MATH & ENG ECO GENERAL EVALUATION EXAM
Problems and Elements (with Answers and Solutions)
Select the best answer from each of the following questions. On the answer sheet provided, shade the box that
corresponds to your choice. Strictly no erasures allowed.
1.
Which of the following is the standard acceleration due to gravity in the English unit?
a) 980.66 fps2
b) 32.2 fps2
c) 9.8066 fps2
d) 32.2 ips2
Answer: 32.2 fps2
2.
What is the value of 1 radian in degrees?
a) 89.55o
b) 57.3o
c) 60.3o
d) 45.58o
c) 90o
d) 270o
Answer: 57.3o
 180o 
  57.3 deg rees
  radians 


Solution:   1 radians 
3.
How many degrees are 4800 mils?
a) 180o
b) 315o
Answer: 270o
 1 deg ree 
  270o
 17.78 mils 
Solution:   4800 mils 
4.
If the density of a gas is 0.003 slug/ft 3, what is the specific weight of the gas?
a) 15.2 N/m3
b) 9.04 N/m3
c) 98.2 N/m3
d) 76.3 N/m3
Answer: 15.2 N/m3



3
2
3
Solution:   g  0.003 slugs / ft 32,2 fps 14.59 kg / slug 1 ft / 0.3048  15.2 N / m
5.
2
If the specific weight of a liquid is 58.5 lbf per cubic foot, what is the specific volume of the liquid?
a) 1.0675 cm3/g
b) 0.5321 cm3/g
c) 1.5502 cm3/g
d) 0.9504 cm3/g
Answer: 1.0675 cm3/g
Solution:   58.5 lb f / ft3  9189.6 N / m3
6.

 936.8 kg / m3
g
v
1
 1.0675 cm3 / g

From a deck of ordinary cards, what is the probability of drawing a heart or face card?
a) 48.08%
b) 42.31%
c) 5.77%
d) 33.33%
Solution: PA or B  PA   PB  PA and B 
7.

13 12 3 22



 42.131%
52 52 52 52
A perfect gas is expanded polytropically with an initial volume and temperature of 0.06 m3 and 147 0C respectively.
If the final volume and temperature are 0.21 m3 and 21 0C respectively, what is the index of the expansion?
a) 1.285
b) 1.212
c) 1.333
d) 1.400
Solution:
T1
V
 { 1 }n 1 solving for n, n  1.285
T2
V2
1
8.
If the loan was for 15 months at 16.8% interest a year and the repayment on a loan was P12,100.00, how much was
the principal?
a) P8,500.00
b) P9,500.00
c) P10,000.00
d) P10,500.00
Solution: P 
9.
F
12,100 .00

 P9,965 .10  P10,000 .00
n
1  i  1.168 1.25
Determine the accumulated value of P2,000.00 in 5 years it is invested at 11% compounded quarterly.
a) P3,440.00
b) P3,404.00
c) P3,044.00
d) P4,304.00
 i 
Solution: F  P1  n 
m

mn
 0.11 
 2,000.001 

4 

4 5
 P3,440.00
10. The sum of P15,000.00, deposited in an account earning 4% per annum compounded quarterly, will become
P18,302.85. Determine the effective rate of interest per year.
a) 3.06 %
b) 4.06 %
c) 5.06 %
d) 6.06 %
Solution:
 i  m 
 0.04  4 
i e  1  n   1100 %  1 
  1100 %  4.06 %
m
4 




11. If a machine is purchased on installment and the buyer makes an P80,000.00 down payment and owes a balance of
P150,000 in 2 years. Determine the machine cash value if money is worth 14% compounded quarterly.
a) P199,312.00
b) P183,912.00
c) P193,912.00
d) P139,912.00
Solution:
Cash Value = Down payment + Present value of the balance
Cash Value  P80,000.00 
F
 in 
1  
m

mn
 P80,000.00 
150,000.00
 0.14 
1 

4 

4 2 
 P193,912.00
12. Find the number of years when P2,500.00 is compounded to P5,800.00 if invested at 12% compounded quarterly.
a) P6.12 years
b) 7.12 years
c) 8.12 years
d) 5.12 years
Solution:
 in 
1  
m

n
mn

F
P
 F
ln  
P
 i 
ln 1  n 
m

m

  i 
F
mn ln 1  n   ln  
m
P




 5,800.00 
ln 

2,500.00 


 7.12 years
4
 0.12 
ln 1 

4 

13. What is the effective rate equivalent of 12% compounded quarterly?
a) 12.55%
b) 11.55 %
c) 12.98 %
Solution:
d) 13 %
 i  m 
 0.12  4 
i e  1  n   1100 %  1 
  1100 %  12.55 %
m
4 




14. What rate compounded-quarterly is equivalent to 14% compounded semi-annually?
a) 10.76 %
b) 11.76 %
c) 12.76 %
2
d) 13.76 %
Solution:
 i  4 
 0.14  2 
i e  1  n   1100 %  1 
  1100 %
4
2 




4
 in 
1    1.1449
4

1


i n  41.1449 4  1  13.76 %


15. Celestino owes P500, due in 3 years and P800 due in 7 years. He is allowed to settle these obligations by a single
payment on the 6th year. Find how much he has to pay on the 6th year if money is worth 14% compounded semiannually.
a) P1,449.12
b) P 1,559.12
c) P1,339.12
d) P1,669.12
Solution:
 0.14 
F6 th  5001 

2 

23

800
 0.14 
1 

2 

21
 750.37  698.75  P1,449.12
16. Cleofas borrowed P2,000.00 from a bank and agreed to pay the loan at the end of one year. The bank discounted the
loan and gave him P1950 in cash. Determine the rate of discount.
a) 3.75 %
b) 3.12 %
c) 2.5 %
d) 1.2 %
Solution:
 2,000.00  1,950.00 
FP
d
100 %  2.5 %
100 %  
2,000.00
 F 


17. A machine was purchased under these terms: P30,000 down and P5,000 each month for 5 years. If money is worth
12% compounded monthly, what is the cash price of the machine?
a) P144,775.19
b) P245,775.19
c) P542,775.91
d) P254,775.19
Solution:
Cash Price = Down Payment + Present Worth of Annuity
 i  mn 
A 1  n   1
m


Cash Pr ice  Down Payment  
 i 
i 1  n 
m

mn
 0.12 125  
5,000.001 
 1

12 


Cash Pr ice  P30,000.00 
 P 254,775.19
1295
 0.12 
0.121 

12 

18. Determine the amount that must be deposited every 3 months in a fund paying 12% compounded quarterly in order to
have P25,000 in 8 years.
a) P746.71
b) P476.17
c) P674.71
d) P700.00
Solution:
A
 in 
 F
m
 in 
1  
m

mn
 0.12 

25,000.00
4 


 P 476.17
48 
 0.12 
1
1 

4 

19. What is the value of 1 radian in degrees?
a) 89.55o
b) 57.3o
c) 60.3o
3
d) 45.58o
 180o 
  57.3 deg rees
  radians 


Solution:   1 radians 
20. How many degrees are 4800 mils?
a) 180o
b) 315o
c) 90o
d) 270o
 1 deg ree 
  270o
 17.78 mils 
Solution:   4800 mils 
21. If the density of a gas is 0.003 slug/ft 3, what is the specific weight of the gas?
a) 15.2 N/m3
b) 9.04 N/m3
c) 98.2 N/m3



d) 76.3 N/m3
Solution:   g  0.003 slugs / ft 3 32,2 fps 2 14.59 kg / slug 1 ft / 0.3048  15.2 N / m3
2
22. If the specific weight of a liquid is 58.5 lbf per cubic foot, what is the specific volume of the liquid?
a) 1.0675 cm3/g
b) 0.5321 cm3/g
c) 1.5502 cm3/g
d) 0.9504 cm3/g
Solution:   58.5 lb f / ft3  9189.6 N / m3


 936.8 kg / m3
g
v
1
 1.0675 cm3 / g

23. A force of 200 lb acts on a block at an angle of 28 o with respect to horizontal. The block is pushed 2 ft horizontally.
Find the work done by this force.
a) 480 J
b) 408 J
c) 840 J
d) 804 J
Solution: W  F  dx  F cos  x  200 cos 282  353.18 ft  lb  480 J
24. The atomic weight of hydrogen is 1 gram per gram-atom. What is the mass of a hydrogen atom?
a) 1.66 x 10-24 g/atom
b) 6.02 x 10-23 g/atom
c) 1 g/atom
d) The mass is too small to calculate

By definition, the mass of an atom is its atomic weight divided by the Avogadro’s number.
W
1
6.02 x 10
23
 1.66 x 10 24 g / atom
25. A truck starts from rest and moves with a constant acceleration of 6 m/s 2. Find the speed of the truck after 4 seconds.
a) 18 m/s
b) 28 m/s
c) 24 m/s
d) 35 m/s
Solution: For uniformly accelerated motion, V  Vo  at  0  64  24 m / s
2
26. A car starts from rest and has a constant acceleration of 3 fps 3. Determine the average velocity during the first 10
seconds of motion.
a) 15 fps
b) 20 fps
c) 12 fps
d) 18 fps
Solution: The distance traveled by the car, S  Vo t 
VAverage 
1 2
1
2
at  0    310  150 ft
2
2
S 150

 15 fps
t
10
27. A ball is dropped from a height of 60 meters above ground. How long does it take to hit the ground?
a) 4.5 seconds
b) 3.5 seconds
c) 2.5 seconds
d) 1.5 seconds
4
1
2
t
Solution: S  Vot    g t 2
2S  Vo t 

g
260  0
 3.5 sec onds
9.81
28. A 5 meter extension ladder leans against the wall; the bottom is 3 m from the wall. If the bottom stays at the same
place, how much should the ladder be extended so that the top would lean against the wall 1 meter higher?
a) 1.2 m
b) 1.5 m
c) 0.5m
d) 0.83095 m
LET h be the height of the wall then h  5 2  32  4m
If it leans I m higher and let x be the extended length then 5  x 2  5 2  3 2 and x = 0.83095m.
29. If a stone dropped from a balloon while ascending at the rate of 7.5m/s reaches the ground in 6seconds, what was the
height of the balloon when the stone was dropped?
a) 110.12 m
b) 120.25 m
y  vi t 
c) 131.81 m
d) 140.12
gt 2
9.8162
 7.56 
 131.58m
2
2
Therefore the stone is dropped at a height 131.58m above the ground.
30. The salary of an employee’s job has five levels, each one 5% greater than the one below it. Due to circumstances, the
salary of the employee must be reduced from the top (fifth) level to the second level, which means a reduction of
P3000.00 per month. What is the employee’s present salary per month?
a) P22,032.50
b) P23,022.50
c) P22,320.50
d) P22,302.50
Solution: The salary levels can be seen as a geometric sequence. Let S n be the salary at level n.
S3  1.05S2
S4  1.05S3
S5  1.05S4
S5  1.05 1.05S3   1.052 S3  1.052 1.05S2  1.053S2
Due to circumstance, S5  3,000.00  S2
S5  1.053 S5  3,000.00  S5 
30001.053
1.053  1
 P22,032.50
31. Determine the value of each interior angle of a regular pentagon.
a) 108o
b) 120o
c) 98o
d) 135o
Solution: For a regular polygon, the value of each interior angle, ,

 
 
No. of Sides  2
52
180o  
 180o  108o
No. of Sides
 5 
32. A cubical container that measures 50.8 mm on a side is tightly packed with eight marbles and is filled with water. All
eight marbles are in contact with the walls of the container and the adjacent marbles. All of the marbles are the same
size. What is the volume of water in the container?
a) 131 096.51 mm3
b) 62 454.54 mm3
c) 68 641.97 mm3
d) 131 960.51 mm3
Solution: Since marbles are tightly packed, r marble = 12.7 mm
Volume of container, Vcontainer  50.83  131096.5 mm3
5
4
3

4
3
Volume of eight marbles, Vmarbles  8  r 3   8 12.73  68 641.97 mm3

Volume of water, Vwater  Vcontainer  Vmarbles  131096.5  68 641.97  62 454.54 mm3
7 6
 ?
5 9
33. What is the determinant of the 2 x 2 matrix, 
a) – 33
c) – 43
b) 33
Solution: The determinant, D 
7 6
 79   56  33
5 9
1

2
1

1
34. What is the determinant of the 3 x 3 matrix,  2  1
a) 6
d) 43
 1

1 ?
1 
c) – 6
b) 7
d) – 7
1 2 1
Solution: D  2  1 1  1 11  211   112  1 1 1  221  111   7
1 1
1
 cos   sin  
 ?
 sin  cos  
35. What is the inverse of the 2 x 2 matrix, A  
 cos  sin  

  sin  cos  
 cos   sin  

 sin  cos  
a) 
  cos  sin  

 sin  cos  
b) 
1 d
a b
 , the inverse, X-1, is: X 1  
Solution: For 2 x 2 matrix, X  
D  c
c d
Where, D = determinant of X. For matrix A, D 
0
 cos  sin 
2
0
sin

c) 
d) 


 
b 

a 
cos   sin 
 cos2   sin  sin   cos2   sin 2   1
sin  cos 
 cos  sin  

  sin  cos  
Then, A 1  
36. The equation y = a1 + a2x is an algebraic expression for which of the following choices?
a) A cosine expansion series b) A circle in polar form c) Projectile motion
d) A straight line
Answer: d) A straight line.

y = mx + b is the slope-intercept form of the equation of a straight line. Thus, y = a 1 + a2x describes a
straight line.
37. Determine the absolute value of resultant vector of the following vectors: F1 = 4i + 7j + 6k; F2 = 9i + 2j + 11k, F3 = 5i
– 3j – 8k.
a) 21
b) 18
c) 25
d) 9
Solution: The resultant of vectors given in unit-vector form is the sum of the components.
R  4  9  5i  7  2  3j  6  11  8k  18i  6 j  9k
R 
182  62  92
 21
38. Given the following vectors: A = 3i + 2j, B = 2i + 3j + k, C = 5i + 2k. Simplify the expression A x B  C .
a) 20
b) 0
c) 60i + 24k
d) 5i + 2k
6
i j k
Solution: Solving first for A x B, let D = A x B, A x B  3 2 0  i2  0  j3  0  k 9  4  2i  3 j  5k
2 3 1
Let E  D  C , then E  D  C  D x C x  D yC y  D zCz  25  30  52  20
39. Determine the rationalized value of the complex number
a) 1.12 – 0.66i
6  2.5i
.
3  4i
b) 0.32 – 0.66i
c) – 32 + 0.66i
d) – 1.12 + 0.66i
Solution:
 In order to rationalize a complex number, multiply the numerator and denominator by the complex
conjugate of the denominator and simplify.
6  2.5i 6  2.5i 3  4i  28  16.5i


 1.12  0.66i
3  4i3  4i
3  4i
25
40. Determine the first derivative with respect to x of the function: gx   5 10  35 .
3
a) ¾
c) 494
b) 0
d) 35
Solution: The derivative of a constant is zero.
41. Determine the slope of the curve y   x 2 at the point (2, 3).
a) 4
b) – 4
c) 2
Solution: The slope of a curve is given by the first derivative. y' 
d) – 2
 
dy d  x 2

 2x
dx
dx
At point (2, 3): y' x   y' 2  22  4
42. What is the sum of the roots of the equation: 2x2 + 5x + 5 = 0?
a) – 2.5
b) 2.5
c) 2.25
Solution: The sum of the roots is: rsum  x1  x 2  
d) – 2.25
b
5

a
2
43. Determine the distance traveled by a particle between a time interval of 0.2 second to 0.3 second if its velocity is
7
, where V is in cm/s and t is in seconds.
t
V  12 t 4 
a) 3.75 cm
Solution:
b) 2.84 cm
dS
7
 V  12 t 4 
dt
t
S



dS 

c) 2.75 cm
d) 3.84 cm
0.3 
0.2
7
12t 4   dt
t



 t   12 
12 5 5
 0.3 
t 2  t1  7 ln  2     0.35  0.25  7 ln 
  2.84 cm
5
t
5
 0.2 
 1  
44. A force of 200 lb acts on a block at an angle of 28 o with respect to horizontal. The block is pushed 2 ft horizontally.
Find the work done by this force.
a) 480 J
b) 408 J
c) 840 J
d) 804 J
Solution: W  F  dx  F cos  x  200 cos 282  353.18 ft  lb  480 J
7
45. The atomic weight of hydrogen is 1 gram per gram-atom. What is the mass of a hydrogen atom?
a) 1.66 x 10-24 g/atom
b) 6.02 x 10-23 g/atom
c) 1 g/atom
d) The mass is too small to calculate

By definition, the mass of an atom is its atomic weight divided by the Avogadro’s number.
W
1
6.02 x 1023
 1.66 x 10 24 g / atom
46. A truck starts from rest and moves with a constant acceleration of 6 m/s 2. Find the speed of the truck after 4 seconds.
a) 18 m/s
b) 28 m/s
c) 24 m/s
d) 35 m/s
Solution: For uniformly accelerated motion, V  Vo  at  0  64  24 m / s
2
47. A car starts from rest and has a constant acceleration of 3 fps 3. Determine the average velocity during the first 10
seconds of motion.
a) 15 fps
b) 20 fps
c) 12 fps
d) 18 fps
Solution: The distance traveled by the car, S  Vo t 
VAverage 
1 2
1
at  0    3102  150 ft
2
2
S 150

 15 fps
t 10
48. A ball is dropped from a height of 60 meters above ground. How long does it take to hit the ground?
a) 4.5 seconds
b) 3.5 seconds
c) 2.5 seconds
d) 1.5 seconds
1
2
Solution: S  Vot    g t 2
t
2S  Vo t 

g
260  0
 3.5 sec onds
9.81
49. A 5 meter extension ladder leans against the wall; the bottom is 3 m from the wall. If the bottom stays at the same
place, how much should the ladder be extended so that the top would lean against the wall 1 meter higher?
a) 1.2 m
b) 1.5 m
c) 0.5m
d) 0.83095 m
LET h be the height of the wall then h  5 2  32  4m
If it leans I m higher and let x be the extended length then 5  x 2  5 2  3 2 and x = 0.83095m.
50. If a stone dropped from a balloon while ascending at the rate of 7.5m/s reaches the ground in 6seconds, what was the
height of the balloon when the stone was dropped?
a) 110.12 m
b) 120.25 m
c) 131.81 m
d) 140.12
y  vi t 
gt 2
9.8162
 7.56 
 131.58m
2
2
Therefore the stone is dropped at a height 131.58m above the ground.
51. The salary of an employee’s job has five levels, each one 5% greater than the one below it. Due to circumstances, the
salary of the employee must be reduced from the top (fifth) level to the second level, which means a reduction of
P3000.00 per month. What is the employee’s present salary per month?
a) P22,032.50
b) P23,022.50
c) P22,320.50
d) P22,302.50
Solution: The salary levels can be seen as a geometric sequence. Let Sn be the salary at level n.
8
S3  1.05S2
S4  1.05S3
S5  1.05S4
S5  1.05 1.05S3   1.052 S3  1.052 1.05S2  1.053S2
Due to circumstance, S5  3,000.00  S2
S5  1.053 S5  3,000.00  S5 
30001.053
 P22,032.50
1.053  1
52. Determine the value of each interior angle of a regular pentagon.
a) 108o
b) 120o
c) 98o
d) 135o
Solution: For a regular polygon, the value of each interior angle, ,

 
 
No. of Sides  2
52
180o  
 180o  108o
No. of Sides
 5 
7 6
 ?
5 9
53. What is the determinant of the 2 x 2 matrix, 
a) – 33
c) – 43
b) 33
Solution: The determinant, D 
d) 43
7 6
 79   56  33
5 9
 1 2  1


54. What is the determinant of the 3 x 3 matrix,  2  1 1  ?
1 1
1 

a) 6
c) – 6
b) 7
d) – 7
1 2 1
Solution: D  2  1 1  1 11  211   112  1 1 1  221  111   7
1 1
1
 cos   sin  
 ?
 sin  cos  
55. What is the inverse of the 2 x 2 matrix, A  
 cos  sin  

  sin  cos  
 cos   sin  

 sin  cos  
a) 
  cos  sin  

 sin  cos  
b) 
c) 
a b
1 d
 , the inverse, X-1, is: X 1  
Solution: For 2 x 2 matrix, X  
D  c
c d
Where, D = determinant of X. For matrix A, D 
0
 cos  sin 
2
0
sin

d) 


 
b 

a 
cos   sin 
 cos2   sin  sin   cos2   sin 2   1
sin  cos 
 cos  sin  

  sin  cos  
Then, A 1  
56. The equation y = a1 + a2x is an algebraic expression for which of the following choices?
a) A cosine expansion series b) A circle in polar form c) Projectile motion
d) A straight line
Answer: d) A straight line.

y = mx + b is the slope-intercept form of the equation of a straight line. Thus, y = a 1 + a2x describes a
straight line.
57. Determine the absolute value of resultant vector of the following vectors: F1 = 4i + 7j + 6k; F2 = 9i + 2j + 11k, F3 = 5i
– 3j – 8k.
a) 21
b) 18
c) 25
d) 9
9
Solution: The resultant of vectors given in unit-vector form is the sum of the components.
R  4  9  5i  7  2  3j  6  11  8k  18i  6 j  9k
R 
182  62  92
 21
58. Given the following vectors: A = 3i + 2j, B = 2i + 3j + k, C = 5i + 2k. Simplify the expression A x B  C .
a) 20
b) 0
c) 60i + 24k
d) 5i + 2k
i
j k
Solution: Solving first for A x B, let D = A x B, A x B  3 2 0  i2  0  j3  0  k 9  4  2i  3 j  5k
2 3 1
Let E  D  C , then E  D  C  D x C x  D yC y  D zCz  25  30  52  20
59. Determine the rationalized value of the complex number
a) 1.12 – 0.66i
6  2.5i
.
3  4i
b) 0.32 – 0.66i
c) – 32 + 0.66i
d) – 1.12 + 0.66i
Solution:
 In order to rationalize a complex number, multiply the numerator and denominator by the complex
conjugate of the denominator and simplify.
6  2.5i 6  2.5i 3  4i  28  16.5i


 1.12  0.66i
3  4i3  4i
3  4i
25
60. Determine the first derivative with respect to x of the function: gx   5 10  35 .
3
a) ¾
c) 494
b) 0
d) 35
Solution: The derivative of a constant is zero.
61. Determine the slope of the curve y   x 2 at the point (2, 3).
a) 4
b) – 4
c) 2
Solution: The slope of a curve is given by the first derivative. y' 
d) – 2
 
dy d  x 2

 2x
dx
dx
At point (2, 3): y' x   y' 2  22  4
62. What is the sum of the roots of the equation: 2x2 + 5x + 5 = 0?
a) – 2.5
b) 2.5
c) 2.25
Solution: The sum of the roots is: rsum  x1  x 2  
d) – 2.25
b
5

a
2
63. Determine the distance traveled by a particle between a time interval of 0.2 second to 0.3 second if its velocity is
7
, where V is in cm/s and t is in seconds.
t
V  12 t 4 
a) 3.75 cm
Solution:
b) 2.84 cm
dS
7
 V  12 t 4 
dt
t
S


c) 2.75 cm
7
12t 4   dt
t
0.2 
 dS  
0.3 


 t   12 
12 5 5
 0.3 
t 2  t1  7 ln  2     0.35  0.25  7 ln 
  2.84 cm
5
 0.2 
 t1   5 
10
d) 3.84 cm
64. Compute the arithmetic Mean of the following set of numbers: 18, 24, 27, 30, 35, 42, 50.
a. 31.82
b. 32.29
c. 30
d. 29.96
Arithmetic Mean 
18  24  27  30  35  42  50
 32.29
7
65. Find the root mean square of 11, 23, and 35.
a. 25
b. 27
Root Mean Square (RMS),RMS 
c. 26
 (x
2
)' s

d. 24
112  23 2  35 2
 25
3
n
66. Five years ago the father is three times as old as his son. Ten years from now, the father will be twice as old as his
son. How old is the son twelve years from now?
a) 32 years old
b) 20 years old
c) 50 years old
d) 38 years old
Solution: Let x = age of the father
x  5  3y  5
y = age of the son
x  10  2y  10 
x  5  3y  15
x  10  2y  20
x  3y  10
3y  10  2y  10
y  20
x  320   20  40
x  2y  10
Age of the son 12 years from now: 20 + 12 = 32 years old
67. From the top of tower A, the angle of elevation of the top of the tower B is 46 o. From the foot of tower B the angle of
elevation of the top of tower A is 28o. Both towers are on a level ground. If the height of tower B is 120 m, how high
is tower A?
a) 40.7 m
b) 44.1 m
c) 42.3 m
d) 38.6 m
E
Solution: DE = 120 m
44o
DE
CD
In triangle DCE,

Sin 46  28 Sin 44o
o
 sin 44o 

  120  sin 44   86.72 m
CD  DE 
 sin 74o 
 sin 74o 




C
h  CD sin 28o  86.72 sin 28o  40.71 m
h
 x
1
68. Determine the value of
a. 0
3
 x
1
3
Tower B
Tower A

D
 x 5  sin x dx .
b.1.75
1
Solution:
1
46o
28o

 x 5  sin x dx 
c. 3.1416
4
x
4
1

1
6
x
6
d. infinity
1
1
1
 cos x 1  0
69. Determine the distance between the foci of a hyperbola if the lengths of the transverse and conjugate axes are 10 m
and 8 m, respectively.
a. 20.8 m
b. 12.8 m
c. 13.8 m
d. 25.6 m
Solution:
S  2c  2 a 2  b 2  2 102  82

  25.61 m


11
70. Think of a number. Double the number. Subtract 6 from the result and divide the answer by 2. The quotient will be
20. What is the number you think?
a. 12
b. 20
c. 23
d. 32
Solution:
Le: x - be the number
2x  6
 20
2
2x-6 = 40;
x = 23
71. Determine the absolute value of resultant vector of the following vectors: F1 = 4i + 7j + 6k; F2 = 9i + 2j + 11k, F3 = 5i
– 3j – 8k.
a) 21
b) 18
c) 25
d) 9
Solution: The resultant of vectors given in unit-vector form is the sum of the components.
R  4  9  5i  7  2  3j  6  11  8k  18i  6 j  9k
R 
182  62  92
 21
72. An Electrical Engineer obtained a loan of P50,000.00 at the rate of 6% compounded annually in order to repair his
mistress’ house. Mow much must the Electrical Engineer pay monthly to amortize the loan within a period of ten
years?
a) P605.20
b) P550.90
c) P505.90
d) P508.90
Solution:
Converting the interest into effective monthly interest, one peso-one year analysis,
1
11  0.61 year  11  i 12 months
i  1.06 12  1  0.00486 or 0.486 %
A
N = mn = 12(10) = 120
i 1  i N P
1  iN  1

0.004861.00486120 50,000.00
1.00486120  1
73. Determine the diameter of a circle, x 2  y 2  6x  4y  12  0 .
a) 9 units
b) 11 units
c) 12 units
Solution:
x
x 2  y 2  6x  4 y  12  0
x  32  y  22  25
2
 
 P550.90
d) 10 units

 6x  9  y 2  4 y  4  12  13  25
Then, r = 5 units and d = 10 units
74. What is the present value of P5,000.00 due in 8 years if money is worth 12% compounded semi-annually?
a) P1,896.23
b) P1,869.23
c) P1,698.23
d) P1,968.23
Solution:
P
F
 in 
1  
m

mn

5,000.00
 0.12 
1 

2 

28 
 P1,968.23
75. How many permutation can be made out of the letters of the word ENGINEERING?
a) 277 200
b) 272 700
c) 200 277
d) 227 700
Solution:
P
n!
11!

 277 200
p! q!... 3!3! 2! 2!
Where, n = 11 objects with 3E’s, 3N’s, 2G’s, and 2I’s
76. If vector A is 10 units and vector B, which makes 60 0 with vector A, is 20 units. What is the difference of vectors A
and B?
12
a) 15.34 units
Solution:
b) 13.45 units
c) 18.76 units
d) 17.32 units
c  a 2  b 2  2ab cos   17.32 units
by cosine law,
77. From a deck of ordinary cards, what is the probability of drawing a heart or face card?
a) 48.08%
b) 42.31%
c) 5.77%
d) 33.33%
PA or B  PA   PB  PA and B 
13 12 3 22



 42.131%
52 52 52 52
78. A perfect gas is expanded polytropically with an initial volume and temperature of 0.06 m3 and 147 0C respectively.
If the final volume and temperature are 0.21 m3 and 21 0C respectively, what is the index of the expansion?
a) 1.285
b) 1.212
c) 1.333
d) 1.400
T1
V
 { 1 }n 1 solving for n, n  1.285
T2
V2
79. If the loan was for 15 months at 16.8% interest a year and the repayment on a loan was P12,100.00, how much was
the principal?
a) P8,500.00
b) P9,500.00
c) P10,000.00
d) P10,500.00
Solution:
P
F
1  i 
n

12,100.00
1.1681.25
 P9,965.10  P10,000.00
80. Determine the accumulated value of P2,000.00 in 5 years it is invested at 11% compounded quarterly.
a) P3,440.00
b) P3,404.00
c) P3,044.00
d) P4,304.00
Solution:
 i 
F  P1  n 
m

mn
 0.11 
 2,000.001 

4 

4 5
 P3,440.00
81. The sum of P15,000.00, deposited in an account earning 4% per annum compounded quarterly, will become
P18,302.85. Determine the effective rate of interest per year.
a) 3.06 %
b) 4.06 %
c) 5.06 %
d) 6.06 %
Solution:
 i  m 
 0.04  4 
i e  1  n   1100 %  1 
  1100 %  4.06 %
m
4 




82. If a machine is purchased on installment and the buyer makes an P80,000.00 down payment and owes a balance of
P150,000 in 2 years. Determine the machine cash value if money is worth 14% compounded quarterly.
a) P199,312.00
b) P183,912.00
c) P193,912.00
d) P139,912.00
Solution:
Cash Value = Down payment + Present value of the balance
Cash Value  P80,000.00 
F
 in 
1  
m

mn
 P80,000.00 
150,000.00
 0.14 
1 

4 

4 2 
 P193,912.00
83. Find the number of years when P2,500.00 is compounded to P5,800.00 if invested at 12% compounded quarterly.
a) P6.12 years
b) 7.12 years
c) 8.12 years
d) 5.12 years
 i 
Solution: 1  n 
m

mn

F
P

  i 
F
mn ln 1  n   ln  
m
P

 
13
n
 F
ln  
P
 i 
ln 1  n 
m

m
 5,800.00 
ln 

2,500.00 
 
 7.12 years
4
 0.12 
ln 1 

4 

84. What is the effective rate equivalent of 12% compounded quarterly?
a) 12.55%
b) 11.55 %
c) 12.98 %
Solution:
d) 13 %
 i  m 
 0.12  4 
i e  1  n   1100 %  1 
  1100 %  12.55 %
m
4 




85. What rate compounded-quarterly is equivalent to 14% compounded semi-annually?
a) 10.76 %
b) 11.76 %
c) 12.76 %
d) 13.76 %
Solution:
 i  4 
 0.14  2 
i e  1  n   1100 %  1 
  1100 %
4
2 




4
 in 
1    1.1449
4

1


i n  41.1449 4  1  13.76 %


86. Celestino owes P500, due in 3 years and P800 due in 7 years. He is allowed to settle these obligations by a single
payment on the 6th year. Find how much he has to pay on the 6th year if money is worth 14% compounded semiannually.
a) P1,449.12
b) P 1,559.12
c) P1,339.12
d) P1,669.12
Solution:
 0.14 
F6 th  5001 

2 

23

800
 0.14 
1 

2 

21
 750.37  698.75  P1,449.12
87. Cleofas borrowed P2,000.00 from a bank and agreed to pay the loan at the end of one year. The bank discounted the
loan and gave him P1950 in cash. Determine the rate of discount.
a) 3.75 %
b) 3.12 %
c) 2.5 %
d) 1.2 %
Solution:
 2,000.00  1,950.00 
FP
d
100 %  2.5 %
100 %  
2,000.00
 F 


88. A machine was purchased under these terms: P30,000 down and P5,000 each month for 5 years. If money is worth
12% compounded monthly, what is the cash price of the machine?
a) P144,775.19
b) P245,775.19
c) P542,775.91
d) P254,775.19
Solution:
Cash Price = Down Payment + Present Worth of Annuity
 i  mn 
A 1  n   1
m


Cash Pr ice  Down Payment  
 i 
i 1  n 
m

mn
 0.12 125  
5,000.001 
 1

12 


Cash Pr ice  P30,000.00 
 P 254,775.19
1295
 0.12 
0.121 

12 

14
89. Determine the amount that must be deposited every 3 months in a fund paying 12% compounded quarterly in order to
have P25,000 in 8 years.
a) P746.71
b) P476.17
c) P674.71
d) P700.00
Solution:
A
 in 
 F
m
 in 
1  
m

mn
 0.12 

25,000.00
4 

 P 476.17
48 
 0.12 
1
1 

4 

90. What is the acid test ratio?
a. The ratio of owner’s equity to total current liabilities
b. The ratio of all assets to actual current liabilities
c. The ratio of current assets (exclusive of inventory) to the total current liabilities.
d. The ratio of gross margin to operating, sates, and administrative expenses
91. How do call an energy required to move 1 Coulomb of charge through an element.
a) Current
b) Voltage
c) Power
d) Resonance
dw
Answer: b) Voltage
where q = charge in C
w = energy in Joules
V
dq
92. This is a number sequence where the succeeding term is obtained by adding the last pair of preceding terms such as
the sequence (1, 1, 2, ,3 5, 8 …). How do you call this number sequence?
a) Euler’s number
b) Fermat number
c) Fibonacci number
d) Fourier series
93. If the roots of an equation are zero, then, how do you classify the solutions?
a. Extranous solutions
b. Trivial solutions
c. Conditional solutions
d. Ambiguous solutions
94. In electricity, how do you call the rate of charge flow?
a) Potential difference
b) Current
c) Voltage
d) Power
95. This law in electrical circuits states, “The algebraic sum of currents entering a node (or a closed boundary) is zero”.
How do you call this law?
a) Kirrchoff’s current law b) Ohm’s current law
c) Kirchhoff’s voltage law
d) Ohm’s voltage law
96. This law in electrical circuits state, “The algebraic sum of all voltages around a closed path (or loop) is zero”. How
do you call this law?
a) Kirrchoff’s current law
b) Ohm’s current law
c) Kirchhoff’s voltage law
d) Ohm’s voltage law
97. In electrical, what is the SI unit of conductance?
a) Ohm
b) Mho
c) Siemens
d) Ampere
98. Which of the following is the equivalent of 1 Ampere?
a) 1 Coulomb per second
b) 1 Joule per Coulomb c) 1 Volt per Ampere
d) 1 Ampere per Coulomb
Answer: a) 1 Coulomb per second
1 Ohm = 1 Volt/Ampere
1 Siemens = 1 Ampere/Volt
1 Volt = 1 Joule/Coulomb
1 Ampere = 1 Coulumb per second
99. This is the process of expressing a polynomial as the product of another polynomial or monomial of lower degree.
What is this mathematical process?
a) Decomposition
b) Rationalization
c) Factoring
d) Polynomial damping
100. This is a point where the concavity of a curve changes or when the slope of the curve is neither increasing nor
decreasing. What is this point commonly called?
a) Maximum point
b) Minimum point
c) Point of tangency
d. Point of inflection
101. How do you call the axis of the hyperbola that passes through the center, the foci and vertices?
a) Transverse axis
b) Conjugate Axis
c) Asymptotic axis
d) Major Axis
102. What is a number, which could not be expressed as a quotient of two integers?
a. Natural
b. Rational
c. Irrational
103. How do you call the opposite of the prefix nano?
a) Peta
b) Tera
c) Giga
15
d. Surd
d) Hexa
104. What do you call a triangle having three unequal sides?
a) Obtuse
b) Oblique
c) Scalene
105. How do you call the distance of a point from the y-axis?
a) Polar distance
b) Coordinate
c) Abscissa
d) Isosceles
d) Ordinate
106. This is the measure of central tendency defined as the most frequent score. How do you call this measure of central
tendency?
a) Median
b) Mode
c) Mean
d) Deviation
107. Which of the following is the equivalent of 1 mil?
a) One-tenth of an inch b) One-thousandth of an inch c) One millionth of an inch c) One-half of an inch
108. A polygon with ten sides is said to be:
a. Dodecagon
b. Decagon
c. Decahedron
109. Any number expressed in place-value notation with base 12 is known as:
a. Duodecimal
b. Deontic
c. Decile
110. Another name for derivative is said to be:
a. Differential manifold
b. Partial derivative
111. Another term for rhombus is said to be:
a. Dichotomy
b. Diamond
c. Differential form
c. Cyclic quadrilateral
d. Dodecahedron
d. Dedekind
d. Differential coefficient
d. Bi-rectangular
112. A prefix denoting a multiple of ten times any of the physical units of the system international.
a. Deka
b. Nano
c. Hecto
d. Exa
113. The father of plane geometry.
a. Euclid
b. Pythagoras
c. Aristotle
d. Galileo
114. This is the case of a solution of a plane triangle where the given data leads to two solutions. How do you call this
case?
a) Ambiguous case
b) Quadratic case
c) Extraneous case
d) Conditional case
115. It is a type of polygon in which each interior angle must be less than or equal to 180°, and all vertices 'point outwards'
away from the interior. How do you call this polygon?
a) Concave Polygon
b) Convex polygon
c) Regular polygon
d) Irregular polygon
116. It is a series of equal payments occurring at equal intervals of time where the first payment is made after several
periods, after the beginning of the payment. How do you call this payment?
a) Deferred annuity
b) Delayed annuity
c) Progressive annuity
d) Simple annuity
117. What do you think is the negotiation of wage rates, conditions of employment, etc. by representatives of the labor
force and management?
a) Union trade
b) Union rally
c) Collective bargaining
d) Cooperative
118. How do you call a type of bond where the corporation’s owner name is recorded and the interest is paid periodically
to the owners with their asking for it?
a) Registered bond
b) Preferred bond
c) Incorporator’s bond
d) Bail bond
119. How do you call the integral of any quotient whose numerator is the differential of the denominator?
a) Co-logarithm
b) Logarithm
c) Product
d) Derivative
120. What is a regular polygon that has 27 diagonals?
a) Nonagon
b) hexagon
c) Pentagon
d) Heptagon
121. How do you call the formula used to compute the value of n factorial, which is in symbolic form (n!), where n is
large number?
a) Matheson formula b) Diophantine formula c) Richardson-Duchman formula d) Stirling’s Approximation
122. What is the reason why an ivory soap floats in water?
a) All matter has mass
b) The specific gravity of ivory soap is greater than that of water
c) The density of ivory soap is unity
d) The specific gravity of ivory soap is less than that of water
16
123. When two planes intersect with each other, the amount of divergence between the two planes is expressed by
measuring the:
a) Reflex angle
b) Dihedral angle
c) Polyhedral angle
d) Plane angle
124. What do you think is the output or sales at which income is insufficient to equal operating cost?
a) Break even point
b) Depreciation
c) Investment
d) Cash flow
125. What is an estimate of assets’ net market value at the end of its estimated life?
a) Book value
b) Depreciation
c) Salvage value
d) Cash flow
126. What do you think is the lessening of the value of an asset due to a decrease in the quantity available as a coal, oil
and timber in forests?
a) Depletion
b) Amortization
c) Depreciation
d) Investment
127. What can you say about the present worth of all depreciation over the economic life of the item?
a) Maintenance
b) Capital recovery
c) Depreciation recovery
d) Annuity
128. What do you think is the provision in the contract that indicates the possible adjustment of material cost and labor
cost?
a) Secondary clause
b) Specification
c) Escalatory clause
d) General provision
129. This is the process of determining the value of certain property for specific reasons. Guess, what is this?
a) Amortization
b) Investment
c) Appraisal
d) Depreciation
130. How do you call those products or services that are directly used by people to satisfy their wants?
a) Consumer goods and services
b) Producer goods and services
c) Necessity products and services
d) Luxury products and services
131. These are used to produce consumer goods and services. Guess, what are these?
a) Consumer goods and services
b) Producer goods and services
c) Necessity products and services
d) Luxury products and services
132. What do you think are those products or services that are required to support human life and activities that will be
purchased in somewhat the same quantity even though the price varies considerably?
a) Consumer goods and services
b) Producer goods and services
c) Necessity products and services
d) Luxury products and services
133. How do you call a cylinder with elliptical cross section?
a. Ellipsoid
b. Cylindroid
c. Hyperboloid
d. Paraboloid
134. How do you call a market whereby there is only one buyer of an item for which there are no goods substitutes?
a) Monopoly
b) Monopsony
c) Oligopoly
d) Oligopsony
135. Which statement about a charge placed on a dielectric material is true?
a. The charge increases the conductivity of the material
b. The charge is confined to the region in which the charge was placed.
c. The charge is immediately lost to the atmosphere
d. The charge is instantly carried to the material’s surface

In a dielectric, all charges are attached to specific atoms or molecules.
136. Which of the following is not a property of magnetic field lines?
a) Magnetic field lines have no beginnings and no ends
b) The lines cross themselves only at right angles
c) The line intersect surfaces of equal intensity at right angles
d) The field is stronger where the lines are closer together

Magnetic field lines do not cross. Their direction at any given point is unique.
137. Tesla is a unit of which of the following?
a) Magnetic induction
b) Inductance
138. What is a pole pitch?
a) The angle at which the pole windings are wound
c) The space on the stator allocated to one pole
c) Capacitance
d) magnetic flux
b) The space on the stator allocated to two poles
d) The mica used to insulate the poles from each other
17

Pole pitch is defined as the periphery of the armature divided by the number of poles. Thus, it is the space
on the stator allocated to one pole.

139. How do you call a polygon with 10 000 sides?
a) Hectogon
b) Chilliagon
c) Myriagon
d) Octacontagon
140. Any line segment joining a vertex of a triangle to a point on the opposite side is called as:
a) Newton line
b) Secant
c) Cevian
d) Euclidian line
141. It is any influence capable of producing a change in the motion of an object.
a) Force
b) Acceleration
c) Friction
d) Velocity
142. How do you call the amount needed at the beginning of operations and permits the enterprise to begin functioning
before it receives any income from the sales of its product or service.
a) Initial working capital
b) Regular working capital
c) Equity
d) Annuity
143. In the problem of writing the equation of a certain curve with respect to another axes in which the new axes are
parallel to the original axes and similarly directed is known as:
a) Translation of axes
b) Reversal of axes
c) Notation of axes
d) Relocation of axes
144. How do you call a ring shaped surface or solid obtained by rotating a circle about a coplanar line that does not
intersect?
a) Torus
b) Annulus
c) Circoloid
d) Annular
145. If the eccentricity is less than one, then curve is known as:
a) Ellipse
b) Hyperbola
c) Parabola
d) Circle
146. Determine the outside diameter of a hollow steel tube that will carry a tensile load of 500 kN at a stress of 140 MPa.
Assume the wall thickness to be 0ne-tenth of the outside diameter.
a) 123 mm
b) 103 mm
c) 113 mm
d) 93 mm
147. What can you say to the following statement: “the volume of a circular cylinder is equal to the product of its base and
altitude.”?
a) Postulate
b) Corollary
c) Theorem
d) Axiom
148. What is the study of the properties of figures of three dimensions?
a) Physics
b) Solid geometry
c) Plane geometry
d) Trigonometry
149. A type of bond, without any security behind them except a promise to pay by the issuing corporation is known as:
a. Collateral trust bond
b. Mortgage bond
c. Debenture bond
d. Joint bond
150. A situation whereby payment is made for work not done. The term also applies to the case where more workers are
used than a reasonable requirement for efficient operation.
a. Downtime pay
b. Check-in-pay
c. Feather bidding
d. Moon lighting
151. The difference between what a negotiable paper is worth in the future and its present worth is known as:
a. Book value
b. Salvage value
c. Sunk value
d. Discount
152. The temperature to which the air must be cooled at constant temperature to produce saturation.
a. Absolute temperature
b. 273 K
c. Dew point
d. Critical temperature
153. A net force that will give to a mass of one gram an acceleration of 1 cm/s 2 is said to be:
a. Newton
b. Ergs
c. Kilogram force
d. Dyne
154. A change in position, specified by a length and a direction is said to be:
a. Displacement
b. Acceleration
c. Velocity
d. Dynamic equilibrium
155. The process of one substance mixing with another because of molecular motion is known as:
a. Adhesion
b. Diffusion
c. Cohesion
d. Confusion
156. Those cost that arise at the result of a change in operations or policy or it is the ratio of a small increment cost and a
small increment of output.
a. Increment cost
b. Differential cost
c. Marginal cost
d. Promotion cost
157. The index that gives the rate earned per share based on current price per share is called as:
a. Price-earning ratio
b. Operating expense ratio c. Dividend yield
d. Equity ratio
158. A regular polyhedron having 12 regular pentagons is called as:
18
a. Icosahedron
b. Octahedron
c. Dodecahedron
d. Tetrahedron
159. Two angles whose sum is 360 o is called:
a. Explementary angles
b. Complimentary angles c. Supplementary angles d. Elementary angles
160. What is an annuity?
a) The future worth of a present amount.
b) A series of uniform amounts over a period of time
c) The present worth of a future amount
d) An annual repayment of a loan
161. When using net present worth calculations to compare two projects, which of the following could invalidate the
calculation?
a) Use of the same discount rate for each period
b) Differences in the magnitudes of the projects
c) Evaluating over different time periods
d) Mutually exclusive projects

a), b) and d) are all problems with internal rate of return calculations that net present worth handles nicely.
However, the net present worth of two projects must be calculated for the same time period.
162. What must two investments with the same present worth and unequal lives have?
a) Different equivalent uniform annual cash flows
b) Identical salvage values
c) Different salvage values
d) Identical equivalent uniform annual cash flows
163. Which of the following is true regarding the minimum attractive rate of return used in judging proposed investments?
a. It is much smaller than the interest rate used to discount expected cash flows from investments
b. It is frequently a policy decision made by an organization’s management
c. It is larger than the interest rate used to discount expected cash flow from investments
d. It is not relevant in engineering economy studies
164. Which of the following situations has a conventional cash flow so that an internal rate of return can be safely
calculated and used?
a. Your company undertakes a mining project in which the land must be reclaimed at the end of the project.
b. You invest in a safe dividend stock and receive dividends each year.
c. You lease a car and pay by the month
d. Your company invests heavily in a new product that will generate profits for two years. To keep profits high
for 10 years, the company plans to reinvest heavily after two years.

The situation in choice b) has a negative cash flow, one sign change, then positive cash flow. Thus, it is the
only situation that has a conventional cash flow so that an IRR can be safely calculated and used.
165. The economic order quantity (EOQ) is defined as the order quantity which minimizes the inventory cost per unit
time. Which of the flowing is not an assumption of the basic EOQ model with no shortages?
a) Reordering is done when the inventory is zero
b) There is an upper bound on the quantity ordered
c) The entire reorder quantity I delivered instantaneously
d) The demand rate is uniform and constant

Recall that, EOQ 
2aK
, where a = the constant depletion rate (items per unit time); K = the fixed cost per
h
order in dollars; h = the inventory storage cost (Pesos per item per unit time). Thus, there is no upper bound
on the quantity ordered.
166. Which of the following events will cause the optimal lot size, given by the classic EOQ model with no shortages, to
increase?
a) A decrease in inventory carrying cost
b) A decrease in demand
c) An increase in demand
d) a) or c) above

EOQ 
2aK
, where a = the constant depletion rate (items per unit time); K = the fixed cost per order in
h
dollars; h = the inventory storage cost (Pesos per item per unit time). Thus, a decrease in inventory carrying
cost, h, or an increase in demand, a, will cause the optimal lot size to increase.
19
167. What is a borrower of a particular loan almost always required to do during repayment?
a) Pay exactly the same amount of principal each payment
b) Repay the loan over an agreed-upon amount of time
c) Pay exactly the same amount of interest each payment
d) Pay the interest only whenever failure to pay the principal
168. How to you classify work-in-process?
a) A liability
b) An expense
c) A revenue
d) An asset

Work-in-process is included in the working fund investments. The working fund investments is an asset not
subjected to depreciation.
169. What is the indirect product cost (IPC) spending variance?
a. The IPC volume adjusted budget minus the total IPC absorbed
b. The IPC volume adjusted budget [fixed + volume (variable IPC rate)]
c. The difference between actual IPC and IPC volume adjusted budget
d. The difference between actual IPC and IPC absorbed
170. A leak from a faucet comes out in separate drops. Which of the following is the main cause of this phenomenon?
a) Air resistance
b) Gravity
c) Surface tension
d) Viscosity of the fluid
171. Which of the following elements and compounds is unstable in its pure form?
a) Hydrochloric acid
b) Carbon dioxide
c) Sodium
172. What is the actual geometric shape of the methane molecule?
a) Tetrahedral
b) Pyramidal
c) Square planar
d) Helium
d) Linear
173. A substance is oxidized when which of the following occurs?
a) It losses electrons
b) It becomes more negative
c) It gives off heat
d) It absorbs energy

By definition, a substance is oxidized when it losses electrons.
174. Reactions generally proceed faster at higher temperatures because of which of the following?
a) The molecules are less energetic
b) The activation energy is less
c) The molecules collide more frequently
d) Both b) & c) above
175. Which one of the following statements regarding organic substances is false?
a. Organic matter is generally stable at very high temperatures
b. Organic substances generally dissolve in high-concentration acids
c. All organic matter contains carbon
d. Organic substances generally do not dissolve in water.
176. Which of the following affects most of the electrical and thermal properties of materials?
a) The weight of the atoms
b) The weight of the protons
c) The electrons, particularly the outermost one d) The magnitude of electrical charge of the protons

The outermost electrons are responsible for determining most of the material’s properties.
177. What are the valence electrons?
a) The electrons of complete quantum shells
c) The outer-shell electrons

b) Electrons with positive charge
d) The K-quantum shell electrons
By definition, the outermost electrons are the valence electrons
178. How do you call the strong bond between hydrogen atoms?
a) Ionic and metallic bonds
b) The covalent bond
c) The ionic bond

d) The metallic bond
Covalent bonds provide the strongest attractive forces between atoms.
179. What are Van der Waals forces?
a) Forces present only in gases
c) Primary bonds between atoms
b) Forces not present in liquids
d) Weak secondary bonds between atoms
20

By definition, Van der Waals forces are weak attractive forces between molecules.
180. Which of the following materials is not a viscoelastic material?
a) Metal
b) Plastic
c) Rubber

d) Glass
A material which is viscoelastic exhibits time-dependent elastic strain. Of the choices, only metal does not
fit this description. Metal is considered to be an elastoplastic material.
181. In molecules of the same composition, what are variations of atomic arrangements known as?
a) Isomers
b) Polymers
c) Monomers
d) Crystal systems

Isomers are molecules that have the same composition but different atomic arrangements.
182. Which of the following is false?
a. The acceleration of a body rotating with a constant angular velocity is zero.
b. Angular momentum for rigid bodies may be regarded as the product of angular velocity and inertia.
c. The radius of gyration for a mass of uniform thickness is identical to that for a planar area of the same
shape.
d. Kinematics is the study of the effects of motion, while kinetics is the study of the causes of motion.

A body rotating at a constant angular velocity has no angular acceleration. It does have a linear acceleration.
183. Which statement about a charge placed on a dielectric material is true?
a. The charge increases the conductivity of the material
b. The charge is confined to the region in which the charge was placed.
c. The charge is immediately lost to the atmosphere
d. The charge is instantly carried to the material’s surface
o
In a dielectric, all charges are attached to specific atoms or molecules.
184. Which of the following is not a property of magnetic field lines?
a) Magnetic field lines have no beginnings and no ends
b) The lines cross themselves only at right angles
c) The line intersect surfaces of equal intensity at right angles
d) The field is stronger where the lines are closer together
o
Magnetic field lines do not cross. Their direction at any given point is unique.
185. Tesla is a unit of which of the following?
a) Magnetic induction
b) Inductance
c) Capacitance
d) magnetic flux
186. What is a pole pitch?
a) The angle at which the pole windings are wound
b) The space on the stator allocated to two poles
c) The space on the stator allocated to one pole
d) The mica used to insulate the poles from each other

Pole pitch is defined as the periphery of the armature divided by the number of poles. Thus, it is the space
on the stator allocated to one pole.
187. How do you call a polygon with 10 000 sides?
a) Hectogon
b) Chilliagon
c) Myriagon
d) Octacontagon
188. Any line segment joining a vertex of a triangle to a point on the opposite side is called as:
a) Newton line
b) Secant
c) Cevian
d) Euclidian line
189. It is any influence capable of producing a change in the motion of an object.
a) Force
b) Acceleration
c) Friction
21
d) Velocity
190. How do you call the amount needed at the beginning of operations and permits the enterprise to begin functioning
before it receives any income from the sales of its product or service.
a) Initial working capital
b) Regular working capital c) Equity
d) Annuity
191. In the problem of writing the equation of a certain curve with respect to another axes in which the new axes are
parallel to the original axes and similarly directed is known as:
a) Translation of axes
b) Reversal of axes
c) Notation of axes
d)
Relocation of axes
192. How do you call a ring shaped surface or solid obtained by rotating a circle about a coplanar line that does not
intersect?
a) Torus
b) Annulus
c) Circoloid
d) Annular
193. If the eccentricity is less than one, then curve is known as:
a) Ellipse
b) Hyperbola
c) Parabola
d) Circle
194. What can you say to the following statement: “the volume of a circular cylinder is equal to the product of its base and
altitude.”?
a) Postulate
b) Corollary
c) Theorem
d) Axiom
195. What is the study of the properties of figures of three dimensions?
a) Physics
b) Solid geometry
c) Plane geometry
d) Trigonometry
196. Points that lie in the same plane:
a) Coplanar
b) Collinear
c) Oblique
d) Parallel
197. What do you call the one-fourth of a great circle?
a) Cone
b) Pyramid
c) Chord
d) Quadrant
198. A plane closed curve, all points of which are the same distance from a point within, called the center.
a) Arc
b) Radius
c) Circle
d) Chord
199. What do you call the replacement of the original cost of an investment?
a) Pay off
b) Return on investment c) Breakeven
d) Capital recovery
200. This is the case of a solution of a plane triangle where the given data leads to two solutions. How do you call this
case?
a) Ambiguous case
b) Quadratic case
c) Extraneous case
d) Conditional case
201. What do you think is the provision in the contract that indicates the possible adjustment of material cost and labor
cost?
a) Secondary clause
b) Specification
c) Escalatory clause
d) General provision
202. This is the process of determining the value of certain property for specific reasons. Guess, what is this?
a) Amortization
b) Investment
c) Appraisal
d) Depreciation
203. If f " (x1 )  0 , then the point (x1, y1) is called;
a) Minimum point
b) Maximum point
c) Inflection point
d) Critical point
Solution: if the second derivative of the function is zero then this is the inflection point.
204. Adding more solute to an already saturated solution will cause the excess solute to settle to the bottom of the
container. What is this process called?
a) Precipitation
b) Hydration
c) Dehydration
d) Saturation
205. The length of time at which the original cost of capital used to purchase a unit has already been recovered.
a) Economic life
b) Write off period
c) Physical life
d) Salvage life
206. The actual interest earned by a given principal is known as:
a) Compound interest
b) Simple interest
c) Effective interest
22
d) Nominal interest
MATHEMATICS PROBLEM WITH
ANSWERS AND SOLUTIONS
INSTRUCTION: Select the correct answer for each of the following questions. Mark only one answer for
each item by shading the box corresponding to the letter of your choice on the answer sheet provided.
STRICTLY NO ERASURES ALLOWED. Use pencil No. 1 only.
1. How do call an energy required to move 1 Coulomb of charge through an element.
a) Current
b) Voltage
c) Power
d) Resonance
Answer: b) Voltage
V
dw
dq
where q = charge in C w = energy in Joules
2. This is a number sequence where the succeeding term is obtained by adding the last pair of preceding
terms such as the sequence (1, 1, 2, ,3 5, 8 …). How do you call this number sequence?
a) Euler’s number
b) Fermat number
c) Fibonacci number
d) Fourier series
Answer: c) Fibonacci number
3. Determine the sum of the coefficient of the variables in the expression (2x + 3y –z)8.
a) 65 536
b) 56 563
c) 63 655
d) 66 535
Solution: sum  21  31  1  56 563
8
4. If the roots of an equation are zero, then, how do you classify the solutions?
a. Extranous solutions
b. Trivial solutions
c. Conditional solutions
solutions
d.
Ambiguous
Answer: b) Trivial Solutions
5. Find the voltage drop to move 2 C of charge from point a to point b that requires – 30 Joules of energy.
a) – 15 V
b) + 15 V
c) – 5 V
d) + 5 V
Solution:
v
w  30 J

 15 V
q
2C
6. This is the process of expressing a polynomial as the product of another polynomial or monomial of
lower degree. What is this mathematical process?
a) Decomposition
b) Rationalization
c) Factoring d) Polynomial damping
Answer: c) Factoring
7. This is a point where the concavity of a curve changes or when the slope of the curve is neither
increasing nor decreasing. What is this point commonly called?
a) Maximum point
b) Minimum point
c) Point of tangency
d. Point of inflection
Answer: d) point of inflection
8. How do you call the axis of the hyperbola that passes through the center, the foci and vertices?
a) Transverse axis
b) Conjugate Axis
c) Asymptotic axis
d) Major Axis
Answer: a) Transverse axis
9. How many permutations can be made out of the letters in the word DIEGO taken 3 at a time?
a) 50 ways
b) 60 ways
c) 120 ways
d) 80 ways
Solution: Pn, r   P5,3 
10. What is the
a) 0 oC
n!
5!

 60 ways
n  1! 5  3!
temperature in degrees Celsius of a molecule at absolute zero?
b) – 273 oC
c) – 32 oC
d) 273 oC
1
Answer: b) – 273 oC
11. If at an angle measures x degrees, what is the measure in radians?
a)

x
180
b)
Solution: a)
180
x

c)
180
x
d)
180
x
x
180 o
12. In electricity, how do you call the rate of charge flow?
a) Potential difference
b) Current
i
Answer: b) Current
dq
dt
c) Voltage
d) Power
where q = charge, C; t = time, sec.
13. What is a number, which could not be expressed as a quotient of two integers?
a. Natural
b. Rational
c. Irrational
d. Surd
Answer: c) Irrational
14. This law states, “The voltage, v, across a resistor is directly proportional to the current, i, flowing
through the resistor”. How do you call this law?
a) Kirchhoff’s Law
b) Ohm’s Law
c) Ampere’s Law
d) Gauss’ Law
Answer: b) Ohm’s Law
15. How do you call an angle that is greater then 180 degree but less than 360 degrees?
a) Complex
b) Reflex
c) Obtuse
d) Exterior
16. This law in electrical circuits states, “The algebraic sum of currents entering a node (or a closed
boundary) is zero”. How do you call this law?
a) Kirrchoff’s current law
b) Ohm’s current law
c) Kirchhoff’s voltage law
d) Ohm’s voltage law
Answer: a) Kirchhof’s current law
17. How do you call the opposite of the prefix nano?
a) Peta
b) Tera
Solution: c) Giga
c) Giga
d) Hexa
Note: The prefix nano represents 10-9 which is the opposite of giga (109).
18. What do you call a triangle having three unequal sides?
a) Obtuse
b) Oblique
c) Scalene
d) Isosceles
Answer: c) Scalene
19. An area of 25.6 cm2 on the map represents a lot having an area of 640 m2. If the scale on the map is 1:x,
what is the value of x?
a) 50
b) 100
c) 500
d) 900
2
Solution:
Map Area
25.6
1
  
2
Actual Area  x 
640 100 
x = 500
20. If the z  1  1  1  ... , what is the value of z?
a) 0.453
b) 0.618
c) 0.816
Solution: Squaring both sides of the equation


 z  1  1  1  ... 


2
2
d) 0.681


z  1  1  1  1  .... 


2
z  1 z
z2  z 1  0
2
2
z
1
12  41 1 0.618

 1.619
21
21. Solve for the value of x from the following equation: x
a) 1.258925
b) 1.892525
c) 1.85925
Solution:
ln x
xx
..
x.
1  1  1  ....  z
but
 ln 10  x
xx
..
x.
xx
..
x.
 10 .
d) 1.528925
 but x
ln x  ln 10
xx
..
x.
 10
1
x  10 10  1.258925
10 ln x  ln 10  ln x 10  ln 10  x10  10
22. This law in electrical circuits state, “The algebraic sum of all voltages around a closed path (or loop) is
zero”. How do you call this law?
a) Kirrchoff’s current law
b) Ohm’s current law
c) Kirchhoff’s voltage law
d) Ohm’s voltage law
Answer: Kirchhoff’s voltage law
23. How do you call the distance of a point from the y-axis?
a) Polar distance
b) Coordinate
c) Abscissa
d) Ordinate
24. In electricity, it is an ability of an element to resist the flow of current. What is this?
a) Resonance
b) Conductance
c) Inductance
d) Resistance
Answer: d) Resistance
25. In electrical circuits, how do you call the reciprocal of resistance?
a) Resonance
b) Conductance
c) Inductance
d) Resistance
Answer: b) Conductance
26. In electrical, what is the SI unit of conductance?
a) Ohm
b) Mho
Answer: c) Siemens
4
3
b)
x 4
Solution: 
y 3
d) Ampere
1 Mho = 1 Siemens
27. If 4y = 3x, then, what is the value of
a)
c) Siemens
3x 2
?
4y 2
3
4
 x 4
   
 y 3
c)
2

x2
y
2

2
3
d)
16
9
Then,
3x 2
4y
2

3
2
3  16  4
 
4 9  3
28. Which of the following is the equivalent of 1 Ampere?
a) 1 Coulomb per second b) 1 Joule per Coulomb c) 1 Volt per Ampere d) 1 Ampere per Coulomb
Answer: a) 1 Coulomb per second
1 Ohm = 1 Volt/Ampere
1 Volt = 1 Joule/Coulomb
1 Siemens = 1 Ampere/Volt
1 Ampere = 1 Coulumb per second
29. This is the measure of central tendency defined as the most frequent score. How do you call this measure
of central tendency?
3
a) Median
b) Mode
c) Mean
d) Deviation
30. When the expression x4 + ax3 + 5x2 + bx + 6 is divided by (x – 2), the remainder is 16. When it is divided
by (x + 1) the remainder is 10. Determine the value of the constant a.
a) 6
b) 9
c) 5
d) 7
Solution: f x   x 4  ax 3  5x 2  bx  6
f 2  24  a 23  522  b2  6  16
8a  2b  26

4a  b  13
Eq. 1
f  1   14  a  13  5 12  b 1  6  10
a  b  2
 ab  2
 b  2a
Eq. 2
Substituting 2 to 1, 4a  2  a  13  3a  15
a
15
 5
3
the , b  2   5  7
31. What is the logarithm of a negative number?
a) Complex number
c) Irrational number
b) Real number
d) Imaginary number
Solution: The logarithm of a negative number can be evaluated as follows:
log  x   log x  x 
where, i 2  1
log  x   log x i 2  log x  log i 2  log x  2 log i

i 
Considering the exponential form of an imaginary number, i  e  2 
log  x   log x  2 log

i 
e 2

 log x  2i  log e  log x  i log e
2
Thus, the logarithm of a negative number is a complex number.
32. Which of the following is the equivalent of 1 mil?
a) One-tenth of an inch
c) One millionth of an inch
b) One-thousandth of an inch
c) One-half of an inch
Answer: a) One-thousandth of an inch
33. This is the case of a solution of a plane triangle where the given data leads to two solutions. How do you
call this case?
a) Ambiguous case
b) Quadratic case
c) Extraneous case
d) Conditional case
Answer: a) Ambiguous case
34. What is the value of k to make the expression kx 2 – 3kx + 9 a perfect square?
a) 2
b) 4
c) 3
d) 5
Solution: The expression Ax2 + Bx + C is a perfect square if B2 = 4AC.
From the given expression: A = k
Then,  3k 2  4k 9
B = -3k
C=9
 k4
35. It is a type of polygon in which each interior angle must be less than or equal to 180°, and all vertices
'point outwards' away from the interior. How do you call this polygon?
a) Concave Polygon
b) Convex polygon
c) Regular polygon
d) Irregular polygon
4
Answer: b) Convex polygon
36. Two times the mother’s age is 8 more than six times her daughter’s age. Ten years ago, the sum of their
ages was 44. What is the daughter’s age?
a) 15 yrs old
b) 18 yrs old
c) 12 yrs old
d) 16 yrs old
Solution: Let x = daughter’s age
y = mother’s age
Present Ages: 2y  6x  8
Ten years ago:
 y  3x  4
eq. 1
x  10   y  10   44
x  y  64
eq. 2
Substituting 1 to 2, x  3x  4  64
 4x  60
 x
60
 15
4
37. How do you call a line segment from the center of a regular polygon to the midpoint of a side? It is also
called as inradius, the radius of an incircle.
a) Radius
b) Apothem
c) Circumradius
d) Inradius
Answer: b) Apothem
38. If the daily wage of CPM and a Plumber are in the ratio 2:1. In a day, a CPM has to work 8 hrs but the
Plumber only 6 hrs. Determine the ratio of their hour wages.
a. 4:3
b. 5:3
c. 3:2
d. 8:3
Solution: Let
x = hourly wage of CPM
y = hourly rate of the Plumber
x
8 x 8 x 2
x 8



 ;
y y
6 6 y 6 y 1
8
8
x 62 6 3
   
y 81 4 2
Then, the ratio is 3:2
39. Which of the following is the equivalent of one circular mil?
a)

0.012
4
Answer: b)
b)

0.0012
4
c)

0.00012
4
d)

0.000012
4

0.0012
4
A circular mil is the area of a circle whose diameter is 1 mil or 0.001 inch.
40. How do you call a method of describing a set where the elements are separated by commas and enclosed
by braces?
a) Tabular or roster form
b) Equal form
c) Rule form
d) Equivalent form
Answer: a) Tabular or roster form
Two Ways of Describing a Set: a) Tabular or roster form; and b) Rule form, a method which makes use
of the description  x . . . .
41. Which of the following is the equivalent of the expression 2Logb 6 – Logb 4?
a) 2Logb 3
b. 3Logb 2
c. 2Logb 2
d. 3Logb 3
 36 
  log b 9  2 log 3
 4
Solution: 2 log b 6  log b 4  log b 36  log b 4  log 
5
42. It is a series of equal payments occurring at equal intervals of time where the first payment is made after
several periods, after the beginning of the payment. How do you call this payment?
a) Deferred annuity
b) Delayed annuity
c) Progressive annuity
d) Simple annuity
Answer: a) Deferred annuity
43. A 100-kg salt solution originally 4 % by weight salt in water is boiled to reduce water content until the
concentration is 5 % by weight salt. How much water is evaporated?
a) 20
b) 25
c) 15
d) 22.5
Solution:
4 % salt
96 % H2O
In Salt:
100 - x
x
100 kg
-
4 % 100   0  5 % 100  x 
5 % salt
95 % H2O
=
100 % H2O
 400  500  5x  then , x  20 kg
In Water (Checking):
96 % 100   100 % x   95 % 100  x   1920  20 x  1900  19 x  then , x  20 kg
44. Tukmol can paint a fence of 50 % faster than Kikoy and 20 % faster than Tiburcio and together thay can
paint a given fence in 4 hours. How long will it take Tukmol to paint the same fence if he had to work
alone?
a) 11
b) 8
c) 9
d) 10
Solution:
Let, x = no. of hours for Tukmol alone to paint the fence y = no. of hours for Kikay to paint the fence
z = no. of hours for Veronica
With the three of them finishing the work together in 4 hours,
1
4  1 4  1 4  1
x
y
z

1 1 1 1
  
x y z 4
Eq. 1
1
2

y 3x
Eq. 2
With Tukmol being 50 % than Kikay,
1 2
1 1
  0.50  
x y
 y  3y

With Tukmol being 20 % faster than Veronica,
1 1
1 6
  0.20  
x z
 z  5x

1
5

x 6x
Eq. 3
Substituting 1/y in Eq. 2 and 1/z in Eq. 3 to Eq. 1,
1 2
5 1



x 3x 6x 4
5 1

2x 4

 x  10 hours
45. It is now between 3 and 4 o’clock and twenty minutes the minute hand will be as much as the hour-hand
as it is now behind it. What is the time now?
a) 3:06.36
b) 3:03.66
c) 3:36.06
d) 3:30.66
x
Solution:
12
1
2

3
x/12

6
4
20/12
5
6
20
At present (now), the minute hand is behind the hour hand by ,
  15 
x
11
 x  15  x
12
12
After 20 minute, the minute hand is ahead the hour hand by ,
  x  20  15 
x
11
10
 20 / 12  x 
12
12
3
As the given condition,  = ,
11
10
11
x   15  x
12
3
12
 then , x  6.36 min utes
Therefore, the time now is 3:06.36.
46. This is the amount of a property in which a willing buyer will pay to a willing seller for the property
when neither one is under the compulsion to buy or sell. What do you call this value?
a) Fair value
b) Goodwill value
c) Book value
d) Market value
Answer: d) market value
47. Determine the diameter of a circle, x 2  y 2  6x  4 y  12  0 .
a) 9 units
b) 11 units
c) 12 units
Solution:
x 2  y 2  6x  4 y  12  0
x
2
 

 6x  9  y 2  4 y  4  12  13  25
x  3
2
 y  2  25
2
48. What is the minimum point of y  x 
a) (1, 2)
Solution:
d) 10 units
Then, r = 5 units and d = 10 units
1
?
x
b) (1.5, 2)
yx
1
x

c) (1, 1.5)
d) (2, 1)
dy
1
 1 2  0
dx
x
Then, x = 1, and y = 2
49. The volume of the cube is increasing at a rate of 5 cu. m per minute. Determine the rate at which the
surface area is increasing, in m2/min, when its side is 10 m.
a) ½
b) 1.75
c) 1.5
d) 2
Solution:
V = x3
A = 6 x2
dV
dx
dx
1 dV
 3x 2

 2
dt
dt
dt 3x dt
dA
dx
 1  dV  4 dV 4
 12 x
 12 x 2 
 5  2 m 2 / min

dt
dt
 3x  dt  x dt 10
50. What is the simple interest rate if an investment of P37,500.00 accumulates to P45,937.5 in 18 months?
a) 0.15
b) 0.2
c) 0.21
d) 0.3
Solution:
F  P1  i n 
7
F 
 1


100 %    F  P 100 %   45,937 .5  37,500 .00 100 %   15 %
iP
 n 
 nP 
 1.537,500 .00  




51. What do you think is the negotiation of wage rates, conditions of employment, etc. by representatives of
the labor force and management?
a) Union trade
b) Union rally
c) Collective bargaining
d)
Cooperative
52. What is the simple interest rate if an investment of P37,500.00 accumulates to P45,937.5 in 18 months?
a) 0.15
b) 0.2
c) 0.21
d) 0.3
Solution:
F  P1  i n 
F 
 1


100 %    F  P 100 %   45,937 .5  37,500 .00 100 %   15 %
iP
 n 
 nP 
 1.537,500 .00  




53. What is the value of Lim
x 
x2 1
?
x3 1
a) 0
Solution:
b) 0.25
c) 1.25
d) indeterminate
x  1x  1  Lim x  1  Lim
x 2 1
1
Lim 3
 Lim
x  x  1
x  x  1 x 2  x  1
x  x 2  x  1
x  x 2  x  1
x 1
1
1
1
Lim

 0
x 
1
1

x

x 1
 1


54. What is the present value of P5,000.00 due in 8 years if money is worth 12% compounded semiannually?
a) P1,896.23
b) P1,869.23
c) P1,698.23
d) P1,968.23
Solution:
P
F
 in 
1  
 m
mn

5,000.00
 0.12 
1 

2 

2 8 
 P1,968.23
55. This is a type of bond whose guaranty is in lieu on railroad equipment. What is this type of bond?
a) Equipment
b) Debenture bond
c) Registered bond
d) Infrastructure bond
Answer: d) Infrastructure bond
56. How do you call a type of bond where the corporation’s owner name is recorded and the interest is paid
periodically to the owners with their asking for it?
a) Registered bond
b) Preferred bond
c) Incorporator’s bond d) Bail bond
Answer: a) Registered bond
57. Twice the middle digit of a three-digit number is the sum of the other two. If the number is divided by
the sum of its digit, the answer is 56 and the remainder is 12. If the digits are reversed, the number
becomes smaller by 594. Find the number.
a) 852
b) 285
c) 825
d) 582
Solution: Let x, y, and z be the hundred’s, ten’s, and unit’s digits, respectively.
The number is: 100x + 10y + z
The reversed number is: 100z +10y + x
8
2y = x + z
Eq. 1
100x  10y  z
12
 56 
xyz
xyz

10x  10y  z   12  56
xyz
100x  10y  z  12  56x  56y  56z
44x  99y  55z  12
Eq. 2
100z  10y  x  100x  10y  z  594
99z  99x  594
x  6z
Eq. 3
Substituting x in Eq. 3 to Eq 1,
2 y  x  z   z  6  2z
y  3 z
Eq. 4
Substituting x in Eq. 3 to Eq. 2,
44 6  z   46 3  z   55 z  12
Then, z = 2
x=8
y=5
The number is 852
Note: This problem can be solved by inspection.
58. A man left Sta. Rosa City to drive to Lopez, Quezon at 6:15 pm and arrived at 11:45 pm. If he averaged
50 kph and stopped 1 hour for dinner, how far is Lopez, quezon from Sta. Rosa City?
a) 225 km
b) 522 km
c) 252 km
d) 215 km
Solution:
Total time, 6:15 pm to 11:45 pm, = 5.5 hours
Time of travel = 5.5 – 1 = 4.5 hours
Distance, S = Vt = 50 (4.5) = 225 km
59. If x varies directly as y and inversely as z, and x = 14 when 7 = 7 and z = 2, find the value of x when z =
4 and y = 16.
a) 12
b) 18
c) 14
d) 16
Solution: x 
y
z
z
2
k  x   14   4
7
 y
 y
 x  k 
z
 y
z
 16 
  16
4
Then, x  k   4
60. Lucy sold 100-pirated DVD. Eighty of them were sold at a profit of 30 % while the rest were sold at a
loss of 40 %. What is the percentage gain or loss on the whole stock?
a) 15 %
b) 20 %
c) 16 %
d) 12 %
Solution:
Let x = the buying price of each DVD
Total Capital = 100x
Income for 80 DVD = 80 (x + 0.30x) = 104x
Income for 20 DVD = 20(x – 0.40x) = 12x
Total sales = 104x + 12x = 116x
9
Profit = total sales – capital = 116x – 100x = 16x
 16x 
% Gain  
 100 %  16 %
 100x 
61. How many terms of the sequence – 9, - 6, - 3, … must be taken so that the sum is 66?
a) 11
b) 6
c) 4
d) 9
Solution: The given sequence is a form of arithmetic progression with common difference of,
d =- 6 – (- 9) = 3
S
n
2a 1  n  1d  66   n 2 9  n  13
2
2
132  18 n  3n 2  3n
3n 2  21n  132  0
3n  12 n  11  0
Therefore, n = 11
62. There are 6 geometric means between 4 and 8748. Find the sum of all terms.
a) 12 310
b) 12 130
c) 13 210
d) 13 120
Solution:
8th term, a8 = 8748
First term, a1 = 4
nth term, a n  a 1r n 1  8748  4r 81  8748r 7
1
 8748  7
Common ratio, r  
 3
 4 
Sum, S 

 

a 1 r n  1 4 38  1

 13120
r 1
3 1
63. How many permutation can be made out of the letters of the word ENGINEERING?
a) 277 200
b) 272 700
c) 200 277
d) 227 700
Solution:
P
n!
11!

 277 200
p! q!... 3!3! 2! 2!
Where, n = 11 objects with 3E’s, 3N’s, 2G’s, and 2I’s
64. A bag contains 3 white and 5 red balls. If two balls are drawn at random, find the probability that both
are white.
a) 0.375
b) 0.10714
c) 0.46667
d) 0.28571
Solution: First draw, white, P1 
3
8
Second draw, white, P1 
32
87
Probability, both white    
3
 0.10714
28
65. Determine the absolute value of the complex number 3 + 4i.
a) 4
b) 5
c) 8
Solution: r 
32  42
2
7
d) 6
5
66. Simplify i1997 + i1999, where I is an imaginary number.
a) 0
b) i
c) 1 + i
 
Solution: i 1997  i 1999  i 1996 i   i 1998 i   i 2
998
d) 1 – I
i   i 2  i    i 998   i 999  i  i  0
10
999
67. The sum of the two interior angles of the triangle is equal to the third angle and the difference of the two
angles is equal to 2/3 of the 3rd angle. Find the 3rd angle.
a) 60o
b) 30o
c) 90o
d) 40o
Solution: Let x = 1st angle
x  y  z  180
y = 2nd angle
z = 3rd angle
xyz
Eq. 1
z
xy  z
3
Eq. 2
Eq. 3
Substituting Eq. 2 to Eq. 1, z = 90o
68. Evaluate the integral of (3x2 + 9y2)dxdy if the interior limit has an upper limit of y and a lower limit of
0, and whose outer limit has an upper limit of 2 and lower limit of 0.
a) 50
b) 30
c) 45
d) 40
Answer: d) 40
69. How do you call the integral of any quotient whose numerator is the differential of the denominator?
a) Co-logarithm
b) Logarithm
c) Product
d) Derivative
Answer: b) Logarithm
70. If a = b, then b = a. This illustrates of which of the following axioms in algebra?
a) Transitive axiom b) Reflexive axiom
c) Replacement axiom d) Symmetric axiom
Answer: d) Symmetric axiom
71. What is a regular polygon that has 27 diagonals?
a) Nonagon
b) hexagon
c) Pentagon
d) Heptagon
Answer: a) Nonagon
72. How do you call the formula used to compute the value of n factorial, which is in symbolic form (n!),
where n is large number?
a) Matheson formula
b) Diophantine formula c) Richardson-Duchman formula
d)
Stirling’s Approximation
73. What is the reason why an ivory soap floats in water?
a) All matter has mass
b) The specific gravity of ivory soap is greater than that of water
c) The density of ivory soap is unity
d) The specific gravity of ivory soap is less than that of water
74. If the product of the slopes of any two straight lines is negative 1, one of these lines is said to be:
a) Parallel
b) perpendicular
c) Skew
d) Non-intersecting
75. When two planes intersect with each other, the amount of divergence between the two planes is
expressed by measuring the:
a) Reflex angle
b) Dihedral angle
c) Polyhedral angle
d) Plane angle
76. These are product or services that are required to support human life and activities, that will be purchased
in somewhat the same quantity even though the price varies considerably.
a) Utilities
b) Necessities
c) Luxuries
d) Producer goods and services
77. The angle which the line of sight to the object makes with the horizontal which is above the eye of the
observer is called as:
a) Angle of elevation
b) Acute angle
c) Angle of depression
d) Bearing
78. This is a number sequence where the succeeding term is obtained by adding the last pair of preceding
terms such as the sequence (1, 1, 2, ,3 5, 8 …). How do you call this number sequence?
a. Euler’s number
b. Fermat number
c. Fibonacci number
d. Fourier
series
11
79. If the roots of an equation are zero, then, how do you classify the solutions?
a. Extranous solutions
b. Trivial solutions
c. Conditional solutions d.
solutions
Ambiguous
80. This is the process of expressing a polynomial as the product of another polynomial or monomial of
lower degree. What is this mathematical process?
a. Decomposition
b. Rationalization
c. Factoring
d.
Polynomial
damping
81. This is a point where the concavity of a curve changes or when the slope of the curve is neither
increasing nor decreasing. What is this point commonly called?
a. Maximum point
b. Minimum point
c. Point of tangency
d. Point of inflection
82. How do you call the axis of the hyperbola that passes through the center, the foci and vertices?
a. Transverse axis
b. Conjugate Axis
c. Asymptotic axis
d. Major Axis
83. What is a number, which could not be expressed as a quotient of two integers?
a. Natural
b. Rational
c. Irrational
d. Surd
84. How do you call an angle that is greater then 180 degree but less than 360 degrees?
a. Complex
b. Reflex
c. Obtuse
d. Exterior
85. What do you call a triangle having three unequal sides?
a. Obtuse
b. Oblique
c. Scalene
d. Isosceles
86. How do you call the distance of a point from the y-axis?
a. Polar distance
b. Coordinate
c. Abscissa
d. Ordinate
87. This is the measure of central tendency defined as the most frequent score. How do you call this measure
of central tendency?
a. Median
b. Mode
c. Mean
d. Deviation
88. This is the case of a solution of a plane triangle where the given data leads to two solutions. How do you
call this case?
a. Ambiguous case
b. Quadratic case
c. Extraneous case
d. Conditional case
89. This is a sequence of numbers where every term is obtained by adding the squares of all preceding terms
such as (1, 5, 14, 30, 55…). How do you call this numbers?
a. Triangular numbers
b. Tetrahedral numbers c. Cubic numbers
d.
Pyramidal numbers
90. It is a process of reasoning wherein other conclusions or formulas are obtained or derived by
mathematical manipulations of previously proven theorems or formulas. How do you call this process?
a. Mathematical induction b. Mathematical deduction
c. Mathematical conversion
d.
Mathematical inversion
91. What is a solid bounded by the spherical zone and the planes of the zone’s base?
a. Spherical wedge b. Spherical solid
c. Spherical triangle
segment
d.
Spherical
92. How do you call the line passing through the focus and perpendicular to the directrix of a parabola?
a. Latus rectum
b. Axis of the parabola
c. Transverse axis
`
d. Major axis
93. What is the ratio of the distance between the foci to the distance between the vertices in either hyperbola
or ellipse?
a. Eccentricity
b. Latus rectum
c. Variance
d. Deviation
94. It is a statement that one mathematical expression is greater than or less than another. How do you call
this?
a. Conditional expression b. Inequality
c. Interval
d. Domain
95. What is the point of concurrency of the altitude of a triangle?
a. Centroid
b. Incenter
c. Orthocenter
12
d. Circumcenter
96. What is the logarithm of a number to have a base e=2.718…?
a. Briggsian logarithm
b. Naperian logarithm
Mantissa
c. Cologarithm
d.
97. What is a process of finding maximum or minimum values of a linear function under limiting conditions
or constraints?
a. Iteration
b. Linear programming
c. Differentiation
d.
Integration
98. Which of the following items classified a polygon?
a. Angles
b. Diagonals
c. Sides
d. Number of nodes
99. When a line y = mx + b slopes downwards from left to right, the slope m is:
a) Less than zero b) Greater than zero
c) Equal to zero
d) Equal to 1
100.
101.
The ratio between the quick assets to the current liabilities
a. Acid test ratio b. Current ratio
c. Working amount
d. Marginal ratio
It is the additional cost of producing one more unit of a product.
a. Sunk cost
b. Marginal cost
c. Variable cost
d. Fixed cost
102.
What is the quantity in addition to the economic order quantity use to anticipate sudden change of
demand and the delay of the ordered quantity?
a. safety stock
b. safety allowance
c. tolerance stock
d. none of these
103.
The ratio of a number is 4:7 where number 4 is referred to as the antecedent. How do you call
number 7 in this ratio?
a. Consequent
b. Minuend
c. Augend
d. Dividend
104.
What is a pair of angles when added together will be equal to 360 o?
a. Supplementary angle
b. Conjugate angle
c. Complimentary angle d. Explimentary angle
105.
What is a line segment joining a vertex of a triangle to a point on the opposite side?
a. Cevian
b. Secant
c. Euclidian line
d) Newton’s line
106.
How do you call a cylinder with elliptical cross section?
a. Ellipsoid
b. Cylindroid
c. Hyperboloid
d. Paraboloid
107.
For a given function, it is found that f(t) = f(- t). What type of symmetry does f(t) have?
a) Odd Symmetry b) Even Symmetry
c) Rotational Symmetry d) Quarter-wave Symmetry
108.
Which is true regarding the signs of the natural functions for angles between 90o and 180o?
a) The tangent is positive b) The cotangent is positive
c) The cosine is negative d) The sine is
negative
109.
What is the inverse natural function of the cosecant?
a) Secant
b) Sine
c) Cosine
d) Tangent
110.
What type of curve is generated by a point, which moves in uniform circular motion about an axis,
while traveling with a constant speed, V, parallel to the axis?
a) A cycloid
b) An epicycloids
c) A hypocycloid
d) A helix
111.
Forty liters of a 60 % salt solution are produced to a 45 % solution. How much solution must be
drained off and replaced with distilled water so that the resulting solution contains only 45 % solution.
a) 6 liters
b) 8 liters
c) 10 liters
d) 12 liters
Answer: c) 10 liters
Solution: Let x represents the number of liters of salt solution to be drained off and replaced with
distilled water.
60 % salt
40 % water
40 liters
-
60 % salt
40 % water
+
0 % salt
100 % water
x liters
x liters
13
=
55 % salt
45 % water
40 liters
Based on salt solution: 0.60 40   0.60 x  0.0 x  0.4540 
x = 10 liters
Based on water solution: 0.40 40   0.40 x  x  0.5540 
x = 10 liters
112.
How do you call the area bounded by two concentric circles?
a) Disk
b) Annulus
c) Ring
d) Sector
113.
Determine, which of the following is incorrect between lease and outright purchase of equipment?
a) Leasing fees needed working capital
b) Leasing reduces maintenance and administrative
expenses
c) Leasing offers certain tax advantage
d) Leasing offers less flexibility with respect to technical
obsolescence.
114.
What do you call the replacement of the original cost of an investment?
a) Pay off
b) Return on investment
c) Breakeven
d) Capital recovery
115.
What do you think is the output or sales at which income is insufficient to equal operating cost?
a) Break even point
b) Depreciation
c) Investment
d)
Cash
flow
116.
What do you think is the lessening of the value of an asset due to a decrease in the quantity available
as a coal, oil and timber in forests?
a) Depletion
b) Amortization
c) Depreciation
d) Investment
117.
How do you call the integral of any quotient whose numerator is the differential of the denominator?
a) Co-logarithm
b) Logarithm
c) Product
d) Derivative
118.
If a = b, then b = a. This illustrates of which of the following axioms in algebra?
a) Transitive axiom b) Reflexive axiom
c) Replacement axiom d) Symmetric axiom
119.
What is a regular polygon that has 27 diagonals?
a) Nonagon
b) hexagon
c) Pentagon
d) Heptagon
120.
How do you call the formula used to compute the value of n factorial, which is in symbolic form
(n!), where n is large number?
a) Matheson formula
b) Diophantine formula c) Richardson-Duchman formula
d)
Stirling’s Approximation
121.
What is the reason why an ivory soap floats in water?
a) All matter has mass
b) The specific gravity of ivory soap is greater than
that of water
c) The density of ivory soap is unity
d) The specific gravity of ivory soap is less than that of
water
122.
If the product of the slopes of any two straight lines is negative 1, one of these lines is said to be:
a) Parallel
b) perpendicular
c) Skew
d) Non-intersecting
123.
When two planes intersect with each other, the amount of divergence between the two planes is
expressed by measuring the:
a) Reflex angle
b) Dihedral angle
c) Polyhedral angle
d) Plane angle
124.
These are product or services that are required to support human life and activities, that will be
purchased in somewhat the same quantity even though the price varies considerably.
a) Utilities
b) Necessities
c) Luxuries
d) Producer goods and services
125.
The angle which the line of sight to the object makes with the horizontal which is above the eye of
the observer is called as:
a) Angle of elevation
b) Acute angle
c) Angle of depression
d) Bearing
126.
This is a number sequence where the succeeding term is obtained by adding the last pair of preceding
terms such as the sequence (1, 1, 2, ,3 5, 8 …). How do you call this number sequence?
a. Euler’s number
b. Fermat number
c. Fibonacci number
d. Fourier
series
127.
If the roots of an equation are zero, then, how do you classify the solutions?
14
a. Extranous solutions
b. Trivial solutions
c. Conditional solutions d.
Ambiguous
solutions
128.
This is the process of expressing a polynomial as the product of another polynomial or monomial of
lower degree. What is this mathematical process?
a. Decomposition
b. Rationalization
c. Factoring
d.
Polynomial
damping
129.
This is a point where the concavity of a curve changes or when the slope of the curve is neither
increasing nor decreasing. What is this point commonly called?
a. Maximum point
b. Minimum point
c. Point of tangency
d. Point of inflection
130.
How do you call the axis of the hyperbola that passes through the center, the foci and vertices?
a. Transverse axis
b. Conjugate Axis
c. Asymptotic axis
d. Major Axis
131.
What is a number, which could not be expressed as a quotient of two integers?
a. Natural
b. Rational
c. Irrational
d. Surd
132.
How do you call an angle that is greater then 180 degree but less than 360 degrees?
a. Complex
b. Reflex
c. Obtuse
d. Exterior
133.
What do you call a triangle having three unequal sides?
a. Obtuse
b. Oblique
c. Scalene
d. Isosceles
134.
How do you call the distance of a point from the y-axis?
a. Polar distance
b. Coordinate
c. Abscissa
d. Ordinate
135.
This is the measure of central tendency defined as the most frequent score. How do you call this
measure of central tendency?
a. Median
b. Mode
c. Mean
d. Deviation
136.
This is the case of a solution of a plane triangle where the given data leads to two solutions. How do
you call this case?
a. Ambiguous case
b. Quadratic case
c. Extraneous case
d. Conditional case
137.
This is a sequence of numbers where every term is obtained by adding the squares of all preceding
terms such as (1, 5, 14, 30, 55…). How do you call this numbers?
a. Triangular numbers
b. Tetrahedral numbers c. Cubic numbers
d.
Pyramidal numbers
138.
It is a process of reasoning wherein other conclusions or formulas are obtained or derived by
mathematical manipulations of previously proven theorems or formulas. How do you call this process?
a. Mathematical induction b. Mathematical deduction
c. Mathematical conversion
d.
Mathematical inversion
139.
What is a solid bounded by the spherical zone and the planes of the zone’s base?
a. Spherical wedge b. Spherical solid
c. Spherical triangle
d.
segment
Spherical
140.
How do you call the line passing through the focus and perpendicular to the directrix of a parabola?
a. Latus rectum
b. Axis of the parabola
c. Transverse axis
`
d. Major axis
141.
What is the ratio of the distance between the foci to the distance between the vertices in either
hyperbola or ellipse?
a. Eccentricity
b. Latus rectum
c. Variance
d. Deviation
142.
It is a statement that one mathematical expression is greater than or less than another. How do you
call this?
a. Conditional expression b. Inequality
c. Interval
d. Domain
143.
What is the point of concurrency of the altitude of a triangle?
a. Centroid
b. Incenter
c. Orthocenter
144.
What is the logarithm of a number to have a base e=2.718…?
15
d. Circumcenter
a. Briggsian logarithm
Mantissa
b. Naperian logarithm
c. Cologarithm
d.
145.
What is a process of finding maximum or minimum values of a linear function under limiting
conditions or constraints?
a. Iteration
b. Linear programming
c. Differentiation
d.
Integration
146.
Which of the following items classified a polygon?
a. Angles
b. Diagonals
c. Sides
d. Number of nodes
147.
When a line y = mx + b slopes downwards from left to right, the slope m is:
a) Less than zero b) Greater than zero
c) Equal to zero
d) Equal to 1
148.
149.
The ratio between the quick assets to the current liabilities
a. Acid test ratio b. Current ratio
c. Working amount
d. Marginal ratio
It is the additional cost of producing one more unit of a product.
a. Sunk cost
b. Marginal cost
c. Variable cost
16
d. Fixed cost
MATHEMATICS/ENG ECO/BASIC ENG TRIVIA EXAMINATION
MULTIPLE CHOICE QUESTIONS
Select the best answer from each of the following questions. On the answer sheet provided, shade the box that corresponds to your
choice. Strictly no erasures allowed.
1.
The roots of the quadratic equation are 1/3 and 3/2. What is the equation?
a. 6x 2  5x  3  0
b. 6x 2  7 x  3  0
c. 6 x 2  7 x  3  0
d. 6 x 2  7 x  3  0
2.
Mr. PME covered a distance of 55 km in 4 hours by driving his car 40 kph, part of the way, and by walking the
remainder of the way at 5 kph. What part of the total distance did Mr PME go by car?
7
8
9
10
a.
b.
c.
d.
11
11
11
11
3.
The water tank in Calamba Water District can be filled by pipe A in half the time the pipe B can empty the tank.
When both pipes are operating, the tank can be filled in 1 hour and 12 minutes. Determine the time, in hours, for pipe
A to fill the tank alone.
a. 0.6
b. 0.7
c. 0.75
d. 0.8
4.
What is the value of k to make the expression kx2 – 3kx + 9 a perfect square?
a) 2
b) 4
c) 3
5.
Which of the following is the standard acceleration due to gravity in the English unit?
a) 980.66 fps2
6.
d) 5
b) 32.2 fps2
What is the value of Lim
x 
a) 0
x2 1
x3 1
c) 9.8066 fps2
d) 32.2 ips2
?
b) 0.25
c) 1.25
d) indeterminate
7.
Two times the mother’s age is 8 more than six times her daughter’s age. Ten years ago, the sum of their ages was 44.
What is the daughter’s age?
a) 15 yrs old
b) 18 yrs old
c) 12 yrs old
d) 16 yrs old
8.
How many terms of the sequence – 9, - 6, - 3, … must be taken so that the sum is 66?
a) 11
b) 6
c) 4
9.
d) 9
A farmer is to plant rice in a rectangular field 30 meters by 40 meters. He started on the edge and plant around the perimeter. How
wide a strip should he plant for each side in order to do half the work?
a) 5 m
b) 2.5 m
c) 3 m
d) 5.5 m
10. There are 6 geometric means between 4 and 8748. Find the sum of all terms.
a) 12 310
b) 12 130
c) 13 210
d) 13 120
11. Compute the arithmetic Mean of the following set of numbers: 18, 24, 27, 30, 35, 42, 50.
a. 31.82
b. 32.29
c. 30
d. 29.96
12. Find the root mean square of 11, 23, and 35.
a. 25
b. 27
d. 24
c. 26
13. Water is pouring into a swimming pool. After t hours, there are t +
into the pool when t = 9 hours?
a) 0.0194
b) 1.167
c) 1.235
t
gallons in the pool. At what rate, in GPM is water pouring
d) 3.6
14. Determine the distance traveled by a particle between a time interval of 0.2 second to 0.3 second if its velocity is
V  12 t 4 
a) 3.75 cm
7
, where V is in cm/s and t is in seconds.
t
b) 2.84 cm
c) 2.75 cm
d) 3.84 cm
15. A pole cast a shadow 15-m long when the angle of elevation of the sun is 61°. If the pole has lean 15° from the vertical directly
toward the sun, what is the length of the pole?
1
a. 54.23 m
b. 48.64 m
c. 36.84 m
d. 64.84 m
16. The volume of the cube is increasing at a rate of 5 cu. m per minute. Determine the rate at which the surface area is increasing, in
m2/min, when its side is 10 m.
a) ½
b) 1.75
c) 1.5
d) 2
17. What is the supplement of an angle whose compliment is 62o?
a) 152o
b) 118o
c) 28o
d) 60o
18. A certain angle has a supplement five times its compliment. What is the angle?
a) 186o
b) 168.5o
c) 67.5o
d) 157.5o
19. Determine the accumulated value of P2,000.00 in 5 years it is invested at 11% compounded quarterly.
a) P3,440.00
b) P3,404.00
c) P3,044.00
d) P4,304.00
20. The sum of P15,000.00, deposited in an account earning 4% per annum compounded quarterly, will become P18,302.85.
Determine the effective rate of interest per year.
a) 3.06 %
b) 4.06 %
c) 5.06 %
d) 6.06 %
21. What is the effective rate equivalent of 12% compounded quarterly?
a) 12.55%
b) 11.55 %
c) 12.98 %
d) 13 %
22. Celestino owes P500, due in 3 years and P800 due in 7 years. He is allowed to settle these obligations by a single payment on the
6th year. Find how much he has to pay on the 6th year if money is worth 14% compounded semi-annually.
a) P1,449.12
b) P 1,559.12
c) P1,339.12
d) P1,669.12
23. Cleofas borrowed P2,000.00 from a bank and agreed to pay the loan at the end of one year. The bank discounted the loan and gave
him P1950 in cash. Determine the rate of discount.
a) 3.75 %
b) 3.12 %
c) 2.5 %
d) 1.2 %
24. From the top of tower A, the angle of elevation of the top of the tower B is 46o. From the foot of tower B the angle of elevation of
the top of tower A is 28o. Both towers are on a level ground. If the height of tower B is 120 m, how high is tower A?
a) 40.7 m
b) 44.1 m
c) 42.3 m
d) 38.6 m
 x
1
25. Determine the value of
a. 0
1
3

 x 5  sin x dx .
b.1.75
c. 3.1416
d. infinity
26. Think of a number. Double the number. Subtract 6 from the result and divide the answer by 2. The quotient will be 20. What is the
number you think?
a. 12
b. 20
c. 23
d. 32
27. Determine the absolute value of resultant vector of the following vectors: F1 = 4i + 7j + 6k; F2 = 9i + 2j + 11k, F3 = 5i – 3j – 8k.
a) 21
b) 18
c) 25
d) 9
28. Find the voltage drop to move 2 C of charge from point a to point b that requires – 30 Joules of energy.
a) – 15 V
b) + 15 V
c) – 5 V
d) + 5 V
29. If the z  1  1  1  ... , what is the value of z?
a) 0.453
b) 0.618
30. Solve for the value of x from the following equation:
a) 1.258925
b) 1.892525
c) 0.816
xx
x
..
x.
d) 0.681
 10 .
c) 1.85925
d) 1.528925
31. A 100-kg salt solution originally 4 % by weight salt in water is boiled to reduce water content until the concentration is 5 % by
weight salt. How much water is evaporated?
a) 20
b) 25
c) 15
d) 22.5
32. Determine the diameter of a circle, x 2  y 2  6 x  4 y  12  0 .
a) 9 units
b) 11 units
c) 12 units
33.
d) 10 units
1
What is the minimum point of y  x  ?
x
a) (1, 2)
b) (1.5, 2)
c) (1, 1.5)
2
d) (2, 1)
34. A man left Sta. Rosa City to drive to Lopez, Quezon at 6:15 pm and arrived at 11:45 pm. If he averaged 50 kph and stopped 1
hour for dinner, how far is Lopez, quezon from Sta. Rosa City?
a) 225 km
b) 522 km
c) 252 km
d) 215 km
35. If x varies directly as y and inversely as z, and x = 14 when y = 7 and z = 2, find the value of x when z = 4 and y = 16.
a) 12
b) 18
c) 14
d) 16
36. Determine the absolute value of the complex number 3 + 4i.
a) 4
b) 5
c) 8
d) 6
37. Simplify i1997 + i1999, where i is an imaginary number.
a) 0
b) i
c) 1 + i
d) 1 – i
38. If vector A is 10 units and vector B, which makes 600 with vector A, is 20 units. What is the difference of vectors A and B?
a) 15.34 units
b) 13.45 units
c) 18.76 units
d) 17.32 units
39. A ball is dropped from a height of 60 meters above ground. How long does it take to hit the ground?
a) 4.5 seconds
b) 3.5 seconds
c) 2.5 seconds
d) 1.5 seconds
40. A change in position, specified by a length and a direction is said to be:
a. Displacement
b. Acceleration
c. Velocity
d. Dynamic equilibrium
41. The process of one substance mixing with another because of molecular motion is known as:
a. Adhesion
b. Diffusion
c. Cohesion
d. Confusion
42. Those cost that arise at the result of a change in operations or policy or it is the ratio of a small increment cost and a small
increment of output.
a. Increment cost
b. Differential cost
c. Marginal cost
d. Promotion cost
43. The sum of all the costs incurred by the originators of the project up to the time that the promoters of the project accept the project
is known as:
a. Development cost
b. Marginal cost
c. Construction cost
d. Promotion cost
44. It is now between 3 and 4 o’clock and twenty minutes the minute hand will be as much as the hour-hand as it is now behind it.
What is the time now?
a) 3:06.36
b) 3:03.66
c) 3:36.06
d) 3:30.66
45. What is the acid test ratio?
a. The ratio of owner’s equity to total current liabilities
b. The ratio of all assets to actual current liabilities
c. The ratio of current assets (exclusive of inventory) to the total current liabilities.
d. The ratio of gross margin to operating, sates, and administrative expenses
46. How do call an energy required to move 1 Coulomb of charge through an element.
a) Current
b) Voltage
c) Power
d) Resonance
47. This is a number sequence where the succeeding term is obtained by adding the last pair of preceding terms such as the sequence
(1, 1, 2, ,3 5, 8 …). How do you call this number sequence?
a) Euler’s number
b) Fermat number c) Fibonacci number
d) Fourier series
48. If the roots of an equation are zero, then, how do you classify the solutions?
a. Extranous solutions
b. Trivial solutions
c. Conditional solutions
49. In electricity, how do you call the rate of charge flow?
a) Potential difference
b) Current
c) Voltage
d. Ambiguous solutions
d) Power
50. This law in electrical circuits states, “The algebraic sum of currents entering a node (or a closed boundary) is zero”. How do you
call this law?
a) Kirrchoff’s current law
b) Ohm’s current law
c) Kirchhoff’s voltage law
d) Ohm’s voltage law
51. This law in electrical circuits state, “The algebraic sum of all voltages around a closed path (or loop) is zero”. How do you call this
law?
a) Kirrchoff’s current law
b) Ohm’s current law
c) Kirchhoff’s voltage law
d) Ohm’s voltage law
52. In electrical, what is the SI unit of conductance?
3
a) Ohm
b) Mho
53. Which of the following is the equivalent of 1 Ampere?
a) 1 Coulomb per second
b) 1 Joule per Coulomb
c) Siemens
c) 1 Volt per Ampere
d) Ampere
d) 1 Ampere per Coulomb
54. This is the process of expressing a polynomial as the product of another polynomial or monomial of lower degree. What is this
mathematical process?
a) Decomposition
b) Rationalization
c) Factoring
d) Polynomial damping
55. This is a point where the concavity of a curve changes or when the slope of the curve is neither increasing nor decreasing. What is
this point commonly called?
a) Maximum point
b) Minimum point
c) Point of tangency
d. Point of inflection
56. How do you call the axis of the hyperbola that passes through the center, the foci and vertices?
a) Transverse axis
b) Conjugate Axis
c) Asymptotic axis
d) Major Axis
57. What is a number, which could not be expressed as a quotient of two integers?
a. Natural
b. Rational
c. Irrational
58. How do you call the opposite of the prefix nano?
a) Peta
b) Tera
c) Giga
d. Surd
d) Hexa
59. What do you call a triangle having three unequal sides?
a) Obtuse
b) Oblique
c) Scalene
d) Isosceles
60. How do you call the distance of a point from the y-axis?
a) Polar distance
b) Coordinate
c) Abscissa
d) Ordinate
61. This is the measure of central tendency defined as the most frequent score. How do you call this measure of central tendency?
a) Median
b) Mode
c) Mean
d) Deviation
62. Which of the following is the equivalent of 1 mil?
a) One-tenth of an inch b) One-thousandth of an inch
Answer: a) One-thousandth of an inch
c) One millionth of an inch
63. A polygon with ten sides is said to be:
a. Dodecagon
b. Decagon
c. Decahedron
64. Any number expressed in place-value notation with base 12 is known as:
a. Duodecimal
b. Deontic
c. Decile
c) One-half of an inch
d. Dodecahedron
d. Dedekind
65. Which of the following is true regarding the minimum attractive rate of return used in judging proposed investments?
a. It is much smaller than the interest rate used to discount expected cash flows from investments
b. It is frequently a policy decision made by an organization’s management
c. It is larger than the interest rate used to discount expected cash flow from investments
d. It is not relevant in engineering economy studies
66. Which of the following situations has a conventional cash flow so that an internal rate of return can be safely calculated and used?
a. Your company undertakes a mining project in which the land must be reclaimed at the end of the project.
b. You invest in a safe dividend stock and receive dividends each year.
c. You lease a car and pay by the month
d. Your company invests heavily in a new product that will generate profits for two years. To keep profits high for 10
years, the company plans to reinvest heavily after two years.
67. The economic order quantity (EOQ) is defined as the order quantity which minimizes the inventory cost per unit time. Which of
the flowing is not an assumption of the basic EOQ model with no shortages?
a) Reordering is done when the inventory is zero
b) There is an upper bound on the quantity ordered
c) The entire reorder quantity I delivered instantaneously
d) The demand rate is uniform and constant
68. Which of the following events will cause the optimal lot size, given by the classic EOQ model with no shortages, to increase?
a) A decrease in inventory carrying cost
b) A decrease in demand
c) An increase in demand
d) a) or c) above
69. What is a borrower of a particular loan almost always required to do during repayment?
a) Pay exactly the same amount of principal each payment
b) Repay the loan over an agreed-upon amount of time
c) Pay exactly the same amount of interest each payment
d) Pay the interest only whenever failure to pay the principal
70. How to you classify work-in-process?
4
a) A liability
b) An expense
c) A revenue
d) An asset
71. What is the indirect product cost (IPC) spending variance?
a. The IPC volume adjusted budget minus the total IPC absorbed
b. The IPC volume adjusted budget [fixed + volume (variable IPC rate)]
c. The difference between actual IPC and IPC volume adjusted budget
d. The difference between actual IPC and IPC absorbed
72. Which of the following does not affect owner’s equity?
a) Expense to get license of start business b) Investment capital
c) License to start business
paid
73. How do you call an increase in the value of a capital asset?
a) Profit
b) Capital gain
c) Capital expenditure
d) Capital stock
74. Another name for derivative is said to be:
a. Differential manifold
b. Partial derivative
c. Differential form
75. Another term for rhombus is said to be:
a. Dichotomy
b. Diamond
76. A polygon with twelve sides is known as:
a. Dodecagon
b. Decagon
Dividends
d. Differential coefficient
c. Cyclic quadrilateral
d. Bi-rectangular
c. Decahedron
d. Dodecahedron
77. A prefix denoting a multiple of ten times any of the physical units of the system international.
a. Deka
b. Nano
c. Hecto
d. Exa
78. The father of plane geometry.
a. Euclid
d. Galileo
b. Pythagoras
d)
c. Aristotle
79. This is the case of a solution of a plane triangle where the given data leads to two solutions. How do you call this case?
a) Ambiguous case
b) Quadratic case
c) Extraneous case d) Conditional case
80. It is a type of polygon in which each interior angle must be less than or equal to 180°, and all vertices 'point outwards' away from
the interior. How do you call this polygon?
a) Concave Polygon
b) Convex polygon
c) Regular polygon
d) Irregular polygon
81. It is a series of equal payments occurring at equal intervals of time where the first payment is made after several periods, after the
beginning of the payment. How do you call this payment?
a) Deferred annuity
b) Delayed annuity
c) Progressive annuity
d) Simple annuity
82. What do you think is the negotiation of wage rates, conditions of employment, etc. by representatives of the labor force and
management?
a) Union trade
b) Union rally
c) Collective bargaining
d) Cooperative
83. How do you call a type of bond where the corporation’s owner name is recorded and the interest is paid periodically to the owners
with their asking for it?
a) Registered bond
b) Preferred bond
c) Incorporator’s bond
d) Bail bond
84. How do you call the integral of any quotient whose numerator is the differential of the denominator?
a) Co-logarithm
b) Logarithm
c) Product
d) Derivative
Answer: b) Logarithm
85. What is a regular polygon that has 27 diagonals?
a) Nonagon
b) hexagon
c) Pentagon
d) Heptagon
Answer: a) Nonagon
86. How do you call the formula used to compute the value of n factorial, which is in symbolic form (n!), where n is large number?
a) Matheson formula
b) Diophantine formula
c) Richardson-Duchman formula
d) Stirling’s Approximation
87. What is the reason why an ivory soap floats in water?
a) All matter has mass
b) The specific gravity of ivory soap is greater than that of water
c) The density of ivory soap is unity
d) The specific gravity of ivory soap is less than that of water
88. When two planes intersect with each other, the amount of divergence between the two planes is expressed by measuring the:
a) Reflex angle
b) Dihedral angle
c) Polyhedral angle d) Plane angle
5
89. What do you think is the output or sales at which income is insufficient to equal operating cost?
a) Break even point
b) Depreciation
c) Investment
90. What is an estimate of assets’ net market value at the end of its estimated life?
a) Book value
b) Depreciation
c) Salvage value
d) Cash flow
d) Cash flow
91. What do you think is the lessening of the value of an asset due to a decrease in the quantity available as a coal, oil and timber in
forests?
a) Depletion
b) Amortization
c) Depreciation
d) Investment
92. What can you say about the present worth of all depreciation over the economic life of the item?
a) Maintenance
b) Capital recovery c) Depreciation recovery
d) Annuity
93. What do you think is the provision in the contract that indicates the possible adjustment of material cost and labor cost?
a) Secondary clause
b) Specification
c) Escalatory clause
d) General provision
94. This is the process of determining the value of certain property for specific reasons. Guess, what is this?
a) Amortization
b) Investment
c) Appraisal
d) Depreciation
95. How do you call those products or services that are directly used by people to satisfy their wants?
a) Consumer goods and services
b) Producer goods and services
c) Necessity products and services
d) Luxury products and services
96. These are used to produce consumer goods and services. Guess, what are these?
a) Consumer goods and services
b) Producer goods and services
c) Necessity products and services
d) Luxury products and services
97. What do you think are those products or services that are required to support human life and activities that will be purchased in
somewhat the same quantity even though the price varies considerably?
a) Consumer goods and services
b) Producer goods and services
c) Necessity products and services
d) Luxury products and services
98. How do you call a cylinder with elliptical cross section?
a. Ellipsoid
b. Cylindroid
c. Hyperboloid
d. Paraboloid
99. How do you call a market whereby there is only one buyer of an item for which there are no goods substitutes?
a) Monopoly
b) Monopsony
c) Oligopoly
d) Oligopsony
100. Which statement about a charge placed on a dielectric material is true?
a. The charge increases the conductivity of the material
b. The charge is confined to the region in which the charge was placed.
c. The charge is immediately lost to the atmosphere
d. The charge is instantly carried to the material’s surface
101. Which of the following is not a property of magnetic field lines?
a) Magnetic field lines have no beginnings and no ends
b) The lines cross themselves only at right angles
c) The line intersect surfaces of equal intensity at right angles d) The field is stronger where the lines are closer together
102. Tesla is a unit of which of the following?
a) Magnetic induction
b) Inductance
c) Capacitance
103. What is a pole pitch?
a) The angle at which the pole windings are wound
c) The space on the stator allocated to one pole
b) The space on the stator allocated to two poles
d) The mica used to insulate the poles from each other
104. How do you call a polygon with 10 000 sides?
a) Hectogon
b) Chilliagon
c) Myriagon
d) magnetic flux
d) Octacontagon
105. Any line segment joining a vertex of a triangle to a point on the opposite side is called as:
a) Newton line
b) Secant
c) Cevian
d) Euclidian line
106. It is any influence capable of producing a change in the motion of an object.
a) Force
b) Acceleration
c) Friction
d) Velocity
107. How do you call the amount needed at the beginning of operations and permits the enterprise to begin functioning before it
receives any income from the sales of its product or service.
6
a) Initial working capital
b) Regular working capital
c) Equity
d) Annuity
108. In the problem of writing the equation of a certain curve with respect to another axes in which the new axes are parallel to the
original axes and similarly directed is known as:
a) Translation of axes
b) Reversal of axes
c) Notation of axes
d) Relocation of axes
109. How do you call a ring shaped surface or solid obtained by rotating a circle about a coplanar line that does not intersect?
a) Torus
b) Annulus
c) Circoloid
d) Annular
110. If the eccentricity is less than one, then curve is known as:
a) Ellipse
b) Hyperbola
c) Parabola
d) Circle
111. Determine the outside diameter of a hollow steel tube that will carry a tensile load of 500 kN at a stress of 140 MPa. Assume the
wall thickness to be 0ne-tenth of the outside diameter.
a) 123 mm
b) 103 mm
c) 113 mm
d) 93 mm
112. What can you say to the following statement: “the volume of a circular cylinder is equal to the product of its base and altitude.”?
a) Postulate
b) Corollary
c) Theorem
d) Axiom
113. What is the study of the properties of figures of three dimensions?
a) Physics
b) Solid geometry
c) Plane geometry
d) Trigonometry
114. Points that lie in the same plane:
a) Coplanar
d) Parallel
b) Collinear
c) Oblique
115. When a line y = mx + b slopes downwards from left to right, the slope m is:
a) Less than zero b) Greater than zero
c) Equal to zero
d) Equal to 1
116. “Whenever a net force acts on a body, it produces acceleration in the direction of the resultant force, an acceleration which is
directly proportional to the resultant force and inversely proportional to the resultant force and inversely proportional to the mass
of the body”. How do you call this theory?
a) Newton’s First law of motion
b) Newton’s Second Law of motion
c) Farday’s law of forces
d) Hook’s law of equilibrium
117. It is defined that the momentum of a moving object is the product of its mass, m, and velocity, V. In Newton’s Law of Motion,
what is the rate of change of momentum with respect to time?
a) Power
b) Momentum
c) energy
d) Force
118. The loss of weight of a body submerged in a fluid is:
a) Proportional to the weight of the body
c) Equal to the weight of the fluid displaced
b) Proportional to the depth of submergence
d) Independent of the volume of the body
119. The amount of company’s profits that the board of directors of the corporation decides to distribute to ordinary shareholders.
a) Dividend
b) Return
c) Share of stock
d) Par value
120. Which of the following is not a theorem on limits?
a) The limit of the algebraic sum of several functions is equal to the sum of their limits
b) The limit of the product of several function is equal to the product of their limits
c) The limit of the difference of several functions is equal to the difference of their limits
d) The limit of the quotient of two functions is equal to the quotient of their limits, provided the denominator is not zero
121. When a homogeneous, flexible cord is held at the two ends and allowed to sag freely on its own weight, it will produce a curve
very similar to a parabola opening upwards. How do you call this curve?
a) Parabola
b) Catenary
c) Cycloid
d) Epicycloids
122. Which of the following Common wealth Acts is known as the oldest Mechanical Engineering law?
a) Commonwealth Act 394
b) Commonwealth Act 594
c) Commonwealth Act 294
d) Commonwealth Act 8394
123. What is a borrower of a particular loan almost always required to do during repayment?
a) Pay exactly the same amount of interest each payment.
b) Repay the loan over an agreed-upon amount of time
c) Pay exactly the same amount of principal each payment
d) The choices a and c above
124. To be a member of the Board of Mechanical Engineering, he/she must be at least how many years old?
7
a) 25 years
b) 30years
c) 35 years
d) 40yeras
125. How do you call the line passing through the focus and perpendicular to the directrix of a parabola?
a. Latus rectum
b. Axis of the parabola
c. Transverse axis
d. Major axis
126. What is the ratio of the distance between the foci to the distance between the vertices in either hyperbola or ellipse?
a. Eccentricity
b. Latus rectum
c. Variance
d. Deviation
127. It is a statement that one mathematical expression is greater than or less than another. How do you call this?
a) Conditional expression
b) Inequality
c) Interval
d) Domain
128. It is a method of depreciation where a fixed sum of money is regularly deposited at compound interest in a real or imaginary fund
in order to accumulate an amount equal to the total depreciation of an asset at the end of the assets estimated life. How do you call
this depreciation?
a) Straight line method
b) Declining balance method
c) SYD method
d) Sinking fund method
129. What is an artificial expense that spreads the purchase price of an asset or other property over a number of years?
a) Depreciation
b) Amnesty
c) Sinking fund
d) Bond
130. How do you classify this interest rate, which specifies the actual rate of interest on the principal for one year?
a) Nominal rate
b) Rate of return
c) Exact interest rate
d) Effective rate
131. What type of curve is generated by a point, which moves in uniform circular motion about an axis, while traveling with a constant
speed, V, parallel to the axis?
a) A cycloid
b) An epicycloids
c) A hypocycloid
d) A helix
132. What do you call the possible outcome of an experiment?
a) A sample space
b) A random point c) An event
d) A finite set
133. How do you call a sequence of numbers where the succeeding term is greater than the preceding term?
a) Dissonant series
b) Isometric series c) Convergent series
d) Divergent series
134. A branch of mathematics which uses the properties of numbers by using symbols or letters to represent numbers in arithmetic
operations which usually variables and unknown quantities which usually involves the use and rearranging or equations.
a. Trigonometry
b. Algebra
c. geometry
d. calculus
135. This is a series of sequential method for carrying out a desire procedure to solve problem.
a. Algorithm
b. hypsogram
c. logarithm
d. angstrom
136. This is use for expressing wavelengths of light or ultraviolet radiation with a unit or length equal to 10 – 10 metre.
a. Mersenne number
b. Midac
c. Light year
d. Angstrom
137. It refers to a straight line, which a curve approaches closely, but never meets or touches the curve.
a. Asymptote
b. Directrix
c. Latus rectum
d. Line segment
138. It is a collection of numbers or letters used to represent a number arranged properly in rows and columns.
a. Determinant
b. Matrix
c. Array
d. equation
139. It is a high – level programming language for the computer used to express mathematical and scientific problems in a manner that
resembles. English rather than computer notations.
a. Algol
b. Cobol
c. Pascal
d. Aldus
140. In any triangle, the length of a line which is equal to the square root of the sides adjacent to the point where this line started minus
the product of the segments of the third side is known as:
a. Angle bisector
b. Median
c. Perpendicular bisector
d. Trisector
141. The whole is greater than any one of its parts. This statement is known as:
a. Postulate
b. Axiom
c. Hypothesis
d. Theorem
142. A perpendicular segment from a vertex of the triangle to the line containing the opposite side is known as:
a. Median
b. altitude
c. Angular bisector d. Perpendicular bisector
143. An S.I. unit of area equal to 100 sq. m.
a. Arc
b. Acre
c. Hectares
8
d. Are
144. The angle that the line of sight to the object, makes with the horizontal, which is above the eye of the observer, is called as:
a. Angle of elevation
b. Angle of depression
c. Acute angle
d. Obtuse angle
145. In complex algebra, we use a diagram to represent a complex plane commonly called as:
a. Venn diagram
b. Histogram
c. Argand diagram
d. Funicular diagram
146. The area bounded by two concentric circles is called as:
a. Annulus
b. Ring
c. Disk
d. Sector
147. A series of numbers in which each number or term is derived from the preceding number by adding a constant value to it is
known as:
a. Geometric sequence b. Arithmetic sequence
c. Analytical sequence
d. Differential sequence
148. 10 to the negative power of 18 is the value of the prefix:
a. Atto
b. Femto
c. Micro
d. Pico
149. A series of equal payments occurring at equal periods of time.
a. Annuity
b. Sinking fund
c. Cash flow
d. annual cost
150. The ratio of annual sales to the average of assets used in producing these sales.
a. Inventory turnover
b. Asset turnover c. Operating – expense ratio d. Quick ratio
151. Quick ratio is defined as the ratio of quick assets to the current liabilities, sometimes this is called:
a. Acid test ratio
b. Debt ratio
c. Equity ratio
d. Current ratio
152. Form of business/company ownership:
a. Partnership
b. Corporation
c. Single proprietorship
d. All of the above
153. It is defined to be any method of repaying a debt, the principal and interest included usually by a series of equal payments at
periodic intervals of time.
a. Amortization
b. Annuity
c. Deferred annuity d. Preferred annuity
9
MATHEMATICS/ENGINEERING ECONOMY
MATHEMATICS/ENG ECO/BASIC ENG TRIVIA EXAMINATION
MULTIPLE CHOICE QUESTIONS
Select the best answer from each of the following questions. On the answer sheet provided, shade the box that corresponds to your choice.
Strictly no erasures allowed.
1.
What is the acid test ratio?
a) The ratio of owner’s equity to total current liabilities
b) The ratio of all assets to actual current liabilities
c) The ratio of current assets (exclusive of inventory) to the total current liabilities.
d) The ratio of gross margin to operating, sates, and administrative expenses
2.
How do call an energy required to move 1 Coulomb of charge through an element.
a) Current
b) Voltage
c) Power
d) Resonance
3.
This is a number sequence where the succeeding term is obtained by adding the last pair of preceding terms such as the sequence (1,
1, 2, ,3 5, 8 …). How do you call this number sequence?
a) Euler’s number
b) Fermat number
c) Fibonacci number
d) Fourier series
4.
Determine the absolute value of resultant vector of the following vectors: F1 = 4i + 7j + 6k; F2 = 9i + 2j + 11k, F3 = 5i – 3j – 8k.
a) 21
b) 18
c) 25
d) 9
5.
Determine the sum of the coefficient of the variables in the expression (2x + 3y –z)8.
a) 65 536
b) 56 563
c) 63 655
d) 66 535
If the roots of an equation are zero, then, how do you classify the solutions?
a. Extranous solutions
b. Trivial solutions
c. Conditional solutions
d. Ambiguous solutions
6.
7.
Find the voltage drop to move 2 C of charge from point a to point b that requires – 30 Joules of energy.
a) – 15 V
b) + 15 V
c) – 5 V
d) + 5 V
8.
This is the process of expressing a polynomial as the product of another polynomial or monomial of lower degree. What is this
mathematical process?
a) Decomposition
b) Rationalization
c) Factoring
d) Polynomial damping
9.
This is a point where the concavity of a curve changes or when the slope of the curve is neither increasing nor decreasing. What is this
point commonly called?
a) Maximum point
b) Minimum point
c) Point of tangency
d. Point of inflection
10. How do you call the axis of the hyperbola that passes through the center, the foci and vertices?
a) Transverse axis
b) Conjugate Axis
c) Asymptotic axis
d) Major Axis
11. How many permutations can be made out of the letters in the word DIEGO taken 3 at a time?
a) 50 ways
b) 60 ways
c) 120 ways
d) 80 ways
12. What is the temperature in degrees Celsius of a molecule at absolute zero?
a) 0 oC
b) – 273 oC
c) – 32 oC
d) 273 oC
13. If at an angle measures x degrees, what is the measure in radians?
a)

x
180
b)
180
x

c)
14. In electricity, how do you call the rate of charge flow?
a) Potential difference
b) Current
180
x
c) Voltage
15. What is a number, which could not be expressed as a quotient of two integers?
a. Natural
b. Rational
c. Irrational
d)
180
x
d) Power
d. Surd
16. This law states, “The voltage, v, across a resistor is directly proportional to the current, i, flowing through the resistor”. How do you call
this law?
a) Kirchhoff’s Law
b) Ohm’s Law
c) Ampere’s Law
d) Gauss’ Law
17. How do you call an angle that is greater then 180 degree but less than 360 degrees?
a) Complex
b) Reflex
c) Obtuse
d) Exterior
18. This law in electrical circuits states, “The algebraic sum of currents entering a node (or a closed boundary) is zero”. How do you call
this law?
a) Kirrchoff’s current law
b) Ohm’s current law
c) Kirchhoff’s voltage law
d) Ohm’s voltage law
19. How do you call the opposite of the prefix nano?
a) Peta
b) Tera
c) Giga
d) Hexa
20. What do you call a triangle having three unequal sides?
a) Obtuse
b) Oblique
c) Scalene
d) Isosceles
c) 0.816
d) 0.681
21. If the z
 1  1  1  ...
a) 0.453
, what is the value of z?
b) 0.618
1
MATHEMATICS/ENGINEERING ECONOMY
22. Solve for the value of x from the following equation:
a) 1.258925
b) 1.892525
x
xx
..
x.
 10 .
c) 1.85925
d) 1.528925
23. This law in electrical circuits state, “The algebraic sum of all voltages around a closed path (or loop) is zero”. How do you call this law?
a) Kirrchoff’s current law
b) Ohm’s current law
c) Kirchhoff’s voltage law
d) Ohm’s voltage law
24. How do you call the distance of a point from the y-axis?
a) Polar distance
b) Coordinate
c) Abscissa
d) Ordinate
25. In electricity, it is an ability of an element to resist the flow of current. What is this?
a) Resonance
b) Conductance
c) Inductance
d) Resistance
26. In electrical circuits, how do you call the reciprocal of resistance?
a) Resonance
b) Conductance
c) Inductance
d) Resistance
27. In electrical, what is the SI unit of conductance?
a) Ohm
b) Mho
c) Siemens
d) Ampere
28. If 4y = 3x, then, what is the value of
a)
4
3
b)
3x
2
4y 2
?
3
4
c)
29. Which of the following is the equivalent of 1 Ampere?
a) 1 Coulomb per second
b) 1 Joule per Coulomb
2
3
c) 1 Volt per Ampere
d)
3
2
d) 1 Ampere per Coulomb
30. This is the measure of central tendency defined as the most frequent score. How do you call this measure of central tendency?
a) Median
b) Mode
c) Mean
d) Deviation
31. Which of the following is the equivalent of 1 mil?
a) One-tenth of an inch b) One-thousandth of an inch
c) One millionth of an inch
c) One-half of an inch
32. This is the case of a solution of a plane triangle where the given data leads to two solutions. How do you call this case?
a) Ambiguous case
b) Quadratic case
c) Extraneous case
d) Conditional case
33. What is the value of k to make the expression kx2 – 3kx + 9 a perfect square?
a) 2
b) 4
c) 3
d) 5
34. It is a type of polygon in which each interior angle must be less than or equal to 180°, and all vertices 'point outwards' away from the
interior. How do you call this polygon?
a) Concave Polygon
b) Convex polygon
c) Regular polygon
d) Irregular polygon
35. Two times the mother’s age is 8 more than six times her daughter’s age. Ten years ago, the sum of their ages was 44. What is the
daughter’s age?
a) 15 yrs old
b) 18 yrs old
c) 12 yrs old
d) 16 yrs old
36. How do you call a line segment from the center of a regular polygon to the midpoint of a side? It is also called as inradius, the radius of
an incircle.
a) Radius
b) Apothem
c) Circumradius
d) Inradius
37. If the daily wage of CPM and a Plumber are in the ratio 2:1. In a day, a CPM has to work 8 hrs but the Plumber only 6 hrs. Determine
the ratio of their hour wages.
a. 4:3
b. 5:3
c. 3:2
d. 8:3
38. Which of the following is the equivalent of one circular mil?
a)

0.012
4
b)

0.0012
4
c)

0.00012
4
d)

0.000012
4
39. How do you call a method of describing a set where the elements are separated by commas and enclosed by braces?
a) Tabular or roster form
b) Equal form
c) Rule form
d) Equivalent form
40. Which of the following is the equivalent of the expression 2Logb 6 – Logb 4?
a) 2Logb 3
b. 3Logb 2
c. 2Logb 2
d. 3Logb 3
41. It is a series of equal payments occurring at equal intervals of time where the first payment is made after several periods, after the
beginning of the payment. How do you call this payment?
a) Deferred annuity
b) Delayed annuity
c) Progressive annuity
d) Simple annuity
42. A 100-kg salt solution originally 4 % by weight salt in water is boiled to reduce water content until the concentration is 5 % by weight
salt. How much water is evaporated?
a) 20
b) 25
c) 15
d) 22.5
43. Tukmol can paint a fence of 50 % faster than Kikoy and 20 % faster than Tiburcio and together they can paint a given fence in 4 hours.
How long will it take Tukmol to paint the same fence if he had to work alone?
a) 11
b) 8
c) 9
d) 10
44. It is now between 3 and 4 o’clock and twenty minutes the minute hand will be as much as the hour-hand as it is now behind it. What is
the time now?
2
MATHEMATICS/ENGINEERING ECONOMY
a) 3:06.36
b) 3:03.66
c) 3:36.06
d) 3:30.66
45. This is the amount of a property in which a willing buyer will pay to a willing seller for the property when neither one is under the
compulsion to buy or sell. What do you call this value?
a) Fair value
b) Goodwill value
c) Book value
d) Market value
46. Determine the diameter of a circle, x  y
a) 9 units
b) 11 units
2
47.
2
 6x  4 y  12  0 .
c) 12 units
d) 10 units
c) (1, 1.5)
d) (2, 1)
1
What is the minimum point of y  x  ?
x
a) (1, 2)
b) (1.5, 2)
48. The volume of the cube is increasing at a rate of 5 cu. m per minute. Determine the rate at which the surface area is increasing, in
m2/min, when its side is 10 m.
a) ½
b) 1.75
c) 1.5
d) 2
49. What is the simple interest rate if an investment of P37,500.00 accumulates to P45,937.5 in 18 months?
a) 0.15
b) 0.2
c) 0.21
d) 0.3
50. What do you think is the negotiation of wage rates, conditions of employment, etc. by representatives of the labor force and
management?
a) Union trade
b) Union rally
c) Collective bargaining
d) Cooperative
51. What is the value of Lim
x 
a) 0
x 2 1
x3 1
?
b) 0.25
c) 1.25
d) indeterminate
52. What is the present value of P5,000.00 due in 8 years if money is worth 12% compounded semi-annually?
a) P1,896.23
b) P1,869.23
c) P1,698.23
d) P1,968.23
53. This is a type of bond whose guaranty is in lieu on railroad equipment. What is this type of bond?
a) Equipment
b) Debenture bond
c) Registered bond
d) Infrastructure bond
54. How do you call a type of bond where the corporation’s owner name is recorded and the interest is paid periodically to the owners with
their asking for it?
a) Registered bond
b) Preferred bond
c) Incorporator’s bond
d) Bail bond
55. A man left Sta. Rosa City to drive to Lopez, Quezon at 6:15 pm and arrived at 11:45 pm. If he averaged 50 kph and stopped 1 hour for
dinner, how far is Lopez, quezon from Sta. Rosa City?
a) 225 km
b) 522 km
c) 252 km
d) 215 km
56. If x varies directly as y and inversely as z, and x = 14 when y = 7 and z = 2, find the value of x when z = 4 and y = 16.
a) 12
b) 18
c) 14
d) 16
57. How many terms of the sequence – 9, - 6, - 3, … must be taken so that the sum is 66?
a) 11
b) 6
c) 4
d) 9
58. There are 6 geometric means between 4 and 8748. Find the sum of all terms.
a) 12 310
b) 12 130
c) 13 210
d) 13 120
59. How many permutation can be made out of the letters of the word ENGINEERING?
a) 277 200
b) 272 700
c) 200 277
d) 227 700
60. A bag contains 3 white and 5 red balls. If two balls are drawn at random, find the probability that both are white.
a) 0.375
b) 0.10714
c) 0.46667
d) 0.28571
61. Determine the absolute value of the complex number 3 + 4i.
a) 4
b) 5
c) 8
d) 6
62. Simplify i1997 + i1999, where i is an imaginary number.
a) 0
b) i
c) 1 + i
d) 1 – i
63. The sum of the two interior angles of the triangle is equal to the third angle and the difference of the two angles is equal to 2/3 of the
3rd angle. Find the 3rd angle.
a) 60o
b) 30o
c) 90o
d) 40o
64. If vector A is 10 units and vector B, which makes 600 with vector A, is 20 units. What is the difference of vectors A and B?
a) 15.34 units
b) 13.45 units
c) 18.76 units
d) 17.32 units
65. How do you call the integral of any quotient whose numerator is the differential of the denominator?
a) Co-logarithm
b) Logarithm
c) Product
d) Derivative
66. What is a regular polygon that has 27 diagonals?
a) Nonagon
b) hexagon
d) Heptagon
c) Pentagon
67. How do you call the formula used to compute the value of n factorial, which is in symbolic form (n!), where n is large number?
a) Matheson formula
b) Diophantine formula
c) Richardson-Duchman formula
d) Stirling’s Approximation
68. What is the reason why an ivory soap floats in water?
3
MATHEMATICS/ENGINEERING ECONOMY
a) All matter has mass
c) The density of ivory soap is unity
b) The specific gravity of ivory soap is greater than that of water
d) The specific gravity of ivory soap is less than that of water
69. When two planes intersect with each other, the amount of divergence between the two planes is expressed by measuring the:
a) Reflex angle
b) Dihedral angle
c) Polyhedral angle
d) Plane angle
70. What do you think is the output or sales at which income is insufficient to equal operating cost?
a) Break even point
b) Depreciation
c) Investment
d) Cash flow
71. What is an estimate of assets’ net market value at the end of its estimated life?
a) Book value
b) Depreciation
c) Salvage value
d) Cash flow
72. What do you think is the lessening of the value of an asset due to a decrease in the quantity available as a coal, oil and timber in
forests?
a) Depletion
b) Amortization
c) Depreciation
d) Investment
73. What can you say about the present worth of all depreciation over the economic life of the item?
a) Maintenance
b) Capital recovery
c) Depreciation recovery
d) Annuity
74. What do you think is the provision in the contract that indicates the possible adjustment of material cost and labor cost?
a) Secondary clause
b) Specification
c) Escalatory clause
d) General provision
75. This is the process of determining the value of certain property for specific reasons. Guess, what is this?
a) Amortization
b) Investment
c) Appraisal
d) Depreciation
76. How do you call those products or services that are directly used by people to satisfy their wants?
a) Consumer goods and services
b) Producer goods and services
c) Necessity products and services
d) Luxury products and services
77. These are used to produce consumer goods and services. Guess, what are these?
a) Consumer goods and services
b) Producer goods and services
c) Necessity products and services
d) Luxury products and services
78. What do you think are those products or services that are required to support human life and activities that will be purchased in
somewhat the same quantity even though the price varies considerably?
a) Consumer goods and services
b) Producer goods and services
c) Necessity products and services
d) Luxury products and services
79. How do you call a cylinder with elliptical cross section?
a. Ellipsoid
b. Cylindroid
c. Hyperboloid
d. Paraboloid
80. How do you call a market whereby there is only one buyer of an item for which there are no goods substitutes?
a) Monopoly
b) Monopsony
c) Oligopoly
d) Oligopsony
81. When a line y = mx + b slopes downwards from left to right, the slope m is:
a) Less than zero
b) Greater than zero
c) Equal to zero
d) Equal to 1
82. “Whenever a net force acts on a body, it produces acceleration in the direction of the resultant force, an acceleration which is directly
proportional to the resultant force and inversely proportional to the resultant force and inversely proportional to the mass of the body”.
How do you call this theory?
a) Newton’s First law of motion
b) Newton’s Second Law of motion
c) Farday’s law of forces
d) Hook’s law of equilibrium
83. It is defined that the momentum of a moving object is the product of its mass, m, and velocity, V. In Newton’s Law of Motion, what is
the rate of change of momentum with respect to time?
a) Power
b) Momentum
c) energy
d) Force
84. The loss of weight of a body submerged in a fluid is:
a) Proportional to the weight of the body
c) Equal to the weight of the fluid displaced
b) Proportional to the depth of submergence
d) Independent of the volume of the body
85. The amount of company’s profits that the board of directors of the corporation decides to distribute to ordinary shareholders.
a) Dividend
b) Return
c) Share of stock
d) Par value
86. Which of the following is not a theorem on limits?
a) The limit of the algebraic sum of several functions is equal to the sum of their limits
b) The limit of the product of several function is equal to the product of their limits
c) The limit of the difference of several functions is equal to the difference of their limits
d) The limit of the quotient of two functions is equal to the quotient of their limits, provided the denominator is not zero
87. When a homogeneous, flexible cord is held at the two ends and allowed to sag freely on its own weight, it will produce a curve very
similar to a parabola opening upwards. How do you call this curve?
a) Parabola
b) Catenary
c) Cycloid
d) Epicycloids
88. Which of the following Common wealth Acts is known as the oldest Mechanical Engineering law?
a) Commonwealth Act 394
b) Commonwealth Act 594
c) Commonwealth Act 294
d) Commonwealth Act 8394
89. What is a borrower of a particular loan almost always required to do during repayment?
a) Pay exactly the same amount of interest each payment.
b) Repay the loan over an agreed-upon amount of time
c) Pay exactly the same amount of principal each payment
d) The choices a and c above
4
MATHEMATICS/ENGINEERING ECONOMY
90. To be a member of the Board of Mechanical Engineering, he/she must be at least how many years old?
a) 25 years
b) 30years
c) 35 years
d) 40yeras
91. How do you call the line passing through the focus and perpendicular to the directrix of a parabola?
a. Latus rectum
b. Axis of the parabola
c. Transverse axis
d. Major axis
92. What is the ratio of the distance between the foci to the distance between the vertices in either hyperbola or ellipse?
a. Eccentricity
b. Latus rectum
c. Variance
d. Deviation
93. It is a statement that one mathematical expression is greater than or less than another. How do you call this?
a) Conditional expression
b) Inequality
c) Interval
d) Domain
94. It is a method of depreciation where a fixed sum of money is regularly deposited at compound interest in a real or imaginary fund in
order to accumulate an amount equal to the total depreciation of an asset at the end of the assets estimated life. How do you call this
depreciation?
a) Straight line method
b) Declining balance method
c) SYD method
d) Sinking fund method
95. What is an artificial expense that spreads the purchase price of an asset or other property over a number of years?
a) Depreciation
b) Amnesty
c) Sinking fund
d) Bond
96. How do you classify this interest rate, which specifies the actual rate of interest on the principal for one year?
a) Nominal rate
b) Rate of return
c) Exact interest rate
d) Effective rate
97. What type of curve is generated by a point, which moves in uniform circular motion about an axis, while traveling with a constant
speed, V, parallel to the axis?
a) A cycloid
b) An epicycloids
c) A hypocycloid
d) A helix
98. What do you call the possible outcome of an experiment?
a) A sample space
b) A random point
c) An event
d) A finite set
99. How do you call a sequence of numbers where the succeeding term is greater than the preceding term?
a) Dissonant series
b) Isometric series
c) Convergent series
d) Divergent series
100. A branch of mathematics which uses the properties of numbers by using symbols or letters to represent numbers in arithmetic
operations which usually variables and unknown quantities which usually involves the use and rearranging or equations.
a. Trigonometry
b. Algebra
c. geometry
d. calculus
THE FOLLOWING ITEMS ARE FOR YOUR READING AND FAMILIARIZATION
101. This is a series of sequential method for carrying out a desire procedure to solve problem.
a. Algorithm
b. hypsogram
c. logarithm
d. angstrom
102. This is use for expressing wavelengths of light or ultraviolet radiation with a unit or length equal to 10 – 10 metre.
a. Mersenne number
b. Midac
c. Light year
d. Angstrom
103. It refers to a straight line, which a curve approaches closely, but never meets or touches the curve.
a. Asymptote
b. Directrix
c. Latus rectum
d. Line segment
104. It is a collection of numbers or letters used to represent a number arranged properly in rows and columns.
a. Determinant
b. Matrix
c. Array
d. equation
105. It is a high – level programming language for the computer used to express mathematical and scientific problems in a manner that
resembles. English rather than computer notations.
a. Algol
b. Cobol
c. Pascal
d. Aldus
106. In any triangle, the length of a line which is equal to the square root of the sides adjacent to the point where this line started minus the
product of the segments of the third side is known as:
a. Angle bisector
b. Median
c. Perpendicular bisector
d. Trisector
107. The whole is greater than any one of its parts. This statement is known as:
a. Postulate
b. Axiom
c. Hypothesis
d. Theorem
108. A perpendicular segment from a vertex of the triangle to the line containing the opposite side is known as:
a. Median
b. altitude
c. Angular bisector
d. Perpendicular bisector
109. An S.I. unit of area equal to 100 sq. m.
a. Arc
b. Acre
c. Hectares
d. Are
110. The angle that the line of sight to the object, makes with the horizontal, which is above the eye of the observer, is called as:
a. Angle of elevation
b. Angle of depression
c. Acute angle
d. Obtuse angle
111. In complex algebra, we use a diagram to represent a complex plane commonly called as:
a. Venn diagram
b. Histogram
c. Argand diagram
d. Funicular diagram
112. The area bounded by two concentric circles is called as:
a. Annulus
b. Ring
d. Sector
c. Disk
113. A series of numbers in which each number or term is derived from the preceding number by adding a constant value to it is known as:
a. Geometric sequence
b. Arithmetic sequence
c. Analytical sequence
d. Differential sequence
114. 10 to the negative power of 18 is the value of the prefix:
5
MATHEMATICS/ENGINEERING ECONOMY
a. Atto
b. Femto
115. A series of equal payments occurring at equal periods of time.
a. Annuity
b. Sinking fund
c. Micro
d. Pico
c. Cash flow
d. annual cost
116. The ratio of annual sales to the average of assets used in producing these sales.
a. Inventory turnover
b. Asset turnover
c. Operating – expense ratio
d. Quick ratio
117. Quick ratio is defined as the ratio of quick assets to the current liabilities, sometimes this is called:
a. Acid test ratio
b. Debt ratio
c. Equity ratio
d. Current ratio
118. Form of business/company ownership:
a. Partnership
b. Corporation
d. All of the above
c. Single proprietorship
119. It is defined to be any method of repaying a debt, the principal and interest included usually by a series of equal payments at periodic
intervals of time.
a. Amortization
b. Annuity
c. Deferred annuity
d. Preferred annuity
120. Grand total of the assets operational capability of a corporation.
a. Authorized capital
b. investment
c. Earning value
d. Money market
121. The process of recording all the transactions of the company, which affect any investment of capital so that at any time the results of
investment, may be known as:
a. Bookkeeping
b. Balancing accounts
c. Profit & loss statement
d. Accounting
122. A system of units based on time, length and mass is called:
a. Absolute system
b. Gravitational system
c. cgs system
d. mks system
123. A US unit capacity used to measure solids equal to 7056 cubic inches (0.1156 m 3)
a. Furlong
b. Barrel
c. Bushel
d. Bar
124. It refers to a statistical distribution having two distinct peaks of frequency distribution.
a. Bimodal
b. Binomial
c. Biaxial
d. Bilingual
125. The straight line or plane that divides a line, a plane, or an angle into two equal parts.
a. Divisor
b. Trisector
c. Eliminator
d. Bisector
126. A law, which states that the curvature of the central fiber is proportional to the bending moment in homogenous bar.
a. Euclid
b. Thailus
c. Bernoulli – Euler
d. Torrecilli
127. A mathematical method that combines two numbers, quantities, etc., to give a third quantity. An example is the multiplication of two
numbers in arithmetic.
a. Binary Operation
b. Polynomial
c. Trinomial
d. sequence
128. An algebraic expression having two variables in it. For example, 3x+y is called
a. Binary
b. Binomial
c. Polynomial
d. Trinomial
129. An algebra of sets that has two binary operations called addition and multiplication which may be used to represent binary logic is
called:
a. Boolean Algebra
b. Elementary Algenra
c. Matric
d. Laplace
130. A logarithm having a base 10 is called:
a. Natural logarithm
b. Briggsian logarithm
c. Complex ogarithm
d. Naperian logarithm
131. Any two points along a streamline in an ideal fluid in steady flow, the sum of the pressure, the potential energy per unit volume and the
kinetic energy per unit volume has the same value. This concept is known as the:
a. Pascal’s Theorem
c. Fluid Theory
c. Hydraulic Theorem
d. Bernoulli’s Energy Theorem
132. If the temperature of a confined gas does not change, the product of the pressure and volume is constant. This is known as:
a. Boyles Law
b. Pascal’s Law
c. Archimedes principle
d. Torrecillis’s Principle
133. The quantity of heat required to raise the temperature of one pound mass of water through one degree Fahrenheit is know as:
a. Calorie
b. specific heat
c. British thermal unit
d. Energy
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