CE Board Exam 1997

CE BOARD 1997

PHILIPPINE INSTITUTE OF CIVIL ENGINEERS – UAE CHAPTER

CIVIL ENGINEERING BOARD EXAM 2013 PREPARATION

Design and Construction “CE Board Exam Nov.

1997″

A simply supported steel beam has a span of 6m. and is

subjected to a vertical concentrated load of 150 kN acting

at midspan. An allowance of 100% for impact is made for

the concentrated load only. The beam is laterally supported

only at the supports. The 1992 National Structural Code of

the Philippines States that the allowable tensile stress for

laterally unsupported members subject to bending is 0.60

Fy while the allowable compressive stress for laterally

unsupported members subject to bending is given by the equation.

Where Cb maybe taken as 1.0 since the maximum moment

does not occur at the supports, rt is the radius of the

compression web area, taken about the axis in the plane of the web.

Steel is A 36 steel with yield strength Fy = 248MPa. Which

of the following most nearly gives the most economical

(lightest) section that will limit the flexural stress to the allowable value.


1997″

The preliminary design of a roadway established two

tangents meeting at the point of intersection at station 200

+ 130. The first tangent has an azimuth equal to 169° while

the second tangent has an azimuth equal to 118°. A simple

horizontal curve with radius equal to 100m. is to be

provided. Which of the following gives the tangent distance “T”.


1997″

The implementing rules and regulations of P.D. 1594 states

that for a unit price contract, quantity overruns or under

runs of not more than 15% of the estimates per major pay

item and 25% per minor item need not be covered by a

change order provided that the same is authorized by the approving and contract prices of a project are as follows.

Item Quantity Unit Price (Pesos)

1 100 1,000

2 50 10,000

3 500 5,000

4 60 6,000

5 1,000 3,000

6 400 1,500

7 3,000 2,000

8 20 25,000

Which of the following quantity need not be covered by a

change order.


1997″

A projectile is fired upward and to the right at an initial

slope of 4 vertical to 3 horizontal and hits the ground at a

point 2m lower than the origin. The maximum height is

attained 8m away from the origin. Compute the value of the

total horizontal distance.

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CE BOARD 1997




1997″

The approved agency estimate (AAE) of a Gov’t. project is 500M. The bids are:

Bidder A : P354,000,000

Bidder B : P639,000,000

Bidder C : P483,000,000

Bidder D : P583,000,000

Bidder E : P295,000,000

Bidder F : P385,000,000

The implementing rules and regulation of Pres. Decree No.

1594 states that no award of contract shall be made to a

bidder whose bid price is higher than Allowable

Government Estimate(AGE) or the Approved Agency

Estimate(AAE) is defined as one half the sum of the (AAE)

and the average of all responsive bids. For the purposes of

determining the average of responsive bids, bids higher

than 120% of the AAE or lower than 60% of AAE shall not

be considered. Which bidder wins the contract for the

Gov’t. project?


1997″

A 50mm diameter split barrel sample is driven into the

ground and the load of a cased burbale by means of blows

form 65kg mass hammer falling freely through a distance

of 760mm. The sample is driven a total of 450mm into the

soil. Which of the following is the test best described by this procedure?

a) Dutch Cone Penetration Test

b) Standard Proctor Test

c) Standard Penetration Test

d) Vane shear test


1997″

A block weighing 200 N rests on a plane inclined upward

to the right at a slope of 4 vertical to 3 horizontal. The

block is connected by a cable initially parallel to the plane

passing through a pulley which is connected to another

block weighing 100N moving vertically. The coefficient of

kinetic friction between the 200N block and the inclined

plane is 0.10, which of the following most nearly gives the acceleration of the system.


1997″

A beam 8.5m. long is fixed at the left end and supported by

a roller at a point 1.5m from the right end. There is an

internal hinge at a point 2.5m. from the fixed end. The

beam is loaded by a clockwise couple equal to 50kN.m at a

point 4.5m to the right of the fixed end and a downward

uniform vertical load equal to 5kN/m starting at a point

4.5m. from the fixed end up to the right end of the beam.

Which of the following most nearly gives the maximum moment.


1997″

A floor is made up of 150mm thick concrete slab and

50mm thick finish both of which has a unit weight of

24kN/m3. The floor also carries ceiling whose weight is

720Pa and a live load of 2400Pa. The floor is supported by

simply supported steel beams with a span of 10m spaced at

4.6m on centers with compression flange rigidly attached to

the concrete floor. The steel is A36 with yield strength (Fy)

= 248MPa. The allowable shear stress specified in the 1992

NSCP is 0.40Fy. Considering the weight of the beam,

which of the following sections is the most economical

(lightest) section for the given load assuming that shear stress governs the design.











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CE BOARD 1997




1997″

A steel plate is 360mm wide and 20mm thick with four bolt

holes cut into the plate as shown in the figure s-3. The

general expression for the specification method for computing the net area is:

Where:

T = thickness of plate

B = width

H = diameter of holes

S = pitch

g = gage

Which of the following most nearly gives the critical net

area (An) of the section in accordance with the 1992 NSCP.


1997″

A simply supported beam has a span o f4.5m. The beam is

subjected to an axial tensile force of 250kN. And a vertical

concentrated load P acting at its midspan. The member is

fully laterally supported for its entire length. The effect of

any bolts can be neglected. The beam consists of 2-

150×90x12mm angles with long legs back to back spaced

at 10mm apart. For this problem the properties of one 150×90x12mm angles are:

Area (A) = 2751 mm2

Section modulus (Sx) = 0.000063m3

Steel is A36 with yield strength (Fy) = 248MPa

Allowable tensile stress = 0.60Fy

Allowable flexural stress = 0.66Fy

Neglecting the weight of the beam, which of the following

most nearly gives the maximum value of the load P that the

member can support.


1997″

A beam is fixed at both ends and has an internal hinge

along the span. Classify the beam as either unstable,

statically indeterminate or statically determinate and degree

of indeterminacy. Assume all loads can act anywhere in any direction of the beam.

a) Statically indeterminate to the first degree

b) Unstable

c) Statically indeterminate to the second degree

d) Statically determinate


1997″

A 2 N weight is swing in a vertical circle of 1m radius and

the end of the cable will break if the tension exceeds 500N.

Which of the following most nearly gives the angular

velocity of the weight when the cable breaks?










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CE BOARD 1997




1997″

In accordance with sections 5.4.7.2.3 of the 1992 NSCP,

strength level of an individual class of concrete shall be

considered satisfactory if both of the following

requirements are met.

a) Average of all sets of three consecutive strength tests equal or exceeds fc’

b) No individual strength test (average of two cylinders) falls below fc’ by more than 3.5MPa.

The required fc’ for a project is 28MPa. The results of four sets of cylinder tests with 5 samples are as follows.

Set A Set B Set C Set D

Sample # 1 24.0 28.5 32.0 21.0

Sample # 2 23.5 28.0 30.5 24.5

Sample # 3 25.0 32.0 25.0 20.5

Sample # 4 35.0 25.0 25.0 22.0

Sample # 4 30.5 29.0 28.0 20.0

Which of the following set is acceptable for the project

requirements?


1997″

The result of standard Proctor Test is as follows:

Water content (%) Weight (W) of moist soil in

Proctor mold (grams)

10 1.485

12 1.606

14 1.696

16 1.755

18 1.741

20 1.651

The volume of the mold for this test is 1/30cu.ft. (946,000

cubic millimeters). Which of the following most nearly

gives the value of the optimum moisture content of the soil?


1997″

March 22nd, 2010 admin No comments Section 5.10.11.5

of the 1992 NSCP, discuss the provisions for moment

magnification. Compression members shall be designed

using the factored axial load Pu from a conventional frame

analysis and a magnified factored moment Mc defined by:

Mc = δs M2b + δb M2s

Where:

M2b = the value of larger factored end moment on

compression member due to loads that result in no

appreciable sideways, calculated by conventional elastic

frame analysis.

M2s = value of larger factored end moment on compression

member due to loads that result in appreciable sideways, calculated by conventional elastic frame analysis.

∑Pu and ∑Pc are the summations for all columns in a story.

For frames not braced against sideways, both δb and δs shall

be computed. For frames braced against sideway, δs shall

be taken as 1.0.

In equation (5.10.7) for members braced against sideway

and without transverse loads between supports Cm maybe taken as:

But not less than 0.40. For all other cases,

Cm shall be taken as 1.0

A rectangular tied concrete column has dimensions of

300mm x 380mm. The column length is 4.5m. is to be

constructed in a frame braced against sideway (the effective

length factor K can be taken as 1 and EI = 34MN-m2.. The

column is loaded in single curvature by the ultimate

factored moment of 110kN.m at its top end and 120kN.m at







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CE BOARD 1997



its bottom end. The column carries factored axial loads due to dead load of 150kN, 350kN due to live load.

Which of the following gives the magnified factored

moment (Mc) that will be used it design the steel reinforcement in accordance with the NSCP 1992.


1997″

The development length (Ld) of a steel reinforcing bar with

given stress (Fs) embedded in concrete anchorage bond

strength (u) and diameter of bar (D) is given by the expression.


1997″

A ball is shot at a ground level at an angle of 80ball is shot

at a ground level at an angle of 80 degrees with the

horizontal with an initial velocity of 10m/sec. Which of the

following most nearly gives the maximum height (h)

attained by the ball?


1997″

Section 5.10.3.2 and 5.10.3.3 of the 1992 National Code of

the Phil. States as follows: Balanced strain conditions exists

at a cross section when tension reinforcement reaches the

strain corresponding to its specified yield strength fy just as

concrete in compression reaches its ultimate strain of 0.003.

For flexural members subject to combined flexure and

compressive axial load, when the design axial load strength

θPn is less than the smaller of 0.10 fc’ Ag or θPb. the ratio

of reinforcement ρ provided shall not exceed 0.75 of the

ratio ρb that would produced balanced strain conditions for

the section under the flexure without axial load. For

members with compression reinforcement, the portion of ρb

equalized by compression reinforcement need not be

reduced concrete beam has a width of 300mm and an

effective of 400mm. Concrete strength is 24MPa and steel

yield strength is 340MPa. Which of the following most

nearly gives the maximum allowable steel area (As) in

accordance with the 1992 NSCP strength design method.


1997″

A non-prismatic simply supported beam has a total span of

8m. The 4m. long middle section of the beam has a

moment of inertia twice the moment of inertia of the

section beside the supports. The beam is acted upon by

downward concentrated load acting at mid span equal to

10kN. Which of the following most nearly gives the slope

(theta) at a point 2m. to the right of the left support (at the

change in cross section.)


1997″

A rod with cross-sectional area of 100sq.mm is stretched

between two fixed points such that the initial tensile load is

10kN. The rod has an initial modulus of elasticity (E) equal

to 180GPa. And a coefficient of linear expansion (alpha)

equal to 0.00001 mm/degree centigrade. The initial tension

is designed such that the rod will have a zero stress when

there is a certain change in temperature of the rod. Which

of the following most nearly gives the value of this temperature change T:


1997″

The H2O table in a deposit of silt is lowered from a depth

of 3m to a depth of 6m. all the silt is saturated even after the H2O table is lowered and the water content is 22%.

Which of the most nearly gives the change in effective

pressure at a depth of 12m. on account of lowering of water table Sp.gr. of soil is 2.60













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CE BOARD 1997




1997″

The soil is said to be non-plastic if the liquid limit is less than:

a) 90

b) 50

c) 20

d) 60


1997″

According to implementing Rules and Regulation PD 159,

which of the following is not authorized to be a member of

the PBAC.

a) Representative of Phil. Constructors Association

b) Representative of PICE

c) Representative of CPA

d) Representative of Road Engineers Association of the

Phil.

Design and Construction “CE Board Exam May

1997″

A concrete beam of rectangular cross section, 120mm x

300mm is to be reinforced by six, high tensile pre-stressing

tendons each having a cross sectional area of 300mm2. If

the level of pre-stress in the tendon is 150N/mm2 and if the

reinforced beam is subjected to an axial tensile load of

150kN, determine the final stress in the concrete assuming

that the ration of the elastic modulus of steel to that of concrete is 15:


1997″

A simply supported beam 400mm by 800mm and span of

10.0m, is pre-stressed by a straight tendon with a force of

1200kN at an eccentricity of 200mm from the centroid. The

beam supports a total weight. Calculate the stresses at the

top fiber.


1997″

Based on the AISC Specifications, the effective net area Ae

at the root of the thread of a threaded tension member is Ae

= 0.7854 (D – 0.9743/n)2 Where D is the nominal outside

diam. Of the threads and n is the number of threads per

25.4mm. if the load is 250kN and the number of threads per

inch of the threaded tension member is 4, Fy = 250MPa the

diameter sufficient to carry the load is:


1997″

A tied column is subjected to axial load and end moments. The conditions of the column are as follows:

Unsupported length, Lu 5.00m

Effective length factor, K 0.90

Flexural rigidity, EI 7500 x 109 N-mm2

Magnification factor, delta 1.20

Moment magnifying coef., Cm 0.533

Determine the ultimate load Pu in kN that this colum can

carry. Use phi = 0.70.


1997″

The rotation or twist in degrees of a shaft, 800mm long,

subjected to a torque of 80N-m, 20mm in diameter, and shear modulus G of 80,000MPa is:



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CE BOARD 1997




1997″

A cubic meter of soil in its natural state weighs 1.75kN;

after being dried, it weighs 15.08kN. The specific gravity

of the soil is 2.70. Determine the void ratio of the original

soil sample:


1997″

The allowable capacity of a 10mm thick fillet weld, E60 electrode (Fu = 415MPa) is:


1997″

A reinforced concrete beam has the following properties;

Beam with, b …………………………… 320mm

Effective depth, d ……………………… 640mm

Concrete strength, fc …………………… 25MPa

Reinforcing steel strength, fy …………. 400MPa

Compute the shear capacity of stirrups


1997″

A W 410 x 74.4 supports a slab with a thickness of 150mm.

The effective width of the slab was computed to be

2000mm. The structural steel section of the composite

system has the following properties:

Beam depth, d 413mm

Flange width, bf 180mm

Cross sectional area, As 9480mm2

Moment of inertia 274.3 x 106mm4

Where is the new location of the neutral axis from the top

of the slab in mm. Use n = 10m transform the area of concrete to steel.


1997″

A steel beam 7.2m long carries a uniformly distributed load

of 36kN/m throughout the span. It is simply supported at its

end and at its center (a two 3.6m span continuous beam). If

the shear (reaction) at the end support is 48.6kN, the

maximum positive moment is developed at this distance

from the end support.


1997″

A footing is 2.40m by 1.50m. The total load P of 1,000kN

on the footing has an eccentricity of 0.40m in the direction

of the longer dimension. Determine the maximum soil pressure at the base.













CE BOARD 1997



Hydraulics “CE Board Exam Nov. 1997″

A vertical wall retains a cohesionless soil which has a unit

weight of 14 kN/m3, and angle of internal friction of 26

degrees. If the wall is 5.0m high, what is the total active

soil pressure in kN on the wall. Assume a unit length of

wall.


Determine the discharge in MLD of a 2800 mm gravity

flow concrete aqueduct 4km long with a head loss of 5.6m.

Assume pipe is flowing just full with roughness coeff. of 0.015.


A H2O tank with 3 mØ is filled with H2O. The H2O level is

2.30 m above a nozzle. What is the velocity of H2O coming

out of the nozzle? Neglect losses


Determine the magnitude of the force on the inclined gate

1.5m. by 0.5m. shown in the figure. The tank is completely

closed and the pressure gage at the bottom of the tank reads 90000 N/m2. Use 9800 N/m3 for H2O.


A drainage canal in the shape of trapezoidal with bottom

width of 2.5m and side slopes of 1 horizontal to 1.5

vertical, carries H2O at a depth of 3m. Find the discharge in m3/s using the chezy’s Formula. S = 0.0009, n = 0.615.


An aeration basin with a vol. of 400 m3 contains a mixed

liquor (aerating activated sludge) with a suspended solids

concentration of 2000 milligrams per liter. How many kg of mixed liquor suspended solids are in the tank.


A pipe 60cm. in length is connected at the end by a nozzle

and the total energy produce in the nozzle is 250m. Compute the velocity of the jet.


A drainage canal in the shape of trapezoidal with a bottom

width of 2.5m. side slopes 1:1 carries water at a depth of

3m. Find the velocity using chezy’s formula, S = 0.0009, n = 0.015


Determine the discharge in MLD of a 2800 mm gravity

flow concrete aqueduct with a hydraulic gradient of 0.0015.

Assume pipe is flowing full with coefficient of roughness = 0.015


A rectangular channel 1 meter in width carries water of 3

m3/s at a depth of 0.6 m. Determine the type of flow.


Precipitation station x was inoperative for part of a month

during which a storm occurred. The respective storm totals

at three surrounding stations A, B and C were 98.80 and

110mm. The normal annual precipitation amounts at

stations x A, B and C are respectively, 880, 1008, 842 and 1080mm. Estimate the storm precipitation for station x.


Find the discharge of a Cipolleti weir if it has a length

equal to 1.67m. and the head of weir is one fifth of its length.

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CE BOARD 1997




A trapezoidal flume of most efficient proportion has a base

width of 1.5m. Its full discharge is 3 m3.s. If the same

material were used for a most efficient rectangular section. What is the discharge of the new section?


A block of wood (s = 0.65) is 20 mm thick is floating in sea

water (s = 1.03). Find the area of a block of wood which

will just support a man weighing 80kg when the top surface is just at the water surface.


A spillway controls reservoir 4 hectares in area. The

permanent crest is at elevation 40m. the length of the

spillway crest is at elevation 40 m. the length of the

spillway is 35.20ft. initially the level of H2O is at elev. 41.8

m. After 25 minutes H2O goes down at a certain level. What is the final elevation.


An open vessel 3m. in diameter contains water at a depth of

3.05m and 0,91 m of oil (S = 0.8) the tank is accelerated upward at 3 m/s2. Find the pressure at the bottom.


A device attached at the end of the pipe with a cover use

for cleaning.

a) clean out

b) man hole

c) culvert

d) none


Fluid particles move in a straight line along a smooth pipe.

The factor that causes coeff. of friction. .

a) viscous shear

b) density of liquid

c) pressure head

d) froude number


A circular pipe 2m. in diameter carries water at a depth of ¾ of its diameter. What is the hydraulic radius?


Tow pipes with the same friction factor and length are

parallel. If the first pipe has twice the diameter of the second, what must be the ratio of their flow?


An open vessel 30cm. in diameter and 90cm high is filled

with water to a depth of 45 cm. Find the magnitude of the velocity such that the vortex is just at the bottom.

Hydraulics “CE Board Exam May 1997″

A rectangular weir was installed to control the flow. If the

flow is set at 3cu.m/s, Cd = 0.6 and the length is 0.8m.,

what must the height be?


A rectangular weir was installed to control the flow. If the

flow is set at 3cu.m/s, Cd = 0.6 and the length is 2m., what must the height be?









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CE BOARD 1997




Water has velocity of 4 m/s through a 40 cm pipe. The discharge through the pipe is:


For adiabatic conditions

a) pv = constant

b) pvk = constant

c) pvn = constant

d) none of these


A drainage line 1.4 km long is designed base on a storm on

a 6 ha. Property which produced 40 mm per hour assuming

a velocity flow of 0.8 m/s. With a runoff coefficient of C = 0.5. what peak discharge can be expected from the area.


Determine the drag on a torpedo with area 0.01 sq.m. moving horizontally at 80 m/s and Cd = 0.5.


Determine the discharge over a suppressed rectangular weir has L = 4 m. and H = 1.2m, and Cw = 0.62.


A type of dam having a smallest cross-section.

a) Buttress Dam

b) Arch Dam

c) Gravity Dam

d) Rock Dam


A 12cm.diameter solid cylinder of height 8 cm. weighing

0.5kg is immersed in liquid with density 800 kg/cm

contained in a tall metal cylinder having a diameter 15cm,

Before immersion the liquid was 8cm. deep. How deep is it

submerged?


A gate slanted 60 degree from the horizontal with width =

1.6m and height = 2.4m is submerged by a depth of 1.8m., determine the pressure at the top of the gate.


A process at which no heat is added to or taken away from

the flow system.

a) Isothermal

b) Isentropic

c) Adiabitic

d) Isotropic


A pressure gauge at elevation 6m. at the side of a tank

containing a liquid reads 90 KPa. Another gauge at elevation 4m. reads 110 KPa. What is the density?


A 12cm. diameter solid cylinder of height 8cm. weighing

0.5 kg is immersed in liquid with density 800 kg/cm

contained in a tall metal cylinder having a diameter 15cm.

Before immersion the liquid was 8cm. deep. What is the

volume of liquids displaced?












CE BOARD 1997




A pressure gauge at elevation 6m. at the side of a tank

containing a liquid reads 90 kPa. Another gauge at

elevation 4m. reads 110 kPa. Compute for the specific weight.


Water has a velocity of 4 m/s through 40 cm pipe. The

discharge through the pipe is:


An open tank 1.82m square, weighs 3,425 N and contains

0.91 m of water. It is acted upon by an unbalanced force of

10,400 N parallel to a pair of sides. What must be the

height in m of the sides. What must be the height in m of the sides of the tank so that no water will be spilled?


Weber Number is defined as:

a) The ratio of inertia forces to surface tension

b) The ratio of inertia forces to the pressure forces

c) The ratio of inertia forces to the elastic forces

d) The ratio of inertia forces to the gravity forces


Determine the discharge over a triangular weir with angle = 73.74 deg. And H = 1.2m and Cw = 0.70.


It is the increased pressure developed on impact with a pilot

tube as a result of localized kinetic energy reduction to

zero.

a) Oritical Pressure

b) Stagnation Pressure

c) Hydrodynamics

d) Pressure Relief


The water supply for city is pumped to a distribution

reservoir. The pumping rate is 600 cu.m. per 4 hours. The

estimated water requirements every 4 hours. The estimated water requirements every 4 hours is shown below.

HOUR DEMAND

0400 200

0800 800

1200 1100

1600 700

2000 500

2400 300

What is the maximum requirement from the reservoir?


A rectangular channel has a base width of 7.0m. and a

depth of 2.5m. carries a discharged of 21.81 m3/s. It is

required to change this channel into a most efficient

trapezoidal section having the same material. Determine the increase in discharge of the new section.

Hydraulics “CE Board Exam May 1997″ The maximum quantity of water which can be guaranteed

during a critical dry period.

a) Reservoir reliability

b) Secondary yield

c) Safe yield

d) reservoir yield


The removal of course and settle able solids by

interception.

a) Screening

b) Comminution

c) Flocculation

d) Floatation


A vertical jet of water supports a load of 200 N at a

constant vertical height of 12m. from the tip of the nozzle.

The diameter of the jet is 25mm Ø. Find the velocity of the jet nozzle tip:












CE BOARD 1997




Evaporation of water from the leaves of plants is called.

a) Eutrophication

b) Saturation

c) Transpiration

d) Interception


The science that treats of the water on earth, their

occurrence, circulation and distribution, their chemical and

physical properties and their reaction with their

environment including their relation to living things:

a) Hydrology

b) Hydrograph

c) Kinetics

d) Unography


Pipes 1, 2 and 3 are 300m., 150 and 250m. long and lf

25cm., 12cm. and 20cm. diam. With f1, f2 and f3 equal to

0.019, 0.019, 0.021 and 0.02 respectively and are connected

in series. If the difference in elevation of the ends of the pipe is 10m., what is the rate of flow in cu.m./sec.


A submarine, which maybe supposed to approximate a

cylinder 3m Ø and 15m long travels submerged at 1.55 m/s

at sea water at 5°C. Viscosity is 1.519x 10-6 m2/s. Find the Reynolds Number for this condition:


What spillway of a dam is used when a space is limited:

a) shaft spillway

b) siphon spillway

c) side channel spillway

d) none of these





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CE BOARD 1997



Mathematics “CE Board Exam Nov. 1997″

From the following differential leveling notes, compute the difference in elevation between station 5 and 6.

STA B.S. F.S. ELEV.

1 2.565 33.971

2 10.875 5.821

3 7.035 1.946

4 3.560 5.741

5 7.186 9.736

6 4.123 7.977

1 4.123


Using the prismoidal correction formula, find the corrected

volume of cut between stations 80 m. apart if the areas of

irregular sections in cut at stations are 26 sq.m. and 68

sq.m. respectively. Base width = 8 m. and side slope is 1:1.


The elements of a compound curve are as follows:

I1 = 18° D1 = 2°

I2 = 23.5° D2 = 4°

Determine the stationing of the P.C. if the stationing

of P.I. = 42 + 89.6. Use arc basis.


Given the following data of a closed traverse. Compute the bearing of line DE.

LINE BEARING DIST(m.)

AB N. 72°10’ E. 64.86

BC S. 48°28’ E. 107.72

CD S. 35°30’ W. 44.37

DE ————– 137.84

EA ————– 12.83


Find the determinants of x:


The correct distance between point E and f IS 213.5 m. If a

100m. tape that is 0.025 m. too long is used to measure EF, what will be the measured distance in meters?


Locate the center of the curve 9x2 – 144x + 16y2 + 96y+495 = 0


Find the remainder if 3x3 – 4x2y + 5xy2 + 6y3 is divided by

x2 – 2xy + 3y2

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CE BOARD 1997




The bases of a right prism is a hexagon with one of each

side equal to 6 cm. The bases are 12 cm. apart. What is the volume of the right prism?


A train starting at initial velocity of 30 kph travels a

distance of 21 km. in 18 min. Determine the acceleration of

the train at this instant.


Determine the length of the latus rectum of the ellipse

having an equation 4x2 + 9y2 – 64x + 54y + 301 = 0.


The base of a right prism is pentagon with one of each side

is 6 cm. long. If the bases are 12 cm. apart, what is the volume of the right prism in cu.m.


Evaluate the log6 845 = x


The volume of a pyramid is 140 cu.m. If it has a

rectangular upper base of 3 m. x 4 m. and an altitude of 5 m., determine the dimensions of the lower base.


Find the remainder if we divide 4y3 + 18y2 + 8y – 4 by 2y + 3


A turbine started from rest to 180 rpm in 6 min. at a

constant acceleration. Find the number of revolutions that it makes within the elapse time.



The cost of equipment is P500,000 and the cost of

installation is P30,000. If the salvage value is 10% of the

cost of equipment at the end of 5 years, determine the book

value at the end of the fourth year. Use straight line method.


The sides of the triangle are 12, 16 and 21. Find the area of

the triangle.



Find the derivative of Arc Sin 3x with respect to x:














CE BOARD 1997




Find the area of the region bounded by the curve r2 = 16 Cos θ.


The angle of elevation of the top of tower B from the top of

tower A is 28° and the angle of elevation of the top of

tower A from the base of tower B is 46°. The two towers

lie in the same horizontal plane. If the height of tower B is 120 m., find the height of tower A.


Find the number of terms for a progression 5,8,11,14……whose sum is 1025.


Points A and B are 100 m. apart and are of the same

elevation as the foot of the bldg. The angles of elevation of

the top of the bldg. from points A and B are 21 degrees and

32 degrees respectively. How far is A from the bldg. in meters?


Find the slope of the line having the parametric equations x = t – 1 and y = 2t.


Find the radius of curvature of a parabola y2 – 4x =0 at point (4,4)


Find the volume of a cone to be constructed from a sector having a diameter of 72 cm. and a central angle of 210°.

Mathematics “CE Board Exam May 1997″

Car A moves due East at 30 kph at the same instant car B is

moving S. 30° E. with a speed of 30 kph. The distance from

A to B is 30 km. Find how fast is the speed between them are separating after one hour.


A corporation uses a type of motor truck which costs P5000

with life 2 yrs. and final salvage value of P800. How much

could the corporation afford to pay for another type of truck

of the same purpose whose life is 3 yrs. with a final salvage value of P1000. Money is worth 4%.


A parabolic curve having a forward tangent of -3%

intersects a back tangent of 6.5% at station 10 + 800 whose

elevation is 5260 m. If the length of the curve is 400 m., find the stationing of the highest point of curve.


A quadrilateral has sides equal to 12 m., 20 m., 8 m. and

16.97 m. respectively. If the sum of the two opposite angles is equal to 225°, find the area of the quadrilateral.


JA 5cm. x 5cm. is cut from a corner of 20cm x 30cm,

cardboard, find the centroid from the longest side.







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CE BOARD 1997




Find the differential equations of the family of lines passing through the origin.


A frustum of a regular pyramid has an upper base of 8 m. x

80 m. and a lower base of 10 m. x 100 m. and an altitude

of 5 m. Find the volume of the pyramid.


From the given close traversed, find the corrected bearing of line EA.

LINE DIST(m.) BEARING

AB 895 S. 70°29’ E.

BC 315 S. 26°28’ E.

CD 875 S. 65°33’ W.

DE 410 N. 45°31’ W.

EA 650 N. 10° E.


What time after 3 o’clock will the hands of the clock be together for the first time?



A spherical triangle ABC has an angle C = 90° and sides a = 50° and c = 80°., Find the value of “b” degrees?


Find the minimum amount of thin sheet that can be made

into a closed cylinder having a volume of 108cu.in. in square inches.


Differentiate Arc Cos 4x:


A deposit of P110,000 was made for 31 days. The net

interest after deducting 20% withholding tax is P890.36. Find the rate of return annually.


Find the area enclosed by the curve x2+8y+16=0, the x-

axis, and the line x – 4 = 0.


In the sum of the interior angles of a polygon with an equal sides is 1080°, find the number of sides of a polygon?


Find the distance from point A(4,2) to B(-5,1).













CE BOARD 1997




Find the slope of a line having a parametric equation of x = 2 + t and y = 5 – 3 t


A circular cone having an altitude of 9 m. is divided into 2

segments having the same vertex. If the smaller altitude is 6

m., find the ratio of the volume of small cone to the big

cone.


A circular curve having an azimuth of back tangent equal to

205° and the azimuth of the forward tangent equal to 262°.

If the middle ordinate is 5.6 m. find the length of the tangent.


The corners of a cubical block touched the closed spherical

shell that encloses it. The volume of the box is 2744 cubic

centimeter. What volume in cubic centimeter inside shell is

not occupied by the block?



A projectile leaves at a velocity of 50 m/s at an angle of 30°

with the horizontal. Find the maximum height that it could

reach?


A line was measured with a 50m. tape. There were 2 tallies,

8 pins, and the distance from the last pin to the end of the line was 2.25 m. Find the length of the line in meters?


Which of the following numbers should be change to make

all the numbers form an Arithmetic progression when

properly arranged?


From the given differential leveling notes, find the elevation of BM2.

STA B.S. F.S. ELEV.

BM1 ********2.565 33.971

TP1 ********10.875 5.821

TP2 *********7.035 1.946

BM1 *********5.741


Find the value of “w” in the following equations:

3x – 2y + w =11

x + 5y – 2w = -9

2x + y – 3w = -6


From station 0 + 0.40 with center height of 1.2 m. in fill,

the ground line makes a uniform slope of 6.5% to station 0

+ 100, whose center height in cut is 3.5m. Find the grade of the finished roadway.











http://ce-review.com/2010/01/25/mathematics-%e2%80%9cce-board-exam-may-1997/

Documents

CE Board Exam 1997