Ang Ibon
July 21, 2022 | Author: Anonymous | Category: N/A
Short Description
Download Ang Ibon...
Description
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 gravi gravity ty 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 radians 57.3 deg rees
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 Solution:
g
0.003 slugs / ft 3 32,2 fps2 14.59 kg / slug 1 ft / 0.3048
2
15.2 N / m3
5. If the specific weight of a liquid is 58.5 lb f per 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
g
936.8 kg / m3
v
1
1. 0675 cm3 / g
6. 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: PA or B PA PB PA and and B
13 52
12 52
3
22
52
52
42.131%
7. A perfect gas gas is expanded polytropically wi with th an initial v volume olume and temperature temperature of 0.06 m3 and 147 0C respectively. 3 0 If the final volume and temperature are 0.21 m and 21 C respectively, what is the index of the expansion? a) 1.285 b) 1.212 c) 1.333 d) 1.400 Solution: T1 T2
1 }n 1 {V
V2
solving for n, n
1.285
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? c) P10,000.00 a) P8,500.00 b) P9,500.00 d) P10,500.00 Solution: P
F
1 i
n
12,100.00
1.1681.25
P10,000.00 P9,965.10
9. 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 P1 n m
mn
0.11 2,000.00 1 4
45
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 Determine the effective rate of interest per year. a) 3.06 % b) 4.06 % c) 5.06 % d) 6.06 %
Solution:
ie
i n m 0.04 4 1 1100 % 1 1100 % 4 .06 % 4 m
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. c) P193,912.00 a) P199,312.00 b) P183,912.00 d) P139,912.00 Solution:: Solution
Cash Value = Down payment + Present value of the balance Cash Value
P80,000.00
F i n
1 m
mn
P80,000.00
150,000.00 4 2 1 0.14 4
,912.00 P193
12. Find the number of years when P2,500.00 is compounded to P5,800.00 if invested at 12% compounded quarterly. b) 7.12 years a) P6.12 years c) 8.12 years d) 5.12 years
Solution:
i n 1 m
n
mn
F
P
ln F P
i ln 1 n m
m
mn ln 1
ln 5,800.00 2,500.00
0.12 ln 1 4
4
i n
F ln m P
7.12 years
13. What is the effective rate equivalent of 12% compounded quarterly quarterly?? a) 12.55% b) 11.55 % c) 12.98 %
Solution:
ie
d) 13 %
i n m 0.12 4 1 1100 % 1 1100 % 12 .55 % 4 m
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:
ie
i n 4 0.14 2 1 1100 % 1 1100 % 2 4 in
4
i n 1 1.1449 4
1 41 .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 o n the 6th year. Find how much he has to pay on the 6 th 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:
F6th
0.14 500 1 2
23
800
1 0.14 2
21
.75 P1,449.12 750.37 698
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 discoun d iscount. t. a) 3.75 % b) 3.12 % c) 2.5 % d) 1.2 % Solution:
.00 1,950.00 F P 100 % 2,000 100 % 2 .5 % 2,000.00 F
d
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? d) P254,775.19 a) P144,775.19 b) P245,775.19 c) P542,775.91
Solution:
Cash Price = Down Payment + Present Worth of Annuity
Cash Pr ice
Cash Pr ice
i n mn A 1 1 m Down Payment mn i i 1 n m 0.12 125 1 5,000.001 12 P30,000.00 P254,775.19 1295 0.12 0.121 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. b) P476.17 a) P746.71 c) P674.71 d) P700.00
Solution:
i n 0.12 25,000.00 F m 4 A P476.17 mn 4 8 0.12 i n 1 1 1 4 m
19. What is the value of 1 radian in degrees? a) 89.55o b) 57.3o
c) 60.3o 3
d) 45.58o
180o radians 57.3 deg rees
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 Solution:
d) 76.3 N/m3
g 0.003 slugs / ft 3 32,2 fps2 14.59 kg / slug 1 ft / 0.30482 15.2 N / m3
22. If the specific weight of a liquid is 58.5 lb f per 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
g
936.8 kg / m3
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
cos 282 353.18 ft lb 480 J Solution: W F dx F cos x 200 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
23
6.02 x 10
1.66 x 1024 g / atom
25. A truck starts from rest and moves with a constant acceleration of 6 m/s2. Find the speed of the truck after 4 seconds. c) 24 m/s a) 18 m/s b) 28 m/s d) 35 m/s Solution: For uniformly accelerated motion, V
Vo at 0 642 24 m / s
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
at 2
1 ft 0 3102 150 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
4
d) 1.5 seconds
1 2
2 S Vo t
t
Solution: S Vot g t 2
g
260 0 9.81
3.5 sec onds
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 much should the lladder adder be extended sso o that the top would llean ean against the wall wall 1 meter higher? 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 32 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 c) 131.81 m d) 140.12
y vi t
2
gt 2
7.56
2
9 .816
131.58m
2
Therefore the stone is dropped at a height 131.58m 131 .58m above the ground.
30. The salary of an employee’s job has five levels, each one o ne 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? 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
S5
1.051.05S3 1.05 2 S3 1.052 1.05S2 1.053S 2
S4
1.05 S3
S5
1.05S4
.00 S2 Due to circumstance, circumstance, S5 3,000 S5
1.053 S5 3,000.00 S5
3
30001.05
P 22,032.50
1.053 1
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
No. of Sides
180 5 5 2 180 108 o
o
o
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 t he container and the adjacent marbles. marbles. All of the marbles are the same size. What is the volume of water in the container? b) 62 454.54 mm3 a) 131 096.51 mm3 c) 68 641.97 mm3 d) 131 960.51 mm3 Solution: Since marbles are tightly packed, r marble marble = 12.7 mm Volume of container, Vcontainer 50.83 131096 .5 mm3
5
4 3
4 3
Volume of eight marbles, Vmarbles 8 r 3 8 12.73 68 641 .97 mm3
Volume of water, Vwater Vcontainer Vmarbles 131096 .5 68641.97 62 454.54 mm3 7 6 ? 33. What is the determinant of the 2 x 2 matrix, 5 9 b) 33 a) a) – – 33 33
Solution:: The determinant, D Solution
7
6
5
9
c) – c) – 43
d) 43
79 56 33
1 2 1 34. What is the determinant of the 3 x 3 matrix, 2 1 1 ? 1 1 1 a) 6
b) 7 1
2
Solution: D 2 1 1
1
c) – c) – 6 6
d) d) – – 7 7
1 1
1 11 211 1 12 1 1 1 221 111 7
1
35. What is the inverse of the 2 x 2 matrix, A cos sin ? sin cos
cos sin
a)
cos sin
cos sin c) sin cos
cos sin sin cos
b)
a c
Solution: For 2 x 2 matrix, X
b
, the inverse, X-1, is: d
Where, D = determinant of X. For matrix A, D
X 1
1 d
c D
0 cos sin d) 0 sin 2
b a
cos
sin cos2 sin sin cos2 sin 2 1 sin cos
cos sin Then, A 1 sin cos 36. The equation y = a1 + a2x is an algebraic expression for which of o f the following choices? a) A cosine expansion expansio n 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 + a 2 x describes a straight line.
37. Determine the absolute value of resultant vector of the t he following vectors: F1 = 4i + 7j + 6k; F2 = 9i + 2j + 11k, F 3 = 5i – 3j – 3j – 8k. 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. Solution R 4 9 5i 7 2 3 j 6 11 8k 18i 6 j 9k
R
182 62 92 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 6
d) 5i + 2k
i
j
k
Solution: Solving first for A x B, let D = A x B, A x B 3 2 0 i2 0 j3 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 DzCz 25 30 52 20 39. Determine the rationalized value of the complex number a) 1.12 – 1.12 – 0.66i 0.66i
6 2.5i
.
3 4i
b) 0.32 0.32 – – 0.66i
c) – c) – 32 + 0.66i
d) d) – – 1.12 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 3 4i
6 2.5i 3 4i 28 16.5i 1.12 0.66i 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) 494
b) 0
d) 35
Solution:: The der Solution derivative ivative of a constant is zero. 41. Determine the slope of the curve y x 2 at the point (2, 3). b) – b) – 4 4 a) 4 c) 2 Solution: The slope of a curve is given by the first derivative. y'
d) d) – – 2 2 dy dx
2x
d x2 dx
At point (2, 3): y' x y' 2 22 4
42. What is the sum of the roots of the equation: 2x 2 + 5x + 5 = 0? a) – 2.5 2.5 b) 2.5 c) 2.25 Solution: The sum of the roots is: r sum x1 x 2
b
d) d) – – 2.25 2.25
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 V
7
12 t 4 , where V is in cm/s and t is in seconds.
t
b) 2.84 cm
a) 3.75 cm Solution:
dS dt
V 12t 4
S
t 5
12
5 2
7 t
d) 3.84 cm
7 12t 4 dt t 0.2
dS
c) 2.75 cm
0.3
t 12 0.3 t15 7 ln 2 0 .35 0.25 7 ln 2.84 cm 0.2 t1 5
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
cos 282 353.18 ft lb 480 J Solution: W F dx F cos x 200 7
d) 804 J
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
23
6.02 x 10
1.66 x 1024 g / atom
46. A truck starts from rest and moves with a constant acceleration of 6 m/s2. Find the speed of the truck after 4 seconds. c) 24 m/s a) 18 m/s b) 28 m/s d) 35 m/s Solution: For uniformly accelerated motion, V
Vo at 0 642 24 m / s
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
at 2
1 ft 0 3 102 150 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? gro und? 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
260 0 9.81
3.5 sec onds
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 much should the lladder adder be extended extended so that the top w would ould lean aagainst gainst 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 32 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 2
2
7.56
9 .816 2
131.58m
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 o ne 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? 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. Solution
8
S3
1.05S2
S5
1.051.05S3 1.05 2 S3 1.052 1.05S2 1.053S 2
S4
1.05 S3
S5
1.05S4
.00 S2 Due to circumstance, circumstance, S5 3,000 S5
1.053 S5 3,000.00 S5
3
30001.05
P 22,032.50
1.053 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
180 5 5 2 180 108 o
o
No. of Sides
7 6 ? 53. What is the determinant of the 2 x 2 matrix, 5 9 b) 33 a) a) – – 33 33
Solution:: The determinant, D Solution
7
6
5
9
2
54. What is the determinant of the 3 x 3 matrix, 2 1
1
c) – c) – 43
2
Solution: D 2 1 1
1
d) 43
1
1 1 ? 1
b) 7 1
79 56 33
1
a) 6
o
c) – c) – 6 6
d) d) – – 7 7
1 1
1 11 211 1 12 1 1 1 221 111 7
1
cos sin ? 55. What is the inverse of the 2 x 2 matrix, A sin cos
cos sin
a)
cos sin
cos sin c) sin cos
cos sin sin cos
b)
a c
Solution: For 2 x 2 matrix, X
b
, the inverse, X-1, is: d
Where, D = determinant of X. For matrix A, D
X 1
1 d
c D
0 cos sin d) 0 sin 2
b a
cos
sin cos2 sin sin cos2 sin 2 1 sin cos
cos sin Then, A 1 sin cos 56. The equation y = a1 + a2x is an algebraic expression for which of o f the following choices? d) A straight line a) A cosine expansion expansio n series b) A circle in polar form c) Projectile motion Answer: d) A straight line.
y = mx + b is the slope-intercept form of the equation of a straight line. Thus, y = a 1 + a 2 x describes a straight line.
57. Determine the absolute value of resultant vector of the t he following vectors: F1 = 4i + 7j + 6k; F2 = 9i + 2j + 11k, F 3 = 5i – 3j – 3j – 8k. 8k. a) 21 b) 18 c) 25 d) 9 9
Solution:: The resultant o Solution off vectors given in unit-vector form is the sum of the components. R 4 9 5i 7 2 3 j 6 11 8k 18i 6 j 9k
R
182 62 92 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 i
j
d) 5i + 2k
k
Solution: Solving first for A x B, let D = A x B, A x B 3 2 0 i2 0 j3 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 DzCz 25 30 52 20 59. Determine the rationalized value of the complex number a) 1.12 – 1.12 – 0.66i 0.66i
6 2.5i 3 4i
b) 0.32 0.32 – – 0.66i
.
c) – c) – 32 + 0.66i
d) d) – – 1.12 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 3 4i
6 2.5i 3 4i 28 16.5i 1.12 0.66i 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) 494
b) 0
d) 35
Solution:: The der Solution derivative ivative of a constant is zero. 61. Determine the slope of the curve y x 2 at the point (2, 3). a) 4
b) – b) – 4 4
c) 2
Solution: The slope of a curve is given by the first derivative. y'
d) d) – – 2 2 dy dx
2x
d x2 dx
At point (2, 3): y' x y' 2 22 4 62. What is the sum of the roots of the equation: 2x 2 + 5x + 5 = 0? a) – 2.5 2.5 b) 2.5 c) 2.25 Solution: The sum of the roots is: r sum x1 x 2
b a
d) d) – – 2.25 2.25
5
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 V
7
12 t 4 , where V is in cm/s and t is in seconds.
t
b) 2.84 cm
a) 3.75 cm Solution:
dS dt
V 12t 4
S
t 5
12
5 2
7 t
7 12t 4 dt t 0.2
dS
c) 2.75 cm
0.3
t 12 0.3 t15 7 ln 2 0 .35 0.25 7 ln 2.84 cm 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
7
32.29
65. Find the root mean square of 11, 23, and 35. a. 25 b. 27 Root Mean Square (RMS),RM RMS S
c. 26
(x
2
)' s
112
23 2 35 2
25 n 3 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
d. 24
x 5 3y 5
y = age of the son
x 10 2y 10
x 5 3y 15
x 10 2y 20
x 3y 10
3y 10 2y 10
y 20
x
x 2y 10
320 20 40
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 28 o. 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 In triangle DCE,
DE Sin46 28
44o
CD Sin 44o
o sin 44o 120 sin 44 86.72 m sin 74o sin 74o
CD DE
h CDsin 28o
C
86.72 si sin n 28o 40.71 m
h
68. Determine the value of a. 0
x 1
3
x 1
3
Tower B
46 28o
Tower A
x 5 sin x dx .
D
b.1.75 1
Solution:
1
o
sin x dx x 5 sin
c. 3.1416 x 4 4
1
1
x6 6
d. infini infinity ty
1 1
cos x 1 0 1
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. d. 25.6 m a. 20.8 m b. 12.8 m c. 13.8 m Solution:
S 2c 2 a 2 b 2
2 2 2 .61 m 10 8 25
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? c. 23 a. 12 b. 20 d. 32 Solution:
Le: x - be the number 2 x 6 2
20
2x-6 = 40;
x = 23
71. Determine the absolute value of resultant vector of the t he following vectors: F1 = 4i + 7j + 6k; F2 = 9i + 2j + 11k, F 3 = 5i – 3j – 3j – 8k. 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. Solution R 4 9 5i 7 2 3 j 6 11 8k 18i 6 j 9k
R
182 62 92 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:: Solution 11 0.6
Converting the interest into effective monthly interest, one peso-one year analysis, analysis, 1 year
1
11 i 12 months
i 1 .0612 N
A
N = mn = 12(10) 12(10) = 120
i 1 i P N
1 i 1
1 0.00486
120
0.004861.00486
x2
x
y 2 6x 4y 12 0
x 32 y 22 25
2
120
1.00486
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:
or 0.486 486 %
50,000.00 1
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? d) P1,968.23 a) P1,896.23 b) P1,869.23 c) P1,698.23 Solution:
F
P
i n 1 m
mn
5,000.00
0.12 1 2
28
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! p!q!...
11! 3!3! 2! 2!
277 200
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
b) 13.45 units
Solution:
c a 2 b 2
by cosine law,
c) 18.76 units
d) 17.32 units
2ab cos 17.32 units
77. From a deck of ordinary cards, what is the probability of drawing a heart or face card? b) 42.31% a) 48.08% c) 5.77% d) 33.33%
PA or B PA PB PA an and d B
13 52
12
3
22
52
52
52
42.131%
78. A perfect gas gas is expanded polytropically wi with th an initial v volume olume and temperature 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 T2
V
{ 1 }n 1 V2
solving for n, n
1.285
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? c) P10,000.00 a) P8,500.00 b) P9,500.00 d) P10,500.00 P
Solution:
F n
1 i
12,100.00
P9,965. 10 P10,000.00
1.1681.25
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
i F P1 n m
Solution:
mn
0.11 2,000.001 4
45
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 Determine the effective rate of interest per year. a) 3.06 % b) 4.06 % c) 5.06 % d) 6.06 %
Solution:
ie
i n m 0.04 4 1 1100 % 1 1100 % 4 .06 % 4 m
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:: Solution
Cash Value = Down payment + Present value of the balance Cash Value
P80,000.00
F
i n 1 m
mn
P80,000.00
150,000.00 4 2 1 0.14 4
,912.00 P193
83. Find the number of years when P2,500.00 is compounded to P5,800.00 if invested at 12% compounded quarterly. b) 7.12 years a) P6.12 years c) 8.12 years d) 5.12 years Solution: 1
i n mn
m
F P
mn ln 1
i n
F ln m P
13
5,800.00 F ln 2,500.00 P 7.12 years n m 4 i n 0.12 ln 1 ln 1 4 m ln
84. What is the effective rate equivalent of 12% compounded quarterly? a) 12.55% b) 11.55 % c) 12.98 %
Solution:
ie
d) 13 %
i m 0.12 4 1 n 1100 % 1 1 100 % 12 .55 % 4 m
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:
ie
i n 4 0.14 2 1 1100 % 1 1100 % 2 4 in
4
i n 1 1.1449 4
1 41 .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 o n the 6th year. Find how much he has to pay on the 6 th 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:
F6th
0.14 500 1 2
23
800
0.14 1 2
21
.75 P1,449.12 750.37 698
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 discoun d iscount. t. c) 2.5 % a) 3.75 % b) 3.12 % d) 1.2 %
Solution:
2,000.00 1,950.00 F P d F 100 % 2,000.00 100 % 2 .5 %
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 pr ice 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
Cash Pr ice
Cash Pr ice
i n mn A 1 1 m Down Payment mn i n i 1 m 0.12 125 5,000.001 1 12 P254,775.19 P30,000.00 1295 0.12 0.121 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. b) P476.17 a) P746.71 c) P674.71 d) P700.00
Solution:
i n 0.12 F 25,000.00 m 4 A P476.17 mn 4 8 1 0.12 i n 1 1 4 m
90. What is the acid test ratio? a. The ratio of owner’s equity to total current liabilities liabilities b. The ratio of all assets to actual current liabilities liabilities c. The ratio of current assets (exclusive of inventory) to the total current liabilities. d. The ratio of gross margin to operating, o perating, sates, and administrative administrative expenses 91. How do call an energy required to move 1 Coulomb of charge through an element. b) Voltage a) Current c) Power d) Resonance dw Answer: b) Voltage V where q = charge in C w = energy in Joules 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? c) Fibonacci number a) Euler’s number b) Fermat number d) Fourier series 93. If the roots of an equation are zero, then, how do you classify the solutions? b. Trivial solutions a. Extranous solutions c. Conditional Conditional solutions
d. Ambi Ambiguous guous solutions
94. In electricity, electricity, how do you call the rate of charge flow? b) Current a) Potential difference 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 law c) Kirchhoff’s voltage law law d) Ohm’s voltage law 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 law b) Ohm’s current law law c) Kirchhoff’s voltage law d) Ohm’s voltage law law 97. In electrical, what is the SI unit of o f conductance? c) Siemens a) Ohm b) Mho 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 Ampere/Vo lt 1 Volt = 1 Joule/Coul Joule/Coulomb omb 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? c) Factoring a) Decomposition Decomposition b) Rationali Rationalization zation d) Polyn Polynomial omial damping 100. This 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? d. Point of inflection a) Maximum point b) Minimum point c) Point of tangency 101. How How do you call the axis of the hyperbola that passes through the center, the foci and vertices? a) Transverse axis b) Conjugate Conjugat e Axis c) Asymptotic axis d) Major Axis 102. What is a number, which could not be expressed as a quotient of two integers? c. Irrational a. Natural b. Rational 103. How How do you call the opposite of the prefix nano? a) Peta b) Tera c) Giga 15
d. Surd d) Hexa
104. What What do you call a triangle having three unequal sides? a) Obtuse b) Oblique c) Scalene 105. How How do you call the distance of a point from the y-axis? c) Abscissa a) Polar distance b) Coordinate
d) Isosceles d) Ordinate
106. This This is the measure of central tendency defined as the most frequent score. How do you call this measure of central tendency? b) Mode a) Median c) Mean d) Deviation Deviation 107. Which 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
d. Dodecahedron
110. Another name for derivative is said to be: a. Differential Differentia l manifold b. Partial derivat ive 111. Another Another term for rhombus is said to be: a. Dichotomy b. Diamond
d. Differential coefficient
c. Differential Differentia l form c. Cyclic quadrilateral
d. Dedekin Dedekind d
d. Bi-rectangular 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 The father of plane geometry. a. Euclid b. Pythagoras c. Aristotle Aristotle d. Galile Galileo o 114. This 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 Conditional case 115. It 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? b) Convex polygon a) Concave Polygon c) Regular polygon d) Irregul Irregular ar polygon 116. It It is a series of equal payments occurring at equal intervals of time where the first payment is made after several periods, after after the beginning beginning of the paymen payment. t. How do you call call this paym payment? ent? a) Deferred annuity b) Delayed annuity c) Progressive Progressive annuity d) Simple annuity 117. W What hat 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 bond d) Bail bond 119. How How do you call the integral of any quotient whose numerator is the d differen ifferential tial of the denominator? deno minator? b) Logarithm a) Co-logarithm c) Product d) Derivativ Derivativee 120. What What is a regular polygon that has 27 diagonals? a) Nonagon b) hexagon c) Pentagon d) Heptagon 121. How 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? Approximation a) Matheson formula formula b) Diophantine formula c) Richardson-Duchman Richardson-Duchman formula d) Stirling’s Approximation 122. W What hat is the reason why an ivory soap floats in water? a) All matter has mass b) The specific specific gravity of iv ivory ory soap is greater than that of w water ater c) The density of ivory soap is unity d) The specific gravity of ivory soap is i s less than that of water 16
123. W When hen two planes intersect with each other, the amount of divergence between the two planes is expressed by measuring the: b) Dihedral angle a) Reflex angle c) Polyhedral Polyhedral angle d) Plane angle 124. What What do you think is the output or sales at which income is insufficient to equal operating cost? a) Break even point b) Depreciation Depreciat ion c) Investment d) Cash flow 125. W What hat is an estimate of assets’ net market value at the end of its estimated life? life? a) Book value b) Depreciati Depreciation on c) Salvage value d) Cash flow 126. W What hat 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 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) Annui Annuity ty 128. What 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) Specificati Specification on c) Escalatory clause d) General provision 129. This This is the process of determining the value of o f certain property for specific reasons. Guess, what is this? a) Amortization Amortization b) Investment c) Appraisal d) Depreciati Depreciation on 130. How How do you call those products pro ducts or services that are directly used by people to satisfy satisfy their wants? a) Consumer goods and services b) Producer goods and services c) Necessity Necessity products and services d) Luxury products and services 131. These These are used to produce consumer goods and services. Guess, what are these? a) Consumer Consumer goods and services b) Producer goods and services c) Necessity Necessity products and services d) Luxury products and services 132. W What hat do you think are those products or services that are required to support human life and activities that will be purchased in somewhat somewhat the sam samee quantity even though the price varies varies considerably? considerably? a) Consumer Consumer goods and services b) Producer goods and services c) Necessity products and services d) Luxury products and services 133. How How do you call a cylinder with elliptical cross section? a. Ellipsoid b. Cylindroid c. Hyperboloi Hyperboloid d d. Parabol Paraboloid oid 134. How How do you call a market whereby there is only one buyer of an item for which there are no goods substitutes? b) Monopsony a) Monopoly c) Oligopoly d) Oligopsony 135. Which 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 carrie d to the t he material’s surface surface
In a dielectric, all charges are attached to specific atoms or molecules.
136. W Which hich 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 Tesla is a unit of which of the following? a) Magnetic induction b) Inductance
c) Capacitance Capacitance
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
d) magneti magneticc flux
b) The space on the stator all allocated ocated to two poles d) The mica used to insula insulate te 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 o ne pole.
139. How How do you call a polygon with 10 000 sides? c) Myriagon a) Hectogon b) Chilliagon d) Octacontagon 140. A Any ny line segment joining a vertex of a triangle to a point on the opposite side is called as: c) Cevian a) Newton line b) Secant d) Euclidian line 141. It It is any influence capable of producing a change in the motion of an object. a) Force b) Acceleration c) Frictionand permits the d) Velocity Velocityto begin functioning 142. How H ow do you call the amount needed at the beginning of operations enterprise before it receives receives any income income from the sales sales of its produc productt or service. a) Initial working capital b) Regular working capital c) Equity d) Annui Annuity ty
143. In 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 ax axes es and simil similarly arly directed is known as: a) Translation of axes b) Reversal of axes c) Notati Notation on of axes d) Relocati Relocation on of axes 144. How 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 Circoloid d) Annular 145. IIff the eccentricity is less than one, then curve is known as: a) Ellipse b) Hyperbola Hyperbo la c) Parabola d) Circle 146. Determine Determine the outside diameter of a hollow steel tube that will carry a tensile load of 500 kN at a stress of o f 140 MPa. Assume the wall thickness to be 0ne-tenth of o f the outside diameter. c) 113 mm a) 123 mm b) 103 mm d) 93 mm 147. What What can you say to the foll following owing statement: “the volume of a circular cylinder is equal to the product of its base and altitude.”? altitude.”? c) Theorem a) Postulate b) Corollary d) Axi Axiom om 148. W What hat is the study of the properties of figures of three dimensions? b) Solid geometry a) Physics c) Plane geometry d) Trigon Trigonometry ometry 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 co oled at constant temperature to produce saturation. a. Absolute temperature b. 273 K c. Dew point d. Critical 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 Kilogram force d. Dyne 154. A change in position, specified by a length and a direction is said to be: a. Displacement b. Accelerati Acceleration on c. Velocity Velocity d. Dynami Dynamicc equilibrium 155. The process of one substance mixing with another because of molecular motion is known as: a. Adhesion Adhesion b. Diffusion c. Cohesion d. Confusi Confusion on 156. Those 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. Prom Promotion otion cost 157. The index that gives the rate earned per share based on current price per share is called as: a. Price-earning 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 Tetrahedron
159. Two Two angles whose sum is 360 o is called: a. Explementary angles b. Complimen Complimentary tary angles c. Supplemen Supplementary tary angles d. Elementary Elementary angles 160. What 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 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 c) Evaluating over different time periods
b) Differences in the magnitudes of the projects 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 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 Which of the following is true regarding the minimum attractive 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 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 t he 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 t hat 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. T The he 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 h
, where a = the constant depletion rate (items per unit time); K = the fixed cost per
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 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 d) a) or c) above c) An increase in demand
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 co st (Pesos per item per unit time). Thus, a decrease in inventory carryi carrying ng cost, h, or an increase in demand, a, will cause the optimal lot size to increase. 19
167. What What is a borrower of a particular loan almost always required to do during repayment? a) Pay exactly the same amount of o f principal each payment b) Repay the loan over an agreed-upon amount of time c) Pay exactly the same amount of o f interest each payment d) Pay the interest only whenever failure to pay the principal 168. How How to you classify work-in-process? d) An asset a) A liability b) An expense c) A revenue
Work-in-process is included in the working fund investments. The working fund investments is an asset not subjected to depreciation. depreciation.
169. What What is the indirect product cost (IPC) spending 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) Viscosi Viscosity ty of the fluid 171. Which Which of the following elements and compounds is unstable in its pure form? c) Sodium a) Hydrochloric Hydrochloric acid b) Carbon dioxide 172. What 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. R Reactions eactions generally proceed faster at higher temperatures because because of which of the following? a) The molecules are less energet ic b) The activat activation ion energy is less d) Both b) & c) above c) The molecules collide more frequently 175. Which Which one of the following statem statements ents 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. W Which hich 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 magni magnitude tude of electrical charge of the protons
The outermost electrons are responsible for determining most mo st of the material’s properties. properties.
177. What 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 How do you call the strong stro ng bond between hydrogen atoms? b) The covalent bond a) Ionic and metallic bonds 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. W Which hich 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 e lastoplastic material material..
181. In 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 Which of the following is false? a. The acceleration of a body rotating with wi th 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 ha ve a linear acceleration.
183. Which Which statement about a charge placed on a dielectric material material is true? a. The charge increases the conductivity of the material
b. chargeisisimmediately confined to lost the to region in which the charge was placed. c. The The charge 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. W Which hich 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 Tesla is a unit of which of the following? a) Magnetic induction b) Inductance
c) Capacitance Capacitance
d) magneti magneticc flux
186. What What is a pole pitch? a) The angle at which the pole windings are wound b) The space space on the stator all allocated ocated 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 o ne pole.
187. How How do you call a polygon with 10 000 sides? c) Myriagon a) Hectogon b) Chilliagon d) Octacontagon 188. A Any ny line segment joining a vertex of a triangle to a point on the opposite side is called as: c) Cevian a) Newton line b) Secant 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 Velocity
190. H How ow do you call the amount needed at the beginning of operations and permits the enterprise to begin functioning before it receives receives any income income from the sales sales of its product or service. a) Initial working capital b) Regular working capital c) Equity d) Annui Annuity ty 191. In 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 ax axes es and simil similarly arly directed is known as: a) Translation of axes b) Reversal of axes c) Notati Notation on of axes d) Relocation of axes
192. intersect? How do you call a ring shaped surface or solid obtained by rotating a circle about a coplanar line that does not a) Torus
b) Annulus
c) Circoloid Circoloid
d) Annular Annular
193. IIff the eccentricity is less than one, then curve is known as: a) Ellipse b) Hyperbola Hyperbo la c) Parabola
d) Circle
194. W What hat can you say to the following statement: “the volume of a circular cylinder i s equal to the product of its base and altitude.”? altitude.”? c) Theorem a) Postulate b) Corollary d) Axi Axiom om 195. W What hat is the study of the properties of figures of three dimensions? b) Solid geometry a) Physics c) Plane geometry d) Trigon Trigonometry ometry 196. Points Points that lie in the same plane: a) Coplanar b) Collinear
c) Oblique
d) Parallel 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. c) Circle a) Arc b) Radius 199. What What do you call the replacement of the original cost of an investment? a) Pay off b) Return on investment investment c) Breakeven
d) Chord
d) Capital recovery
200. T This his 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 Conditional case 201. What What do you think t hink is the provision in the contract that indicates the possible adjustm adjustment ent of material cost and labor cost? a) Secondary clause b) Specificati Specification on c) Escalatory clause d) General provision 202. This This is the process of determining the value of o f certain property for specific reasons. Guess, what is this? a) Amortization Amortization b) Investment c) Appraisal d) Depreciati Depreciation on "
203. IIff f (x1 )
0 , then the point point
a) Minimum point
(x1, y1) is called;
b) Maximum point
c) Inflection point
d) Critical point
Solution: if the second derivative of the ffunction unction is zero then this is the iinflection nflection point. 204. Adding 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 Dehydration d) Saturation Saturation 205. T The he 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
206. The The actual interest earned by a given principal is known as: a) Compound interest b) Simple interest c) Effective interest 22
d) Salvage life 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 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 dw
V
Answer: b) Voltage
dq
where q = charge in C
d) Resonance w = energy in Joules
2. This is a number sequence where the succeeding term is obtained by adding the last pair o off preceding terms such as the sequence (1, 1, 2, ,3 5, 8 …). How do you call this number sequence? 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) z)8. a) 65 536 b) 56 563 c) 63 655 d) 66 535
8
Solution: sum 21 31 1
563 3 56 56
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 Ambiguous
Answer: b) Trivial Solutions 5. Find the voltage drop to move 2 C of charge from point a to point b that requires – requires – 30 30 Joules of energy. a) – a) – 15 15 V b) + 15 V c) c) – – 5 V d) + 5 V Solution:
v
w 30 J 15 V 2C q
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) Rationalizati Rationalization on 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 c) 120 ways d) 80 ways b) 60 ways
Solution: Pn, r P5,3 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) b) – – 273 273 oC c) c) – – 32 32 oC d) 273 oC
1
Answer: b) – b) – 273 273 oC 11. If at an angle measures x degrees, what is the measure in radians? a)
180 180
x
Solution: a)
b)
x 180 o
180
x
c)
180 x
d)
180
x
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? law? a) Kirchhoff’s Law Law b) Ohm’s Law c) Ampere’s Law d) Gauss’ Law Law Answer: b) Ohm’s Law 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”. zero”. How do you call this law? law? b) Ohm’s current law law a) Kirrchoff’s current law c) Kirchhoff’s voltage law law d) Ohm’s voltage law law Answer: a) Kirchhof’s current law 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 (10 9).
18. What do you call a triangle having three unequal sides? a) Obtuse b) Oblique c) Scalene
d) Isosceles
Answer: c) Scalene
19. what An area of 25.6 on the map represents a lot having an area of 640 m2. If the scale on the map is 1:x, is the valuecm2 of x? a) 50 b) 100 d) 900 c) 500
Solution:
20. If the z
2
1 25.6 2 Actual Area x 640100 Map Ma p Area
x = 500
1 1 1 ... , what is the value of z?
a) 0.453
b) 0.618
c) 0.816
d) 0.681
Solution: Squaring both sides of the equation
z 1 1 1 ...
2
2
z 1 1 1 1 ....
2
2
1 1 1 ....
but
z
2
z
1 z
z2
z 1 0
1 12 41 1 0.618 z 1.619 21 21. Solve for the value of x from the following equation: x b) 1.892525 c) 1.85925 a) 1.258925
Solution:
ln x x
xx
. ..
ln 10 x x
xx
x
xx
. ..
10 .
. ..
ln x ln 10
but x x
d) 1.528925 xx
. ..
10 1
10 ln x ln 10
ln
x 10
ln 10
x 10
10
x
10 10
1.258925
22. This law in electrical circuits state, “The algebraic sum of all voltages around a closed path (or loop) is zero”. How do you yo u call this law? a) Kirrchoff’s current law law b) Ohm’s current law law d) Ohm’s voltage law law c) Kirchhoff’s voltage law Answer: Kirchhoff’s voltage law 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 re ciprocal of resistance? a) Resonance c) Inductance b) Conductance
d) Resistance
Answer: b) Conductance 26. In electrical, what is the SI unit of conductance? a) Ohm b) Mho Answer: c) Siemens
c) Siemens
d) Ampere
1 Mho = 1 Siemens 2
27. If 4y = 3x, then, what is the value of 3x 2 ?
4y
a)
4 3
Solution:
b)
x y
4 3
3 4
c)
x 4 y 3
2
x2 y
2
16 9
2 3
d)
Then,
3 2
3x 2
3 16 4 4 9 3 4y 2
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 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 x 4 + ax3 + 5x2 + bx + 6 is divided by (x – (x – 2), 2), the remainder is 16. When it is divided by (x + 1) the remainder is 10. Determine the value of the constant 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 23 522 b2 6 16
f 1 1
4
8a 2 b 26
4a b 13
a 13 5 12 b 1 6 10 a b 2
a b 2
b 2 a
Substituting 2 to 1, 4a 2 a 13 3a 15 a
15 3
5
31. What is the logarithm of a negative number? a) Complex number
the , b 2 5 7 the
b) Real number
Eq. 2
Eq. 1
c) Irrational 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
2
log x log x i
2
log x log i
log x 2 log i
i 2
Considering the exponential form of an imaginary number, i e log x log x 2 log e 2 i
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 3kx + 9 a perfect square? a) 2 c) 3 d) 5 b) 4 Solution: The expression Ax 2 + Bx + C is a perfect square if B 2 = 4AC. From the given expression: A = k Then, 3k 2 4k 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? age? b) 18 yrs old c) 12 yrs old d) 16 yrs old a) 15 yrs old Solution: Let x = daughter’s age age
y = mother’s age age
Present Ages: 2y 6x 8
y 3x 4
eq. 1
Ten years ago: x 10 y 10 44 x y 64
eq. 2
Substituting 1 to 2, x 3x 4 64
4 x 60
x
60 4
15
37. How do you call a line l ine 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, da y, 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
Solution: Let
x = hourly wage of CPM
x x y
d. 8:3
c. 3:2
8 y 8
8
6
x 8 x 6 6 y y 8
y = hourly rate of the Plumber
2 1
;
x y
6 2 6 3 8 1 4 2
Then, the ratio is 3:2 39. Which of the following is the equivalent of one circular cir cular mil? a)
0.012
4
Answer: b)
b)
4
0.0012
c)
4
0.00012
4
d)
0.000012
4
2
0.001
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 2Log b 6 – 6 – Log Log b 4? a) 2Logb 3 b. 3Log b 2 c. 2Log b 2 d. 3Log b 3 Solution: 2 log b 6 log b 4 log b 36 log b 4
36 log log b 9 2 log 3 4
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? b) Delayed annuity a) Deferred 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? b) 25 c) 15 d) 22.5 a) 20
100 - x
x
100 kg
Solution:
4 % salt 96 % H2O
-
5 % salt 95 % H2O
=
100 % H2O
In Salt: 4 % 100 100 0 5 % 10 100 0 x
40 400 0 500 500 5x
then , x
20
kg
In Water (Checking): 96 % 10 100 0 100 100 % x 95 % 100 100 x
1920 20x 1900 19x 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 x
1
1
y
z
4 4 4 1
1
1
1
1
y
z
4
x
Eq. 1
With Tukmol being 50 % than Kikay,
1 2 1 0.50 x y y 3y 1
1
y
2
3x
Eq. 2
With Tukmol being 20 % faster than Veronica, 1 x
1 6 1 0.20 z z 5x
1 x
5 6x
Eq. 3
Substituting 1/y in Eq. 2 and 1/z in Eq. 3 to Eq. 1, 1 x
2 3x
5 6x
1 4
5 2x
1
x 10 hours
4
45. It is now between 3 and 4 o’clock and twenty minutes the minute hand will be as much as the hour -hand hour -hand as it is now behind it. What is the time now? b) 3:03.66 c) 3:36.06 a) 3:06.36
d) 3:30.66
x
Solution: 12
1 2
3
x/12
20/12
4
20
5
6
6
At present (now), the minute hand is behind the hour hand by ,
15
x 12
x 15
11 12
x
After 20 minute, the minute hand is ahead the hour hand by ,
x 20 15
x 12
11
20 / 12
12
x
10 3
As the given condition, = , 11 12
x
10 3
15
11 12
then , x 6.36 min utes
x
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 y a) 9 units b) 11 units 2
Solution:
x2
2
6x 4 y 12 0 . c) 12 units
d) 10 units
y 2 6x 4 y 12 0
62x 9 y22 4 y 4 12 13 25 x 3 y 2 25 Then, r = 5 units and d = 10 units
x
2
48. What is the minimum point of y x a) (1, 2)
Solution:
1 x
?
b) (1.5, 2)
y x Then,
1 x
dy dx
1
c) (1, 1.5)
1 x2
d) (2, 1)
0
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 m 2/min, when its side is 10 m.
surface area is increasing, in m /min, when its side is 10 m. a) ½ b) 1.75 Solution:
V = x3
dV dt dA dt
c) 1.5
d) 2
A = 6 x2
3x 2
dx
dt dx 12x dt
dx
1 dV
3x 2 dt dV 4 dV 12x 2 3x dt x dt dt 1
4 10
5 2 m 2 / mi min n
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:
FP 1 i n 7
F 1 45,937 F P .5 37,500.00 P 100 % i 100 % 15 % 100 % nP 1 . 5 37 , 500 . 00 n 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 d) c) Collective bargaining 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
FP 1 i n
Solution:
F 1 45,937 .5 37,500.00 F P P 100 % i 100 % 15 % 100 % nP 1.5 37,500.00 n 53. What is the value of Li Lim m x
b) 0.25
a) 0
Solution:
1 ? x3 1
x2
Lim Lim x
x2 x
3
c) 1.25
x 1 x 1x 1 1 Lim m Lim m 2 Lim m Li Li Li 2 1 x x 1x x 1 x x x 1 x 1
Li Lim m x
x
1 x 1
1
1
1
d) indeterminate
1 x
2
x 1 x 1
0
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 i n
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 int erest is paid periodically to to the owners with their their asking for it? a) Registered bond b) Preferred bond c) Incorporator’s bond 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 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. respectively. The number is: 100x + 10y + z The reversed number is: 100z +10y + x 8
2y = x + z 100x 10y z xyz
56
12 xyz
Eq. 1
10x 10y z 12 56 xyz
100x 10y z 12 56x 56y 56z 44x 99y 55z 12
Eq. 2
100z 10y x 100 x 10y z 594
99z 99 x 594 x 6 z
Eq. 3
Substituting x in Eq. 3 to Eq 1, 2 y x z z 6 2z
y 3 z
Substituting x in Eq. 3 to Eq. 2, 446 z 46 3 z 55 z 12
Eq. 4
Then,
z=2
x=8
y=5
The number is 852 Note: This problem can can be solved by inspection. 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 6:15 pm to to 11:45 11:45 pm, = 5.5 hours Time of travel = 5.5 – 5.5 – 1 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 14 4 7 y
y x k z
k x
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 sstock? tock? a) 15 % b) 20 % d) 12 % c) 16 % 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 – 20(x – 0.40x) 0.40x) = 12x Total sales = 104x + 12x = 116x 9
Profit = total sales – sales – capital capital = 116x – 116x – 100x 100x = 16x % Gain
16x % 100 % 16 100x
61. How many terms of the sequence – sequence – 9, 9, - 6, - 3, … must be taken so that the sum is 66? 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 – 6 – ( (- 9) = 3 n S 2 2a 1 n 1d 132 132
n 66 2 2 9 n 1 3
18 n 3n 2 3n
3n 2
21n 13 132 2 0
132 132
18n 3n
3n
3n
0
21n 13 132 2
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 81 8748 r 7
1
7 8748 Common ratio, r 3 4
Sum, S
1 4 38 1 13120 r 1 3 1
a 1 r n
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! p! q!...
11! 3!3! 2! 2!
277 200
Where, n = 11 objects with 3E’s, 3N’s, 2G’s, and 2I’s 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
3
8 7
28
Probability, both white
7
0.10714
65. Determine the absolute value of the complex number 3 + 4i. a) 4 b) 5 c) 8 Solution: r
2
d) 6
3 2 42 5
66. Simplify i1997 + i1999, where I is an imaginary number. b) i c) 1 + i a) 0
d) 1 – II
i i i i
1997 i 1999 i 1996 i i 1998 i i 2 Solution: i
998
2 999
998
i 999 i i 0
10
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 3 rd angle. Find the 3rd angle. d) 40o a) 60o b) 30o c) 90o
Solution: Let x = 1st angle
y = 2nd angle
x y z 180
z = 3rd angle x y z
Eq. 1
z z 3
xy
Eq. 2
Eq. 3
Substituting Substituti ng Eq. 2 to Eq. 1, z = 90 o 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 c) Product d) Derivative b) Logarithm Answer: b) Logarithm 70. If a = b, then b = a. This illustrates of which of the following 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 2 7 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 Diophantine formula c) Richardson-Duchman formula d) Stirling’s Approximation Approximation 73. What is the reason why an ivory soap floats in water? a) All matter has mass b) The specific gravity gravity of ivory soap is greater 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 negative 1, one of these lines is said to be: a) Parallel b) perpendicular c) Skew d) Non-intersecting 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 p urchased 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, 2 , ,3 5, 8 …). How do you call this number sequence? 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 solution solutions? s? a. Extranous solutions c. Conditional solutions d. b. Trivial solutions solutions
Ambiguous 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 Rationalization d. Polynomial c. Factoring 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? b. Conjugate Axis c. Asymptotic axis d. Major Axis a. Transverse axis 83. What is a number, which could not be expressed as a quotient of two integers? a. Natural b. Rational d. Surd c. Irrational 84. How do you call an angle that is greater then 180 degree but less than 360 degrees? a. Complex c. Obtuse d. Exterior b. Reflex 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 c. Mean d. Deviation Deviation b. Mode 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? b. Quadratic case c. Extraneous case d. Conditional Conditional case a. Ambiguous 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? 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 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 foc us 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
d. Circumcenter
12
96. What is the logarithm of a number to have a base e=2.718…? 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? b. Linear programming a. Iteration c. Differentiation d. Integration 98. Which of the following items classified a polygon? a. Angles b. Diagonals Diagonals c. Sides
d. Number of nodes
99. When a line y = mx + b slopes downw downwards ards from left to right, the slope m is: c) Equal to zero d) Equal to 1 a) Less than zero b) Greater than zero 100. The ratio between the quick assets to the current liabilities c. Working amount a. Acid test ratio b. Current ratio
d. Marginal ratio
101. 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? b. safety allowance c. tolerance stock d. none of these a. safety stock 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? b. Minuend c. Augend d. Dividend a. Consequent 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 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
106. How do you call a cylinder c ylinder with elliptical cross section? a. Ellipsoid b. Cylindroid c. Hyperboloid
d) Newton’s line line 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 90 o 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
55 % salt 45 % water 40 liters
13
Based on salt solution: 0.6040 0.60 x 0.0 x 0.4540
x = 10 liters
Based on water solution: 0.4040 0 .40 x x 0.5540
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 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 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 c) Product d) Derivative b) Logarithm 118. If a = b, then b = a. This illustrates of which of the followin following g axioms in algebra? a) Transitive axiom b) Reflexive axiom c) Replacement axiom d) Symmetric axiom 119. What is a regular polygon that has 27 2 7 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 Diophantine formula c) Richardson-Duchman formula d) Stirling’s Stirli ng’s Approximation 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 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 c) Polyhedral angle d) Plane angle b) Dihedral angle 124. These are product or services that are required to support human life and activities, that will be purchased in somewhat somewhat the same quantity even though though the price varies con considerably. siderably. a) Utilities c) Luxuries d) Producer goods and services b) Necessities 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: b) Acute angle c) Angle of depression d) Bearing a) Angle of elevation 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? sequence? a. Euler’s number b. Fermat number d. Fourier c. Fibonacci number series 127.
If the roots of an equation are zero, then, how do you classify the solutions? 14
a. Extranous solutions c. Conditional solutions d. Ambiguous Ambiguous b. Trivial solutions 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 Rationalization d. Polynomial c. Factoring 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? b. Conjugate Axis c. Asymptotic axis d. Major Axis a. Transverse axis 131. What is a number, which could not be expressed as a quotient of two integers? a. Natural b. Rational d. Surd c. Irrational 132. How do you call an angle that is greater then 180 degree but less than 360 degrees? a. Complex c. Obtuse d. Exterior b. Reflex 133.
What do you call a triangle having three unequal sides?
a. Obtuse
b. Oblique
c. Scalene
134. How do you call the distance of a point from the y-axis? a. Polar distance b. Coordinate c. Abscissa
d. Isosceles
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? b. Quadratic case c. Extraneous case d. Conditional Conditional case a. Ambiguous 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? 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 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 f ocus 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
143. What is the point of concurrency of the altitude of a triangle? a. Centroid b. Incenter c. Orthocenter 144.
d. Domain
d. Circumcenter
What is the logarithm of a number to have a base e=2.718…? e=2.718…?
15
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 c. Differentiation d. b. Linear programming Integration 146.
Which of the following items classified a polygon?
a. Angles 147.
b. Diagonals Diagonals
c. Sides
d. Number of nodes
When a line y = mx + b slopes downwards downwards from left to right, the slope m is:
a) Less than zero b) Greater than zero
c) Equal to zero
148. The ratio between the quick assets to the current liabilities c. Working amount a. Acid test ratio b. Current ratio
d) Equal to 1 d. Marginal ratio
149. It is the additional cost of producing one more unit of a product. a. Sunk cost c. Variable cost b. Marginal cost
16
d. Fixed cost
MATHEMATICS/ENG MATHEMATICS/EN G ECO/BASIC ENG TRIVIA EXAMINATION MULTIPLE CHOICE QUESTIONS Select the best answer from each each of the following questions. On the answer sheet provided, shade the box that corresponds to your choice. Strictly no erasures allowed.
1.
The ro roots ots of th thee qua quadra dratic tic equat equation ion are are 1/3 and and 3/ 3/2. 2. What What is the the equati equation? on? 2
2
2
a. 6x 5x 3 0
2
c. 6 x 7 x 3 0
b. 6x 7 x 3 0
d. 6x 7 x 3 0
2.
Mr. PME cov covered ered a dis distance tance of of 55 km in 4 hours hours by driving driving his car 40 k kph, ph, part of the way, way, and by walkin walking g 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. c. d. b. 11 11 11 11
3.
The w water ater tan tank k in Calamb Calambaa Water District District can be be filled by pipe pipe A in half half the time the pipe B ccan an em empty pty 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. b. 0.7 c. 0.75 d. 0.8 a. 0.6
4.
Wha Whatt is the the va value lue o off k to m make ake the exp expres ression sion kx2 – – 3kx 3kx + 9 a perfect square? a) 2 c) 3 b) 4
5.
Which of the following is the standard acceleration due to gravity in the English unit? b) 32.2 fps2
a) 980.66 fps2
6.
d) 5
Wh What at is the the valu valuee of Lim x
x2 1 x3 1
c) 9.8066 9.8066 fps2
? b) 0.25
a) 0
d) 32.2 ips2
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? b) 18 yrs old c) 12 yrs old d) 16 yrs old a) 15 yrs old
8.
How How m many any term termss of the the seq seque uenc ncee – – 9 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 rec rectangular tangular field 30 meters by 40 meters. He started on the edge aand nd 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 aare re 6 ge geometric ometric m means eans between 4 and 8748. F Find ind the sum of aall ll term terms. s. 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 35,, 42, 50. a. 31.82 b. 32.29 c. 30
d. 29.96
12. Find tthe he root mea mean n square of 11, 2 23, 3, and 35. a. 25 b. 27
d. 24
c. 26
13. Wat Water er is pour pouring ing into a sswimm wimming ing pool pool.. Afte Afterr 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. Determ Determine ine the distan distance ce traveled by a partic particle le between a time interval interval of 0.2 second to 0.3 secon second d if its velocity is V 12 t 4
a) 3.75 cm
7 t
, where V is in cm/s and t is in seconds. c) 2.75 cm
b) 2.84 cm
d) 3.84 cm
15. A pole cast a shadow 15-m long when tthe he angle of eleva elevation tion of the sun is 61°. If the pole has llean ean 15° from the vertical directly toward the sun, what is the length of the pole?
1
b. 48.64 m
a. 54.23 m
c. 36.84 m
d. 64.84 m
16. The volume of tthe he cube is increasing at a rate of 5 cu. m per minute. De Determine termine tthe he rate aatt which the surface area is increasi increasing, ng, in m2 /min, when its side is 10 m. d) 2 a) ½ b) 1.75 c) 1 .5 17. What iiss the suppl suppleme ement nt of an angl anglee whose ccomplim ompliment ent is 62o? o o a) 152 b) 118
c) 28o
d) 60o
18. A certain angle has a supplement five times its compliment. W What hat is the angle? c) 67.5o a) 186o b) 168.5o
d) 157.5o
19. Dete Determine rmine the ac accumul cumulate ated d value of P2,000. P2,000.00 00 in 5 years it is invest invested ed at 11% compoun compounded ded quarte quarterly. rly. 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 eearning arning 4% per annum compounded quarter quarterly, ly, will become P18,302.85. Determine the effective effective rate of interest per yea year. r. b) 4.06 % a) 3.06 % c) 5.06 % d) 6.06 % 21. What is the eff effecti ective ve rate equiv equivalent alent of 12% comp compounded ounded quar quarterl terly? y? a) 12.55% b) 11.55 % c) 12.98 %
d) 13 %
22. Celestino owes P500, due in 3 y years ears and P800 due in 7 years. He is allowed tto o settle tthese hese 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 agre agreed ed to pay the loan at the end of one yea year. r. 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 ttower ower A, tthe he angl anglee of elev elevation ation of tthe he top of the ttower ower B is 4 46 6 o. From the foot of tower B the angle of elevation of o the top of tower A is 28 . 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 1
25. Det Determ ermine ine the value value o of f
x 1
3
x 5 sin x dx .
a. 0
b.1.75
c. 3.1416
d. infinity
26. Think of a number. Double the num number. ber. Subtract 6 from the re result sult and divide tthe he answer by 2. The quotient w will ill be 20. W What hat is the number you think? a. 1 2 b. 20 c. 23 d. 32 27. Determine the absolute value of resultant vec vector tor of the following vect vectors: ors: F1 = 4i + 7j + 6k; F 2 = 9i + 2j + 11k, F3 = 5i – 5i – 3j 3j – – 8k. 8k. a) 21 b) 18 c) 25 d) 9 28. Find the v volta oltage ge drop to mov movee 2 C of charg chargee from poin pointt a to point b that req requires uires – – 30 30 Joules of energy. – 15 a) a) – 15 V b) + 15 V c) – 5V d) + 5 V – 5 29. If the z 1 1 1 ... , what is the value of z? a) 0.453
b) 0.618
30. Solve for the v value alue of x ffrom rom tthe he fo followi llowing ng equa equation: tion: 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 wa water ter is boiled to re reduce duce water content until the co concentration ncentration is 5 % by weight salt. How much water is evaporated? a) 20 b) 25 c) 15 d) 22.5 32. Dete Determine rmine the di diame ameter ter of a cir circle, cle, x 2 y 2 6x 4 y 12 0 . a) 9 units b) 11 units c) 12 units 33. Wha Whatt is tthe he m mini inimum mum poi point nt of y a) (1, 2)
x 1 ? x
b) (1.5, 2)
c) (1, 1.5)
2
d) 10 10 units units
d) (2, 1)
34. A man left Sta. R Rosa osa 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? c) 252 km a) 225 km b) 522 km d) 215 km 35. If x varies direct directly ly 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. d) 16 a) 12 b) 18 c) 14 36. Dete Determine rmine tthe he absol absolute ute val value ue of the com complex plex num number ber 3 + 4i. b) 5 a) 4 c) 8
d) 6
37 37.. Si Simp mpli lify fy i1997 + i1999, where i is an imaginary number. a) 0 b) i c) 1 + i
d) 1 – – ii
38. If vec vector tor A is 10 unit unitss and ve vector ctor B B,, whic which h make makess 600 with vector A, is 20 units. What is the difference d ifference of vectors A and B? a) 15.34 units b) 13.45 units c) 18.76 units d) 17.32 units 39. A ball iiss dropped from a height of 60 m meters eters above ground. How long does it take to hit the ground? b) 3.5 seconds a) 4.5 seconds c) 2.5 seconds d) 1.5 seconds 40. A change iin n position position,, speci specified fied by a leng length th and a direc direction tion is sai said d to be: a. Displacement b. Acceleration c. Velocity 41.
d. Dynamic equilibrium
The proce process ss of one substa substance nce mix mixing ing wit with h another bec because ause of mole molecula cularr motion is know known n as: Diffusion a. Adhesion b. c. Cohesion d. Confusion
42. Those cost that aarise rise at the result of a cha change nge in operations or policy or it is the ratio of a small increment increment cost and a small increment of output. a. Increment cost
b. Differential cost
c. Marginal cost
d. Promotion cost
43. The sum of al alll the costs incurred by the originat originators ors of the project up to the tim timee that the promoters of the projec projectt accept tthe he 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 hou r-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. Wha Whatt is the aacid cid ttest est rrat atio? io? a. The ratio of owner’s equity to total current liabilitie liabilitiess b. The rati ratio o of all asse assets ts to to ac actual tual current current liabi liabiliti lities es c. The ratio of current assets (exclusive of inventory) to the total current liabilities . d. The ra ratio tio of gr gross oss ma margin rgin to o operat perating, ing, sa sates, tes, aand nd admi administr nistrativ ativee expe expenses nses 46. How do ca call ll an energy required to move 1 Coulomb of charge through aan n eleme element. nt. a) Current
c) Power
b) Voltage
d) Resonance
47. This is a number se sequence quence where the succ succeeding eeding term is obtai obtained ned by adding the last pa pair ir of preceding term termss such as the sequence (1, 1, 2, ,3 5, 8 …). How do you call this number sequence? b) Fermat number c) Fibonacci number d) Fourier series a) Euler’s number 48. If the roots of an equ equation ation ar aree zero, the then, n, how do you clas classify sify the sol solutions utions?? a. Extranous solutions b. Trivial solutions c. Con Condi diti tion onaal solut olutio ions ns 49. In ele electri ctricity city,, how do y you ou cal calll the rate of cha charge rge flow? a) Potential difference b) Current
c) Voltage
d. Ambigu biguou ouss ssol olut utiions ons
d) Power
50. This law in electrical circuits circuits states, “The algebraic sum of currents entering a node (or a closed boundary) bound ary) is zero”. How d o you call this law? a) Kirrchoff’s current law b) Ohm’s current law law c) K Kiirchh hho off’s voltage law d) Ohm’s voltage law 51. This law in electrical circuits circuits state, “The algebraic sum of all voltages around a closed path (or loop) is zero”. How do you call this law? a) Kirrchof hoff’s curr urrent law
c) Kirchhoff’s Kirchhoff’s voltage law
b) Ohm hm’’s curr rreent law
52. In elec electric trical, al, wha whatt is the SI uni unitt of conduc conductance tance??
3
d) Ohm’s voltage law
a) Ohm
b) Mho
53. Whic Which h of the foll following owing iiss the equi equivale valent nt of 1 Amper Ampere? e? a) 1 Coulomb per second b) 1 Joule per Coul Coulomb omb
d) Ampere
c) Siemens
c) 1 Volt per Ampe Ampere re
d) 1 Ampe Ampere re per Coulom Coulomb b
54. This is the process of expressing a polynomial as the product of another polynomial polynomial or monomial of lower lower degree. What is this mathematical mathematic al process? a) Decomposition b) Rationalization c) Factoring d) Polynomial Polynomial dampin damping g 55. This is a point whe where re the concavity of a curve changes or when the slope of the curve is neither neither increasing nor dec decreasing. reasing. What is this point commonly called? a) Maximum point
b) Minimum point
c) Point of tangency
d. Point of inflection
56. How do you cal calll the axis of the hy hyperbol perbolaa that pass passes es throug through h the cente center, r, the foci an and d vertic vertices? es? a) Transverse axis b) Conjugate Axis c) Asymptotic axis d) Major Axis 57. What is a num number, ber, whi which ch could not be expr expresse essed d as a quotient of ttwo wo integ integers? ers? c. Irrational a. Natural b. Rational 58. How do y you ou cal calll the o opposit ppositee of the the pref prefix ix nan nano? o? c) Giga a) Peta b) Tera
d) Hexa
59. What do y you ou call a tr triangl ianglee havin having g three une unequal qual si sides? des? a) Obtuse b) Oblique
c) Scalene
d) Isosceles
60. How do you ca call ll the di distanc stancee of a point fr from om the yy-axis? axis? a) Polar distance b) Coordinate
c) Abscissa
d) Ordinate
d. Surd
61. This is the me measure asure of central te tendency ndency defined as the most frequent score. How do you call call this meas measure ure of central tendency tendency?? a) Median
c) Mean
b) Mode
62. Whic Which h of the ffollow ollowing ing is tthe he equi equivale valent nt of 1 mi mil? l? 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 poly polygon gon wi with th te ten n sides is sa said id to be: a. Dodecagon b. Decagon 64.
c. Decahedron
Any numbe numberr expre expressed ssed in pla place-va ce-value lue nota notation tion wi with th base 12 iiss known as as:: a. Duodecimal b. Deontic c. Decile
d) Deviation c) One-half of an inch
d. Dodecahedron
d. Dedekind
65. Which of the following is true regarding the minimum aattractive ttractive rate of return used in judging pr proposed oposed investme investments? nts? a. It is muc much h small smaller er than tthe he inter interest est ra rate te used tto o discou discount nt expec expected ted ca cash sh flows ffrom rom inve investme stments nts b. It is frequently a policy decision made by an organization’s management c. It is larger larger than the iintere nterest st ra rate te use used d to disco discount unt ex expecte pected d cash cash flow from iinvestm nvestments ents d. It is n not ot re relev levant ant iin n eng engine ineeri ering ng ec econom onomy y stu studie diess 66. Which of the following si situations tuations has a conventi conventional onal cash flow so that that an internal rate of return can be safe safely ly calculated aand nd used? a. Your com company pany unde undertak rtakes es a mini mining ng projec projectt in whic which h the lan land d must be re reclai claimed med at the end end of the pro project ject.. b. You invest in a safe dividend dividend sto stock ck and and rec receive eive d dividend ividendss each year. c. You You le leas asee a ccar ar aand nd p pay ay by tthe he m mont onth h d. Your com company pany iinvest nvestss heavily heavily in a ne new w produc productt tha thatt will gener generate ate pr profits ofits for tw two o years years.. To kee keep p profits high fo forr 10 years, the company plans to reinvest heavily after two years. 67. The economic order quantity (EOQ) is def defined ined as the order quant quantity ity which minim minimizes izes the inventory cost per unit tim time. e. 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 entire reorde reorderr qu quant antit ity y I del delive ivered red insta instanta ntaneo neousl usly y d) T The he d dem emand and rat ratee iiss un unifo iform rm and con consta stant nt 68. Which of the following eevents vents will cause the optimal lot si size, ze, given by the cclassic lassic EOQ model w with ith no shortages, to iincrease? ncrease? 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 aalways lways 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 Pay exactl exactly y tthe he ssam amee am amount ount of iinte nteres restt ea each ch p paym ayment ent
d) Pa Pay y the the iinte nteres restt onl only yw whene henever ver fai failure lure to p pay ay the pri princi ncipal pal
70. How to y you ou cl classif assify yw work-in-p ork-in-proces rocess? s?
4
a) A liability
b) An expense
c) A revenue
d) An asset
71. What is the iindire ndirect ct produc productt cost (IPC (IPC)) spendi spending ng varia variance? nce? a. The IPC v volum olumee aadjuste djusted d budg budget et minus the total IPC absorbe absorbed d b. The IIPC PC vol volume ume aadjuste djusted d budge budgett [fi [fixed xed + volum volumee (va (variable riable IPC ra rate)] te)] c. The di diffe fferenc rencee between between ac actua tuall IPC an and d IPC volum volumee adju adjusted sted b budg udget et d. The d diff iffere erence nce b betw etwee een n act actual ual IIPC PC an and d IPC aabsor bsorbed bed 72. Which of the following does not affect owner’s equity? c) License to start business a) Expen Expense se to get llice icense nse of sstar tartt bus busine iness ss b) Inv Invest estme ment nt ca capit pital al paid 73. How do you ca call ll an inc increas reasee in the va value lue of a ca capita pitall asse asset? t? b) Capital gain a) Profit c) C Caapit pital eex xpend pendiiture d) Capital st stock ock 74.
Anot Another her na name me ffor or deriva derivativ tivee is sa said id to be be:: a. Differential manifold b. Partial derivative
c. Cyclic quadrilateral
d. Bi-rectangular
c. Decahedron
d. Dodecahedron
77. A prefix denoting a multiple of ten tim times es any of tthe he physical units of the system international. a. Deka b. Nano c. Hecto
d. Exa
78. The ffath ather er of pl plane ane g geom eometr etry. y. a. Euclid
d. Galileo
b. Pythagoras
Dividends
d. Differential coefficient
c. Differential form
75. Anothe Anotherr ter term m for rhombus is sa said id to be: a. Dichotomy b. Diamond 76. A poly polygon gon wi with th tw twelve elve sides is know known n as: a. Dodecagon b. Decagon
d)
c. Aristotle
79. This is the ca case se of a solution of a pla plane ne triangle where the given data le leads ads to two solutions. How do you call this cas case? e? a) Ambiguous case b) Quadratic case c) Extraneous case d) Conditional case 80. It is a type of polygon in which each interior aangle ngle must be less than or equal to 180°, and al alll vertices 'point outwards' outwards' away from the interior. How do you call this polygon? a) Concave Polygon b) Convex polygon c) Re Regular po polygon d) Ir Irregular po polygon 81. It is a series of eequal qual payments occurring at equal intervals of time where the first payme payment nt is ma made de after seve several ral 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 tthe he negotiation of wage rates, conditi conditions ons of employment, eetc. tc. by representati representatives ves 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 bo nd 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 d) Bail bond c) Incorporator’s bond 84. How do you call the iintegr ntegral al of any quotie quotient nt whose num numerat erator or is the diffe differenti rential al of the denom denominator inator?? a) Co-logarithm b) Logarithm c) Product d) Derivative Answer: b) Logarithm 85. What iiss a regu regular lar pol polygon ygon tha thatt has 27 diago diagonals? nals? a) Nonagon b) hexagon
c) Pentagon
d) Heptagon
Answer: a) Nonagon 86. How do you call the form formula ula used to compute the value value of n factorial factorial,, which is in symbolic form (n!), where n is la large rge number? a) Math Mathes eson on form formul ulaa b) Diop Diopha hant ntin inee fo form rmul ulaa c) Rich Richar ards dson on-D -Duc uchm hman an form formul ulaa d) Stirling’s Approximation 87. What is the the reas reason on why an iv ivory ory soa soap p floa floats ts in wat water? er? 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 w with ith each other, the amount of divergence betw between een the two planes is expr expressed essed by mea measuring suring the: b) Dihedral angle a) Reflex angle c) Polyhedral angle d) Plane angle
5
89. What do you thi think nk is the output o orr sales at w which hich incom incomee is insuffi insufficient cient to equ equal al operat operating ing cost 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 aasset sset due to a decrease in the quantity av available ailable as a coal, oil aand nd timber in forests? a) Depletion b) Amortization c) Depreciation d) Investment 92. What can y you ou say about the present worth of all deprecia depreciation tion over the economic life of the item item?? a) Maintenance b) Capital recovery cc)) Depreciation recovery d) Annuity 93. What do you think is the provision in the contract that indicates the possible adjustm adjustment ent of material cost and labor cost? a) Secondary clause b) Specification c) Escalatory clause d) General provision 94. This is the process of dete determining rmining the value of certain pr property operty for specifi specificc reasons. Guess, what is tthis? his? a) Amortization b) Investment c) Appraisal d) Depreciation 95. How do you cal calll those products or services that are dire directly ctly 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 aare re used tto o produce consume consumerr goods and services. G Guess, uess, 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 th those ose product productss or service servicess that are requ required ired to support hum human an life and acti activitie vitiess that will be purc purchase hased d 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 y you ou cal calll a cy cylinde linderr wit with h elli elliptica pticall cross cross sec section? tion? a. Ellipsoid b. Cylindroid
c. Hyperboloid
d. Paraboloid
99. How do you cal calll a ma market rket whereby there is only one buye buyerr of an ite item m for which there are no g goods oods substitutes? a) Monopoly b) Monopsony c) Oligopoly d) Oligopsony 100. Which statement about a charge pl placed aced on a dielectric material material is true? a. The cchar harge ge inc increa reases ses tthe he con conduc ducti tivit vity y of the m mate ateria riall b. The charge charge is is confine confined d to the rregio egion n in whi which ch the the charge charge was p plac laced. ed. c. The charge charge is iimme mmedia diatel tely y lost lost to the the atm atmosph osphere ere d. The charge is instantly carried to the material’s surface 101. Which of the following iiss not a property of magneti magneticc field lines? ac)) The M Maagn ticinter ffiieldsect li linessurfac s ha hav ves en no o be bequal eginni ning ngss an aity nd at no noright eght ndsangl liene line intersect urfaces of iintens ntensity rien angles es
b) The The fie lines cross themselves only at right angles d) field ld is stro stronger nger whe where re the li lines nes are ccloser loser to togethe getherr
102. Tesla is a unit of which of the follow following? ing? a) Magnetic induction b) Inductance
c) Capacitance
103. What is a pole pi pitch? tch? a) The angl ngle at at whi whicch the the po pole le wind ndiings ngs are are wound ound c) The space on the stator allocated to one pole
b) The spa pacce on on the the sta stator all lloc ocaated to to tw two pol polees d) The mica used to insulate the poles from each other
104. How do you call a polygon wi with th 10 000 sides sides?? a) Hectogon b) Chilliagon
c) Myriagon
105. Any line segment joining a vertex of a triangle to a point on the opposite side is ca called lled as: c) Cevian a) Newton line b) Secant
d) magnetic flux
d) Octacontagon
d) Euclidian line
106. It is any influence capable of producing a change in the m motion otion of an obje object. ct. 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 o r service.
6
a) Initial working capital
b) Regular working capital
c) Equity
d) Annuity
108. In the problem of w writing riting the equation of a certain curve w with ith respect to another axes in which tthe he new axes are pa parallel rallel 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 coplanar line that does not intersect? a) Torus b) Annulus c) Circoloid d) Annular 110. If the eccentricity iiss less than one, then curve is known as: a) Ellipse b) Hyperbola
c) Parabola
d) Circle
111. Determine the outside dia diameter meter of a hollow steel steel tube that will carry a tensile load of 500 kN at a stress stress of 140 MPa. Assume the wall thickness to be 0ne-tenth of the outside diameter. c) 113 mm a) 123 mm b) 103 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.”? c) Theorem a) Postulate b) Corollary d) Axiom 113. What is the study of the properties of fig figures ures of three dimensions? a) Physics b) Solid geometry c) Plane geometry
d) Trigonometry
114. Points that lie in the same pla plane: ne: 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 resultant force and inversely proportional to the resultant resultant force and inversely proportional to the mass of the body”. How do you call this theory? b) Newton’s Second Law of motion a) Newton’s First 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 o f directors of the corporation decides to distribute to ordinary shareholders shareholders.. a) Dividend b) Return c) Share of stock d) Par value 120. Which of theoffollowing iiss notsum a theorem on functions lim limits? its? is equal to the sum of their limits a) The limit the algebraic of several 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 ccord ord is held at the two ends and allowed 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 Act Actss 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 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) same amount of principal each payment d) Pay The exactly choicesthe a and c above 124. To be a mem member ber of the Board of Mechanic Mechanical al Engineering, he/s he/she he must be at le least ast 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? parabola? b. Axis of the parabola a. Latus rectum c. Transverse axis
d. Major axis
126. What is the ratio of the distance betwe between en the foci to the distance between between the vertices in either hyperbola or ellipse? a. Eccentricity b. Latus rectum c. Variance d. Deviation 127. It is a statement that one ma mathematical thematical ex expression pression is greater than or less than another. How do you call this? b) Inequality a) Conditional expression c) Interval d) Domain 128. It is a method of depreci depreciation ation where a fixed sum of money iiss regularly deposited at compound inte interest rest in a real or im imaginary aginary fund in order to accumulate an amount equal to the total depreciation of an asset asset at the end of the assets estimated lif life. e. How do you call this depreciation? a) Straight line method b) Declining balance method d) Sinking fund method c) SYD method 129. What is an artifi artificial cial ex expense pense that spreads the purchase price of an aasset sset 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, w which hich specifies the actual rate 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 circula circularr 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? c) An event a) A sample spac pace b) A rand ndom om po poiint
d) A finite set
133. How do you call a se sequence quence of numbers where the ssucceeding ucceeding term is grea greater ter 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 m method ethod 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 radia radiation tion with a unit or length equal to 10 – 10 – 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, 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 lette letters rs used to represent a number arranged properly in rows and columns. c. Array a. Determinant b. Matrix d. equation 139. It is is a h high igh – – level 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 adja adjacent cent to the point where this line started 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 statement is known as: b. Axiom a. Postulate c. Hypothesis
d. Theorem
142. A perpendicular segment from a verte vertex x of the triangle to the line containing the opposite side is known as: b. altitude a. Median c. Angular Angular bisector d. Perpendic Perpendicular ular bisec bisector tor 143. An S.I. unit of area equal to 100 sq. m m.. a. Arc b. Acre
c. Hectares
8
d. Are
144. The angle that the line of sight to the objec object, t, makes with the horizontal, which is above the eye 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 com complex plex plane commonly calle called d as: c. Argand diagram a. Venn diagram b. Histogram d. Funicular diagram 146. The area bounded by two concentric circle circless is called as: a. Annulus b. Ring
c. Disk
d. Sector
147. A series of numbers in whic which h each number or term is derived derived from the preceding number by adding a constant constant value to it is known as: a. Geometric sequence b. Arithmetic sequence c. A Ana naly lyti tica call sequ sequeence nce d. D Diiffe fere rent ntia iall sequ sequeence nce 148. 10 to the nega negative tive pow power er of 18 is the value of the pref prefix: ix: a. Atto b. Femto
c. Micro
d. Pico
149. A series of equal pa payments yments 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 avera average ge of assets used in producing these sales. b. Asset turnover c. Operating – a. Inventory turnover Operating – exp expens ensee ra ratio tio d. Qu Quick ick rat ratio io 151. Quick ratio is defined as the ratio of quick assets to the current liabilities, liabilities, sometimes sometimes this is called: a. Acid test ratio b. Debt ratio c. Equity ratio d. Current ratio 152. Form of busine business/c ss/compan ompany y ownersh ownership: ip: a. Partnership b. Corporation
c. Single proprietorship
d. All of the above
153. It is defined to be any m method ethod of repaying a debt, tthe he principal aand nd interest included usually by a serie seriess of equal payments aatt periodic intervals of time. a. Amortization
b. Annuity
c. Deferred annuity d. d . Preferred annuity
9
MATHEMATICS/ENGINEE MATHEMATI CS/ENGINEERING RING 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 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. liabilities. d) The ratio of gross margin to operating, sates, and administrative expenses
2.
How do cal calll an e energy nergy required b) to Voltage move 1 Coulomb of charge through an element. a) Current Voltage c) Power
3.
This is a number sequence where the succeeding term iis s obtained by a adding dding the last pair of preceding terms such as the sequence (1 (1,, 1, 2, ,3 5, 8 …). How do you call this number sequence? sequence? a) Euler’s number b) Fermat number c) Fibonacci number d) Fourier series
4.
Determine the absolute v value alue of resultant vector of the following vectors: F1 = 4i + 7j + 6k; F 2 = 9i + 2j + 11k, F 3 = 5i – 5i – 3j 3j – – 8k. 8k. a) 21 21 b) 18 c) 25 d) 9
5.
Determine the sum of the coefficien coefficientt of the variables in the expression (2x + 3y 3y – –z) z)8. a) 65 536 536 b) 56 563 c) 63 655
6.
7.
If the roots of an equation are zero, then, how do you class classify ify the solutions? a. Extranous solutions b. Trivial solutions solutions c. Conditional solutions
d) Resonance
d) 66 535
d. Ambiguous solutions
Find the vol voltage tage drop to move 2 C of charge from point a to point b that requires requires – – 30 30 Joules of energy. a) a) – – 15 15 V V
b) + 15 V
c) – c) – 5 V
d) + 5 V
8.
This is the pro process cess of expres expressing sing a poly polynomial nomial as the product o off another polynomial polynomial or monomial of llower ower degree. What is this mathematical process? a) Decomposition b) Rationalization c) Factoring Factoring d) Polynomial damping
9.
This is a point where the concavi concavity ty of a curve changes or when the slope of the curve is neither increa increasing sing 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 hy hyperbola perbola that passes through the center, the foci and vertices? a) Transverse axis axis b) Conjugate Axis c) Asymptotic Asymptotic axis
d) Major Axis
11. How many permutations can be made out of the letters in the word DIEGO DIEGO taken 3 at a time? a) 50 ways b) 60 ways ways c) 120 ways
d) 80 ways
12. What is the temperature in degrees Cel Celsius sius of a molecule at absolute absolute zero? o
o
a) 0 C
b) b) – – 273 273 C
o
o
c) – c) – 32 32 C
d) 273 C
13. If at an angle me measures asures x degrees, what is the mea measure sure in radians? a) a)
180
x
b)
180
x
14. In electricity electricity,, how do you call the rate of charge flow? a) Potential difference b) Current Current
c)
180 x
c) Voltage
15. What is a number, which could not be expre expressed ssed as a quotient of two integers? integers? a. Natural b. Rational c. Irrational 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”. resistor” . How do you call this law? a) Kirchhoff’s Law Law b) Ohm’s Law Law c) Ampere’s Law d) Gauss’ Law Law 17. How do you call an angle that is greater then 180 degree but les less s than 360 degrees? a) Complex b) Reflex Reflex c) Obtuse
d) Exterior
18. This law in electrical circuits states, 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 law b) Ohm’s current law law c) Kirchhoff’s voltage law law d) Ohm’s voltage law law 19. How do you call the opposite of the pre prefix fix nano? a) Peta b) Tera
c) Giga Giga
d) Hexa
20. What do you cal calll a triangle having three unequal sides? a) Obtuse b) Oblique
c) Scalene Scalene
d) Isosceles
21. If the z
1 1 1 ...
a) 0.453
, what is the value of z? b) 0.618 0.618
c) 0.816
d) 0.681
c) 1.85925
d) 1.528925
1
MATHEMATICS/ENGINEE MATHEMATI CS/ENGINEERING RING ECONOMY
22. Solve for the value of x from the following equation: a) 1.258925 1.258925 b) 1.892525
xx
xx
. ..
10 .
23. This law in electrical circuits state, “The algebraic sum sum of all voltages around a closed path (or loop) is zero”. How do you call you call this law? a) Kirrchoff’s current law law b) Ohm’s current law law c) Kirchhoff’s voltage law law d) Ohm’s voltage law law 24. How do you call the distance of a poin pointt from the y-ax y-axis? is? a) Polar distance b) Coordinate
c) Abscissa Abscissa
d) Ordinate
25. In electricity electricity,, it is an ability of an element to resis resistt the flow of current. What is this? this? a) Resonance b) Conductance c) Inductance
d) Resistance Resistance
26. In electrical circuit circuits, s, how do you call the reciprocal of resistance? a) Resonance b) Conductance Conductance
c) Inductance
d) Resistance Resistance
27. In electrical, what is the SI unit of condu conductance? ctance? a) Ohm b) Mho
c) Siemens Siemens
d) Ampere
28. If 4y = 3x 3x,, then, what is the value of
a)
4 3
b)
3 4
3x 2 4y 2
?
c)
2 3
d)
3 2
29. Which of the foll following owing is the equiva equivalent lent of 1 Ampe Ampere? re? a) 1 Coulom Coulomb b per second second
b) 1 Joule per Coulomb
c) 1 Volt per Ampere
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 tendency? ? a) Median b) Mode Mode c) Mean d) Deviation 31. Which of the foll following owing is the equiva equivalent lent of 1 mil? a) One-tenth of an inch b) One-thousandth of an inch 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 case b) Quadratic case c) Extraneous case d) Conditional case 33. What is the valu value e of k to ma make ke the expression kx2 – 3kx – 3kx + 9 a perfect square? a) 2 b) 4 4 c) 3
d) 5
34. It is a type of polygon in which ea each ch interior angle must be less than or equal to 180°, 180°, and all vertices 'point ou outwards' twards' away from the interior. How do you call this polygon? a) Concave Polygon b) Convex polygon 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? age? a) 15 yrs old 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 of a side? It is also called as inradius, the radius of an incircle. a) Radius b) Apothem Apothem c) Circumradius d) Inradius 37. If the daily wage of CPM and a Plumber are in the ratio 2:1 2:1.. In a day, a CPM has to work 8 hrs bu butt 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 foll following owing is the equiva equivalent lent of one circu circular lar mil? a)
4
0.012
b)
4
0.0012
c)
4
0.00012
d)
4
0.000012
39. How do you call a method of describi describing ng a set where the elements are separated by commas and enclosed by braces? a) Tabular or roster form form b) Equal form c) Rule form d) Equivalent form 40. Which of the foll following owing is the equiva equivalent lent of the ex expression pression 2Logb 6 6 – – Log Logb 4? a) 2Logb 3 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 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 20 b) 25 c) 15 d) 22.5 43. Tukmol can paint a fence of 50 % faster than Kik Kikoy oy 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 t he hour -hand -hand as it is now behind it. What is the time now? 2
MATHEMATICS/ENGINEE MATHEMATI CS/ENGINEERING RING ECONOMY
a) 3:06.36 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 buye buyerr 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 value 2
2
46. Determine the diameter of a circle, x y a) 9 units b) 11 units 47. What is the minimum poin pointt of y a) (1, 2) 2)
x
1 x
b) (1.5, 2)
6x 4 y 12 0 .
c) 12 units
d) 10 units
c) (1, 1.5)
d) (2, 1)
?
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 iiff an investment of P37,500.00 P37,500.00 accumulate accumulates s to P45,937.5 in 18 months? a) 0.15 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 bargaining d) Cooperative 51. What is the value of Li Lim m
x
a) 0
x 2 1 x3 1
? b) 0.25
c) 1.25
d) indeterminate
52. What is the present value of P5,00 P5,000.00 0.00 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 P1,968.23 53. This is a type of bond whose guaran guaranty ty 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 wit h their asking for it? a) Registered bond bond b) Preferred bond c) Incorporator’s bond 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 km d) 215 km 56. If x varies directl directly y 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 sequence – – 9, 9, - 6, - 3, … must be taken so that the sum is 66? 66?
View more...
Comments
