reservations
will cancel at the last minute. A certain hotel chain finds 20% of the reservation will not be
used. If 4 reservations are made, what is the probability fewer than two will cancel?
a. 0.8192
b. 0.3825
c. 0.7241
d. 0.5211
13. Find the area bounded by the parabolas x2 - 2x + 2y + 5 = 0 and x2 - 2x + y + 1 = 0.
a. 14
b. 14/13
c. 16
d. 16/3
14. Find the general solution of y' = y sec x.
a. y = C sec2x tan x
b. y = C(sec x + tan x)
c. y = C sec x tan x
d. y = C sec x
15. A company manufactures industrial laminates (thin nylon-based sheets) of thickness 002
tolerance of 0.004 in. Solve the inequality involving absolute values that describes the rand
thickness for the laminate.
a. 0.017 ≤ 𝑥 ≤ 0.024
b. 0.014 ≤ 𝑥 ≤ 0.022
c. 0.017 ≤ 𝑥 ≤ 0.025
d. 0.016 ≤ 𝑥 ≤ 0.023
16. Determine all the values of (1 + i)i.
a. cos (2sq. root of 2kπ) + i sin (2sq. root of 2 kπ)
b. cos (1/2 ln 2) + i sin (1/2 ln 2)
c. e^-π/4 + 2lπ (cos (1/2 ln2) + i sin (1/2 ln2))
d. e^-π/4 + 2kπ
17. Judy's English quiz scores are 56. 93 72 99 and 87 What is the median of her quizzes?
a. 87
b. 56
c. 72
d. 85
18. Find the equation of the line passing 3 units from the origin and parallel to 3x + 4y – 10 = 0.
a. 3x + 4y -15 = 0
b. 4x + 3y + 1 = 0
c. x-3y + 15 = 0
d. 3x + 4y – 5 = 0
19. Which ratio best express the following: five hours is what percent of a day?
a. 5/24 = x/100
b. 5/24 = 24/x
c. 5/100 = x/24
d. x/100 = 24/5

20. What is the graph of the curve whose equation is 5x2 + 5y2 – 5x – 10y - 33 = 0
a. parabola
b. ellipse
c. hyperbola
d. circle
21. if a school buys three computers a, b, and c pesos each, gets a discount of 90%, which
expression would determine the average price paid by the school?
a. (a + b + c) 09/3
b. (a + b + c) / 3
c. (a + b + c) /0.9
d. (a + b + c) 0.9
22. Find the equation of the family of orthogonal trajectories of the system of parabolas
y2 = 2x + C.
a. y = Ce^2x
b. y = Ce^-2x
c. y = Ce^x
d. y = Ce^ -x
23. A laboratory keeps two acid solutions on hand. One is 20% acid and the other is 35% acid
How many liters of distilled water should be added to a liter of 35% acid solution in order to
dilute it to a 20% acid solution?
a. 0.45
b. 0.75
c. 0.25
d. 0.57
24. Solve xy’(2y - 1) = y(1 - x).
a. ln xy = x - 2y +Ć
b. ln xy = 2y – x + C
c. ln xy = x + 2y + C
d. In xy = 2(x - y) + C
25. in an arithmetic series, the terms of the series are equally spread out. For example, in 1 + 5 +
9 + 13 + 17, consecutive terms are 4 apart. If the first term in an arithmetic, series is 3. The
last term is 136, and the sum is 1,390. what are the first 3 terms?
1
a. 3, 36 3 , 70
b. 3, 10, 17
c. 3. 23,43
1
d. 3, 69 2 , 138
26. Find the equation of the circle tangent to 4x-3y + 12 = 0 at (-3,0) and tangent also to
3x + 4y – 18 = 0 at (4.1).
a. x2 + y2 + 4x - 3y + 6 = 0
b. x2 +y2 + x - 2y + 3=0
c. x2 +y2 + x - y + 5 = 0
d. x2 +y2 - 2x + 6y - 15 = 0
27. Joseph gave 1/4 of his candies to Joy and Joy gave 1/5 of what she got to Tim. if Tim
received 2 candies, how many candies did Joseph have originally?
a. 30
b. 20
c. 50
d. 40
28. A line that is perpendicular to the y-axis has a slope equal to ______________.
a. one
b. infinity
c. indeterminate
d. zero
29. What is the value of x if logx 1296 = 4?
a. 3
b. 6
c. 5
d. 4
30. It represents the distance of a point from y-axis.
a. coordinate
b. ordinate
c. abscissa
d. polar distance
31. What is the next term in the geometric sequence 16, -4,1, -/4, ...?
a. 1/16
b. 1/8
c. 1/8
d. 0
32. A steel girder 8 m long is moved on rollers along a walkway 4 m wide and into a corridor
perpendicular to the walkway. How wide must the corridor be to successfully move the
girder?
a. 1.8m
b. 18 m
c. 10 m
d. 8 m
33. Find the centroid of the solid generated by revolving about x = 0 the first quadrant arc x2 + y2
= a2, the fourth quadrant arc of x2 - y2 = a2 , the fourth quadrant arc of 2x – y = 2a and x = 0.
a. (0, 2/3)
b. (0, -1/3)
c. (0, 1/3)
d. (0, -2/3)
34.Jeff burns 500 calories per hour bicycling. How long will he have to bike to burn 750
calories?
a. 1.5 hours
b. 2 hours
c. 0.5 hour
d. 3 hours
35. Evaluate ∫ 𝑑𝑥/(𝑥 + 2) from x = -10 to x = -6
a. In (1/2)
b. ln 1
c. ln 2
d. 2 ln 2
36. Find all the real solutions to the logarithmic equation In x + In 2 = 3
a. e^½
b. e^2
c. e^3/2
d. e
37. On a particular morning, the temperature went up 1 degree every 2 hours. If the temperature
was 53 degrees at 5 AM. at what time was it 57 degrees?
a. 12 P.M.
b. 8 A.M.
c. 1 P.M.
d. 7AM
𝑥 2−4
38. Evaluate lim
𝑥→2 𝑥−2
a. 8
b. 4
c. 0
d. 16
39. Aubrey measured the width of her dining room in inches. It is 150 inches How many feet
wide is her dining room?
a. 10.5 ft
b. 21.5 ft
c. 12.5 ft
d. 9.5 ft
40. Find the angle in mils subtended by a line 10 yards long at a distance of 5000 yards
a. 2.5 mils
b. 1 mil
c. 4 mils
d. 2.04 mils
41. Find x. arctan x + arctan (1/3) = π/4
a. 1/4
b. 1/5
c. 1/2
d. 1/3
42. Assuming that the soap bubble retains its spherical shape as it expands, how fast is its radius
increasing when its radius is 2 in, if air is blown into it at the rate of 4 in^3/sec?
a. 1/π in/sec
b. 3/2π in/sec
c. 1/4π in/sec
d. 2/3π in/sec
43. Approximately how many liters of water will a 10-gallon container hold?
a. 42
b. 32
c. 9
d. 38
44. If csc2θ = x2 + 1, what is cot2θ?
a. х
b. 1+x
c. x2
d. 1-x2
45. How many ancestors does a set of triplets have in the eleven generations before them?
Assume there are no duplicates.
a. 4085
b. 4005
c. 4009
d. 4095
46. A point where the concavity of a curve changes or when the slope of the curve is neither
increasing nor decreasing is known as
a. inflection point
b. maximum point
c. minimal point
d. point of tangency
47. A cone shaped icicle is dripping from the roof. The radius of the icicle is decreasing at a rate
of 0.2 cm/hr, while the length is increasing at a rate of 0.8 cm/hr. If the icicle is currently 4
cm in radius and 20 cm long, is the volume of the icicle increasing or decreasing, and at what
rate?
a. decreasing at 20 cu. сm/hr
b. increasing at 24 cu. сm/hr
c. decreasing at 24 cu. сm/hr
d. increasing at 20 cu. сm/hr
48. Find the equation of the normal to x2 + y2 = 1 at the point (2, 1).
a. x-y=0
b. x = 2y
c. y = 2x
d. x+y=1
49. Marvin helps his teachers plan a field trip. There are 125 persons to the field trip and each
school bus holds 48 persons. What is the minimum number of school buses is needed to
reserve for the trip?
a. 5
b. 4
c. 3
d. 2
50. The drivers at F and M trucking must report the mileage on their vehicle each week. The
mileage reading of Ed's vehicle was 20,907 at the beginning of one week, 21,053 at the end
of the same week. What is the total number of miles driven by Ed that week?
a. 145 miles
b. 1046 miles
c. 146 miles
d. 46 miles
51. Find the area bounded by x? - 2x + 2y + 5 = 0 and x? - 2x + y + 1 = 0.
a. 14
b. 16/3
c. 16
d. 14/3
52. _____________represents the distance of a point from the y-axis.
a. abscissa
b. coordinate
c. polar distance
d. ordinate
53 Give one indicated root of (-16i)1/2
a. 2 cis 330°
b. 2 cis 165°
c. 2 cis 167°
d. 2 cis 67.5°
54. From a ship sailing due east a light house was seen to bear N 45° E. After sailing 5 km, the
lighthouse as a bearing of N 69° W. How far was the lighthouse from both points of
observationi?
a. 3.87 km
b. 3.00 km
c. 0.87 km
d. 3 33 km
55. Each of the question on a quiz is a five-part multiple choice question with exactly one correct
answer. A student, totally unprepared for the quiz, guesses on each of 15 question If at least
11 questions must be answered correctly to pass the quiz, what is the chance the student
passes?
a. 0.10
b. 0.20
c. 0.50
d. 0
56. Find the volume generated when the area bounded by the curve y = cosh x and the x-axis
from x = 0 to x = 1 is revolved about the x-axis.
a. 2.42
b. 1.42
c. 4.42
d. 3.42
57. Bobby is 2 years as twice as old as Ellen. The sum of twice Bobby’s age and three times
Ellen’s age is 56. How old is Ellen?
a. 10
b. 18
c. 20
d. 12
58. Water is running out of a conical funnel at a rate of 1 cu. in / sec If the radius of the abse of
the funnel is 4 in and the altitude is 8 in. find the rate at which the water level is dropping
when it is 2 in from the top.
a. -1/9π in/sec
b. -1/2π in/sec
c. -1/π in/sec
d. -2/π in/sec
59. Wat curve is described by the equation 4x2-y2+8x + 4y = 15?
a. Ellipse
b. Parabola
c. Hyperbola
d. Circle
60. Carbon is a radioactive form of carbon that is found in all living plants and animals. After a
plant and animal dies, the carbon 14 disintegrates Scientists determine the age of the remains
by comparing its carbon 14 with the amount found in living plants and animals and follows
exponential growth pattern. Charcoal from an ancient fire pit Java had 1/4 the amount of
carbon 14 found in a living sample of wood with the same size Estimate the age of the
charcoal.
a. 11.350 years
b. 11.500 years
c. 11,280 years
d. D. 11,200 years
61 A tangent to a conic is a line which
A passes incide

70. According to Newton's Law of Cooling the rate at which a substance cools in air is directly
proportional to the difference between the temperature of the substance and that of air. If the
temperature of the air is 30° and the substance cools from 100° to 70° in 15 minutes, how long
will it take to cool 100° to 50°?
a. 45.30 min
b. 33.59 min
c. 35.39 min
d. 43.50 min
71. Find the maximum area of a rectangle which can be inscribed in an ellipse having the
equation x2 + 4y2 = 4.
a. 4
b. 3
c. 2
d. 5
72. A square has a side 5 cm shorter than the side of a second square. The area of the larger
square is four times the area of the smaller square. Find the side of each square.
a. 15,6
b. 15, 5
c. 10,5
d. 10,6
73. Find the approximate increase in the volume of the sphere of the radius increases from 2 to
2.05 in one second
a. 5.51
b. 2.12
c. 5.55
d. 2.51
74. A car consumes 16 gallons of gasoline to travel 448 miles. How many miles/gallon is the
cars consumption?
a. 26
b. 24
c. 22
d. 28
75. A pebble dropped into a lake creates an expanding circular ripple. If the radius of the ripple is
increasing at the rate of 2 in/sec, at what rate is its area increasing when its radius is 10 in. ?
a. 12.56 sq. in/sec
b. 125.66 sq. in/sec
c. 62.33 sq. in/sec
d. 253.54 sq. in/sec
76. If sinθ = a and cos2 θ = b then what is the value of sin2 θ- 2cos θ?
I. a2 + 2 square root of b
II. a2- 2 square root of b
III. b2 + 2 square root of a
IV. b2 - 2 square root of a
a. I and II only
b. III only
c. III and IV only
d. I only
77. Find the domain of the following function: f(x) = 3x, -6 ≤ 𝑥 ≤ 8.
a. (-6, 8)
b. [-18, 24)
c. (-18, 24)
d. (-6, 8]
78. Three circles of radii 3, 4, and 5 inches, respectively are tangent to each other externally.
Find the largest angle of a triangle formed by joining the centers.
a. 75.1°
b. 72.6°
c. 73.3°
d. 73.4°
79. If the general equation of the conic is Ax2 + Bxy + Cy2 + DX + Ey + F = 0. If B2 - 4AC > 0,
the equation describes a __________.
a. ellipse
b. hyperbola
c. parabola
d. circle
80. Determine the equation that expresses that G is proportional to k and inversely proportional
to C and z. Symbols a, b and care constants.
𝑐𝑘
a. 𝐺 = 𝐺𝐺
𝑎
b. 𝐺 =
𝑏𝑐
𝑐𝑘
c. 𝐺 = 𝑧𝐶
𝑏𝐶
d. 𝐺 = 𝑧𝑘
81. Find L^-1 {1/(s2 + b2)2}.
a. 1/ (s2 +b2)
b. b/ (s2 +b2)
c. s/ (s2 +b2)
d. 1/ (s2 -b2)
82. Bob notices that the ratio of boys to the total students in his class is 3:4. If there are 28
students in his class, how many of them are boys?
a. 24
b. 21
c. 7
d. 14
83. Evaluate ∫(sin 5x + cos3x) dx from x = 0 to x = π/2.
a. 0.0347
b. 0.0213
c. 0.0123
d. 0.0417
86. Solve for x in the equation: arctan 2x + arctan x = 7/4.
a. 0.182
b. 0.218
c. 0.821
d. 0.281
87. Find the vertex of the parabola x2 = 8y.
a. (2, 4)
b. (0,0)
c. (-2, 0)
d. (0,8)
88. Find the equation of the line which is perpendicular to the line 3x – 2y - 5 = 0 and which
passes through the point of intersection of 4x - y - 5 = 0 and x - y - 5 = 0.
a. 2x - 3y + 2 = 0
b. 2x – 3y - 15 = 0
c. 2x + 3y + 15 = 0
d. 2x + 3y - 2 = 0
89. Which of the following linear equations has a negative slope?
a. y = 4x - 5
b. -5x + y = 1
c. 6y + x =7
d. 6 = y – x
90. Mrs. Farrell's class has 26 students. Only 21 were present on Monday. How many were
absent?
a. 5
b. 15
c. 16
d. 4
91. A chicken farmer has 750 eggs. 4% of the eggs are cracked, 5% of the remainder are found to
be defective. How many eggs could be sold if only eggs without cracks and defects are sold?
a. 483
b. 508
c. 458
d. 684
92. In the polar coordinate system, the distance from a point to the pole is _____________.
a. polar angle
b. radius vector
c. y-coordinate
d. x-coordinate
93. x2 - y2 = 16 is the equation of a:
a. ellipse
b. hyperbola
c. circle
d. parabola