Preboard 2 Math

CIVIL ENGINEERS LICENSURE EXAM (EERC Preboard - MANILA) OCTOBER 2019 MATHEMATICS, SURVEYING, AND TRANSPORTATION ENGINEERING

8.

The correct distance between points X and Y is 375.50 m. If a 100-m tape that is 0.0115 m too long is used to

INSTRUCTION: Select the correct answer for each of the following

measure, what will be the measured distance?

questions. Mark only one answer for each item by shading the

a.

375.5432 m

box corresponding to the letter of your choice on the answer

b.

375.6221 m

c. d.

375.4568 m 375.3997 m

sheet provided. STRICTLY NO ERASURES ALLOWED. Use pencil no. 1 only.

9.

A stadia intercept factor of 4.6 m was measured on a stadia rod by a transit with stadia constant and stadia interval factor of 0.28 m and 100.92, respectively. If the

MULTIPLE CHOICE

line of sight was inclined at an angle of 6°40’ with the horizontal, determine the horizontal distance from the

Situation 1: Line AB 70 m long was paced by a surveyor four times

1.

with the following data: 92, 93, 91 and 95.

transit to the rod.

Another line CB was paced for 123, 122, 125

a.

464.5120 m

c.

449.0972 m

and 124.

b.

458.2534 m

d.

461.3730 m

10.

Determine the pace factor of the surveyor.

A transit has a stadia interval factor of 98.96 and stadia

a.

0.7547

c.

0.5668

constant of 0.30 m. Compute the vertical distance from

b.

3.0189

d.

2.2672

the stadia rod’s middle hair reading to the lens of transit when the stadia intercept is 0.8 m if the angle of sight

2.

3.

is 4°50’.

Determine the actual length of CB. a.

94.33

c.

92.56

a.

6.6958 m

c.

6.3201 m

b.

91.89

d.

93.21

b.

6.2158 m

d.

6.6721 m

If the line AB was at elevation 700 m above sea level,

Situation 2: A transit with stadia constant equal to 0.28 is used to

determine the reduced sea level distance.

determine the horizontal distance between

a.

69.9923 m

c.

69.9889 m

points B and C, with a stadia intercept reading

b.

69.9998 m

d.

69.8972 m

of 2.15 m, the distance BC is equal to 209.55 m

4.

5.

Compute the grid distance if the grid factor is 0.9988. a.

69.9049 m

c.

69.9158 m

b.

69.8133 m

d.

69.9083 m

11.

Compute the stadia interval factor of the instrument. a.

97.3349

c.

100.0221

b.

99.0346

d.

98.0192

A line was measured to have 7 tallies, 3 marking pins 12.

and 6 links. How long is the line?

If it was also used to determine the difference in

a.

7,306 pins

c.

7,306 perch

elevation between B and D having a stadia intercept

b.

7,306 feet

d.

7,306 vara

reading of 2.51 m at D at a vertical angle of +7°30’, determine the difference in elevation.

6.

A line was measured with a 50-m tape. There were 3

a.

32.20 m

c.

31.87 m

tallies, 10 pins, and the distance from the last pin to end

b.

32.53 m

d.

31.65 m

of the line was 13 m. Find the length of the line.

7.

a.

2,013 feet

b.

2,013 meters

c.

2,013 rod

d.

2,013 vara

13.

Compute the horizontal distance between B and D. a.

240.43 m

c.

244.62 m

b.

247.06 m

d.

242.11 m

The distance was measured and was recorded to have a value of 11 perch, 4 rods and 20 vara. Compute the total

Situation 3: A transit with stadia interval factor of 99.8 was set at C on the line between points A and B, and the

distance in meters. a.

90.93 m

c.

92.23 m

b.

93.67 m

d.

91.75 m

following stadia readings were observed.

ENGR. ERICKNEIL D. REALUYO, MSCE, ME-1. SO, MP

CIVIL ENGINEERS LICENSURE EXAM (EERC Preboard - MANILA) OCTOBER 2019

POSITION

VERTICAL

OF ROD

ANGLE

At A At B

HAIR READINGS

15.

b.

N 52°13’ W

c.

N 59°13’ W

d.

N 52°43’ W

Middle

Lower

+12°35’

1.430

1.185

1.030

a.

0°19’12”

c.

0°02’12”

-9°08’

2.072

1.874

1.836

b.

0°02’24”

d.

0°19’24”

22.

23.

Find the secular variation per year.

A 50-m tape which is of standard length at a temperature of 22° is used to measure a line with a measured distance of 512 m. During measurement, the

What is the horizontal distance between A and B? a.

60.981 m

c.

60.825 m

b.

61.346 m

d.

61.725 m

temperature was 53°C. If the coefficient of thermal expansion of the tape is 0.0000116/°C, determine the correct length of the line.

What is the difference in elevation between points A and B?

16.

N 59°43’ W

Upper

If the stadia constant is 0.377 m, 14.

a.

a.

12.26 m

c.

12.09 m

b.

13.01 m

d.

13.73 m

a.

511.8159 m

c.

512.2091 m

b.

512.1841 m

d.

511.3015 m

Situation 6:

A close traverse has the following data.

What is the horizontal distance from the transit to the rod held at B?

LINE

LATITUDE

DEPARTURE

1-2

+76.30

+43.18

a.

27.22 m

c.

23.33 m

2-3

+33.80

b.

38.39 m

d.

35.04 m

3-4

-16.39

-80.58

4-5

+64.12

-31.93

367.2 m was measured by a 30 m tape which is 0.02 m too

5-6

-73.87

+10.72

short.

6-1

Situation 4: A rectangular lot having a dimension of 238.5 m by

24. 17.

Compute the correct length of the lot. a.

367.44 m

c.

366.82 m

b.

366.96 m

d.

367.51 m 25.

18.

Find the error in the area. a.

116.8085 m2

c.

116.6645 m2

b.

116.7307 m2

d.

116.5091 m2

Find the length of line 6-1. a.

93.960 m

c.

93.690 m

b.

93.609 m

d.

93.096 m

Find the bearing of line 6-1. a.

N 25°35’46” E

c.

N 25°35’46” W

b.

S 25°35’46” W

d.

S 25°35’46” E

Situation 7: 19.

+40.22

A bag contains 3 white, 5 black and 4 yellow balls.

If the same tape was used to set a baseline with length of 700 m, determine the distance to be laid out.

26.

If

three

balls

are drawn

in

succession

without

a.

700.4670 m

c.

699.3913 m

replacement, what is the probability that the drawn balls

b.

699.5333 m

d.

700.5715 m

are all white?

Situation 5: In 1993, the magnetic bearing of line AB measured

a.

1/110

c.

2/55

b.

3/220

d.

1/220

by a compass instrument was N 60°13’ W. The declination of the needle at that time was 4°30’

27.

E.

If

three

balls

are drawn

in

succession

without

replacement, what is the probability that the drawn balls of different colors?

20.

Compute the true bearing of the line. a.

N 64°43’ W

c.

N 55°43’ W

b.

N 55°23’ W

d.

N 64°13’ W

28.

a.

1/22

c.

7/22

b.

5/11

d.

3/11

A bowl contains 4 red, 5 green and 6 blue balls. What is the probability of not getting a red ball in the first

21.

If the declination when year 2018 was 3°30’ W,

draw?

determine the magnetic bearing of the same line during

a.

11/15

c.

2

that year.

b.

1.5

d.

4/15

ENGR. ERICKNEIL D. REALUYO, MSCE, ME-1. SO, MP

CIVIL ENGINEERS LICENSURE EXAM (EERC Preboard - MANILA) OCTOBER 2019 Situation 10: A provincial chapter of a rotary club held a lottery Situation 8:

to raise funds for their organization, with P

Eleven coins were tossed.

10,000.00 top prize and with 2,000 tickets 29.

printed and sold.

Find the probability of getting nine heads. a.

0.106

c.

0.033

b.

0.027

d.

0.041

38.

What is the mathematical expectation of a member if he bought 10 tickets?

30.

Find the probability of getting at least seven heads.

a.

P 50.0

c.

P 110.5

a.

0.106

c.

0.333

b.

P 89.0

d.

P 101.3

b.

0.274

d.

0.411 39.

31.

Find the probability of getting at most six tails.

one ticket is worth P 100.00?

a.

0.185

a.

P 67.1

c.

P 55.4

0.471

b.

P 60.0

d.

P 49.5

b. 32.

What is the mathematical expectation of a member if

0.726 0.556

c. d.

A family has 5 children. Find the probability that among

Situation 11:

the children, 3 are girls.

a vibration test and 5 failed due to having a high resistance.

a.

7/16

b.

5/16

c. d.

When testing 1000 soldered joints, 4 failed during

3/16 9/16

40.

Determine the probability of a joint failing due to vibration or high resistance.

33.

A cat has a litter of seven kittens. If the probability is

a.

0.001

c.

0.005

0.52 that a kitten will be female, what is the probability

b.

0.004

d.

0.009

that exactly two of the seven will be male? a.

0.078

c.

0.144

b.

0.184

d.

0.233

41.

Determine the probability of a joint failing due to vibration and high resistance.

34.

An archer hits 70% of all his targets. What is the

a.

0.00003

c.

0.00004

probability that he will hit exactly 5 of his next 12 shots?

b.

0.00002

d.

0.00001

a.

0.0824

c.

0.0595

b.

0.0619

d.

0.0291

42.

A standard deck of 52 cards is well shuffled. Find the probability that the first four cards dealt are the aces.

Situation 9:

A baseball match consists of 12 innings. A

a.

4 x 10-6

c.

8 x 10-6

league has a chance of winning that is twice of

b.

6 x 10

d.

2 x 10-6

-6

losing and a chance of having a draw that is 43.

twice of losing.

A card is chosen from a pack of cards. Determine the probability that it is either a black or a picture card.

35.

Find the probability of a league that they will have six

a.

8/13

c.

10/13

wins and three losses.

b.

17/26

d.

19/26

a.

0.0111

c.

0.0388

b.

0.0456

d.

0.0556

44.

From three standard decks of cards, what is the probability of getting a diamond from the first deck, an

36.

Find the probability of a league that they will have seven

ace from the second deck and an ace of heart from the

wins.

third deck?

a. b. 37.

0.7112 0.1009

c. d.

0.2931

a.

1/850

c.

1/550

0.4300

b.

1/3300

d.

1/2704

Find the probability of a league that they will have at

45.

One bowl contains four cards numbered 1, 3, 5 and 6. Another box contains three cards numbered 2, 4 and 7.

most seven wins. a.

0.9427

c.

0.7556

One card is drawn from each bag. Determine the

b.

0.2345

d.

0.8889

probability that the sum is even. a.

5/7

c.

5/12

b.

7/12

d.

3/7

ENGR. ERICKNEIL D. REALUYO, MSCE, ME-1. SO, MP

CIVIL ENGINEERS LICENSURE EXAM (EERC Preboard - MANILA) OCTOBER 2019 46.

47.

In a dice game, one fair die is used. The player wins P30

54.

If the population variance is 4200, how many data are

if he rolls either a 1 or a 6. He losses P20 if he turns up

involved?

any other face. What is the expected winning for one

a.

20

c.

10

roll of the die?

b.

15

d.

25

a.

6.667

c.

3.333

b.

-3.333

d.

-6.667

55.

Nikki and Mayrose each throw two dice. If Nikki gets a

What is the sample standard deviation? a.

74.34

c.

108.01

b.

66.14

d.

86.60

sum of 5, what is the probability that Mayrose will get less?

48.

56.

a.

1/7

c.

1/4

a.

0.669

c.

0.903

b.

1/12

d.

1/6

b.

0.864

d.

0.724

Two fair dice are thrown. What is the probability that

Situation 15: In a certain engineering school approximately 11%

the sum shown is divisible by 5?

of people are left – handed. Total population of the school is

a.

1/9

c.

1/12

b.

7/36

d.

1/4

1,100. 57.

Situation 12:

A class of 40 students took an examination. The

58.

that grade?

53.

c.

0.0809

b.

0.0514

d.

0.1929

What is the probability that at most 100 students are left – handed?

82.82

c.

83.12

a.

0.2081

c.

0.0155

b.

81.45

d.

84.03

b.

0.0215

d.

0.1830

If 25% of the class failed the exam, what should be the

59.

What is the probability that between 90 and 140

minimum score of a student in order to pass?

students are left – handed?

a.

60.32

c.

57.20

a.

0.451

c.

0.912

b.

67.55

d.

63.26

b.

0.965

d.

0.309

60.

x, 7, 10, 18, 20, 21, x2

52.

0.2311

a.

Situation 13: Refer to the given data set below.

51.

a.

If 10% of the class will be awarded with a grade of A, what is the minimum score a student must get to have

50.

What is the probability that at least 130 students are left – handed?

mean of their scores is 70 and the standard deviation is 10. 49.

If the mean is 75, what is the relative variability?

If the range is 20, what is the mean? a.

15.14

c.

11.06

b.

12.57

d.

17.45

61.

Find the Laplace transform of 3 when s = 0.5. a.

3.0

c.

1.0

b.

6.0

d.

1.5

Find the Laplace transform of cos(1.4t) when s = 2. a.

−50/149

c.

35/149

b.

−35/149

d.

50/149

What is the interquartile range? a.

17

c.

23

b.

11

d.

14

62.

Find the Laplace transform of e-2tcos(3t) when s = 1.5. a.

14/85

c.

−14/85

b.

2/37

d.

−2/37

What is the 9th decile? a.

14

c.

16

b.

25

d.

21

Situation 14:

The sum of all the product of the individual

frequency and the square of the difference of the datum and

63.

Find the inverse Laplace of (–2s + 6)/(s2 + 4). a.

–3cos(2t) + 2sin(2t)

b.

–2cos(t) + 3sin(t)

c.

–2cos(2t) + 3sin(2t)

d.

–3cos(t) + 2sin(t)

mean is 105,000.

ENGR. ERICKNEIL D. REALUYO, MSCE, ME-1. SO, MP

CIVIL ENGINEERS LICENSURE EXAM (EERC Preboard - MANILA) OCTOBER 2019 64.

A man borrowed P75,000 on September 18, 1898 and promised to pay on May 17, 1904 at a simple interest

72.

A fixed circle with center at (8, 6) has a radius of 5 units.

of 12% per annum. How much will be the total interest?

Find the equation of the locus of points connecting the

a.

P50,957.83

c.

P50,827.87

center of circles tangent to the given fixed circle and the

b.

P50,817.24

d.

P50,967.12

x-axis. a.

x2 – 16x – 22y + 75 = 0

Situation 16: An engineer makes an annual deposit of P5,000.00

b.

x2 – 16x + 22y + 75 = 0

for 5 years. The interest rate is 10% compounded annually.

c.

x2 – 16x – 22y – 75 = 0

d.

x2 – 16x + 22y – 75 = 0

65.

How much is his account after 5 years. a.

P30,525.50

c.

P41,091.61

b.

P32,667.01

d.

P44,710.55

73.

Find the equation of the locus of the center of circles that are tangent to the circle x2 + y2 – 12x – 8y + 43 = 0 and to the y-axis.

66.

67.

a.

How much is his account after 10 years.

y2 – 8y – 18x – 43 = 0

a.

P49,161.62

c.

P44,692.38

b.

y2 + 8y – 18x + 43 = 0

b.

P54,077.79

d.

P38,556.01

c.

y2 – 8y – 18x + 43 = 0

d.

y2 + 8y – 18x – 43 = 0

To prepare his retirement for 20 years, a self-employed engineer deposits P6,000 every end of 3 months in a

74.

Find the distance from the origin to the point (5, 6, 7).

fund that earns 10% compounded quarterly. How much

a.

9.70 units

c.

10.49 units

could he get after his retirement?

b.

10.25 units

d.

11.18 units

a.

P1,856,288.05

b.

P2,002,497.00

c.

P2,300,319.54

d. P1,490,296.28

75.

Find the distance between the points A(3, -5, 0) and B(2, 4, -6).

68.

A man deposits P50,000 annually to an account earning

a.

7.87 units

c.

11.92 units

6% compounded continuously. How many years will it

b.

10.86 units

d.

12.04 units

take him to accumulate P1,000,000?

69.

a.

12.34 yrs

c.

11.34 yrs

b.

14.32 yrs

d.

13.42 yrs

A man paid a 10% down payment of P200,000 for a house and lot and agreed to pay the balance of monthly installments for 5 years at an interest rate of 15% compounded

monthly.

What

was

the

monthly

installment?

70.

a.

P40,389.82

c.

P36,490.32

b.

P38,105.76

d.

P42,821.87

At 6%, find the capitalized cost of a bridge whose cost is P250 M and life is 20 years, if the bridge must be partially rebuilt at a cost of P100 M at the end of each 20 years.

71.

a.

P213.27 M

c.

P295.31 M

b.

P163.27 M

d.

P245.31 M

A company uses a type of truck which costs P2,000,000, with life of 3 years and final salvage value of P320,000. How much could the company afford to pay for another type of truck for the same purpose, whose life is 4 years with a final salvage value of P400,000, if money is worth 4%? a.

P2,805,120

c.

P2,718,480

b.

P2,585,870

d.

P2,642,320

ENGR. ERICKNEIL D. REALUYO, MSCE, ME-1. SO, MP