CE INTEGRATION

Second Semester, SY: 2024 - 2025

EVALUATION EXAM 4

INSTRUCTION: Select the correct answer for each of the following questions. Mark only one answer for
each item by shading the circle corresponding to the letter of your choice on the answer sheet provided.
STRICTLY NO ERASURES ALLOWED.
STATISTICS & PROBABILITY

1. The mean of three numbers is 3 and the variance is 3. A second set of five numbers has a mean of 5 and
variance of 5. What is the variance of the combined set?
a. 5.2 c. 5.6
b. 5.4 d. 5.8
2. If the sum of the squares of five numbers is 165 and their variance is 8. What is the mean of the numbers?
a. 3 c. 5
b. 4 d. 6
3. Consider the following scores of 10 students: 81, 45, 55, 68, 46,96, 65, 49, 67, 67. Which among the following
statements is not correct?
a. The mean is 64 c. The mode is 67
b. The median is 66 d. The range is 51
4. What is the standard deviation of these set of numbers? 43, 52, 81, 95, 53, 58, 41, 32, 89, 60
a. 20.14 c. 24.01
b. 21.04 d. 24.10
5. Consider the following actual indices of university ranking: 886, 903, 858, 920, 491, 827, 819, 873, 751, 867,
807, 655, 794. Calculate the interquartile range.
a. 69 c. 89
b. 79 d. 99
6. Which among the following sets of numbers will yield the minimum standard deviation?
a. {1, 5, 6, 10} c. {1, 4, 7, 10}
b. {2, 3, 4, 5} d. {1, 8, 9, 10}
7. With the data: 33, 10, 9, 30, 21, 21, 30, 30, 28. Find the 37th percentile.
a. 18 c. 21
b. 20 d. 22
8. In how many ways can you select 10 questions from a set of 15 questions, if the first 5 to be selected will come
from the first 7 questions from the set.
a. 3003 c. 756
b. 252 d. 1176
9. In how many ways can you select one architect and 3 civil engineers from a pool of 3 architects and 7 civil
engineers?
a. 38 c. 35
b. 105 d. 630
10. What is the probability of selecting a King in a deck of cards?
a. 1/13 c. 1/4
b. 1/12 d. 1/10
11. Hollow block has been supplied by 4 suppliers. 40% is from Supplier A, 25% from Supplier B, 20% Supplier C
and 15% from Supplier D. If the percentage of defect hollow block in each supplier is as follows: A: 1%, B: 2%,
C: 3% and D: 5%. Find the probability that if a hollow block is defective, it was supplied by Supplier C.
a. 4/15 c. 8/15
b. 2/5 d. 2/3
12. When drawing three cards from standard deck of cards find the probability, that they are all face cards.
a. 11/850 c. 11/1105
b. 33/4420 d. 6/1105
13. PAG-ASA has predicted there is an 80% chance of raining during the week. What is the probability that it is
raining in at least 5 days of that week?
a. 27.53% c. 20.97%
b. 36.70% d. 85.20%
 CE INTEGRATION
Second Semester, SY: 2024 - 2025

14. Five estimators measure the distance of two points. They got an average of 135 meters with the standard
deviation of 2.4 meters. Find the standard error of their measurements
a. 1.073 meters c. 1.386 meters
b. 1.200 meters d. 1.697 meters
15. Find the sum of all cubes of odd number below 20.
a. 16900 c. 18900
b. 17900 d. 19900
16. A restaurant offers 7 types of viands, 3 types of rice, 4 types of drinks. In how many ways can select 2 viands, 1
rice type and a drink if he doesn’t want to order one of the viands?
a. 504 c. 252
b. 360 d. 180
17. What is the probability of getting a sum of 8 in a throw of 2 dice?
a. 1/2 c. 1/9
b. 5/36 d. 1/12
18. In a deck cards, what is the probability of drawing read or a face card?
a. 7/13 c. 9/13
b. 8/13 d. 10/13
19. In a throw of a single die, what is the probability of getting an even or a prime number?
a. 1/3 c. 2/3
b. 1/2 d. 5/6
20. A box has 6 blue balls and 4 red balls. In drawing two balls. Find the probability that they have different color.
a. 2/5 c. 8/15
b. 7/15 d. 3/5

ENGINEERING ECONOMICS

21. A bank load of P50,000 was made at 8% simple interest. How long would it take in years for the amount of the
loan and interest to equal P74,000?
a. 5 c. 7
b. 6 d. 8
22. Compute the equivalent rate of 6% compounded semi-annually to a rate compounded quarterly.
a. 6.59% c. 5.69%
b. 6.95% d. 5.96%
23. Ten years ago, the value of money was P120,000 and now its worth P179,000. Find the single payment amount
factor.
a. 1.492 c. 1.925
b. 1.942 d. 1.429
24. A contractor estimates that he could finish a certain project in 15 days if he has 20 men. At the start, he hired 10
men, then after 6 days, 10 more men are added. How many days the project was delayed?
a. 3 c. 5
b. 4 d. 6
25. An economy is experiencing inflation at an annual rate of 6%. If this continues, what will $100 will be worth five
years from now, in terms of today’s dollar?
a. $84.73 c. $94.73
b. $74.73 d. $64.73
26. A machine costing P1.8M has a salvage value of P300,000 after 5 years. Calculate the depreciation value
(book value) at the end of 3 years using the straight-line method.
a. P900,000 c. P750,000
b. P860,000 d. P700,000
27. A machine costing P1.5M has a salvage value of P600, 000.00 at the end of its economic life. What is the
economic life of this machine if using the sum-of-the-years digit method, its book value at the end of 2 years is
estimated to be 870,000.00?
a. 4 c. 6
b. 5 d. 7
 CE INTEGRATION
Second Semester, SY: 2024 - 2025

28. The revenue selling N number of computer units is R = 80N and the cost to produce them is C = 60N + 10,000.
How many computer units must be sold to break even?
a. 400 c. 500
b. 800 d. 600
29. Determine the approximate size of an annual payment needed to retire P60,000,000 in bonds issued by a city
to build a dam. The bonds must be repaid over a 50-year period, and they earn interest at an annual rate of 6%
compounded annually.
a. P3,810,000 c. P4,125,000
b. P3,540,000 d. P4,326,000
30. A father wants to set aside money for his 5-year old son’s future college education. Money can be deposited in
a bank account that pays 8% per year, compounded annually. What equal deposits should be made by the
father, on his son’s 6th through 7th birthdays, in order to provide P80,000 on his son’s 18 th, 19th, 20th, and 21th
birthdays?
a. P12,547 c. P15,589
b. P14,228 d. P13,963
31. How long does it take an investment of P200,000 to double if its invested 5% interest compounded quarterly?
a. 14 years c. 18 years
b. 15 years d. 20 years
32. If money is invested at a nominal rate of interest of 9% for a period of 5 years. What is the value of the
compound amount factor if it is compounded continuously?
a. 1.458 c. 1.568
b. 1.632 d. 1.365
33. A manufacturing company has a production capacity of 600,000 units with an income of P720, 000. The
company’s fixed expense is P250, 000 and the cost to produce per unit is P0.7. Compute the number of units to
break even.
a. 500,000 c. 550,000
b. 450,000 d. 400,000
34. A loan of $8000 is borrowed to be repaid with uniform periodic payment at a nominal rate of 12% over 5 years.
What is the payment if made annually?
a. $2192 c. $2219
b. $2291 d. $2129
35. Compute the effective annual interest rate equivalent to 5% nominal annual interest compounded continuously.
a. 5.13% c. 5.23%
b. 5.18% d. 5.28%
36. Determine the capitalized cost of a large format printer that has a first cost of P1.2Million and salvage value
after five useful years equal to P600,000.00. The operation and maintenance cost P 100,000.00 every after 3
years. Use interest rate, i=10.1%
a. 2.47M c. 3.41M
b. 2.56M d. 2.89M
37. P10,000 is deposited into a 9% account today. At the end of year 2, another P30,000 will be deposited. In year
5, a P40,000 purchase will be made. Approximately, how much will be left in the account 1 year after the
purchase?
a. P12,500 c. P15,500
b. P13,500 d. P14,500
38. The Department of Highways will be widening a two-lane road into a four-lane freeway this summer. The project
requires to purchase of $22M worth of land for the additional two lanes. If the department uses an interest rate
of 6%, what is the EAC of the right-of-way?
a. $1.23M c. $2.31M
b. $2.13M d. $1.32M
39. A businessman wishes to raise P1.5Million in every year by investing a fixed amount of money every end of the
year for three years. What is the required investment using an interest rate of 8%.
a. 635,740.00 c. 475,360.00
b. 547,630.00 d. 396,134.00
40. Equipment with first cost of P1.8M has a salvage value of P300, 000 at the end of 5 years. Using the constant
percentage method, what is the total depreciation after three years?
 CE INTEGRATION
Second Semester, SY: 2024 - 2025

a. 591,723 c. 985,365
b. 614,302 d. 1,185,691

PHYSICS

SITUATION 41-43. A particle moves along a straight line according to the function s = 3t3 – 36t + 2, where s is the
distance traveled in meters and t is in seconds. Determine the following:
41. The time required for the particle to reach a velocity of 45 m/s.
a. 3 c. 5
b. 4 d. 6
42. The acceleration of the particle when v = 108 m/s
a. 54 m/s c. 72 m/s
b. 27 m/s d. 45 m/s
43. The net displacement of particles from t = 5s to t = 2s.
a. 324 c. 432
b. 243 d. 234
44. As seen in the figure, what is the acceleration between point A and B?
a. 0.594 c. -0.625
b. -0.594 d. 0.625

45. Calculate the velocity v of the 50-kg crate when it reaches the bottom
of the chute at B if it is given an initial velocity of 4 m/s down the
chute at A. The coefficient of kinetic friction is 0.30.
a. 1.25 c. 3.15
b. 3.69 d. 4.78

46. The crate, which has a mass of 100 kg, is subjected to the
action of the two forces. If it is originally at rest, determine the
distance it slides in order to attain a speed of 6 m/s. The
coefficient of kinetic friction between the crate and the surface
is μk 0.20.
a. 1.35 m c. 1.95 m
b. 3.50 m d. 2.25 m

SITUATION 47-48. Starting from rest, a particle moving in a straight line has an acceleration of a = (2t – 6) m/s 2, where t
is in seconds.
47. What is the particle’s velocity when t = 6 s.
a. 0 c. 2
b. 1 d. 3
48. what is its position
a. 92.8 m c. 80.7 m
b. 77.3 m d. 64.8 m
49. Large freight trains accelerate very slowly. Suppose one such train accelerates from rest, giving its 0.350-m-
radius wheels and angular acceleration of 0.250 rad/s 2. After the wheels have made 200 revolutions (assume
no slippage). How far has the train moved down the track?
a. 439.82 m c. 677.01 m
b. 512.88 m d. 493.95 m
50. A bullet in motion hits and gets embedded in a solid block resting on a frictionless table. What is conserved?
a. Momentum and Kinetic Energy
b. Kinetic Energy alone
c. Neither Kinetic Energy nor momentum
d. Momentum alone

51. A massive truck collides head on with a small car. Which of the following are correct?
 CE INTEGRATION
Second Semester, SY: 2024 - 2025

A. Both the car and the truck experience the same force of impact.
B. Car experience greater acceleration
C. Truck experience greater acceleration.
D. Car experience greater force of impact.
E. None of these.
a. A c. B and D
b. A and B d. D
52. A bucket 200 mm in diameter and 300 mm in height is 2/3 full of water. It is swung in a vertical plane such its
bottom of the bucket describes a circle of radius of 1 m. Determine the speed of rotation (in rpm) such that no
water is spilled.
a. 31.5 c. 25.6
b. 18.4 d. 38.5
53. What is the required angle of banking of a 200-m-radius curve such that there is no shearing stress between
tires and the pavement at a speed of 90 kph? The coefficient of friction between tires and the pavement is 0.45.
a. 15.25 degrees c. 16.78 degrees
b. 17.68 degrees d. 12.55 degrees
54. An elevator starting from rest at the first floor of a tall condominium accelerates uniformly at 2m/s 2 for the first 4
seconds, then move at constant speed in the next 10 seconds, then decelerate uniformly in the next 6 seconds
until it stops. If the floors are 3 meters apart, at what floor did the elevator stop?
a. 39 c. 41
b. 40 d. 42
SITUATION 55-57. A jet is issued from the side of a tank under a constant
as shown. The side of the tank has an inclination of 1H to 1V. The total
depth of water in the tank is 8 m and the orifice are located 3 m above the
bottom of the tank. Neglecting air resistance and assuming Cv = 1.0, Note:
vo = Cv√ 2 gH , determine the following:
55. The maximum height to which the jet will rise above the orifice.
a. 2.5 m c. 2.0 m
b. 3.0 m d. 3.5 m
56. The point x2 the jet will strike a horizontal plane 1.2 m bellow the bottom of the tank.
a. 14.7 m c. 15.6 m
b. 11.1 m d. 13.2 m
57. The time it takes for the jet to strike a horizontal plane 1.20 m below the bottom of the tank.
a. 1.88 s c. 1.54 s
b. 2.32 s d. 1.62 s
SITUATION 58-60. A flywheel with radius of 40 cm is rotating at 250 rpm.
58. If the wheel is rotating at a constant angular speed, how many revolutions will it make in 12 seconds?
a. 25 c. 75
b. 50 d. 45
59. If flywheel is decelerating at -2 rad/s, how many revolutions will it make in 10 seconds?
a. 25.75 revolution c. 25.25 revolution
b. 25.50 revolution d. 25. 45 revolution
60. If the flywheel is decelerating at 5 rpm per second, many revolutions will it make before it comes to a complete
stop?
a. 101.4 rev c. 104.1 rev
b. 114.2 rev d. 102.4 rev