CE Board Exam 1998

CE BOARD 1998

PHILIPPINE INSTITUTE OF CIVIL ENGINEERS – UAE CHAPTER

CIVIL ENGINEERING BOARD EXAM 2013 PREPARATION

Design and Construction “CE Board Exam Nov.

1998″

A concurrent force system in space is composed of 3 forces

described as follows P1 has a magnitude of 100kN and acts

through the origin and points x =3, y =4, z=2. P2 has a

magnitude of 60kN and acts through the origin and points x

= 4, y = 1, z = -2. P3 has a magnitude of 80kN and acts through the origin and points x = 2, y = -3, z = 3.

1) Which of the following most nearly gives the x-component of the resultant force.

2) Which of the following most nearly gives the y-component of the resultant force.

3) Which of the following most nearly gives the z-component of the resultant force.


1998″

A bill of quantities is to be prepared for square isolated

reinforced concrete column and footing as shown. The

foundation is strong enough that form works is not required for footing. The swell factor for backfill is 120%.

1) Which of the following most nearly gives the quantity of excavation in m3.

2) Which of the following most nearly gives the quantities

of form works is sq.m.


1998″

A rectangular reinforced concrete beam with width of

300mm and effective depth of 600mm is subjected to a

service (unfactored) bending moment of 200kN.m. The

beam is reinforced with 4-32mmØ bars. The modular ratio n = 8.

1) Using the alternate (working stress) Design method.

Which of the following most nearly gives the distance of the neutral axis from the top of the beam (kb) in mm.

2) Which of the following most nearly gives the maximum stress in concrete in MPa.

3) Which of the following most nearly gives the total comp. force in concrete in kN.

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CE BOARD 1998




1998″

For continuous beams and slabs, approximate coefficients

of shear and bending moments in accordance with the

NSCP Specifications may be utilized when the following conditions are satisfied.

1) Adjacent clear spans may not differ by more than 20%

of the shorter span.

2) Ratio of live load to dead should be less than 3.

3) The loads must be uniformly distributed.

When all conditions are satisfied, the following formulas

maybe used to determine shear forces and bending moments in continuous beam and one way slabs.

A) For positive moment

End span:

1) If discontinuous ends is unrestrained …… (WL’2/11)

2) If discontinuous ends is integral with the support………………………………………. (wL’2/14)

3) Interior spans…………………………….. (wL’2/16)

B) For negative moment

1) Negative moment at exterior face of first interior support.

Two spans ………………………………… -(wL’2/9)

More than two spans ………………………… - (wL’2/10)

2) Negative moment at other faces of interior

supports…………………………………… (wL’2/11)

3) Negative moment at face of all supports for

a) Slabs with spans not exceeding

3m …………………………………….… - (wL’2/12)

b) Beams and girders when the ratio of sum of column stiffness to beam stiffness exceeds 8 at each

end of the span ………………………….. - (wL’2/12)

3) Negative moment at interior faces of exterior supports, for members built integral with their supports.

a. Where the support is a spandrel beam or girder

……… -(wL’2/24)

b. Where the support is a column

……… -(wL’2/16)

C) Shear Forces:

1) Shear in end members at first interior

support………………………………….………(1.15wL’/2)

2) Shear at the other support …………………... (wL’/2)

The figure shown is a continuous beam having given clear

spans of L1 = 6m., L2 = 7m and L3 = 8m. It carries a

uniform dead load of 12 kN/m and a uniform dead load of

12kN/m and a uniform live load of 30 kN/m. It is required to compute the following. Use NSCP moment coefficients.

1) Which of the following most nearly gives the moment at

A.


B.

3) Which of the following most nearly gives the moment at C.



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CE BOARD 1998




1998″

Section 4.5.1.3.1 of the NSCP specifies the allowable axial

compressive members whose cross-sections meet with the

provisions of the code.

A compression member is 3m. long and pinne at both ends.

Effective length of factor K = 1.0. The column is subjected

to an axial compressive load of 590kN. The section is made

up of 2 angles of unequal legs with long legs back to back

and separated by a gusset plate 11mm thick. Use A 36 steel, Fy = 248 MPa and E = 200000 MPa.

1) Which of the following gives the largest allowable

compressive stress.

2) Which of the following gives the smallest allowable

compressive stress.

3) Which of the following gives the most economical

setion.

Section Area(m2) rx(m) ry(m)

2- < 120×80x10 0.0056 0.040 0.018

2- < 1150×90x12 0.0062 0.052 0.021

2- < 180×100x10 0.0079 0.060 0.026


1998″

A W 16 x 58 is connected to W 18 x 31. Use A-36 steel Fy

= 248MPa. Allowable stress Ss = 0.40 Fy. A 502 grade hot

driven rivets with an allowable shearing stress of 120MPa

and allowable bearing stress of 1.5 Fu(AISC). The support

is to be designed using the full strength of W 16 x 58 beam based on the gross section.

Properties of sections

W 16 x 58 W 18 x 31

d = 403mm Flange thickness = 11mm

Web thickness = 10mm

1) Which of the following most nearly gives the minimum

diameter of rivets not the exceed allowable shear stress.

2) Which of the following most nearly gives the minimum diameter of rivets not to exceed allowable bearing stress.

3) Which of the following most nearly gives the minimum diameter of rivets.





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CE BOARD 1998




1998″

A truss shown in the figure is subjected to a horizontal

force at joint C. The term E below refers to the modulus of

elasticity of the material in Pa and the term A refers to the

cross-sectional area of the members. The truss is to be analyzed using the method of superposition.

1) Which of the following most nearly gives the relative

displacement of joint B and D, if member BD is removed in meters.

2) Which of the following most nearly gives the relative

displacement of joint B and D due to two unit loads (N)

acting at joint B and D acting towards each other in the

direction of member BD, if the member BD is removed in m.

3) Which of the following most nearly gives the value of the bar force in member BD in Newtons.


1998″

From the beam shown in the figure.

1) Which of the following gives the fixed end moment at B due to the concentrated load in kN.m.

2) Which of the following most nearly gives the distribution factor at B for the member AB in %


B.


1998″

Three identical cylinders are stacked within a rigid bin as

shown in the figure weight of each cylinder is 500 N. There

is no friction at any contact surface.

1) Which of the following most nearly gives the force at A, in Newtons.

2) Which of the following most nearly gives the force at B, in Newtons.

3) Which of the following most nearly gives the force at C, in Newtons.

Design and Construction “CE Board Exam May

1998″

A piece of equipment was purchased for P4,000,000.00

The useful life is estimated at 5years with no salvage value.

The equipment is estimated to be used 1000 hours every year Operating costs are as follows:

Fuel ………….10 liters/hour @ P10 per liter

Oil ……………1 liter/hour @ P20 per liter

Grease ……….2 liters/hour @ P5 per liter

The equipments uses 6 tires costing P60,000 each.

Estimated life of tires is 4000 cost of money is 15% per

year. Cost of insurance taxes, storage, etc. is 15% per year.

1) Which of the following gives the cost of using the

equipment only in pesos per hour.

2) Which of the following gives the cost of using the tires in pesos per hour.

3) Which of the following gives the cost of using the equipment and tires in pesos per hour.





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CE BOARD 1998




1998″

For the forces in the figure shown

1) Which of the following most nearly gives the magnitude

of the horizontal component of the resultant of the force

system?

2) Which of the following most nearly gives the magnitude

of the resultant force?

3) Which of the following gives the angle that the

equilibrant makes with the horizontal axis.


1998″

1) For the wall footing shown in the figure, which of the

following most nearly gives the effective soil pressure if

the allowable soil pressure is 200kPa. (the effective soil

pressure is the remaining soil pressure available to support

the loads after the effects of the soil an concrete weights are

subtracted) fc’ = 28 MPa fy = 280MPa

Unit weight of concrete = 24kN/m3

Unit weight of soil = 16kN/m3

Allowable soil pressure = 200kPa

PD = 200kN/m

PL = 180kN/m

2) Which of the following most nearly gives the minimum

width of footing rounded to the nearest 0.10m. such that the

effective soil pressure will not be exceeded.

3) Which of the following most nearly gives the ultimate shear due to factored loads acting or, the critical section.


1998″

Given the beam shown in the figure, in equation (1) and (2)

below, the terms are as follows:

Axy = area of the moment diagram of the given load acting

on a simple beam

Xxy = distance of centroid of Axy from point x

I = moment of inertia of member

Lxy = span length of member xy

1) Determine the value of the expression:

Representing the contribution of the uniform load and

concentrated load acting on the span ab, to the three-moment equations of two-span beam.

2) Determine the value of the expression:

Representing the contribution of the triangular load acting

on the triangular load acting on the span bc, to the three-moment equations of two-span beam.

3) Compute the maximum negative moment.







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CE BOARD 1998




1998″

A sand layer of the cross-sectional area shown in the figure

below has been determined to exist for a 450m. length of

levee. The coefficient of permeability of the sand layer is

3m per day. Compute the quantity of water which flows into the ditch.


1998″

A plate with width of 300mm and thickness of 20mm is to

be connected to two plates of the same material with half

the thickness, by 25mm diameter rivets, as shown in the

figure. The rivet holes have a diameter 2mm larger than the

rivet diameter. The plate is A36 steel with yield strength Fy

= 248 megaPascals, allowable tensile stress of 1.35 Fy. The

rivets are A502, Grade 2, hot-driven rivets with allowable shear stress of 150 megaPascals.

1) Which of the following most nearly gives the max. load

in kN that can be applied to the connection without exceeding the allowable shear stress in rivets.


in kN that can be applied to the connection without

exceeding the allowable bearing stress between the plates and the rivets.


in kN that can be applied to the connection without

exceeding the allowable tensile strength of the plates.


1998″

For the shaded area given in the figure.

1) Determine the area, in square meters.

2) Determine the x-coordinate of the centroid, in meters.

3) Determine the y-coordinate of the centroid, in meters.


1998″

Given the figure below:

1) Determine the reinforcement ratio, in percent

2) Determine the ratio of the center spacing of

reinforcement to the column dimension in the direction of

bending.









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CE BOARD 1998



3) Using the interaction Diagram, determine the maximum

downward load that the column can support, in kN, if

eccentricity e = 200mm.


1998″

A simply supported beam with span of 8meters is subjected

to a uniform vertical downward load equal to 50kilo

Newtons/meters, acting on the plane of the minor axis of

the beam section, which includes the beam weight. The

beam is restrained against lateral buck.ing of the top and

bottom flanges for the entire span. The material is A36

steel with fy = 248 megaPascals and modulus of elasticity =

200 gigaPascals. The allowable flexural stress for laterally

braced compact sections is 0.66 fv. The allowable

deflection is 1/360 of the span. Three compact sections are

being considered, as follows, with their respective

properties relevant to this problem (length units are in

meters):

Section Moment of Inertia Beam Depth

1 W 24 x55 0.000558 m4 0.598m.

2 W 21 x 62 0.000554 m4 0.533m.

3 W 21 x 68 0.000616 m4 0.537m.

1) Determine the minimum section modulus Sx, in m3, such

that the maximum flexural stress will not be exceeded.

2) Determine the minimum moment of inertia Ix, in m4,

such that the maximum deflection will not be exceeded.

3) Assuming that shear stress is not critical, which of the

sections being considered is the most economical section

adequate for the given load.


1998″

A simply-supported beam has shear diagram shown in the figure.

1) Determine the maximum positive bending moment, n kN-m.

2) Determine the maximum negative bending moment, in kN-m

3) Determine the location of the inflection point from the support, in meters.


1998″

The result of a grading analysis is the particular size

distribution shown in the figure. Determine the effective grain size D10.

a) 0.10

b) 0.07

c) 0.09

d) 0.08


1998″

A soil sample is placed in a brass box. The soil is gripped

by perforated metal grilles and porous discs are behind the

metal grilles to allow the sample by means of a 500kg

weight and while applying the normal load, a lateral force

is gradually exerted in the box using an electrical screw

jack. The force and the corresponding cross section of specimen are recorded during the test. This is known as:

a) Consolidated drain test

b) Direct shear test

c) Undrained shear test

d) Unconfined compression test







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CE BOARD 1998



Hydraulics “CE Board Exam May 1998″

The velocity at which the change from laminar to turbulent flow occurs is:

a) lower than that from turbulent to laminar

b) equal to that from turbulent to laminar

c) higher than that from turbulent to laminar

d) none of these


A large cylindrical steel tank 4m. high with its bottom

on level ground contains two layers of liquid. The bottom

layer is water 2m. deep. The top layer is occupied by a

liquid whose specific gravity is not known to a depth of

1m. A 50 mm diam. orifice with a coefficient of velocity of

0.98 is situated one meter from the bottom of the tank. The

jet from the orifice hits the ground 2.75m horizontally away from the vena contracta. Determine the sp.gr. of the liquid.


Which of the following statements is not in accordance with Pascal’s Law?

a) The pressure is the same in all directions at any point in

a fluid at rest.

b) The pressure applied at any point to a liquid in a closed

vessel is transmitted undiminished to every portion of the

vessel

c) A body submerged in a fluid apparently weighs less by

an amount equal to the weighs less by an amount equal to

the weight of fluid displaced.

d) None of these


Horizontal orifice under a constant head of 1.30m. issues a

jet which hits a point 5m. below the centerline of the orifice

and 5m horizontally from the vena contrata. What is the coeff. of velocity?


What is the discharge capacity of a concrete pipe culvert 4

ft. in diam. And 10m. long if the difference in water level at

the outlet is 10m. Assume coefficient of discharge C = 0.74.


A watershade covering an area consisting of an equilateral

triangle ABC and a square section on the side BC. AV is

1.5km. long. If the storm precipitation depths as measured

on the rain gages at A, B and C are 75 mm., 125 mm and

100 mm respectively, compute the average precipitation over the watershed using Thiessen’s polygon method.


If the discharge over a 45° triangular weir is 0.021 m3/sec. What is the head if C = 0.594?


A vertical jet of water thru a nozzle supports a load of 150

N. The velocity and diameter of the jet at the nozzle tip are

17.46 m/s and 3 cm. Find the distance of load from the nozzle tip in meters.

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CE BOARD 1998




On slow filter, thin gelatinous surface coat of biological growth maybe develop.

a) facultative

b) biomass

c) sludge bulking

d) Shmuthdecke


Type of bacteria found in water which lives and developed without oxygen.

a) facultative

b) Bacilli

c) sponge

d) anaerobic


Wastewater from a residential community is 400 liters per

person per day containing 200 milligram per liter BOD and

240 milligram per liter suspended solids. Determine the

number of grams of BOD per person per day.


A nozzle situated at ground level issues a jet inclined at 30°

with a velocity of 12 m/s. How long will it take before the jet hit the ground?


Find the discharge through a rectangular suppressed weir in

m3/sec if L = 2.4m. and H = 18cm. Neglect velocity of approach. Use Francis formula.


Assuming the same cross sectional area and slope, which

of the following channel shapes will give the highest

discharge?


Wastewater from residential community is 400 liters per

person per day containing 240 mg/liter suspended solids.

Calculate the number of grams of suspended solids per person per day.


A drainage canal in the shape of trapezoid with a bottom

width of 2.5m. and sideslope of 1 hor. To 1.5 vertical

carries water at a depth of 3m. Find the discharge in m3/sec using Mannings formula. S = 0.0004, n = 0.015.


A spillway 12.9m. long releases flood run off from a

reservoir 5 hectares in area. If the reservoir level drops

from elevation 55m to 54m. in 2520 sec. fond the elevation

of the crest of the spillway in meters. Use Francis formula. Assume constant reservoir surface area.


A storm drain with a radius of 1.8 m. flows half full. Find the hydraulic radius in meters.


If a 5kg steel plate attached to an end of a 0.1 x 0.3 x 1.2m.

wooded pole, what is the length of the pole above the

water? Use sp.gr. of wood equal to 0.50. Neglect buoyant force on steel.













CE BOARD 1998




A dam 4m. on top, 10m at the bottom and 20m. high has

water 15m. depth acting on its vertical side. What is the

factor of safety against sliding if the coefficient of friction is 0.80.


Water flows in a rectangular canal having a width of 1m.

and a depth of 0.6m. at the rate of 0.07 m3/sec. Determine the type of flow.


Compute the critical depth for a rectangular canal having a critical velocity of 4 m/s.


With normal barometric pressure at sea level, the

atmospheric pressure at an elevation of 1215.5m. in terms

of height of mercury is equal to _________. Wt. of air = 11

N/m3 and Hg = 760 mm of air at sea level.


A large square tank has a 200 mm-diameter nozzle 5m. below the water level?


A tank contains oil sp.gr. = 0.80, gasoline sp.gr. = 0.9 and

sea water sp.gr. = 1.05. What is the pressure at a depth of

1.2m in kg/m2 if the depths of liquids are 0.5, 0.6 and 0.8

m. respectively.

Hydraulics “CE Board Exam Nov. 1998″

A trapezoidal drainage canal has a width of 1.2 m. and

1.8m. at the bottom and top respectively. If n = 0.016, what is the hydraulic radius when flowing 1.2m. deep.


A specimen of moist clay has a mass of 183.4 grams. After

oven drying, the mass is reduced to 157.7 grams. Compute

the moisture content of the sample.


Determine the discharge through a trapezoidal weir whose

sides are at an angle of 14°01’11” from the vertical and the crest length is 1.5m. long. The head on the weir is 0.3m.


A tank contains three liquids. Oil with sp.gr. of 0.8,

gasoline with sp.gr. of 0.90 and see water with a sp.gr. of

1.05 with depths of 0.65, 0.45 and 0.55 m. respectively. Compute for the water pressure at a depth of 0.80 m.


A fluid flows through a 1000m. long and 12 mm. diam.

glass tube. In 2 minutes 0.015 m3. of fluid passes through

the tube. If head loss is 0.20 meter, what is the Reynolds

Number. Assume laminar flow.


The discharge in a rectangular flume of most efficient

section(b = 2d) is 9 cu.m/sec. If the velocity of flow is 1.2

m/s, find the slope required for uniform steady flow. Use Chezy’s c = 50 (S.I. units)


A suppressed rectangular weir is under a head of 32m. The

width of the channel upstream of the weir is 2.5m. and

water stands 1.25m. deep. Using the Francis formula, find

the discharge in m3/sec. Neglect velocity of approach.


A dam 40m. high has a spillway discharging at 2m. deep

and a crest length of 10m. If c = 3.2, find the discharge in

cu.m. sec.


A masonry dam 6m. on top, 18m. at the bottom and 24m.

high has water 20m. deep on its vertical side. What is the

factor of safety against sliding? Assume weight of masonry as 2400 kg/m3. and coefficient of friction is 0.80.






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CE BOARD 1998




A 600 mm. diameter water main is bent at an angle of 45°

from the horizontal. What vertical component of dynamic

pressure is developed in the bend if the velocity in the pipe is 2 m/s?


Determine the discharge in MLD in a 3000 mm gravity

flow aqueduct if the depth of flow is 2400 mm. The slope

of the hydraulic gridline is 0.0014 and the value of Mannings “n” is 0.016.


A trapezoidal flume in the shape of a half hexagonal has

abase width of 1.5m. It is laid at a slope “S”, has a

roughness coefficient “n” and the discharge is 3.0 m3/sec.

When flowing full. If the same material were used for the

most efficient rectangular section, by how much would be the discharge decrease in cu.m. per sec.?


A circular orifice is located 5m. below the water surface. If

the tank is large and the diameter of the orifice is 5 mm,

calculate the discharge in m3/sec. if the coefficient of discharge is 0.60.


A vertical gate with width = 1.2 m. is submerged in liquid

with top and bottom edge, 3m. and 6m. below the surface,

respectively. If oil with sp.gr. = 0.80 occupies the top 1

meter of the liquid and the rest is water, calculate the force acting on the gate.


The discharge over a rectangular suppressed weir is 0.333

cu.m/sec. Water stands 1.0 m. depth at the back of the weir.

Find the length of crest of the weir if the head is 20cm. Consider velocity of approached and use Francis Formula.


Piston A has a cross section of 1200 sq.cm. While that of

piston B is 950 sq.cm. with the latter higher than piston A

by 1.75m. If the intervening passages are filled with oil

whose specific gravity is 0.80, what is the difference in

pressure between A and B.


If the maximum flow in a 5 meter wide rectangular channel

is 10 cu.m./sec. what is the critical velocity in m/sec2. Use g = 9.81 m/sec2.


Water flow in a 4m. wide rectangular channel. If the critical

depth was measured to be 0.542m., what is the max. flow in cu.m./sec. use g = 9.81 m/sec2.


A large air tight conical tank is filled with water 3.6m.

above a nozzle located at its sides. The air pressure inside

the tank is 20 kPa. If the side of the tank is inclined 15°

from the vertical and the nozzle is perpendicular to the side

of the tank, what is the horizontal component of the velocity of the jet?


Run off from a 10 sq. km. drained area is discharge over a

weir 45m. long If rainfall with an intensity of 30mm. per

hour fell on the area, find the resulting head of the weir.

Use Francis formula and neglect velocity of approach.












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CE BOARD 1998




In a tri axial test, a specimen of saturated (normally

consolidated) clay was consolidated under a chamber

confining pressure of 80 kPa. The axial stress on the

specimen was then increased until the axial stress at failure

was 120 kPa. The pore pressure (u) at the time was 30 kPa. Compute the consolidated undrained friction angle (phi).


A clay layer 4m. thick rests beneath a deposit of submerged

sand 8m. thick. The top of the sand is located 3m. below

the surface of the lake. The saturated unit weights of sand

and clay is 25 kN/m3. and 18 kN/m3. Compute the effective vertical pressure at mid-height of clay layer.


A conduit, closed or open designed to convey water from a

source to a point usually a reservoir where the distributed system begins.

a) Aqueduct

b) Gravity conduit

c) canal

d) flume


The gravity-fet distribution system will have a flat or level hydraulic gradient or pressure surface when:

a) pipes are more bigger and bigger from the source to the

end

b) there are no leaks and no withdrawal from the system

c) the term is flat

d) the pipe size are uniform


The hydraulic and energy gradients for a straight pipe and uniform diameter are parallel with each other because of:

a) uniform velocity

b) uniform pressure drop

c) constant slope of pipe

d) none of these


A sewer intended to carry only sanitary sewage.

a) sanitary sewer

b) outfall sewer

c) storm sewer

d) combined sewer


Which of the statement is true.

a) center of buoyancy is always below the center of mass

of stability

b) buoyant force on any body is equal to the fluid

displaced

c) center of mass of displaced fluid is coincident with

center of mass of an object

d) none of these


In a flow net construction of determining seepage flow, the

paths along which water can flow through a cross-section

are called:

a) Equipotential lines

b) Flow lines

c) Flow diagrams

d) Flow nets

Hydraulics “CE Board Exam Nov. 1998″ In acceptable dosage, this process in water treatment is

helpful in reducing the incidence of tooth decay.

a) Coagulation

b) Fluorosis

c) Calcium addition

d) Fluoridation









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CE BOARD 1998



Mathematics “CE Board Exam Nov. 1998″

The slope of the curve x=6y3 – 2y2 at (6, 3) is equal to:


Find the sum of the geometric progression 2x, 4x+14, 20x-

14 …. Up to the 10th term.


The volume of the frustum of a regular triangular pyramid

is 135 cu.m. The lower and the upper bases, both

equilateral triangles have edges equal to 9 m. and 3 m. respectively. Find its altitude.


The log of the product MN is equal to 1.62324929 and the

log of the quotient M/N is equal to -0.066946789. Find the value of N.


Eleven (11) men can finish the job in 15 days. Five (5) men

were working at the start and after 6 days four (4) men were added. How many days will it take to finish the job?


Find the area of the region bounded by the polar curve r2 = a2 Cos 2θ



Find the radius of curvature of the curve 4x – y2 = 0 at point (1,2).


A coin is tossed 3 times. What is the probability of getting 3 tails up?


Find the equation of the diameter of the ellipse which

bisects all chords having a slope of 1/5 the equation of

ellipse is 64x2 + 25y2 = 1600.


A truck travels from point M north ward for 30 min., then

eastward for one hour, then shifted N. 30° W. If the

constant speed is 40 kph, how far directly from M in km, will it be after 2 hours?


A traverse has the following data:

LINE BEARING DISTANCE

AB N. 73°23’ E 33.48

BC S. 39°30’ E 8.11

CD S. 43°40’ W 39.42

DE N. 39°50’ W 7.08

EA N. 17°33’ W 22.02

Determine the amount of correction for the latitude of

the line CD using transit rule.

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CE BOARD 1998




A line 100 m. log was placed by a surveyor for four times

with the following data: 142, 145, 145.5 and 146. Then

another line was paced for four times again with the

following results, 893, 893.5, 891 and 895.5. Determine the

length of the line.


A driver traveling at mph is 80 m. from a wall ahead. If the

driver applies the brakes immediately (perception time is 2

seconds) and begins slowing the vehicle at 10 m/sec2

(decelerating), find the distance from the stopping point to

the wall.


A stadia intercept reading of 3.0 m. was taken on a rod

using a transit having a stadia interval factor of 100 and a

stadia constant of 0.3 m. if the line of sight is inclined at an

angle of 3°15’, determine the horizontal distance from the

transit to the rod.


Data on a traffic accident recorded on a certain intersection

for the past 5 years has an accident rate of 4160 per million

entering vehicles (ARMV). If the average daily traffic

entering the intersection is 504, find the total number of accidents during the 5 year period.


The areas of cut of two irregular sections 60 m. apart are 32

sq.m. and 68 sq.m. respectively. The base width is 8 m.

with a side slope of 1:1. Find the corrected volume of cut in cu.m. using prismoidal correction formula.


A vertical sag curve has a descending grade of -1.7% and

an ascending grade of +2.3%. If the sag curve ahs a length

of 135 m., compute the length of the sight distance?


A driver traveling at mph is 80 m. from a wall ahead. If the

driver applies the brakes immediately (perception time is 2

seconds) and begins slowing the vehicle at 10 m/sec2

(decelerating), find the distance from the stopping point to

the wall.


A highway curve has a super elevation of 7°. Find the

radius of the curve so that there will be no lateral pressure between the tires and the roadway at a speed of 40 mph?


A machine costing P720,000 is estimated to have a life of

10 yrs. If the annual rate of depreciation is 25% determine

the total depreciation using a constant percentage of declining balance method.


Compute the surface area of the cone having a slant height of 5 cm. and a diameter of the base equal to 6 cm.


Find the distance from a point (5, -3) to the line 7x – 4y = 28.


If the volume of the sphere is equal to 36 cu.cm, find the

surface area of the sphere.


Water is the flowing into a conical vessel 15 cm. deep and

having a radius of 3.75 cm. across the top. If the rate at

which water is rising is 2 cm/sec. how fast is the water

flowing into the conical vessel when the depth of water is 4

cm?


How many years will P100,000 earned a compound interest

of P50000 if the interest rate is 9% compounded quarterly?


Find the length of the common chord of the curves x2 + y2 = 64 and x2 + y2 – 16x = 0.


The area bounded by the curve x3 = y, the line y = 8 and the y-axis. Determine the centroid of the volume generated.

















CE BOARD 1998




The deflection angles of two intermediate points A and B

of a simple curve are 3°15’ and 8°15’ respectively from the

P.C. if the chord distance between A and B is 40 m, find the length of curve from P.C. to B.


A circle having an area of 201 sq.m. is cut into segments by

a chord which is 3 m. from the center of the circle. Compute the area of the smallest segment

Mathematics “CE Board Exam May 1998″

A closed traverse has the following data. Compute the bearing of line 1-2.

LINE BEARING DISTANCE

1-2 ————- 58.7

2-3 ————- 27.3

3-4 N. 86.78° E. 35.2

4-5 S. 5 – 3° E. 35.0

5-1 S. 72.7° W. 78.96


A manufacturer produces certain items at a labor cost of

P115 each, material cost of P76 each and variable cost of

P2.32 each. If the item has a unit price of P600, how many

number of units must be manufactured each month for the

manufacturer to break even if the monthly overhead is

P428,000.


A man loans P187,400 from a bank with interest at 5%

compounded annually. He agrees to pay his obligations by

paying 8 equal annual payments, the first being due at the end of 10 yrs. Find the annual payments.


The angular speed of a flywheel having a diameter of 6m. is 20 rpm. Compute its tangential velocity.


The radius of the earth is 3960 miles. If the gravitational

acceleration of the earth surface is 32.16 ft/sec2., what is the velocity of escape from the earth in miles/sec.?


The perpendicular offset distance from a point 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., compute the radius of the simple curve.


A tape has a standard length at 20°C. was measured at a

temperature of 3°C. coefficient of thermal expansion is

0.0000116 m./ °C and its true horizontal length is 865.30

m, what is the measured length?


The transit is set up at A and a stadia was placed at a

distance of 194.20 m. from A. The stadia intercept was

recorded to be 1.94. If the stadia constant is 0.30, determine the stadia interval factor.


Find the slope of the line having the parametric equation y = 4t + 6 and x = t + 1.

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CE BOARD 1998




Find the volume of a cone to be constructed from a sector having a diameter of 72 cm. and a central angle of 150°.


From a speed of 60 kph, a train decelerates at the rate of 2

m/min2. along the path. How far in meters will it travel after 14 minutes?


Given a compound curve with I1 = 28°, I2 = 31°, D1 = 3°,

D2 = 4°. Compute the stationing of the P.C.C. if P.I. is at

station 30 + 120.5


Using the prismoidal correction formula, compute the

corrected volume of cut and fill between stations 70 m.

apart if the areas of irregular sections in cut at the stations

are 26 sq.m. and 84 sq.m. respectively. Base width = 8m.,

sideslope is 1:1.


The volume of the water in a hemisphere having a radius of 2m. is 2.05 m3. Find the height of the water.


Determine the diameter of a closed cylindrical tank having a volume of 11.3 cu.m. to obtain minimum surface area.



Determine the velocity sum of the progression if there are 7 arithmetic mean between 3 and 35.


Determine the velocity of progress with the given equation


The boat travels downstream in 2/3 the time as it does

going upstream. If the velocity of the river current is 8 kph, determine the velocity of the boat in still water.


Compute the distance between the directress of the curve

9x2 + 25y2 – 54x – 250y + 481 = 0


Evaluate the integral of 5 Cos6 x Sin2 x dx if the upper limit is π/2 and the lower limit is zero.


Given the two sides of the triangle ABC as AB = 2 cm, BC = 8 cm. Find the possible length of side AC.


A circle having an area of 452 m2 is cut into two segments

by a chord which is 6m. from the center of the circle.

Compute the area of the biggest segment.















CE BOARD 1998




Compute the equivalent rate of 6% compounded semi-annually to a rate compounded quarterly.


A trough having an equilateral triangle end sections has

sides equal to 0.3 m. and 6 m. long. Find the volume of

water in container if the depth of water is one half the depth

of the trough.


Find the length of the arc of the circle x2 + y2 = 64 at x = -1, and x = -3.


The area bounded by the curve y = 2x1/2 and the line y = 6

and the y-axis is to be revolved at the line y = 6. Determine the centroid of the volume generated.


Find the slope of the curve x2 + y2 – 6x + 10y + 5 = 0 at point (1, 0)


The log of the quotient M/N and the log of the product MN

is equal to 1.55630251 and 0.352182518 respectively. Find the value of M.


Find the length of the latus rectum of the curve y2 = -12x

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CE Board Exam 1998

Documents

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1998a driver traveling

allowable shear stress

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stadia interval factor