Rizal Technological University

Electronics Engineering Licensure Examination Assessment

Note: If your score is below 70%, you failed the entire assessment exam.

1. What is the area bounded by the curve 10. A liquid is flowing into a conical
x2 = -9y and the line y+1 = 0. container at the rate of 8 m3/min. If the
a. 6 sq. units b. 5 sq. unit height of the inverted cone is 12m and
c. 2 sq. units d. 4 sq. units the radius of its circular opening is 6m.
How fast is the water level rising when
the water is 4 m deep?
x2
2. Evaluate the integral of
x 3
4
dx a. 0.31 m/min
c. 0.75 m/min
b. 0.46 m/min
d. 0.64 m/min
3
a. 3 ln (x + 4) + C
b. ln (x3 + 4) + C 11. The area of the region bounded by two
c. 1/3 ln (x + 4) + C concentric circles is called
d. 1/3 ln (x3 + 4) a. annulus b. ring
c. washer d. circlic
3. Evaluate the integral of
 sec xdx 12. A ladder 5m long leans against the
a. ln (secx – tanx) wall of an apartment house forming an
b. ln (secx + tanx) angle 50 degree, 32 minutes with the
c. 2ln (secx + tanx) ground. How high up the wall does it
d. –ln (secx – tanx) reach?
a. 3.86 m b. 4.11 m
4. Find the volume of the area bounded by c. 1.12 m d. 3.34 m
the given curve x2 = 8y and the line y =2
and revolve about the line y =2. 13. A statue 3.2 m high stands on a
a. 17.87pi b. 17.07pi pedestal such that its foot is 0.4 m
c. 71.01pi d. 19.93pi above the observer’s eye level. How far
from the statue must the observer stand
5. There are eight balls and are tightly in order that the angle subtended by the
packed in a cubical container that statue will be maximum?
measures 8 x 8 x 8 cm. The balls are a. 1.1 m b. 1.2 m
arranged with 4 balls per layer and in c. 1.3 m d. 1.5 m
contact with the walls of the container
and the adjacent balls. If the container 14. Find the 30th term of the A.P. 4, 7,
is filled with water, what is the volume 10,…
of the water in cubic cm? a.88 b.91
a. 320 b. 422 c.75 d.90
c. 224 d. 244
15. The quartile deviation is a measure
6. Find the equation of the directrix of of
the parabola y2 = 20x. a.frequency b.central tendency
a. x + 20 = 0 b. x + 5 = 0 c.certainty d.dispersion
c. x – 20 = 0 d. x – 5 = 0
16. What is the quotient when 4 + 8i is
7. What is the value of determinants divided by -i3?
whose elements are shown below? a. 8 – 4i b.8 + 4i
1 5 -2 c. -8 + 4i d.-8 – 4i
2 1 -3
3 -2 1 17. Given f(x) = (x – 4) (x + 3) + 4,
when f(x) is divided by x – k, the
a. 46 b. -46 remainder is k. Find k
c. 18 d. 25 a. -12 b.8
c. 4 d.2
8. Amanda left Batangas to drive to
Manila at 6:15 PM and arrived at 11:45 18.A point of the curve where the first
PM. If he averaged 30mph and stopped 1 derivative of a function is zero and the
hour for dinner for she is very hungry, second derivative is positive is called
how far is Manila from Batangas? a. point of inflection
a. 215.86 miles b. maxima
b. 135.01 miles c. minima
c. 200.76 miles d. contraflexture
d. 155 miles

9. It takes Jam 60 seconds to run around 19. Three sides of a trapezoid are each 8
a 440 yard oval track. How long does it cm long. How long is the 4th side when
take Philip to run around the track if the area of the trapezoid has the
they met in 32 sec after they start greatest value?
together at the starting point going in a. 16 cm b. 15 cm
opposite directions? c. 12 cm d. 10 cm
a. 55.27 seconds b. 62.27 seconds
c. 68.52 seconds d. 77.26 seconds

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 32. The area of a circle is 89.42 sq.
20. Find the area bounded by y  11  x ,
inches. What is its circumference?
the lines 3x = 2 and x = 10, and the x- a. 32.25 in b. 33.52 in
axis. c. 35.33 in d. 35.55 in
a.19.456 sq. units b.20.567 sq. units
c.22.567 sq. units d.21.478 sq. units 33. Find the area bounded by y = ex, x=0
and y=0.
21. Find the equation of the curve at a. 1 sq unit
every point of which the tangent line has b. 2 sq units
a slope of 2x. c. 3 sq units
a. x = -y2 + c b. y = -x2 + c d. 4 sq units
2
c. y = x + c d. x = y2 + c
34. What is the maximum point of y = x +
22. Find the equation of the family of 1/x?
orthogonal trajectories of the system of a. (2,1) b. (1,2)
parabolas y2 = 2x + C. c. (3,1) d. (-1,-2)
a. y  Ce  x b. y  Ce x
35. Find the area of a triangle given the
c. y  Ce 2 x d. y  Ce 2 x points of its vertices:
A (-1,-2); B (3,-5); C (3, 4).
23. What is the perimeter enclosed by the a. 12
curve: x2 + y2 - 12x - 8y + 43 = 0? b. 16
a. 81.8 b. 18.8 c. 18
c. 1.29 d. none d. 24

24. One is to fifty-two and one-half as 36. Water is being pumped into a conical
three and one-third is to __________. tank at the rate of 100 ft/min. The
a. 145 b. 205 height of the tank is 20 ft and its
c. 135 d. 175 radius is 5 ft. How fast is the water
level rising when the water height is 10
25. If A is 10% greater than B and B is ft?
20% less than C, express A in terms of a. 2/pi
percentage of C. b. 3/pi
a. 12% b. 88% c. 12/pi
c. 30% d. 52% d. 16/pi

37. Find the point on the line 3x  y  6

26. If x varies directly as y and
closest to (2, 3).
inversely as z, and x  14 when y  7 and a. (11/10, 27/10)
z  2 , find x when z  4 and y  16 . b. (3, 5)
a. 16 b. 12 c. (2/10, 7/10)
c. 15 d. 10 d. (7/10, 26/10)

27. The resistance of a wire varies 38. The two legs of a triangle are 300
directly with its length and inversely and 150 m each, respectively. The angle
with its area. If a certain piece of wire opposite the 150 m side is 26°. What is
10 m long and 0.10 cm in diameter has a the third side?
a. 341.78 m
resistance of 100 ohms, what will its
resistance be if it is uniformly b. 210.3 m
stretched so that its length becomes 12 c. 206.87 m
m? d. 31.2 m
a. 164 b. 120
c. 360 d. 144 39. Find the volume of the solid of
revolution formed by rotating the region
28. Power set of empty set has exactly bounded by the parabola y=x2 and the
_____ subset. lines y=0 and x=2 about the x-axis.
a. One a. 22pi/5 b. 12pi/5
c. 42pi/5 d. 32pi/5
b. Two
c. Zero
d. Three 40. The first term of an arithmetic
progression is 2 and the 6th term is 12.
29. What is the cardinality of the set of Find the sum of the first 12 terms?
a. 156 b. 154
odd positive integers less than 10?
a. 10 c. 148 d. 150
b. 5
c. 3 41. A hotel is to be constructed in a
d. 20 rectangular lot with a perimeter of 800
m. What is the largest area that can be
30. Find the center of the circle x2 + y2 enclosed by fencing the perimeter?
- 6x + 4y – 23 = 0 a. 2 hectares b. 4 hectares
a. (3,-2) b. (-2,3) c. 3 hectares d. 6 hectares
c. (-3,2) d. (3,2)
42. The product of two real numbers is
31. The interior angles of a triangle 18. When 1 is subtracted from each number
measures 2x, x+15 and 2x+15. What is the the product is 9. What is the sum of two
value of x? numbers?
a. 60 b. 45 a. 9 b. 10
c. 30 d. 10 c. 11 d. 8

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43. Let’s see what lim f x    looks like. 46. The hypotenuse of a right triangle is
x a
14m. Find its perimeter if its area is
Which of the following graphs of a maximum.
function f x  such that lim f x    . a. 33.8 m b. 31.8 m
x 0
c. 32.8 m d. 29.8 m
a.
47. Find the rate of the change of volume
of a sphere with respect to its radius
when its radius is 5.
a. 200pi b. 100pi
c. 300pi d. 400pi

48. By integration, solve the area

bounded by the parabola x2 = 3y - 3 and
x2 = y.
a. 1.63 b. 3.61
c. 6.13 d. 3.16

49. What is the integral of sin6θcos4θdθ

if the upper limit is pi/2 and the lower
limit is 0?
b. a. 2pi/512 b. 3pi/512
c. 5pi/512 d. 7pi/512

50. What is the multiplicative identity

element?
a. 0 b. 1
c. –1 d. infinity

“What worries us today may

just be a tiny bit of
c. information that will not even
merit a line when your life
story is written. The Lord
help us to see that HE is
bigger than our biggest
problem. Let’s not be afraid
and worried of any trials
because we have a big GOD that
will work out good in the
end.”

d.
GOD BLESS YOU! 

44. In a physical fitness test, Jommel

did 25 more push-ups than RS. The total
number of push-ups for both men was 173.
Find the number of push-ups RS did.
a. 47 b. 74
c. 84 d. 26

45. What is the maximum value of y if y =

x3-x?
a. 0.385 b. 0.835
c. 0.358 d. 0.853