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CEBEP MAY 2019 PRE REVIEW MODULE

MATHEMATICS , SURVEYING, AND TRANSPORTATION ENGINEERING
ENGINEERING MATHEMATICS
A
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Two planes leave manila for a southern city, a distance of 900 km
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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
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TRIGONOMETRY
1
...
15 meters
...
(83
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Determine the period of the trigonometric function f(x) = sin (π/6 x)

(12)

3
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(72°)
4
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(61/11)
5
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He walks 85 m nearer the tower and
finds its angle of elevation to be 60°
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61 m)
C
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What is the length of the latus rectum x^2 = 20y ? (20)
2
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The cross section of a cooling
tower forms a hyperbola
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Find the diameter of the top of the cooling tower to the nearest foot
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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
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Find the distance between
them
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PLANE AND SOLID MENSURATION GEOMETRY
1
...
thick is 14 inches
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1 oz copper per cubic inch
...
07 lbs)
2
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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
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(410 sq m)
5
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5
...
8
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5 m
...
(16
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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
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(9 and 1)

4
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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
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Find the integral of (x^2 – sec^2 x) dx
...
Find the perimeter of the cardioid r = 1 – cos θ
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Evaluate the following multiple integral: (0
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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
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What is now the chance of drawing a white counter?
(2/3)
4
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(37
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Joel Embiid averages two blocks per game
...
36)
H
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Solve the differential equation: y’ = (y + x) / x
...
Given the following equation
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(x = 3)
1 2
6
|𝑥 −2 1 | = 25
0 1 −1

3
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(2 – 5i)

4
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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
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(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
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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
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Natalie Magtanggol borrowed P 100,000
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He must pay back the
loan over 30 years with uniformly monthly payments due on the first day of each month
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Magtanggol pay each month? (P 839
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A deferred annuity is purchased that will pay P 10,000
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If money is worth 6% compounded quarterly, what is the present value of this annuity?
(P 292,386
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DEPRECIATION, CAPITALIZED COST AND ANNUAL COST
1
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00
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00, how much will be depreciated in the 9th year using 150% declining balance schedule? (P 449
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The cost to equip a condo unit with CCTV system is P 50,000
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If the interest rate is 15% per year and it
has a life of 6 years, find the equivalent annual cost
...
00)
3
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00 and a five year depreciable life
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00 at the end of five years
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(P 36,000
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Determine the capitalized cost of a project that cost P 324,000
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00 at the end of four years , if money is worth 8%
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76)
5
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00 with a salvage value of P 500
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Calculate the
annual depreciation cost by sinking fund method at 4% interest
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26)
C

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