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CEBEP MAY 2019 PRE REVIEW MODULE

MATHEMATICS , SURVEYING, AND TRANSPORTATION ENGINEERING
ENGINEERING MATHEMATICS
A
...
Two planes leave manila for a southern city, a distance of 900 km
...

Plane A arrives in their destination 2 hours and 15 minutes ahead of plane B
...
Solve the root of the given equation: (No Solution)
√2𝑥 − 6 + √9 − 𝑥 = 0
3
...
How long does it take for the arrow to reach 240 feet in the air? (5 secs)
4
...
59)
𝑝 = 30𝑒 −0
...
Find the value of x if 1/4 , 1/6 , 1/x and 2/27 are consecutive terms of a geometric progression
...
TRIGONOMETRY
1
...
15 meters
...
(83
...
Determine the period of the trigonometric function f(x) = sin (π/6 x)

(12)

3
...
(72°)
4
...
(61/11)
5
...
He walks 85 m nearer the tower and
finds its angle of elevation to be 60°
...
61 m)
C
...
What is the length of the latus rectum x^2 = 20y ? (20)
2
...
The cross section of a cooling
tower forms a hyperbola
...
Find the diameter of the top of the cooling tower to the nearest foot
...
Find the area bounded by the points (2,0) , (-2, 4) , and (0,-4)
...
What is the general equation of an ellipse with center at (2,0) , focus at (5,0) and b = 4 ? (16x^2 + 25y^2
– 64x – 336 = 0)
5
...
Find the distance between
them
...
PLANE AND SOLID MENSURATION GEOMETRY
1
...
thick is 14 inches
...
1 oz copper per cubic inch
...
07 lbs)
2
...
PQRS is a square inside ACBD , PQBA , QCRB , RSDC , and SPAD were
identical trapezia, each of area 16 sq cm
...
The sum of interior angles of a pentagon is ________ (540°)
4
...
Each of the
circles has a radius of 9 m and each circle passes through the center of the other
...

(410 sq m)
5
...
5
...
8
...
5 m
...
(16
...
DIFFERENTIAL CALCULUS
1
...
A balloon is rising vertically over a point A on the ground at the rate of 15 ft/sec
...
When the balloon is 40 ft from A, at what rate is its distance from B changing?
(12 ft/s)
3
...

(9 and 1)

4
...
Determine its velocity at the end
of 2 seconds
...
Sand is pouring from a spout at the rate of 25 cc/sec
...
At what rate in cm/sec if the height increasing, when the cone is 50 cm high?
(0
...
INTEGRAL CALCULUS
1
...
(59
...
Find the integral of (x^2 – sec^2 x) dx
...
Find the perimeter of the cardioid r = 1 – cos θ
...
Evaluate the following multiple integral: (0
...
Find the area of the region to the left of the parabola x = 2y^2 , to the right of the y axis and between y=
1 and y = 3
...
PROBABILITY AND STATISTICS
1
...
The mean lifetime is 400 days with
a standard deviation of 50 days
...
In a survey regarding the favorite teen stars , it was found that 55% of them like Kyline , 50% like Pauline
, 40% like Frenny , 30% like Kyline and Pauline , 20% like Kyline and Frenny , 12% like Pauline and Frenny
and only 10% like all of the three
...
A bag contains one counter, known to be either white or black
...
What is now the chance of drawing a white counter?
(2/3)
4
...
(37
...
Joel Embiid averages two blocks per game
...
36)
H
...
Solve the differential equation: y’ = (y + x) / x
...
Given the following equation
...
(x = 3)
1 2
6
|𝑥 −2 1 | = 25
0 1 −1

3
...


(2 – 5i)

4
...
The distance of the
point from y axis is proportional to the time
...
The vector that describes the motion
is: ( y = (3x + 1) e^3x - 1 )
5
...


(x^2 y^2 = 2y^3 + c)

ENGINEERING ECONOMICS
A
...
How much money would you need to deposit today at 9% annual interest compounded monthly to have
P 12,000
...
08)
2
...
The loan is for 3 years
at 10% annual simple interest
...
Find the present value of an annuity of P 25,000 payable annually for 8 years with first payment at the of
10 years if money is worth 5%
...
11)
4
...
Natalie Magtanggol borrowed P 100,000
...
He must pay back the
loan over 30 years with uniformly monthly payments due on the first day of each month
...

Magtanggol pay each month? (P 839
...
A deferred annuity is purchased that will pay P 10,000
...
If money is worth 6% compounded quarterly, what is the present value of this annuity?
(P 292,386
...
DEPRECIATION, CAPITALIZED COST AND ANNUAL COST
1
...
00
...
00, how much will be depreciated in the 9th year using 150% declining balance schedule? (P 449
...
The cost to equip a condo unit with CCTV system is P 50,000
...
If the interest rate is 15% per year and it
has a life of 6 years, find the equivalent annual cost
...
00)
3
...
00 and a five year depreciable life
...
00 at the end of five years
...

(P 36,000
...
Determine the capitalized cost of a project that cost P 324,000
...
00 at the end of four years , if money is worth 8%
...
76)
5
...
00 with a salvage value of P 500
...
Calculate the
annual depreciation cost by sinking fund method at 4% interest
...
26)
C
...
A bridge project is proposed that has total present worth benefit of P 75 million and total present worth
costs of P 55 million
...
Determine the net book
value
...
Pauline Mendoza is planning her retirement from showbiz has decided that she will have to withdrawp
10,000
...
How much money must she have in the bank at
the start of her retirement if her money earns 6% per year, compounded annually and she is planning a 12
year retirement (12 annual withdrawals) ? (P 83,839
...
The revenue R from selling x number of computer boards is given as R = 60x and the cost C of producing
them is given by C = 50x + 5000
...
(30,000)
4
...
00
...
How many kilos of beef needed to break even? (5,000)
5
...
The old machine is expected to require out of pocket
cost of P 85,000 each year for 4 years and then be scared for P 5,000 residual value
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Invested capital should earn a minimum return of 15% before taxes
...
( P 16,021
...
MECHANICS AND OSCILLATIONS AND MECHANICAL WAVES
1
...
It moves 2
...
60 secs
...
What is the tension in the string
during the accelerating process? (T = 62
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A 3m string is driven by a 240 Hz vibrator at its end
...
Consider a 42,000 kg train car travelling at 10 m/s toward another train car
...
What is the mass of the second train car? (28,000 kg)
4
...
The force
you exerted on the door was 50 N, applied perpendicular to the plane of the door
...
1
...

Assuming that you pushed the door at its edge, what was the torque on the swinging door (taking the hinge
as pivot point) ? (50 Joules)
5
...
2 degrees above the
horizontal
...
What is the initial speed of
the projectile? (59 m/s)

B
...
How fast must a 1000 loop coil (each with 20 sq cm area) turn in the Earth’s magnetic field of 0
...
50 volts? (0
...
How many calories are required to heat each of 3 grams of aluminum from 10℃ to 65℃ ? (32 calories)
3
...
0 cm
...
(0
...
In a non-flow process there is heat transfer loss of 1055 kJ and an internal energy increase of 210 kJ
...
(1265 kJ compression)
5
...
3 x 10^11 m with
a speed of 2
...
Determine the current in the orbit
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1 milliamperes)
C
...
Two thin converging lenses shown in the figure of focal lengths of f1 = 10
...
0 cm are
separated by 20
...
An object is placed 30
...
Find the overall magnification of the
system
...
667)

2
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40 m and an ocular focal length of 3
...
the
telescope is aimed at a far away object and the final image is viewed at infinity
...
43)
3
...
What is the period of light? (1
...
Light travels from air into an optical fiber with an index of 1
...
If the angle of incidence on the end of
the fiber is 22° , the find the angle of refraction inside the fiber
...
Light traveling through an optical fiber ( n = 1
...
If the
angle of incidence on the end of the fiber is 30 ° , what is the angle of refraction outside the fiber? (46° )
SURVEYING
A
...
The scale on the map is 1:x
...
6 cm^2 on
the map
...
A line AB between the stations A and B was measured as 348
...
05 m
...
(347
...
A distance of 1500 m was measured with a 20 m chain
...
If the length of chain was perfectly correct while starting measurement, what is the true length
of the line measured? (1503 meters)
4
...
B is at elevation 825 m and is higher than
C
...
(825
...
86
2
6
0
...
75
4
8
1
...
A distance was measured with a 30 m steel tape and recorded as 96
...
What is the correct distance? (96
...
LEVELING AND TRAVERSE AREA
1
...
874m
...
60m above its station (point A) and the prism is at height 2
...
If the reduced levels of A
and B are RLA=+27
...
700m, calculate the horizontal distance from A to B
...
732 m)
2
...
(line DE = N 72° 08’ E)
LINES
A-B
B-C
C-D
D-E
E-A

BEARING
S 35°30’ W
N 57°15’ W
N 1°45’ E
?
?

DISTANCES
44
...
84 m
64
...
86 m
106
...
A line of levels, 6 km long is run between A to B with average backsight and foresight distances of 150 m
...
8 m
...
What is the correct elevation of B if its recorded elevation is 425
...
87 m)
4
...
632

1
...
543

3
...
Point 2 is on the same line as P and Q but not
between them
...
With the wye level at point 1, what is rod
reading at Q for a level sight? (2
...
A closed traverse has the following data shown
...
(202
...
00
258
...
41

Bearing
N 47° 02’ 14” E
S 69° 35’ 59” E
S 39° 35’ 17” W
S 87° 29’ 48” W
N 24° 48’ 09” W

C
...
A device used to detect obstructions such as boulders and ledges that can be plotted in navigational
charts
...
Elevation of triangulation station Alpha is 250m while that of Bravo is 685m
...
The height of transit placed at Alpha is 1
...
The
distance from Alpha to Charlie is 30 km and from Bravo to Charlie is 50km
...
(60
...
A theodolite is set up at one end at a level base line 150 m long
...
The stadia intercept at each location as follows: 0
...
600, 0
...
207 , and 1
...
Determine the average value of stadia interval factor K
...
7)
4
...

Find the interior angle D
...
A tacheometer is placed at a station A and readings on a staff held vertical upon a B
...
of RL =100
...
640, 2
...
760 and 0
...
120, 4
...
The angle of
depression of the telescope in the first case is 6° 19' and in the second case is 7° 42'
...
5
...
434 m;
91
...
SIMPLE, COMPOUND, AND REVERSE CURVES
1
...
54 m using arc basis
...
The perpendicaular distance between two parallel tangents of a reversed curve is 7
...
If the stationing of the PC is at 4 + 560
...
(4 + 625
...
The length of the long tangent of a compound curve is 500m
...
The length from PC to a point on the long tangent that is the intersection of the long tangent and the
common tangent is 100 m
...
Two roads having a deviation angle of 45° at apex point V are to be joined by a 200 m radius circular
curve
...
2 m, find the chainage of the forward tangent
...
44 m)
5
...

It is decided, for construction reasons, that the mid-point of the curve must be moved 4 m towards the

centre, i
...
away from the intersection point
...
Calculate
the radius of the new curve
...
PARABOLIC, SIGHT DISTANCE AND SPIRAL CURVES
1
...
with a design speed of 100 kph
...
5%
...
C (63
...
The tangents of a spiral curve forms an angle of intersection of 25° at station 2 + 058
...
For a radius of central curve of 300 m and a length of spiral of 52
...
Find the length of the central
curve
...
8 meters)
3
...
(114
...
A parabolic sag curve has a grade of the back tangent of -2% and forward tangent of 3%
...
Compute the elevation of the PT
...
20
meters)
5
...

Given t=2
...
7 and brake efficiency of 50 percent in either case
...
(235
...
AREAS AND VOLUMES
1
...
The width of the roadway is 10 m for both cut and fill
...
Find the difference between the volumes
of cut and fill if the side slopes are 1
...
(14,618
...
The center height of the road at 7 +110 is 2 m fill while station 7 + 160 it is 1
...
cut
...
8%
...
(71 + 141
...
The length of a line originally 100 mm long on a map plotted to a scale of 1/1000 was found to be 96 mm
due to shrinkage of the map
...
03 m
...
(307 m^2)
4
...
(51
...
8
3
...
8

Right
11
...
21

5
...
5 meters , 2nd side = 25
...
HIGHWAY and RAILROAD ENGINEERING
1
...
(10 percent)
2
...
(Marshall mix design method)
3
...
Hint: (Tb/Tc) = (Cc/Cb)^(1/5)
(48
...
5 cm
25
...
0 cm

C Value
62
180
25

4
...
(Mountable curbs)
5
...
If the train has a headway
of 20 minutes and an average speed of 45 kph, determine the number of trains required for continuous
operations on the loop from outline terminal to the Shaw Blvd (central terminal)
...
(12 trains)
TRAFFIC ENGINEERING
1
...
Assume a reaction time of 2
...
Coefficient of friction is 0
...
(235
...
The table below shows 15 minute volume counts during the peak hour on an approach of an intersection
...
(1648)
Time
6:00-6:15 am
6:15-6:30 am

Volume
375
380

6:30-6:45 am
6:45-7:00 am

412
390

3
...

(BPR Meter)
4
...
84)
5
...

(Fluorescent Reflective Sheeting)
PORTS AND HARBORS AND AIRPORT ENGINEERING
1
...
C
...

Sometimes stressed slab or beam is also used
...
VFR in the airport flight rules means ________
...
These are constructed for quick arrival and departure of ships and land transport and for cargo sorting
before and after the departure/arrival of ships in the port
...
It refers to the force that makes a floating body to return to its original position when the floating body
moves in still water
...
These are any prominent object , natural or artificially constructed , easily indentifiable and capable of
being used as a means to indicate and guide in navigation

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