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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.
- Which of the following is the standard acceleration due to gravity in the English unit?
a) 980.66 fps^2 b) 32.2 fps^2 c) 9.8066 fps^2 d) 32.2 ips^2
Answer: 32.2 fps^2
- What is the value of 1 radian in degrees?
a) 89.55o^ b) 57.3o^ c) 60.3o^ d) 45. 58 o
Answer: 57.3o
Solution: 57. 3 degrees
radians
180 1 radians
o
- How many degrees are 4800 mils?
a) 180o^ b) 315o^ c) 90o^ d) 270 o
Answer: 270o
Solution: 270 o
- 78 mils
1 degree 4800 mils
- If the density of a gas is 0.003 slug/ft^3 , what is the specific weight of the gas?
a) 15.2 N/m^3 b) 9.04 N/m^3 c) 98.2 N/m^3 d) 76.3 N/m^3
Answer: 15.2 N/m^3
Solution:
3 2 2 3
g 0. 003 slugs/ft 32 , 2 fps 14. 59 kg/slug 1 ft/ 0. 3048 15. 2 N/m
- If the specific weight of a liquid is 58.5 lbf per cubic foot, what is the specific volume of the liquid?
a) 1.0675 cm^3 /g b) 0.5321 cm^3 /g c) 1.5502 cm^3 /g d) 0.9504 cm^3 /g
Answer: 1.0675 cm^3 /g
Solution: 58. 5 lbf /ft^3 9189. 6 N/m^3936. 8 kg/ m^3 g
1. 0675 cm/g
1 v ^3
- 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: ^ ^ ^ ^ ^ ^42.^131 %
P AorBPAPBPAandB
- A perfect gas is expanded polytropically with an initial volume and temperature of 0.06 m^3 and 147 0 C respectively.
If the final volume and temperature are 0.21 m^3 and 21 0 C respectively, what is the index of the expansion? a) 1.285 b) 1.212 c) 1.333 d) 1.
Solution: } solvingforn,n 1. 285 V
V
T
T (^) n 1
2
1
2
- If the loan was for 15 months at 16.8% interest a year and the repayment on a loan was P12,100.00, how much was
the principal? a) P8,500.00 b) P9,500.00 c) P10,000.00 d) P10,500.
Solution:
P 9 , 965. 10 P 10 , 000. 00
1 i
F
P
n 1. 25
- Determine the accumulated value of P2,000.00 in 5 years it is invested at 11% compounded quarterly.
a) P3,440.00 b) P3,404.00 c) P3,044.00 d) P4,304.
Solution:
P 3 , 440. 00 4
m
i F P 1
mn 4 5 n (^)
- The sum of P15,000.00, deposited in an account earning 4% per annum compounded quarterly, will become
P18,302.85. Determine the effective rate of interest per year. a) 3.06 % b) 4.06 % c) 5.06 % d) 6.06 %
Solution: 1 100 % 4. 06 % 4
m
i i 1
m 4 n e
- 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.
Solution: Cash Value = Down payment + Present value of the balance
P^193 ,^912.^00
P 80 , 000. 00
m
i 1
F
Cash Value P 80 , 000. (^00) mn 42 n
- Find the number of years when P2,500.00 is compounded to P5,800.00 if invested at 12% compounded quarterly.
a) P6.12 years b) 7.12 years c) 8.12 years d) 5.12 years
Solution:
P
F
ln m
i mnln 1 P
F
m
i 1 n
mn n
- 12 years
ln 1
ln
m
i ln 1
P
F
ln
n (^) m 4 n
- What is the effective rate equivalent of 12% compounded quarterly?
a) 12.55% b) 11.55 % c) 12.98 % d) 13 %
Solution: 1 100 % 12. 55 % 4
m
i i 1
m 4 n e
- What rate compounded-quarterly is equivalent to 14% compounded semi-annually?
a) 10.76 % b) 11.76 % c) 12.76 % d) 13.76 %
Solution: 57. 3 degrees
radians
180 1 radians
o
- How many degrees are 4800 mils?
a) 180o^ b) 315o^ c) 90o^ d) 270 o
Solution: 270 o
- 78 mils
1 degree 4800 mils
- If the density of a gas is 0.003 slug/ft^3 , what is the specific weight of the gas?
a) 15.2 N/m^3 b) 9.04 N/m^3 c) 98.2 N/m^3 d) 76.3 N/m^3
Solution:
3 2 2 3
g 0. 003 slugs/ft 32 , 2 fps 14. 59 kg/slug 1 ft/ 0. 3048 15. 2 N/m
- If the specific weight of a liquid is 58.5 lbf per cubic foot, what is the specific volume of the liquid?
a) 1.0675 cm^3 /g b) 0.5321 cm^3 /g c) 1.5502 cm^3 /g d) 0.9504 cm^3 /g
Solution: 58. 5 lbf /ft^3 9189. 6 N/m^3936. 8 kg/ m^3 g
1. 0675 cm/g
1 v ^3
- A force of 200 lb acts on a block at an angle of 28o^ with respect to horizontal. The block is pushed 2 ft horizontally.
Find the work done by this force. a) 480 J b) 408 J c) 840 J d) 804 J
Solution: W^ FdxFcosx^200 cos^28 ^2 ^353.^18 ftlb^480 J
- 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.
- 66 x 10 g/ atom
- 02 x 10
1 W 23 ^ ^24
- A truck starts from rest and moves with a constant acceleration of 6 m/s^2. Find the speed of the truck after 4 seconds.
a) 18 m/s b) 28 m/s c) 24 m/s d) 35 m/s
Solution: For uniformly accelerated motion, V V at 0 6 4 24 m/s
2
o
- 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, 3 10 150 ft
at 0
S Vt
2 2
o
15 fps
t
S
VAverage
- A ball is dropped from a height of 60 meters above ground. How long does it take to hit the ground?
a) 4.5 seconds b) 3.5 seconds c) 2.5 seconds d) 1.5 seconds
Solution: g t^2 2
1 S Vot
(^)
- 5 seconds
- 81
g
2 S Vt t o^
- A 5 meter extension ladder leans against the wall; the bottom is 3 m from the wall. If the bottom stays at the same
place, how much should the ladder be extended so that the top would lean against the wall 1 meter higher? a) 1.2 m b) 1.5 m c) 0.5m d) 0.83095 m
LET h be the height of the wall then h 5 3 4 m
2 2
If it leans I m higher and let x be the extended length then 2 2
2 5 x 5 3 and x = 0.83095m.
- 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.
- 58 m 2
gt y vt
2 2 i
Therefore the stone is dropped at a height 131.58m above the ground.
- The salary of an employee’s job has five levels, each one 5% greater than the one below it. Due to circumstances, the
salary of the employee must be reduced from the top (fifth) level to the second level, which means a reduction of P3000.00 per month. What is the employee’s present salary per month? a) P22,032.50 b) P23,022.50 c) P22,320.50 d) P22,302.
Solution: The salary levels can be seen as a geometric sequence. Let Sn be the salary at level n.
S 3 1. 05 S 2 S 4 1. 05 S 3 S 5 1. 05 S 4
S 5 1. 05 1. 05 S 3 1. 05 2 S 3 1. 05 ^21. 05 S 2 1. 05 3 S 2
Due to circumstance, S 5 3 , 000. 00 S 2
P 22 , 032. 50
05 1
05 S 1. 05 S 3 , 000. 00 S 3
3 5 5
3 5
- 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, ,
o^ 180 o 108 o 5
5 2 180 No.ofSides
No. ofSides 2
- A cubical container that measures 50.8 mm on a side is tightly packed with eight marbles and is filled with water. All
eight marbles are in contact with the walls of the container and the adjacent marbles. All of the marbles are the same size. What is the volume of water in the container? a) 131 096.51 mm^3 b) 62 454.54 mm^3 c) 68 641.97 mm^3 d) 131 960.51 mm^3
Solution: Since marbles are tightly packed, rmarble = 12.7 mm
Volume of container, 3
3 Vcontainer 50. 8 131096. 5 mm
Solution: Solving first for A x B, let D = A x B, i 2 0 j 3 0 k 9 4 2 i 3 j 5 k
2 3 1
3 2 0
i j k A xB
Let E DC, then E DCDxC xDyCyDzCz 2 5 3 0 5 2 20
- Determine the rationalized value of the complex number 3 4 i
6 2. 5 i
.
a) 1.12 – 0.66i b) 0.32 – 0.66i c) – 32 + 0.66i d) – 1.12 + 0.66i
Solution: In order to rationalize a complex number, multiply the numerator and denominator by the complex conjugate of the denominator and simplify.
- 12 0. 66 i 25
28 16. 5 i 3 4 i 3 4 i
6 2. 5 i 3 4 i 3 4 i
6 2. 5 i
40. Determine the first derivative with respect to x of the function: g x 5 10 35.
a) ¾ b) 0 c) 4
3 4 9 d) 35
Solution: The derivative of a constant is zero.
- Determine the slope of the curve y x^2 at the point (2, 3).
a) 4 b) – 4 c) 2 d) – 2
Solution: The slope of a curve is given by the first derivative.
2 x dx
d x dx
dy y'
2
At point (2, 3): y' x y' 2 2 2 4
- What is the sum of the roots of the equation: 2x^2 + 5x + 5 = 0?
a) – 2.5 b) 2.5 c) 2.25 d) – 2.
Solution: The sum of the roots is: 2
5 a
b rsum x 1 x 2
- Determine the distance traveled by a particle between a time interval of 0.2 second to 0.3 second if its velocity is
t
7 V 12 t^4 , where V is in cm/s and t is in seconds.
a) 3.75 cm b) 2.84 cm c) 2.75 cm d) 3.84 cm
Solution: t
7 V 12 t dt
dS (^4)
3
2
(^4) dt t
7 dS 12 t
2. 84 cm
2
3
3 0. 2 7 ln 5
12 t
t t t 7 ln 5
12 S 5 5 1
5 2 1
5 2
- A force of 200 lb acts on a block at an angle of 28o^ with respect to horizontal. The block is pushed 2 ft horizontally.
Find the work done by this force. a) 480 J b) 408 J c) 840 J d) 804 J
Solution: W FdxFcosx 200 cos 28 2 353. 18 ftlb 480 J
- 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.
- 66 x 10 g/ atom
- 02 x 10
1 W 23 ^ ^24
- A truck starts from rest and moves with a constant acceleration of 6 m/s^2. Find the speed of the truck after 4 seconds.
a) 18 m/s b) 28 m/s c) 24 m/s d) 35 m/s
Solution: For uniformly accelerated motion, V V at 0 6 4 24 m/s
2
o
- A car starts from rest and has a constant acceleration of 3 fps^3. Determine the average velocity during the first 1 0
seconds of motion. a) 15 fps b) 20 fps c) 12 fps d) 18 fps
Solution: The distance traveled by the car, 3 10 150 ft 2
at 0 2
S Vt
2 2 o
15 fps 10
t
S
VAverage
- A ball is dropped from a height of 60 meters above ground. How long does it take to hit the ground?
a) 4.5 seconds b) 3.5 seconds c) 2.5 seconds d) 1.5 seconds
Solution: g t^2 2
1 S Vot
- 5 seconds
- 81
g
2 S Vt t
o
- A 5 meter extension ladder leans against the wall; the bottom is 3 m from the wall. If the bottom stays at the same
place, how much should the ladder be extended so that the top would lean against the wall 1 meter higher? a) 1.2 m b) 1.5 m c) 0.5m d) 0.83095 m
LET h be the height of the wall then h 5 3 4 m
2 2
If it leans I m higher and let x be the extended length then 2 2
2 5 x 5 3 and x = 0.83095m.
- 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.
- 58 m 2
gt y vt
2 2 i
Therefore the stone is dropped at a height 131.58m above the ground.
- The salary of an employee’s job has five levels, each one 5% greater than the one below it. Due to circumstances, the
salary of the employee must be reduced from the top (fifth) level to the second level, which means a reduction of P3000.00 per month. What is the employee’s present salary per month? a) P22,032.50 b) P23,022.50 c) P22,320.50 d) P22,302.
Solution: The salary levels can be seen as a geometric sequence. Let Sn be the salary at level n.
Solution: The resultant of vectors given in unit-vector form is the sum of the components.
R 4 9 5 i 7 2 3 j 6 11 8 k 18 i 6 j 9 k R 18 6 9 21
2 2 2
58. Given the following vectors: A = 3i + 2j, B = 2i + 3j + k, C = 5i + 2k. Simplify the expression A xB C.
a) 20 b) 0 c) 60i + 24k d) 5i + 2k
Solution: Solving first for A x B, let D = A x B, i 2 0 j 3 0 k 9 4 2 i 3 j 5 k
2 3 1
3 2 0
i j k
A xB
Let E DC, then E DCDxC xDyCyDzCz 2 5 3 0 5 2 20
- Determine the rationalized value of the complex number 3 4 i
6 2. 5 i
.
a) 1.1 2 – 0.66i b) 0.32 – 0.66i c) – 32 + 0.66i d) – 1.12 + 0.66i
Solution: In order to rationalize a complex number, multiply the numerator and denominator by the complex conjugate of the denominator and simplify.
- 12 0. 66 i 25
28 16. 5 i 3 4 i 3 4 i
6 2. 5 i 3 4 i 3 4 i
6 2. 5 i
60. Determine the first derivative with respect to x of the function: g x 5 10 35.
a) ¾ b) 0 c) 4
3 4 9 d) 35
Solution: The derivative of a constant is zero.
- Determine the slope of the curve
2 y x at the point (2, 3).
a) 4 b) – 4 c) 2 d) – 2
Solution: The slope of a curve is given by the first derivative.
2 x dx
d x dx
dy y'
2
At point (2, 3): y' x y' 2 2 2 4
- What is the sum of the roots of the equation: 2x^2 + 5x + 5 = 0?
a) – 2.5 b) 2.5 c) 2.25 d) – 2.
Solution: The sum of the roots is: 2
5 a
b rsum x 1 x 2
- Determine the distance traveled by a particle between a time interval of 0.2 second to 0.3 second if its velocity is
t
7 V 12 t^4 , where V is in cm/s and t is in seconds.
a) 3.75 cm b) 2.84 cm c) 2.75 cm d) 3.84 cm
Solution: t
7 V 12 t dt
dS (^4)
3
2
(^4) dt t
7 dS 12 t
2. 84 cm
2
3
3 0. 2 7 ln 5
12 t
t t t 7 ln 5
12 S 5 5 1
(^52) 1
5 2
- 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.
- Find the root mean square of 11, 23, and 35.
a. 25 b. 27 c. 26 d. 24
Root Mean Square (RMS),
- 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 y = age of the son x 5 3 y 5
x 10 2 y 10
x 5 3 y 15 x 10 2 y 20 x 3 y 10 x 2 y 10
3 y 10 2 y 10 y 20 x 3 20 20 40
Age of the son 12 years from now: 20 + 12 = 32 years old
- From the top of tower A, the angle of elevation of the top of the tower B is 46o. From the foot of tower B the angle of
elevation of the top of tower A is 28o. Both towers are on a level ground. If the height of tower B is 120 m, how high is tower A? a) 40.7 m b) 44.1 m c) 42.3 m d) 38.6 m
Solution: DE = 120 m
In triangle DCE,
Sin 44 o
CD Sin 46 28
DE
- 72 m sin 74
sin 44 120 sin 74
sin 44 CD DE o
o
o
o
h CDsin 28 o^ 86. 72 sin 28 o 40. 71 m
68. Determine the value of
1
1
3 5
x x sinxdx.
a. 0 b.1.75 c. 3.1416 d. infinity
Solution: cosx 0
x
4
x x x sinxdx
1 1
1
1
(^16)
1
1 4
1
- Determine the distance between the foci of a hyperbola if the lengths of the transverse and conjugate axes are 10 m
and 8 m, respectively. a. 20.8 m b. 12.8 m c. 13.8 m d. 25.6 m
Solution: S 2 c 2 a b 2 10 8 25. 61 m
2 2 2 2
- 29 7
18 24 27 30 35 42 50 Arithmetic Mean
25 3
11 23 35
n
(x)'s RMS
(^2222)
D
C
Tower A
Tower B
h
o
o
E
o
a) 15.34 units b) 13.45 units c) 18.76 units d) 17.32 units
Solution: by cosine law, c a^2 b^2 2 abcos 17. 32 units
- 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%
42. 131 % 52
P AorBPA PBPAandB
- A perfect gas is expanded polytropically with an initial volume and temperature of 0.06 m^3 and 147 0 C respectively.
If the final volume and temperature are 0.21 m^3 and 21 0 C respectively, what is the index of the expansion? a) 1.285 b) 1.212 c) 1.333 d) 1.
} solvingforn,n 1. 285 V
V
T
T (^) n 1
2
1
2
- If the loan was for 15 months at 16.8% interest a year and the repayment on a loan was P12,100.00, how much was
the principal? a) P8,500.00 b) P9,500.00 c) P10,000.00 d) P10,500.
Solution:
P 9 , 965. 10 P 10 , 000. 00
1 i
F
P (^) n 1. 25
- Determine the accumulated value of P2,000.00 in 5 years it is invested at 11% compounded quarterly.
a) P3,440.00 b) P3,404.00 c) P3,044.00 d) P4,304.
Solution:
P 3 , 440. 00 4
m
i F P 1
mn 45 n (^)
- The sum of P15,000.00, deposited in an account earning 4% per annum compounded quarterly, will become
P18,302.85. Determine the effective rate of interest per year. a) 3.06 % b) 4.06 % c) 5.06 % d) 6.06 %
Solution: 1 100 % 4. 06 % 4
m
i i 1
m 4 n e
- 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.
Solution: Cash Value = Down payment + Present value of the balance
P 193 , 912. 00
P 80 , 000. 00
m
i 1
F
Cash Value P 80 , 000. 00 mn 42 n
- Find the number of years when P2,500.00 is compounded to P5,800.00 if invested at 12% compounded quarterly.
a) P6.12 years b) 7.12 years c) 8.12 years d) 5.12 years
Solution: (^)
P
F
ln m
i mnln 1 P
F
m
i 1 n
mn n
- 12 years
ln 1
ln
m
i ln 1
P
F
ln
n (^) m 4 n
- What is the effective rate equivalent of 12% compounded quarterly?
a) 12.55% b) 11.55 % c) 12.98 % d) 13 %
Solution: 1 100 % 12. 55 % 4
m
i i 1
m 4 n e
- What rate compounded-quarterly is equivalent to 14% compounded semi-annually?
a) 10.76 % b) 11.76 % c) 12.76 % d) 13.76 %
Solution: 1 100 % 2
i i 1
4 2 n e
i 1
4 n (^)
i 4 1. 1449 4 1 13. 76 %
1 n
- Celestino owes P500, due in 3 years and P800 due in 7 years. He is allowed to settle these obligations by a single
payment on the 6th^ year. Find how much he has to pay on the 6th^ year if money is worth 14% compounded semi- annually. a) P1,449.12 b) P 1,559.12 c) P1,339.12 d) P1,669.
Solution:
750. 37 698. 75 P 1 , 449. 12
F 5001
21
23
6 th
- Cleofas borrowed P2,000.00 from a bank and agreed to pay the loan at the end of one year. The bank discounted the
loan and gave him P1950 in cash. Determine the rate of discount. a) 3.75 % b) 3.12 % c) 2.5 % d) 1.2 %
Solution: 100 % 2. 5 % 2 , 000. 00
F
F P
d (^)
- A machine was purchased under these terms: P30,000 down and P5,000 each month for 5 years. If money is worth
12% compounded monthly, what is the cash price of the machine? a) P144,775.19 b) P245,775.19 c) P542,775.91 d) P254,775.
Solution: Cash Price = Down Payment + Present Worth of Annuity
mn n
mn n
m
i i 1
m
i A 1
CashPrice DownPayment
P 254 , 775. 19
Cash Price P 30 , 000. 00 1295
125
104.What do you call a triangle having three unequal sides?
a) Obtuse b) Oblique c) Scalene d) Isosceles
105.How do you call the distance of a point from the y-axis?
a) Polar distance b) Coordinate c) Abscissa d) Ordinate
106.This is the measure of central tendency defined as the most frequent score. How do you call this measure of central
tendency? a) Median b) Mode c) Mean d) Deviation
107.Which of the following is the equivalent of 1 mil?
a) One-tenth of an inch b) One-thousandth of an inch c) One millionth of an inch c) One-half of an inch
108.A polygon with ten sides is said to be:
a. Dodecagon b. Decagon c. Decahedron d. Dodecahedron
- Any number expressed in place-value notation with base 12 is known as:
a. Duodecimal b. Deontic c. Decile d. Dedekind
- Another name for derivative is said to be:
a. Differential manifold b. Partial derivative c. Differential form d. Differential coefficient
111.Another term for rhombus is said to be:
a. Dichotomy b. Diamond c. Cyclic quadrilateral d. Bi-rectangular
112.A prefix denoting a multiple of ten times any of the physical units of the system international.
a. Deka b. Nano c. Hecto d. Exa
113.The father of plane geometry.
a. Euclid b. Pythagoras c. Aristotle d. Galileo
114.This is the case of a solution of a plane triangle where the given data leads to two solutions. How do you call this
case? a) Ambiguous case b) Quadratic case c) Extraneous case d) Conditional case
115.It is a type of polygon in which each interior angle must be less than or equal to 180°, and all vertices 'point outwards'
away from the interior. How do you call this polygon? a) Concave Polygon b) Convex polygon c) Regular polygon d) Irregular polygon
116.It is a series of equal payments occurring at equal intervals of time where the first payment is made after several
periods, after the beginning of the payment. How do you call this payment? a) Deferred annuity b) Delayed annuity c) Progressive annuity d) Simple annuity
117.What do you think is the negotiation of wage rates, conditions of employment, etc. by representatives of the labor
force and management? a) Union trade b) Union rally c) Collective bargaining d) Cooperative
118.How do you call a type of bond where the corporation’s owner name is recorded and the interest is paid periodically
to the owners with their asking for it? a) Registered bond b) Preferred bond c) Incorporator’s bond d) Bail bond
119.How do you call the integral of any quotient whose numerator is the differential of the denominator?
a) Co-logarithm b) Logarithm c) Product d) Derivative
120.What is a regular polygon that has 27 diagonals?
a) Nonagon b) hexagon c) Pentagon d) Heptagon
121.How do you call the formula used to compute the value of n factorial, which is in symbolic form (n!), where n is
large number? a) Matheson formula b) Diophantine formula c) Richardson-Duchman formula d) Stirling’s Approximation
122.What is the reason why an ivory soap floats in water?
a) All matter has mass b) The specific gravity of ivory soap is greater than that of water c) The density of ivory soap is unity d) The specific gravity of ivory soap is less than that of water
123.When two planes intersect with each other, the amount of divergence between the two planes is expressed by
measuring the: a) Reflex angle b) Dihedral angle c) Polyhedral angle d) Plane angle
124.What do you think is the output or sales at which income is insufficient to equal operating cost?
a) Break even point b) Depreciation c) Investment d) Cash flow
125.What is an estimate of assets’ net market value at the end of its estimated life?
a) Book value b) Depreciation c) Salvage value d) Cash flow
126.What do you think is the lessening of the value of an asset due to a decrease in the quantity available as a coal, oil
and timber in forests? a) Depletion b) Amortization c) Depreciation d) Investment
127.What can you say about the present worth of all depreciation over the economic life of the item?
a) Maintenance b) Capital recovery c) Depreciation recovery d) Annuity
128.What do you think is the provision in the contract that indicates the possible adjustment of material cost and labor
cost? a) Secondary clause b) Specification c) Escalatory clause d) General provision
129.This is the process of determining the value of certain property for specific reasons. Guess, what is this?
a) Amortization b) Investment c) Appraisal d) Depreciation
130.How do you call those products or services that are directly used by people to satisfy their wants?
a) Consumer goods and services b) Producer goods and services c) Necessity products and services d) Luxury products and services
131.These are used to produce consumer goods and services. Guess, what are these?
a) Consumer goods and services b) Producer goods and services c) Necessity products and services d) Luxury products and services
132.What do you think are those products or services that are required to support human life and activities that will be
purchased in somewhat the same quantity even though the price varies considerably? a) Consumer goods and services b) Producer goods and services c) Necessity products and services d) Luxury products and services
133.How do you call a cylinder with elliptical cross section?
a. Ellipsoid b. Cylindroid c. Hyperboloid d. Paraboloid
134.How do you call a market whereby there is only one buyer of an item for which there are no goods substitutes?
a) Monopoly b) Monopsony c) Oligopoly d) Oligopsony
135.Which statement about a charge placed on a dielectric material is true?
a. The charge increases the conductivity of the material b. The charge is confined to the region in which the charge was placed. c. The charge is immediately lost to the atmosphere d. The charge is instantly carried to the material’s surface
In a dielectric, all charges are attached to specific atoms or molecules.
136.Which of the following is not a property of magnetic field lines?
a) Magnetic field lines have no beginnings and no ends b) The lines cross themselves only at right angles c) The line intersect surfaces of equal intensity at right angles d) The field is stronger where the lines are closer together
Magnetic field lines do not cross. Their direction at any given point is unique.
137.Tesla is a unit of which of the following?
a) Magnetic induction b) Inductance c) Capacitance d) magnetic flux
138.What is a pole pitch?
a) The angle at which the pole windings are wound b) The space on the stator allocated to two poles c) The space on the stator allocated to one pole d) The mica used to insulate the poles from each other
a. Icosahedron b. Octahedron c. Dodecahedron d. Tetrahedron
159.Two angles whose sum is 360o^ is called:
a. Explementary angles b. Complimentary angles c. Supplementary angles d. Elementary angles
160.What is an annuity?
a) The future worth of a present amount. b ) A series of uniform amounts over a period of time c) The present worth of a future amount d) An annual repayment of a loan
161.When using net present worth calculations to compare two projects, which of the following could invalidate the
calculation? a) Use of the same discount rate for each period b) Differences in the magnitudes of the projects c) Evaluating over different time periods d) Mutually exclusive projects
a), b) and d) are all problems with internal rate of return calculations that net present worth handles nicely. However, the net present worth of two projects must be calculated for the same time period.
162.What must two investments with the same present worth and unequal lives have?
a) Different equivalent uniform annual cash flows b) Identical salvage values c) Different salvage values d) Identical equivalent uniform annual cash flows
163.Which of the following is true regarding the minimum attractive rate of return used in judging proposed investments?
a. It is much smaller than the interest rate used to discount expected cash flows from investments b. It is frequently a policy decision made by an organization’s management c. It is larger than the interest rate used to discount expected cash flow from investments d. It is not relevant in engineering economy studies
164.Which of the following situations has a conventional cash flow so that an internal rate of return can be safely
calculated and used? a. Your company undertakes a mining project in which the land must be reclaimed at the end of the project. b. You invest in a safe dividend stock and receive dividends each year. c. You lease a car and pay by the month d. Your company invests heavily in a new product that will generate profits for two years. To keep profits high for 10 years, the company plans to reinvest heavily after two years.
The situation in choice b) has a negative cash flow, one sign change, then positive cash flow. Thus, it is the only situation that has a conventional cash flow so that an IRR can be safely calculated and used.
165.The economic order quantity (EOQ) is defined as the order quantity which minimizes the inventory cost per unit
time. Which of the flowing is not an assumption of the basic EOQ model with no shortages? a) Reordering is done when the inventory is zero b) There is an upper bound on the quantity ordered c) The entire reorder quantity I delivered instantaneously d) The demand rate is uniform and constant
Recall that, h
2 aK EOQ (^) , 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 of the following events will cause the optimal lot size, given by the classic EOQ model with no shortages, to
increase? a) A decrease in inventory carrying cost b) A decrease in demand c) An increase in demand d) a) or c) above
h
2 aK EOQ , 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, a decrease in inventory carrying cost, h, or an increase in demand, a, will cause the optimal lot size to increase.
167.What is a borrower of a particular loan almost always required to do during repayment?
a) Pay exactly the same amount of principal each payment b) Repay the loan over an agreed-upon amount of time c) Pay exactly the same amount of interest each payment d) Pay the interest only whenever failure to pay the principal
168.How to you classify work-in-process?
a) A liability b) An expense c) A revenue d) An asset
Work-in-process is included in the working fund investments. The working fund investments is an asset not subjected to depreciation.
169.What is the indirect product cost (IPC) spending variance?
a. The IPC volume adjusted budget minus the total IPC absorbed b. The IPC volume adjusted budget [fixed + volume (variable IPC rate)] c. The difference between actual IPC and IPC volume adjusted budget d. The difference between actual IPC and IPC absorbed
170.A leak from a faucet comes out in separate drops. Which of the following is the main cause of this phenomenon?
a) Air resistance b) Gravity c) Surface tension d) Viscosity of the fluid
171.Which of the following elements and compounds is unstable in its pure form?
a) Hydrochloric acid b) Carbon dioxide c) Sodiu m d) Helium
172.What is the actual geometric shape of the methane molecule?
a) Tetrahedral b) Pyramidal c) Square planar d) Linear
173.A substance is oxidized when which of the following occurs?
a) It losses electrons b) It becomes more negative c) It gives off heat d) It absorbs energy
By definition, a substance is oxidized when it losses electrons.
174.Reactions generally proceed faster at higher temperatures because of which of the following?
a) The molecules are less energetic b) The activation energy is less c) The molecules collide more frequently d) Both b) & c) above
175.Which one of the following statements regarding organic substances is false?
a. Organic matter is generally stable at very high temperatures b. Organic substances generally dissolve in high-concentration acids c. All organic matter contains carbon d. Organic substances generally do not dissolve in water.
176.Which of the following affects most of the electrical and thermal properties of materials?
a) The weight of the atoms b) The weight of the protons c) The electrons, particularly the outermost one d) The magnitude of electrical charge of the protons
The outermost electrons are responsible for determining most of the material’s properties.
177.What are the valence electrons?
a) The electrons of complete quantum shells b) Electrons with positive charge c) The outer-shell electrons d) The K-quantum shell electrons
By definition, the outermost electrons are the valence electrons
178.How do you call the strong bond between hydrogen atoms?
a) Ionic and metallic bonds b) The covalent bond c) The ionic bond d) The metallic bond
Covalent bonds provide the strongest attractive forces between atoms.
179.What are Van der Waals forces?
a) Forces present only in gases b) Forces not present in liquids c) Primary bonds between atoms d) Weak secondary bonds between atoms
