MATH DIAGNOSTIC EXAM SET ONLINE 8.

Find the maximum point of the

curve, y = x3 – 9x2 + 15x – 3.
1. A body moves along a straight A. (5, -28) C. (2, 7)
line according to the law s = B. (3, -12) D. (1, 4)
0.5t3 – 2t. Find its
acceleration at the end of 2 s. 9. The points A (-2, 3), B (6, -
A. 6 C. 5 5), and C (8, 5) are vertices
B. 2 D. 4 of a right triangle. Find the
length of the median from A to
2. A 60 m cable that weighs 4 kg/m side BC.
has a 500 kg weight attached at A. 8.26 C. 7.56
the end. Find the work done in B. 9.48 D. 8.65
winding up the last 20 m of the
cable. 10. Given vectors A = 2i + 4j +
A. 10,000 kg-m C. 11,900 kg- 8k and B = -2i + j – 4k. Find
B. 10,800 kg-m D. 12,500 kg-m the cross product.
A. -24i – 8j + 10k
3. What is the ratio of the sides B. -24i + 8j + 10k
of a triangle if the product of C. -4i – 8j – 32k
the sines of its angle is a D. -4i – 8j + 32k
maximum?
A. 1:2.2 C. 1:2:1 11. If the surface area of a
B. 1:1:1 D. 1:1:3 sphere increases by 21%, find
the increase in its volume.
4. Daniel has one more Algebra A. 13.31% C. 44.1%
exam to take before computing B. 33.1% D. 47.5%
the average of his grades. His
Algebra scores so far are 93, 12. A chemist needs to dilute a
94, 94, 95, 96, 98. What must 50% boric acid solution to a
be his score on this last exam 10% solution by adding water.
so he can maintain his present If it needs 25 liters of the
average? 10% solution, how much water
A. 94 C. 92 should it use?
B. 95 D. 99 A. 10 L C. 20 L
B. 15 L D. 25 L
5. In a certain school, 4% of the
men and 1% of the women are 13. The growth of a population P
taller than 1.8 m. Furthermore, is modeled by the differential
60% of the students are women. equation dP/dt = 0.713P. If the
Now if a student is selected at population is 2 at t = 0, find
random and is taller than 1.8 the population at t = 5.
m, what is the probability that A. 3.15 C. 20.69
the student is a woman? B. 4.56 D. 70.68
A. 1/3 C. 3/11
B. 1/4 D. 1/11 1 4 𝑥 𝑦
14. Given: A = ( ); B = ( ).
0 2 𝑤 𝑧
6. Find the area bounded by the Find z if B is the adjoint of
curves, y = 2/x and y = 3 – x. A.
A. 0.247 C. 0.269 A. -1 C. 1
B. 0.158 D. 0.114 B. -2 D. 2

7. Mary and Rose are 500 m apart. 15. Find the percentage increase
Mary walks 1 kph faster than in the surface of a sphere if
Rose and it tries to catch its radius will be increased by
Rose. If Rose walks 3 kph, find 5%.
the distance traveled by Mary A. 10.25% C. 15.5%
when she catches Rose. B. 12.5% D. 25%
A. 4.2 km C. 2.0 km
B. 2.4 km D. 3.2 km 16. One side of a parallelogram is
10 cm and its diagonals are 16
cm and 24 cm. Find its area.
A. 151.3 cm2 C. 142.8 cm2
B. 147.5 cm2 D. 158.7 cm2
17. Marianne will be x years old 25. The path of a particle, moving
y years from now. How old is in a straight line is given by
she now? s = t3 – 6t2 + 9t + 4. Find s
A. y – x C. x when the particle is moving at
B. x – y D. y constant velocity.
A. 3 C. 5
18. Parcel charges of a courier B. 4 D. 6
company are as follows:
P40 for the first 2 kilograms 26. Find the simplified value of
P15 for each of the succeeding (1 – i) divided by (1 + i) ten
kilogram weight of parcels raised to power 10.
With these rates, what amount A. -1 C. 1
would be charged on a parcel B. 10i D. -10i
weighing 30 kg?
A. P660 C. P460 27. Find the Laplace transform of
B. P450 D. P650 5 sin t + 10 cos t.
A. (5 + 10s)/(s2 + 1)
19. Find the area of a circle B. (5s + 10)/(s2 + 1)
circumscribing a triangle C. (5s + 10)/(s + 1)(s - 1)
having sides of 4 cm, 5 cm, and D. (5 + 10s)/(s + 1)(s - 1)
6 cm respectively.
A. 23.87 cm2 C. 28.73 cm2 28. Find the general solution to
B. 25.41 cm2 D. 21.56 cm2 the DE, (D^2 – 8D + 16)y = 0.
A. y = C1e4x + C2ex
20. Find the sum of coefficients B. y = C1e2x + C2ex
of the expression (4x - 3)9. C. y = C1e-4x + C2e4x
A. 19,684 C. 19,114 D. y = C1e4x + C2xe4x
B. 19,486 D. 19,414
29. Find the radius of the circle
21. As a man walks across a bridge x2 + y2 + 4x – 10y -92 = 0?
at a speed of 1.5 m/s, a boat A. 6 C. 10
passes directly beneath him at B. 9 D. 11
a speed of 3 m/s. The bridge is
9 m above the water. How fast 30. What percent of 50 is 12?
is the boat and the man A. 18% C. 16%
separating after 3 second? B. 24% D. 26%
A. 1.0 m/s C. 2.0 m/s
B. 1.5 m/s D. 2.5 m/s 31. The general solution of dy/dx
= 4x/y is a family of ___.
22. A kite, at a height of 60 ft, A. Ellipses C. Lines
is moving horizontally at a B. Parabolas D. Hyperbolas
rate of 5 ft/s away from the
boy who flies it. How fast is 32. At what time between 4 and 5
the cord being released when o’clock will the hands of the
100 ft are out? clock be opposite each other?
A. 4 ft/s C. 8 ft/s A. 4:54 & 32 sec
B. 6 ft/s D. 12 ft/s B. 4:52 & 23 sec
C. 4:50 & 12 sec
23. Jason ate 3 oz of a 16-oz ice D. 4:53 & 26 sec
cream pack. What percentage of
the pack did he eat? 33. Find the inverse Laplace
A. 18.75% C. 13.25% transform of s/(s + 25).
2

B. 21.45% D. 18.50% A. cos 5t C. 5 cos t

B. sin 5t D. 5 sin t
24. Find the volume generated by
revolving about the line x – 2 34. Find the area of the polygon
= 0, the area in the first and with vertices at 2+3i, 3+I, -
fourth quadrants, bounded by 2-4i, -4-I, -1+2i.
the curve, x2 + y2 – 4 = 0. A. 47 C. 25
A. 40.25 C. 45.45 B. 47/2 D. 25/2
B. 42.50 D. 47.10
35. A rubber ball is made to fall 44. If Jim and Jerry work
from a height of 150 cm and is together, they can finish a job
observed to rebound 2/3 of the in 4 hours. If working alone
height to which it falls. How takes Jim 10 hours to finish
far will the ball travel before the job, how many hours would
coming to rest if it continues it take Jerry to do the job
to fall in this manner? alone?
A. 450 cm C. 725 cm A. 4 C. 6.7
B. 750 cm D. 900 cm B. 6.5 D. 16

36. A line passes through (-2, 5) 45. Find the equation of the
and (h, 1) and has x-intercept normal line of the curve x3 +
of 3. Find h. y3 = 9 at point (1, 2).
A. 1 C. 4 A. x – y = 8 C. x – 2y = 6
B. 2 D. 3 B. 4x – y = 2 D. 2x – y = 10

37. An item is marked down from 46. A whole number from 1 to 12,
its price of P8,200 to a sale inclusive is picked at random.
price of P5,740. What is the What is the probability that
discount rate? the number is less than 7 or is
A. 30% C. 45% a prime?
B. 33% D. 63% A. 2/3 C. 11/12
B. 3/4 D. 7/12
38. Find the length of a line with
a slope of 4/3 from a point (6, 47. How many three digit numbers
4) to the y-axis. greater than 330 can be formed
A. 10 C. 12 from the digits 0, 1, 2, 3, 4,
B. 11 D. 13 5, and 6, if each digit can be
used only once?
39. Find the value of k in the A. 210 C. 90
quadratic equation, 3x2 – kx + B. 180 D. 105
x – 7k = 0, if 3 is one of the
roots. 48. Find the distance from point
A. 3 C. 6 (-1, 0) to the line 3x – 4y =
B. 4 D. 8 22.
A. 10 C. 5
40. Find the angle in mils B. 8 D. 6
subtended by a line 10 yards
long at a distance of 5000 49. Find the volume of a cube
yards. whose surface area is 54 cm2.
A. 2.5 mils C. 4 mils A. 36 C. 27
B. 1 mil D. 2.04 mils B. 64 D. 216

41. It takes 15 minutes to warm up 50. Hotels, like airlines, often

from 10°C to 20°C in a room overbook, counting on the fact
whose temperature is 30°C. that some people with
Assuming Newtons law of reservations will cancel at the
cooling, how long would it take last minute. A certain hotel
to warm up from 10°C to 25°? chain finds 20% of the
A. 15 mins C. 30 mins reservation will not be used.
B. 24 mins D. 32 mins If 4 reservations are made,
what is the chance that fewer
42. The length of a side of a than two will cancel?
regular hexagon is 14 cm. Find A. 0.3825 C. 0.5211
the length of the apothem. B.0.7241 D. 0.8192
A. 13.87 C. 10.24
B. 11.21 D. 12.12 51. The centroid of the area
bounded by the parabola y 2 =
43. The equation |z + 1| - |z + 4ax and the line x = p
2| = 4 is what type of conic? coincides with the focus of the
A. Circle C. Ellipse parabola. Find the value of p.
B. Parabola D. Hyperbola A. 3/5 a C. 2/5 a
B. 5/3 a D. 5/2 a
52. A transmitter with a height of 60. Find the general solution of
15 m is located on top of a the DE, dy/dx + y/x = 3x
mountain, which is 3.0 km high. A. y = x2 + cx C. y = x2 + C/x
What is the farthest distance B. y = cx2 D. y = x2 + C
on the surface of the earth
that can be seen from the top 61. Find the area of an isosceles
of the mountain? Take the triangle whose base is 10 cm
radius of the earth to be 6400 and its base angle is 60°.
km. A. 33.3 C. 43.3
A. 225 km C. 196 km B. 21.7 D. 50.2
B. 152 km D. 205 km
62. Two brothers are respectively
53. What is the next term in the 5 and 8 years old. In how many
geometric sequence 16, -4, 1, years will the ratio of their
-1/4, ...? ages be 3:4?
A. 1/16 C. -1/8 A. 3 C. 5
B. 1/8 D. 0 B. 4 D. 7

54. The cost per hour of running 63. An urn contains four black
a boat is proportional to the balls and six white balls. What
cube of the speed of the boat. is the probability of getting
At what speed will the boat run one black ball and one white
against a current of 4 kph in ball in consecutive draws from
order to go a given distance the urn without replacement?
most economically? A. 0.27 C. 0.24
A. 6 kph C. 20 kph B. 0.35 D. 0.53
B. 12 kph D. 24 kph
64. Mary has $50 in dimes and
55. The polynomial x2 + 4x + 4 is quarters, she has 60 more
the area of a square floor. quarters than dimes. How many
What is the length of its side? quarters does she have?
A. x + 2 C. x + 1 A. 100 C. 180
B. x - 2 D. x - 1 B. 160 D. 120

56. Which ratio best express the 65. Find the discriminant of the
following: five hours is what equation 5x2 – 6x + 1 = 0.
percent of a day? A. 12 C. 18
A. 5/24 = x/100 B. 16 D. 20
B. 5/24 = 24/x
C. 5/100 = x/24 66. In a throw of two dice, what
D. x/100 = 24/5 is the probability of getting
a sum of 7 or 11?
57. A line that is perpendicular A. 1/6 C. 2/9
to the y-axis has a slope equal B. 1/8 D. 5/36
to
A. one 67. From past experience, it is
B. infinity known that 90% of one-year old
C. indeterminate children can recognize their
D. zero mother’s voice from the voice
of a similar sounding female.
58. If coversed sin Ɵ= 0.134, find A random sample of 20 one-year
the value of Ɵ? olds is given this voice
A. 60° C. 45° recognition test. Find the
B. 20° D. 30° probability that all 20
children recognize their
59. Peter sold 2 glasses of milk mother’s voice.
for every 5 sodas he sold. If A. 0.222 C. 0.646
he sold 10 glasses of milk, B. 0.500 D. 0.122
find the number of sodas he
sold.
A. 4 C. 20
B. 12 D. 25
68. Find the sum of all even 78. Jennifer flipped a coin three
integers between 5 and 29. times and got heads each time.
A. 202 C. 216 What is the probability that
B. 204 D. 220 she gets heads on the fourth
flip?
69. Given the equation, (x + yi) A. 1/2 C. 1/4
(1 – 2i) = 7 – 4i, find y. B. 1/16 D. 1
A. 5 C. 2
B. 3 D. 1 79. After paying a commission of
7% of the sale price to her
70. Find the equation of the line broker, Kaye receives P103,000
containing the point (3, 2) and for her car. How much was the
parallel to the line 2x – y + car sold?
7 = 0. A. P95,790 C. P110,420
A. 2x – y =10 C. 2x – y = 8 B. P110,753 D. P110,000
B. 2x + y = 10 D. 2x + y = 8

71. A ranch has cattle and horses 80. How many different eight-
in a ratio of 9:5. If there are letter arrangements can be
80 more head of cattle than formed from the letters in the
horses, how many animals are on word PARALLEL?
the ranch? A. 40,320 C. 20,160
A. 280 C. 200 B. 3,360 D. 6,720
B. 40 D. 140
81. If (sec A – 2)(2 csc A – 1) =
72. The sum of the three numbers 0, what quadrant does A
forming an AP is 33. If the sum terminate?
of their squares is 461, find A. I only C. II and IV
the smallest number. B. I and IV D. IV only
A. 7 C. 6
B. 5 D. 4 82. Find the acute angle between
the vectors (3 – 4i) and (-4 +
73. The 2nd term of a geometric 3i).
progression is 8 and the 6th A. 15°15’ C. 18°18’
term is 128. Find the 12th term. B. 16°16’ D. 21°21’
A. 7296 C. 6080
B. 4096 D. 8192 83. Find the integral of x cos
(2x2 + 7) dx.
74. If log xy = 6 and log (x/y) = A. cos (2x2 + 7) + C
2, find log x. B. cos (2x2 + 7) / 4 + C
A. 100 C. 4 C. sin (2x2 + 7) + C
B. 2 D. 10 D. sin (2x2 + 7) / 4 + C

75. In what quadrant will Ɵ 84. A point is chosen at random

terminate if sec Ɵ is positive inside a circle having a
and csc Ɵ is negative? diameter of 8 cm. Find the
A. I C. III probability that the point is
B. II D. IV at least 1.5 cm away from the
center of the circle.
76. If the side of the triangle A. 5/8 C. 12/45
have ratio of 4:7:5 find the B. 5/64 D. 55/64
smallest angle of the triangle.
A. 25° C. 34° 85. The area in the first quadrant
B. 33° D. 24° bounded by y2 = x, the line x =
4 and the x-axis is revolved
77. Find the equation of the axis about the line x = 4. Find the
of symmetry of the parabola y volume generated.
= 2x2 – 7x + 5. A. 63.89 C. 53.62
A. 7x – 4 = 0 C. 7x + 4 = 0 B. 57.41 D. 60.12
B. 4x – 7 = 0 D. 4x + 7 = 0
86. Find the derivative of tan x.
A. sec2 x C. ln sec x
B. sec x tan x D. ln cot x
87. For what values of x is the 95. Find the numerical value of
derivative of the function x3 the Roman numeral MMDCCCLIX.
equal to the derivative of x2 + A. 2354 C. 2649
x? B. 2859 D. 2559
A. -1 C. 1/2
B. 2 D. 1 96. A circle having an area of 224
cm2 is inscribed in an octagon.
88. Find the area bounded by y = Find the area of the octagon.
x3, the x-axis and the line x = A. 232 cm2 C. 236 cm2
-2 and x = 1. B. 230 cm 2 D. 234 cm2
A. 1.25 C. 4.25
B. 2.45 D. 5.50 97. A retailer purchased ballpens
for P90 and sold all but for a
89. The locus of a point which profit of P2 per ballpen. With
moves so that its distance from the total amount he received,
a fixed point and a fixed line he could buy 5 more ballpens.
are always equal. How many ballpens did he
A. Ellipse C. Parabola originally purchase?
B. Circle D. Hyperbola A. 45 C. 20
B. 15 D. 30
90. Find the limit of (z2 + z – 1
– 3i) / (z2 – 2z + 2) as z 98. Find the equation of a circle
approached (1 + i). tangent to the line 3x – 4y =
A. 1 – 2i C. -4i 32, and the center is at (0,7).
B. 2 – i D. 1 – 1.5i A. x2 + y2 + 14y – 85 = 0
B. x2 + y2 – 14y – 95 = 0
91. In two similar triangles, C. x2 + y2 + 14y – 80 = 0
find the ratio of the lengths D. x2 + y2 – 14y – 90 = 0
of the corresponding sides if
the areas are 72 and 50? 99. Convert the polar equation r
A. 36/25 C. 6/5 = 3/sinƟ to its equivalent
B. 5/6 D. 25/36 rectangular equation.
A. y = 3 – x C. y/x = 3
92. Find the value of log (2 + B. y = 3 D. y = 3 + x
3i).
A. 0.557 + 0.427i 100. In a pile of logs, each layer
B. 0.575 + 0.462i contains one more log than the
C. 0.577 + 0.486i layer above and the top
D. 0.555 + 0.468i contains just one log. If there
are 100 logs in the pile, find
93. Find the equation of the the number of layers in the
straight line through the point pile.
(3, -1) with a slope of -1/2. A. 13 C. 15
A. 2x + y – 1 = 0 B. 14 D. 16
B. 2x + y + 1 = 0
C. x + 2y – 1 = 0
D. x + 2y + 1 = 0

94. A tank is filled with 2 pipes.

The first pipe can fill the
tank in 10 hours. But after it
has been opened for 3 1/3
hours, the second pipe is
opened and the tank is filled
in 4 hours more. How long would
it take the second pipe alone
to fill the empty tank?
A. 10 hrs C. 15 hrs
B. 12 hrs D. 16 hrs