College of Engineering Education

2nd Floor, BE Building

Matina Campus, Davao City
Telefax: (082)296-1084
Phone No.: (082)300-5456/300-0647 Local 133

CE 601- ACHIEVEMENT EXAM E

Instructions:
A. Mark only one answer for each item by shading the box corresponding to the letter of your choice using No. 2 pencil
only.
B. Write your solutions on the papers provided.
C. Borrowing of calculator is not allowed.
D. Once the examination has started, you are not allowed to leave the testing area.
E. Once finished, submit the questionnaire and your answer sheet.
F. If you think the correct answer is not in the choices, select letter “e”.
1. Are funds supplied by others on which a fixed rate of interest must be paid and the debt be repaid at a specific
time.
a. Annuity
b. Equities
c. Borrowed capital
d. Gratuitous
2. Is the length of time on which the property maybe operated at a profit.
a. Economic life
b. Period
c. Depreciation
d. Capitalized cost

3. Given the equation of the lines: 3x+4y-12=0 and 6x+8y+2=0. Find the acute angle between them in degrees.
A. 8 B. 0 C. 6 D. 4

4. Spaceship WilliamX is approaching touchdown on planet Bartz at height y (meters) and time t (seconds) given by
y=100-100t+25t^2. Determine the speed of the spaceship WilliamX as it lands of the surface of Bartz.
A. 50 m/s B. 100 m/s C. 25 m/s D. None in list
5. What is the area of an octagon inscribed in a circle having an area of 126 m2?
A. 113.4 B. 213.4 C. 123.4 D. 122.4
6. How many solutions does the system have?
3y+6=12x
-y=-4x+2

A. One B. Two C. Infinitely many D. None

7. The perimeter of a triangle is 84 m while its area is 102 m2. Determine the diameter of the circle that maybe inscribed
in this triangle.
A. 14.86m B. 4.86m C. 5.38m D. 15.38m

8. Suppose that y varies inversely with x. Write the inverse variation when y=6 and x=8.
A. y=x/48 B. y=48/x C. y=3/(2x) D. y=3x/2

9. A spherical balloon with an initial radius C of 5 inches, begins to leak at time t=0, and its radius t seconds later is C =
DEFG
JK. At what rate (in cubic inches per second) is air leaking from the balloon when t=30 seconds?
HI
A. 6.545 B. 7.545 C. 8.545 D. 9.545

10. Two wheels are rolling along parallel straight lines at the same linear speed. One of the wheels has a diameter of 12 cm
while the other has a diameter of 18 cm. If they are allowed to roll until the larger wheel has revolved 72 times, how
many times has the smaller wheel probably revolved?
A. 92 B. 108 C. 96 D. 120
11. Solve for the solution set of the equation: |3x+2|+7=14
A. 5/3 and -23/3 B. -23/3 and -3 C. 5/3 only D. 5/3 and -3
O
MN
P
12. Which of the following is equivalent to P R ?
N
Q S
A. 16 B. 1 C. 16/x D. 32/x
13. King Ernest is spent 100/x % of his gold deposit yesterday. He is set to earn gold today. What percentage of the
amount of gold King Ernest currently has would he need to earn today to end up with as much gold as he started?
A. 100/x % B. 100/(x-1) % C. x/(x-1) % D. (x-1)/x %
14. Each edge V of a square is increasing at the rate of 2 JK/W. At what rate is the area X of the square increasing when
edge is 10 JK?
A. 10 in2/s B. 20 in2/s C. 30 in2/s D. 40 in2/s

15. What is the area of a regular heptagon with side s=12 cm?
A. 222.32 B. 318.54 C. 503.68 D. 523.28

16. Two sides of a parallelogram measure 68 and 83 cm and its shorter diagonal is 42 cm. What is the largest interior angle
of the parallelogram?
A. 30.27° B. 149.73° C. 132.23° D. 123.65°

17. What is the slope of the curve y=2sinx at x=1°?

A. A. 1 B. B. 2 C. C. 3 D. D. 4
18. A triangular piece of land has vertices A, B and C and is surveyed producing the following data: A=30°, C=50° and
AC=13 m. What should be the length of side AB?
A. 7.89 m B. 8.23 m C. 9.54 m D. 10.11 m

19. A certain radio wave takes the form of a sine curve and is expressed by the equation y=5sin2x. What is the frequency of
this wave?
A. 3.14 B. 2.01 C. 0.32 D.1.87

20. Which of the following could be a product of an even prime number and odd prime number?
A. 6 B. 10 C. 14 D. All of the above

21. A sandwich is made by putting cheese and ham between two pieces of bread. You are given five types of cheese, two
kinds of ham and three choices of bread. How many different sandwiches can you make?
A. 10 B. 20 C. 30 D. 60

22. A steel structural member has a mass of 400 kg. If each of its dimensions are reduced by 30%, determine its new mass.
A. 133.3 kg B. 134.2 kg C. 137.2 kg D. None in list

23. There exist a value x such that the tangent of the expression 2x + 18 is equal to the cotangent of the expression 4x – 12.
Find the value of x.
A. 15 B. 14 C. 13 D. 12

24. Lot ABCDEFA is a closed traverse in the form, of a regular hexagon with each side equal to 100 m. The bearing of AB
is N 25°E. What is the bearing of FA?
a.) N 35° W
b.) N 15° W
c.) N 34° E
d.) N 30° W

25. With the line of sight making an angle of 4°30’ with the horizontal, the length intercepted on the stadia rod is 1.8 m.
the stadia constant is 0.30 and the stadia interval factor is 100.determine the vertical distance of the point sighted
above the instrument.
a.) 14.10 m
b.) 14.5 m
c.) 13.50 m
d.) 15.0 m
26. A train running at 60 kph decelerated at 2m/min^2 for 14 minutes. Find the distance travelled, in km.
within this period.
A. 12.2 C. 13.8
B. 13.2 D. 12.8

27. From a speed of 30 kph at point A, a car accelerated uniformly. After 18 minutes it reached point B, 21 km.
from A. Find the acceleration in m/s^2.
A. 0.0804 C. 0.0633
B. 0.0206 D. 0.0467

28. A car drives East from point A at 30 kph. Another car, starting from B at the same time, drives S 30
degrees toward A at 60 kph. , B is 30 km. away from A. How fast in kph., is the distance between the two
cars changing after one hr.?
 A. 43 C. 45
B. 44 D. 40
29. Annie buys a television set from a merchants who offers P 25,000.00 at the end of 60 days. Annie wishes to pay
immediately and the merchant offers to compute the required amount on the assumption that money is worth 14%
simple interest. What is the required amount?
a) P 23,429.97
b) P 24,429.97
c) P 25,429.97
d) P 26,429.97

30. The tag price of a certain commodity is for 100 days. If paid in 31 days, there is 3% discount. What is the simple
interest paid?
a) 13.14%
b) 14.14%
c) 15.14%
d) 16.14%

31. How long will it take P1,000 to amount to P1,346 if invested at 6% compounded quarterly.
a) 3 years
b) 4 years
c) 5 years
d) 6 years

SIT : Solve the following Solid Mensuration problems.

32. Find the depth of a hopper to hold 35 gantas of grain, if it is to be build in the shape of a frustum of a square pyramid
with the upper and lower bases measuring 60 cm and 35 cm on a side respectively. Note: 1 ganta is equal to 3 liters.
A. 25 cm B. 35 cm C. 45 cm D. 55 cm

33. Find the volume of the largest cube that can be cut from a sphere of diameter 5 cm.
A. 21 cm3 B. 24 cm3 C. 28 cm3 D. 37 cm3

34. The inside diameters of the bases of a flowerpot are 10 cm and 7 cm, and the slant height is 9 cm. How many cubic
meters of soil does it contain when it is completely filled?
A. 509 cm3 B. 576 cm3 C. 622 cm3 D. 693 cm3

SIT : Determine the domain of the following functions:

35. y=sqrt(x-1)
A. {x|x Є ^, x_1` B. {x|x Є ^, x≥1` C. {x|x Є ^, x>1` D. {x|x Є ^, x>-1`
36. y=(x^2+2x-1)/(x^2-1)
A. {x|x Є ^, x_1` B. {x|x Є ^, x_1 ⋃ x_-1` C. {x|x Є ^, x=1` D. {x|x Є ^`

37. y=sin-1(2x+5)
A. {x|x Є ^, -3<x<2` B. {x|x Є ^, -3≥x≥2` C. {x|x Є ^, x≤-3 ⋃ x≥2` D. {x|x Є ^, -3≤x≤2`

SIT : Solve the following algebra problems:

38. In a class of 78 students 41 are taking French, 22 are taking German and 9 students are taking both French and
German. How many students are not enrolled in either course?
A. 12 B. 14 C. 24 D. 54

39. If (x+2), (2x+3), (5x-6) are consecutive terms of arithmetic progression, the value of x equals:
A. 4 B. 5 C. 6 D. 2

40. 145,300,610,1230…
In the above sequence every term after the first is formed by multiplying by x and then adding y, where x and y are
positive integers. What is the value of x + y?
A. 2 B. 10 C. 12 D. 14

SIT : Given the following velocity vectors: VA=3i+4j-k and VB=i-2j+5k.

41. Which of the following gives the value of VA+VB?
A. 4i-6j+6k B. 4i+2j+4k C. 4i-2j-4k D. 4i+4j+2k

42. What is the magnitude of VA+VB?

A. 9.38 B. 6 C. 6.67 D. 7.48

43. What is the magnitude of VA-VB?

 A. 8.72 B. 7.62 C. 7.86 D. 9.50

SIT : A 50 m. tape was standardized and was found to be 0.0042 m. too long than the standard length at an observed
temperature of 58oC and a pull of 15 kilos. The same tape was used to measure a certain distance and was recorded
to be 673.92 m. long at an observed temp. of 68oC and a pull of 15 kilos. Coefficient of linear expansion is
0.0000116/oC.
44. Determine the standard temperature.
a) 50.76oC
b) 40.76oC
c) 30.76oC
d) 20.76oC
45. Determine the total correction.
a) 0.4813 m
b) 0.3481 m
c) 0.1348 m
d) 0.8134 m
46. Determine the true length of the line.
a) 674.401 m
b) 674.733 m
c) 674.268 m
d) 674.055 m
SIT : A company wants to purchase dump truck, which cost P 800 000 and a salvage value of P 100 000 after useful life of 5
years or rent at a cost of P 1255/day. Annual cost of operation and maintenance is P 12 000. How many days that the
dump truck should be used so that the purchased are compensated if the rate is 15%? Use sinking fund method for
depreciation.
47. What is the annual cost for the purchase of truck?
a. P 237 898.48
b. P 212 698.48
c. P 235 820.89
d. P 191 181.76
48. How many days per year that the dump truck will be used so that the purchased are compensated?
a. 188
b. 166
c. 177
d. 199
49. How much is the book value at the end of 10 years?
a. P 35 000
b. P 70 000
c. P 85 000
d. P 15 000

50. A ramp meter operates during the morning peak period. Ramp meter cycles vary with time as shown in the table
below. The metering scheme allows one vehicle per cycle to pass the signal. The table below gives the number of
vehicles demanding service on the ramp during the particular time intervals, the cumulative demand for the ramp
for the morning peak, and the ramp meter cycle for each interval. What are the service rates for meter cycle 12,10,
and 6?
Time Period 15min Vol. Cumulative Vol. Meter cycle, s
6:30 – 6:45 75 75 6
6:45 – 7:00 100 175 10
7:00 – 7:15 125 300 12
7:15 – 7:30 110 410 12
7:30 – 7:45 80 490 10
7:45 – 8:00 65 555 6
A. 85,65,145 veh C. 145,65,85 veh
B. 150,90,75 veh D. 75,90,150 veh

51. The formula log (1-k) = -0.3/H models the relationship between the half-life H of a radioactive material and its rate of
decay k. Find the rate of the decay of the iodine isotope 1-131 if its half-life is H days. Round to four decimal places.
A. 0.1827 C. 0.0627
B. 0.3827 D. 0.0827

52. An industrial engineer has found that when she takes a sample of size 5 of a product, 90% of the time there are no
defectives in the sample, 3% of the time there is 1 defective, 2% of the time there are 2 defectives, 2% of the time there are
3 defectives, 2%of the time there are 4 defectives, and 1% of the time there are 5 defectives. What is the probability of taking
a sample that has at least 3 defectives in the 5?
A. 7% C. 9%
B. 5% D. 15%

53. A circle has its center at (3, -27). It is tangent to the line 3x + 4y – 26 = 0. Compute the point of tangency of the circle.
A. (3,4) C. (6,2)
B. (2,6) D. (3,6)

54. A rectangular swimming pool is 12meters long and 8 meters wide. A tile border of uniform width is to be built around
the pool, using 120 square meters of tile. The tile is from a discounted stock (so no additional materials are available), and
all 120 square meters are to be used. How wide should the border be?
A. 5.4meters C. 3.4meters
B. 2.4meters D. 4.4meters

55. Light travels at a rate of approximately 1.86x10 miles per second. It takes light 5x10^2 seconds to travel from the sun
to earth. What is the distance between Earth and the sun? (Hint: d=rt)
A. 83 million miles C. 103 million miles
B. 73 million miles D. 93 million miles

56. An equipment cost P480,000 and has a salvage value of 10% of its cost at the end of its life of 36,000 operating hours in
a period of 5 years. In the first year of service, it was used for 12,000 hours. If at the end of the 2nd year, it was used for 15,000
hours, find the depreciation at the end of the 2nd year.
A. 324,000 C. 144,000
B. 160,000 D. 180,000

57. A father wants to set aside money for his 5year 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 17th birthdays, in order to provide Php 5000 on the son’s 18th, 19th, 20th, and 21st birthdays?Hint: (PiA,8%,4) = .302
A. Php822.67 C. Php877.67
B. Php827.67 D.Php872.67

58. A point moves in the plane according to equations x = t^2 + 2t and y = 2t^3 – 6t. Find dy/dx when t = 0,2, and 5.
A. -3, -3, -12 C. 3, 3, 12
B. 3, -3, 12 D. -3, 3, 12

59. A nutritionist in a hospital is arranging special diets that consist of a combination of three basic foods. It is important
that patients on this diet consume exactly 310 units of calcium, 190units of iron, and 250units of vitamin A each day. The
amounts of these nutrients in one-ounce food are given in the following table.
Units per Ounce Calcium Iron Vitamin A
Food A 30 10 10
Food B 10 10 30
Food C 20 20 20
How many ounces each food must be used to satisfy the nutrient requirements exactly?
A. 6 ounces of food A, 5 ounces of food B and 3 ounces of food C
B. 3 ounces of food A, 5 ounces of food B and 6 ounces of food C
C. 6 ounces of food A, 3 ounces of food B and 5 ounces of food C
D. 5 ounces of food A, 3 ounces of food B and 6 ounces of food C

60. A trough has an open top 0.30 m by 6 m and closed vertical ends which are equilateral triangles 30 cm on each side. It is
filled with water to half its depth. Find the volume of the water in cu. m.
A. 0.046 C. 0.037
B. 0.058 D. 0.065

61. The eccentricity of an ellipse is 0.6 and the distance between its foci is 6 units. Find the distance between its directrices.
A. 8.33 C. 16.67
B. 15.67 D. 21.33

62. Find the length of the arc of x^2 + y^2 = 64 from x=-1 to x=-3, in the second quadrant
A. 2.24 C. 2.75
B. 2.61 D. 2.07

63. The volume of a closed cylindrical tank is 11.3 cu. m. If the total surface area is minimum, what is its base diameter, in
m?
A. 1.88 C. 2.44
 B. 1.22 D. 3.76

64. A boat takes 2/3 as much time to travel downstream from C to D, as to return, if the rate of the river’s current is 8 kph,
what is the speed of the boat in still water?
A. 38 C. 39
B. 40 D. 41

65. The radius of the earth is 3,960 mi., The gravitational acceleration at the earth’s surface is 32.16 fps^2. What is the
velocity of escape from the earth in mi/s?
A. 7.83 C. 6.94
B. 9.36 D. 8.62

66. When the temperature was 3degrees C, the distance from E to F was measured using a steel tape that has a standard
length at 20degrees C with a coefficient of thermal expansion of 0.0000116/degrees C. If the correct distance from E
to F is 836.5 m., what was the measured distance in m?
A. 835.675 C. 836.005
B. 836.335 D. 836.665

67. What is the slope of the curve x^2 + y^2 – 6x + 10y + 5 = 0 at (1, 0).
A. 2/5 C. -2/5
B. 5/2 D. -5/2

68. A line was observed to have a compass bearing of N52°15’W when the declination is 1°15’E. What is the true bearing of
the line if the local attraction of 3°45’ was existed to the west of vicinity?
a. N45°54’W b. N35°45’W
c. N54°45’W d. N25°54W
69. A stadia intercept of 1.02 m was recorded for a horizontal sight stadia surveying. If the stadia interval factor and stadia
constant are 98.36 and 0.30 respectively, compute for the horizontal distance.
a. 100.63 m b. 106.03 m
c. 600.13 m d. 601.30 m
70. A raindrop has terminal velocity of 45ft per second. At the surface of the earth, the drop enters a 400ft well, if sounds
travels at 1125fps, how long will it take for the drop to reach the bottom?
a. 4.143 s b. 3.261 s
c. 5.231 s d. 6.485 s

SIT :A vertical summit parabolic curve has a vertical offset of 0.375 m. from the curve to grade tangent at sta 10 + 050. The
curve has a slope of 4% and -2% grades intersection at the P.I. The offset distance of the curve at P.I. is equal to 1.5 m.
If the stationing of the P.C. is at 10 + 100.
71. Compute the required length of curve.
a. 100 m c. 150 m
b. 200 m d. 200 m
72. Compute the horizontal distance of the vertical curve turning point from the point of intersection of the grades.
a. 30.42 m c. 33.33 m
b. 42.15 m d. 26.54 m
73. Compute the elevation of the vertical curve turning point if the elevation of P/T. is 86.42 m.
a. 80.22 m c. 84.54 m
b. 91.36 m d. 87.08 m

SIT : The perpendicular offset distance from point A on a simple curve to Q on the tangent line is 64 m. If the distance from
the P.C. to Q on the tangent is 260 m.
74. Compute the radius of the simple curve.
a. 560.13 m c. 557.31 m
b. 549.25 m d. 555.02 m
75. Compute the length of the curve from P.C. to A.
a. 273.09 m c. 263.41 m
b. 267.95 m d. 270.31 m