GEODETIC ENGINEERING
THEORY AND PRACTICE
1. A line 100 m long was paced by a surveyor for four times with the
following data: 142, 145, 145.5 and 146. Then another line was
paced for four times also with the following results: 893, 893.5, 891
and 895.5. What is the distance of the new line?
2. A surveyor used a 30m tape in measuring an inclined distance. The
measured length on the slope was recorded to be 459.20 m long. The
difference in elevation between the initial point and the end point
was found to be 1.25m. The 30m tape is of standard length at a
temperature of 100C and a pull of 50 N. During measurement the
temperature reading was 150C and the tape was supported at both
ends with an applied pull of 75N. The cross-sectional area of the tape
is 6.50 mm2 and the modulus of elasticity is 200 000 MPa. The tape
has a mass of 0.075 kg/m. Coefficient of thermal expansion is
0.0000116 m/0C. What is the true horizontal distance?
3. A line was determined to be 2395.25m when measured with a 30m
steel tape supported throughout its length under a pull of 4 kg at
mean temperature of 350C. Tape used is of standard length at 20 0C
under a pull of 5 kg. Cross-sectional area of tape is 0.03 cm 2.
Coefficient of thermal expansion is 0.0000116 m/ 0C, modulus of
elasticity of tape is 2 x 106 kg/cm2. What is the corrected length of
the line?
4. A line was measured to have 5 tallies, 6 marking pins and 63.5 links.
How long is the line in feet?
5. A line was measured with a 50 m tape. There were 2 tallies, 8 pins
and the distance from the last pin to the end of the line was 2.25 m.
How long is the line in meters?
6. A distance was measured and was recorded to have a value
equivalent to 8 perch, 6 rods and 45 vara. What is the total distance
in meters?
7. A map made as a result of a Cadastral Survey, drawn to appropriate
scale and showing all land parcels and important natural and manmade features within a municipality/project, for purposes of
describing and recording ownership.
a) Reference Map
b) Municipal Map
c) Projection Map
d) Cadastral Map
8. The establishing of precise horizontal and vertical control points for
the detailed survey is one of the functions of:
a) Bureau of Standards
b) Corps of Engineers
c) Coast and Geodetic Survey
d) General Land Office
9. The type of scale used most often by draftsmen to determine
distances is:
a) engineer’s
b) architect’s
c) graphical
d) rhumba
10. The term “station“ when used in connection with distance is
generally considered its broadest sense to be:
a) a unit of distance equal to 100ft
b) any point on a line occupied by a transit or level
c) any point a line set by continuous chaining from a point of
beginning
d) any point on a line where a rod reading is to be taken
11. The usual manner of supporting a steel tape when using it under
general condition is
a) at both ends
b) at ends and quarter points
c) at ends and center
d) throughout its length on a level surface
GEODETIC ENGINEERING
THEORY AND PRACTICE
12. The following interior angles of a triangle traverse were measured
with the same precision:
Angle
A
B
C
Value
410
770
630
15. From the measured values of distance AB, the following trials were
recorded.
No. of Measurements
5
6
2
What is the probalble value of angles A, B and C?
13. Measured from point A, angles BAC, CAD and BAD were recorded
as follows:
Trials
1
2
3
4
Distance
120.68
120.84
120.76
120.64
What is the probable error, the standard deviation, the standard error?
16. A level surface which is used as a reference for measuring vertial
Angle
Value
BAC
CAD
BAD
280 34’ 00”
610 15’ 00”
890 49’ 40”
No. of Measurements
2
2
4
What is the probable value of angles BAC, BAD and CAD?
14. From the given data of a differential leveling as shown in the
tabulation:
STA
BS
1
2
3
4
5
6
7
5.87
7.03
3.48
7.25
10.19
9.29
FS
ELEV
392.25
6.29
6.25
7.08
5.57
4.45
4.94
What is the difference in elevation of station 7 and station 4?
distances is called:
a) bench mark
b) grade surface
c) datum plane
d) horizontal surface
17. The term “ backsight “ in leveling means
a) a sight in the general direction to the rear
b) the vertical distance from the line of sight to a point whose
elevation is to be determined
c) a rod reading on a point whose elevation is known
d) a rod reading on a turning point
18. The height of instrument as used in leveling means
a) tance from the ground to the line of sight
b) elevation of the line of sight above the datum plane
c) height of the line of sight above the turning point or bench mark
d) overall height of the tripod and level combined
19. On a contour map, closely spaced contour lines indicate
a) flat slope
b) very irregular land
c) a relatively sharp slope
d) straight converging lines
GEODETIC ENGINEERING
THEORY AND PRACTICE
20. In two-peg test method of a dumpy level the following observations
were taken
Rod reading on A
Rod reading on B
1
2
3
Instrument
set-up near A
1.505 m
2.054 m
Instrument
set-up near B
0.938 m
1.449 m
What is the difference in elevation between A and B?
What is the error in the line of sight?
What is the correct rod reading on A with the instrument set up
at B?
21. A line of levels 10 km long was run over soft ground starting from
BM1 with elevation 22.5 m to BM2 , the elevation of BM2 was
computed to be 17.25 m. It was found out however that the level
settles 5 mm between the instant of every backsight reading, the rod
also settles 2 mm between the instant of every tuning point reading.
If the backsight and foresight distance average 100 m, what is the
corrected elevation of BM2?
22. A line of levels is run from BM 1 to BM2 which is 12 km long.
Elevation of BM1 was found to be 100 m and that of BM 2 is 125.382
m. Backsight and foresight distances were 150 m and 100 m
respectively. What would be the corrected elevation of BM 2
considering the effect of curvature and refraction correction?
23. A man’s eyes 1.75 m above sea level can barely see the top of a
lighthouse which is at a certain distance away from the man.
1
2
How far is the lighthouse from the man if the top of the
lighthouse is 14.86 m above sea level, considering the effect of
curvature and refraction?
What is the height of the tower at a distance 20 km away from
the man that will just be visible without the line of sight
approaching nearer than 1.75 m to the water, considering the
effect of curvature and refraction?
24. A trigonometric leveling between two points A and B of a certain
rough terrain are each distance 2000 m from a third point C, from
which the measured vertical angle to A is 3 0 30’ and to B is 10 30’.
Point C is located between A and B at elevation 342.60 m.
1
2
What is the difference in elevation between A and B considering
the effect of curvature and refraction?
What is the elevation of A, considering the effect of curvature
and refraction?
25. A point observed by a level or transit appears to be higher than it
really is, because of:
a) curvature of the earth’s surface
b) parallax of the telescope
c) refraction of air
d) convergence of light rays within the telescope
26. Short lines of various widths drawn on a map in the direction of
greatest slope are commonly called
a) form lines
c) hachures
b) contours
d) slope lines
27. The following type of fields notes can best be studied under normal
conditions to construct a contour map of a 35 acre golf course:
a) cross-section notes
c) BM level notes
b) slope stake notes
d) precise level notes
28. In leveling, if the rod is not held vertical, the reading is
a) usually too small
b) usually too large
c) equal too large or small
d) always too large
GEODETIC ENGINEERING
THEORY AND PRACTICE
29. Two hills A and C have elevations of 600 m and 800 m respectively.
In between A and C is another hill B which has an elevation of 705 m
and is located at 12 km from A and 10 km from C.
1
2
3
What is the clearance or obstruction of the line of sight at hill B
if the observer is at A so that C will be visible from A?
If C is not visible from A, what height of tower must be
constructed at C so that it could be visible from A with line of
sight having a clearance of 2 m at hill B?
What height of equal towers at A and C must be constructed in
order that A, B and C will be intervisible?
30. The observed compass bearing of a line in 1981 was S 37 0 30’ E and
the magnetic declination of the place then was known to be 3 0 10’ W.
It was also discovered that during observation local attraction of the
place at that moment of 5 0 E existed. Find the true azimuth of the
line?
31. In a particular year, the magnetic declination was 1 0 10’ E and the
magnetic bearing of line DE was N 16 0 30’ W. If the secular variation
per year is 30 E, determine the magnetic bearing of line DE 5 years
later.
32. From the field notes of a closed traverse shown:
LINES
AB
BC
CD
DE
EA
1
2
3
BEARING
Due North
N 450 E
S 600 E
S 200 W
S 860 59’ W
DISTANCE
400.00 m
800.00 m
700.00 m
600.00 m
966.34 m
What is the relative error or precision?
What is the adjusted distance of line EA using Transit Rule?
What is the adjusted bearing of line EA using Transit Rule?
33. The surveyor’s compass is an instrument which
a) reads horizontal angles
b) gives the horizontal direction of a line
c) is relatively free of all types of errors
d) is an essential part of the engineers transit
34. A clinometer measures
a) angles
b) distances
c) elevations
d) barometric pressures
35. Turning angles with the transit telescope first in the normal or direct
position and then in the reversed position corrects the error due to:
a) plate bubbles not being at right angles to the vertical axis
b) vertical hair not being truly vertical
c) horizontal axis not being truly horizontal
d) plates not being truly horizontal
36. A random line in surveying is
a) an offset line locating buildings
b) a line produced to intersects a traverse line or some other line
c) a trial line run near a true line
d) a line established by swinging a tape from a point to another
line
37. The stadia is a method for measuring
a) horizontal angles
b) vertical angles
c) distances
d) azimuth of lines
GEODETIC ENGINEERING
THEORY AND PRACTICE
38. From the field notes of a closed traverse shown:
LINES
AB
BC
CD
DE
EA
1
2
BEARING
Due North
N 450 E
S 600 E
S 200 W
S 860 59’ W
40. The stadia method of surveying is used when
DISTANCE
400.00 m
800.00 m
700.00 m
600.00 m
966.34 m
What is the adjusted distance of line CD using Compass Rule?
What is the adjusted bearing of line CD using Compass Rule?
39. From the given closed traverse:
LINES
AB
BC
CD
DE
EF
FA
1.
2.
3.
40.
BEARING
N 200 E
N 680 E
S 220 E
S 400 W
S 620 W
---
DISTANCE
17.42
18.46
22.40
12.60
10.20
---
What is the distance of line FA?
What is the bearing of line FA?
What is the area of the closed traverse in acres?
required
b) an accurate representation of great amount of detail in a small
area is required
c) the survey is in open country
d) the area surveyed is to be reproduced on a small scale map
41. If it is necessary to climb over a fence in a field while carrying a
transit or level the instrument man should
a) lean the instrument against the fence, then climb over
b) lay the instrument on the ground, then climb over the fence
c) place the instrument on the other side of the fence with the
tripod legs well spread, then climb over
d) remove the head of the instrument and place it on the other side
of the fence
42. Which of the following charts should a Geodetic Engineer refer to
determine approximate magnetic declination in a particular
location?
a) an isogradient chart
c) an isogonic chart
b) an isohaline chart
d) an isonephlic chart
43. The North, South, East and West points of a compass are also
known as
a) occidental directions
b) collimation directions
Given the filed data below:
1.
2.
3.
a) a rapid method measuring distances over rough ground is
Stations
Azimuths
Distance
T1 to T2
T2 to T3
T3 to T4
T4 to T1
2560 40’ 53’
290 28’ 04”
1040 19’ 39”
1790 23’ 37”
43.520 m
51.784 m
17.076 m
30.828 m
What is the linear error of closure?
What is the relative error?
What is the error of T3 to T4 by Transit Rule?
c) cardinal directions
d) oriental directions
44. Who invented the solar compass where magnetic declination can be
determined
a) William Burt
b) Richard Young
c) Thomas Gunter
d) Charles Morse
GEODETIC ENGINEERING
THEORY AND PRACTICE
45. Given below is the technical description of lot 2081, Cebu Cadastre
LINES
1–2
2–3
3–4
4–1
1
2
3
BEARING
S 320 17’ W
N 360 25’ W
N 150 47’ W
N 730 07’ E
DISTANCE
22.04 m
10.00 m
5.00 m
19.95 m
DISTANCE
44.37 m
137.84 m
12.83 m
64.86 m
106.72 m
What is the bearing of line DE?
What is the bearing of line EA?
What is the area of the closed traverse in acres?
47. In an old survey made when the declination was 2 0 10’ W the
magnetic bearing of a given line was N 35 0 45’ E. The declination
in the same place is now 30 30’ E. What are the true bearing and the
present magnetic bearing that would be used in retracing the line?
48. The transit or theodolites used in official surveys of all types of
lands in the Philippines shall have a stadia constant of:
a) 98
b) 100
50. The standard tension which is adopted by the Bureau of Lands at
which each tape shall be of standard length is:
a) 12 kg
b) 10 kg
c) 15 kg
a) 200
BEARING
S 350 30’ W
N 570 15’ W
N 10 45’ E
?
?
c) 30
d) 250C
d) 18 kg
control in the survey of cadastral projects. One of the general
requirements is that the position of the triangulation stations shall
be selected so that no angle maybe less than:
46. From the given closed traverse:
1
2
3
at which each tape shall be of standard length is:
a) 320C
b) 420C
c) 280C
51. A scheme of triangulation maybe used for establishing points of
What is the area of the lot by DMD method?
What is the area of the lot by DPD method?
What is the DPD of line 3 – 4?
LINES
AB
BC
CD
DE
EA
49. The standard temperature which is adopted by the Bureau of Lands
d) 0.30
b) 300
c) 250
d) 150
52. If the area under survey is 2000 hectares, what quality of control
should be used?
a) primary
b) secondary
c) tertiary
d) none of the above
53. If the area under survey is 30 000 hectares, what quality of control
should be used?
a) primary
b) secondary
c) tertiary
d) none of the above
54. In reading traverse angles
a) two pointings are required for each direction per circle position
with an optical reading theodolite
b) four pointings are needed for each direction per repetition with a
transit
c) less arithmetic is required with the optical-reading theodolite in
reducing the readings
d) considerable time (reading and reduction) is saved by using the
optical-reading theodolite instead of the the transit
GEODETIC ENGINEERING
THEORY AND PRACTICE
55. From the given closed traverse:
LINES
1–2
2–3
3–4
4–5
5–1
1
2
BEARING
S 730 21’ E
S 400 10’ E
S 260 42’ W
N 140 20’ W
N 120 20’ E
58. The movement of the outer spindle on an engineer’s transit is
DISTANCE
247.20
154.30
611.90
?
?
56. From the data shown below, determine the value of the unknown
bearing and distance.
BEARINGS
N 320 27’ E
?
S 80 51’ E
S 730 31’ W
N 180 44’ W
59. The magnetic bearing of a line is
a) the total horizontal angle measured from the south end of the
What is the distance of line 4 - 5?
What is the distance of line 5 - 1?
LINES
AB
BC
CD
DE
EA
controlled by
a) upper tangent screw
b) leveling screws
c) lower tangent screw
d) upper clamp screw
DISTANCES
110.8 m
83.6 m
126.9 m
?
90.2 m
57. In running an azimuth traverse with true south as zero azimuth, at
each set-up the proper method of orienting the transit with
telescope inverted is to
a) backsight along preceding line with A vernier at azimuth of
preceding line
b) backsight along preceding line with A vernier at back azimuth
of preceding line
c) backsight along preceding line with A vernier at 1800
d) sight toward true north with A vernier at 00
magnetic meridian
b) the total horizontal angle measured from north end of the
magnetic meridian
c) the acute angle which the line makes with the meridian
d) the azimuth of the line minus 900
60. The process of determining direction on a map relative to the
earth’s surface is generally called
a) bearing
c) geodetic
b) direction
d) orientation
61. A planimeter is used to
a)
b)
c)
d)
measure horizontal and vertical angles
determine difference in elevation
enlarge maps
determine areas
62. The angle between the geometric meridian and magnetic
needle direction of a line is the
a) interval
c) azimuth
b) bearing
d) declination
GEODETIC ENGINEERING
THEORY AND PRACTICE
63. Three shore stations C, D and E are triangulation observation
points with CD = 615 m and DE = 625 m. Angle EDC is
1250. A hydrographer at point D wanted to know his position
with respect to the triangulation points, he measured angle
CBD = 430 and DBE = 420 30’. What is the angle CDB and
the distance BC?
64. Stations A and B along the bank of a river are measured and
found to be 350 m apart. To find the width of the river, a third
station C is established on the opposite bank and the azimuth
as measured fom A is 2210 45’ and from B is 1430 20’. If the
azimuth of the line AB is 2660 20’, what is the width of the
river?
65. A series of perpendicular offsets were taken from a transit
line to a curved boundary line. These offsets were taken 9m
apart and were taken in the following order: 2m, 3.2m, 4m,
3.5m, 5m, 4.5m and 6m. Determine the area included
between the transit line and the curved using,
1 Trapezoidal Rule
2 Simpson’s One Third Rule
66. The compass rule for balancing a traverse is based upon the
assumption that the precision of angular measurement
compared with linear measurement is
a) greater than
b) consistent with
c) less than
d) unrelated to
67. A mechanical instrument used exclusively in a field survey
with a plane table in making topographic sketches is
generally known as a
a) vernier
b) alidade
c) transit
d) head level
68. The choice of field method for preparing a topographic map,
assuming any type of equipment needed is available, is
governed mainly by
a) the intended use of the map
c) the map scale
b) the area of the tract
d) all of the above
69. A closed hachured contour line represents a
a) ridge
c) summit
b) valley
d) depression
70. Contour interval is the
a) horizontal distance between adjacent contours
b) elevation above sea level
c) difference in elevation between adjacent contours
d) scaled distance between adjacent contour lines on a
map
71. Given the following:
Elevation of triangulation station A
Elevation of triangulation station B
Elevation of mountain C
Height of theodoite at hill A
Distance from A to C
Distance from C to B
=
=
=
=
=
=
995 m
2470 m
1250 m
1.5 m
2000 m
3000 m
From the given data above, you were instructed to build a
tower at triangulation station B in such a way that the line of sight
will pass through mountain C with a clearance of 2 m. How high is
the tower at B?
GEODETIC ENGINEERING
THEORY AND PRACTICE
72. A transit with a stadia interval factor of 100.85 was set up at a
point C between points A and B, the following stadia reading
were observed:
Stadia
Rod
A
B
Vert
Angle
+ 200 25’
- 120 10’
Wire Reading
Upper
Middle
Lower
1.850 m
1.488 m
1.600 m
1.488 m
1.350 m
1.330 m
If the stadia constant is 0.442, what is the horizontal distance
AB and the vertical elevation between A and B?
73. A survey party proceeded to do their stadia survey works as
follows. The transit was set up at A and with the line of sight
horizontal took tod readings at points B and C which is 300m
and 80m respectively.
With rod at B the stadia interval was recorded to be
3.001m and with the rod at C the stadia interval was recorded
to be 0.800m. The distance from the instrument to the
principal focus was recorded to be 0.30m. They then went to
survey other points with some of the data recorded as follows
with the transit at point D, the two points E and F were
sighted.
Rod at E
Stadia interval
=
2.25 m
Vertical angle
=
+40 30’
Rod at F
Stadia interval
=
3.56 m
Vertical angle
=
-30 30’
1 What is the stadia interval factor?
2 What is the horizontal distance DE?
3 What is the difference in elevation between E and F
assuming elevation of D is 350.42m above sea level?
74. The areas bounded by the water line of a reservoir is
determined by using a planimeter. A1 = 20,400 m2 , A2 =
18,600 m2 , A3 = 14,300 m2 , A4 = 10,200 m2 , A5 = 8,000 m2
and A6 = 4,000 m2. The contour interval is 2m. Determine the
volume of water using:
1 End Area Method
2 Prismoidal Formula
75.
Given the following current meter notes. Determine the
discharge of the stream in liter per second. All measurements
are in meters.
Distance
from IP
30
40
55
70
78
Depth
(meters)
0
3.0
3.5
2.0
0
Depth of
Observation
Velocity
1.8
2.1
1.2
0
0.28
0.32
0.22
Mean
Velocity
Area
Discharge
76.
A map can be correctly called a topographic map if it shows
a) location of boundary lines and structures
b) distances and dimensions
c) a record of jurisdiction and owners of property
d) contours and natural features and work of man
77.
The procedure to be followed in performing the main
adjustments of transit is based upon
a) carrying them out in proper order
b) the principle that single reversion doubles the error,
double reversion quadruples it
c) completing each adjustment exactly in all cases
before beginning the next
d) checking the adjustments after they have
completed
GEODETIC ENGINEERING
THEORY AND PRACTICE
78.
79.
A simple curve has a central angle of 36 0 and a degree of
curve of 60.
1 Compute the radius of the curve using arc basis.
2 Compute the tangent distance.
3 Compute the external distance.
4 Compute the middle ordinate.
5 Compute the chord distance.
6 Compute the length of curve.
Two tangents making an angle of 620 from each other is
connected by a simple curve. A point “x” on the curve is
located by a distance along the tangent from the P.C. equal to
240 m and an offset from the tangent equal to 60 m. The P.C.
is at station 10+080.
1 Compute the radius of the curve.
2 Compute the tangent distance of the curve
3 Compute the stationing of point “x” on the curve.
80.
The tangents of a simple curve have bearings of N 20 0 E and
N 800 E respectively. The radius of the curve is 200 m.
1 Compute the external distance of the curve.
2 Compute the middle ordinate of the curve.
3 Compute the stationing of point A on the curve having a
deflection angle of 60 from the P.C. which is at 1+200.
81.
The index error of a transit causes incorrect reading of
a) horizontal angles because of eccentricity of the plate
circles
b) horizontal angles because of errors in the graduation of
the plates
c) vertical angles because the vertical arc is not properly set
d) vertical angles because the line of sight and the telescope
bubble are not parallel
82.
Elimination of the errors due to curvature and refraction in
leveling operation accomplished by
a) keeping lengths of sights less than 300 ft
b) keeping distance to backsights and foresights balanced
c) keeping bubble accurately centered at all times
d) keeping axis of line of sight perpendicular to the
vertical axis
83.
The purpose of the adjustment of the vertical hair in the
transit telescope is to get the
a) line of sight to revolve in a vertical plane
b) vertical hair to revolve in a plane
c) vertical hair to revolve in a vertical plane
d) line of sight to revolve in a plane
84.
The method of laying out points on a circular curve by
deflection angles is based mainly upon the principle that
a) an angle inscribed in the circumference of a circle is
measured by the intercepted arc
b) the angle between a chord and a tangent at a point on a
curve is one-half the angle of arc intercepted by the
chord
c) the intersection angle is equal to the central angle
d) the instrument will be set up on the P.C. or P.T.
85.
In accuracies in measurements which occur because some
aspect of a surveying operation is performed with
carelessness, poor judgement and improper execution
a) Error
b) Personal error
c) Mistakes
d) Instrumental error
GEODETIC ENGINEERING
THEORY AND PRACTICE
86. Given a compound curve:
I1 = 240 ; I2 = 360 ; D1 = 60 ; D2 = 40
1
2
3
Compute the length of the common tangent of the curve.
Compute the stationing of P.C.C if P.C. is at station
10+420.
Compute the stationing of P.T.
87. Two tangents intersect at station 26 + 050. A compound curve
laid on their tangents has the following data:
I1 = 310 ; I2 = 360 ; D1 = 30 ; D2 = 50
1
2
3
Compute the stationing of the P.C.
Compute the stationing of the P.T.
If the P.T. is moved 15 m. out from the center, compute the
stationing of the new P.T. with the P.C.C. remaining
unchanged.
88. On a rail road line, two tangents that intersect at station 10 +
243 so as to form an angle of 360 28’ are to be connected by a
compound curve consisting of two simple curves. The simple
curve beginning at the P.C. which is at station 10 + 163 is to
be a 40 curve whose degree is based on a 20 m chord and is to
have a central angle of 170. Using chord basis.
1 What should be the radius of the other simple curve that
ends at the P.T.?
2 Compute the stationing of the P.C.C.
3 What is the length of the tangent from the P.I. to the P.T.
of the compound curve?
89. A type of error which will always have the same sign and
magnitude as long as field condition remain constant and
unchanged.
a) Natural errors
c) Systematic errors
b) Personal errors
d) Accidental errors
90. An instrument developed by the Greeks sometime in 130 B.C.
which was used for leveling, laying off right angles, and for
measuring horizontal and vertical angles.
a) Libella
c) Diopter
b) Chorobates
d) Merchet
91. A device used for measuring time and meridian.
a) Libella
c) Diopter
b) Chorobates
d) Merchet
92. A type of leveling instrument which is often called
construction level or architects level.
a) Automatic level
c) Dumpy level
b) Wye level
d) Builders level
93. A standard practice to hold the tape horizontally above the
ground and to plumb at one or both ends when taping on
sloping or uneven terrain surfaces. The procedure is known as:
a) breaking tape
c) tallying tape
b) tape measuremnts
d) slope taping
94. An imaginary surface of the sea which is midway between
high and low tides.
a) Mean Sea Level
c) Level Surface
b) Datum
d) Horizontal Surface
GEODETIC ENGINEERING
THEORY AND PRACTICE
95. Two parallel tangents 10 m apart are connected by a reversed
curve. The chord length from the P.C. to the P.T. equals 120 m.
1 Compute the length of tangent with common direction.
2 Determine the equal radius of the reversed curve.
3 Compute the stationing of the P.R.C. if the stationing of
A at the beginning of the tangent with common direction
is 3 + 420.
96. In a rail road layout, the centerline of two parallel tracks are
connected with a reversed curve of unequal radii. The central
angle of the first curve is 16 0 and the distance between parallel
tracks is 27.60 m, stationing of the P.C. is 15 + 420 and the
radius of the second curve is 290 m.
1 Compute the length of the long chord from the P.C. to
P.T.
2 Compute the radius of the first curve.
3 Compute the stationing of the P.T.
97. The method of leveling used to determine the difference in
elevation between two intervisible points located at a
considerable distance apart and between which points leveling
could not be performed in the usual manner.
a) Reciprocal leveling
c) Profile leveling
b) Double rodded leveling
d) Trigonometric leveling
98. A type of leveling usually used in highway or railroad
construction which is often necessary to obtain a
representation of the ground surface on either side of the
centerline.
a) Profile leveling
c) Direct leveling
b) Cross-section leveling
d) Stadia leveling
99. This line is generally adapted reference in surveying practice,
it passes through the geographic north and south poles of the
earth and the observes position.
a) Magnetic meridian
c) Grid meridian
b) Assumed meridian
d) True meridian
100. It is better to observe Polaris for true north at elongation
instead of at culmination because:
a) the star is moving faster at culmination
b) the star is moving faster at elongation
c) watch time must be more nearly correct at culmination
d) watch time must be more nearly correct at elongation
101. True altitude of the sun observed by theodolite is the vertical
angle to center,
a) plus parallax and refraction angles
b) minus parallax and refraction angles
c) minus parallax angle plus refraction angle
d) plus parallax angle minus refraction angle
102. The magnitude of scale error for an area mapped by a
Lambert Conformal projection is fixed by the
a) difference in elevation of land
b) proximity to equator
c) east and west limitation chosen
d) north and south limitation chosen
103. Which grid system considers the portion of the earth between
two selected parallel of altitude to be a horizontal slice of a
cone
a) World polyconic
b) Orthomorphic
c) Transverse mercator
d) None of the above
GEODETIC ENGINEERING
THEORY AND PRACTICE
104. A vertical summit parabolic curve has its P.I. at station
14+750 with elevation of 76.30 m. The grade of the back
tangent is 3.4% and forward tangent of -4%. If the length of
the curve is 300 m:
1 Compute the location of the vertical curve turning point
from the P.I.
2 Compute the elevation of the vertical curve turning point.
3 Compute the stationing of the vertical curve turning
point.
105. A symmetrical vertical summit curve has tangnets of +4%
and -2%. The allowable rate of change is 0.3% per meter
station. Stationing and elevation of P.T. is at 10+020 and
142.63m respectively.
1
2
3
Compute the length of curve.
Compute the distance of the highest point of the curve
from the P.C.
Compute the elevation of the highest point of the curve.
106. A vertical symmetrical sag curve has a descending grade of
-4.2% and ascending grade of +3% intersecting at station
10+020 whose elevation is 100 m. The two grade lines are
connected by a 260 m vertical parabolic sag curve.
1
2
3
What distance from the P.C. is the lowest point of the
curve?
What is the vertical offset of the parabolic curve to the
point of intersection of the tangent grades?
If a 1m diameter culvert is placed at the lowest point of
the curve with the top of the culvert buried 0.60m
below the subgrade, what will be the elevation of the
invert of the culvert?
107. The maximum velocity in a transverse section of a stream
usually occurs
a) at the shallowest part of the cross section
b) at the deepest part of the cross section
c) near the banks
d) at the center of the stream
108. The solar compass used in running some original public land
surveys,
a) automatically corrects for local attraction
b) defines directions based upon the magnetic needle
c) cannot give even approximately correct results
d) is designed for astronomical-type operation
109. A solar observation for meridian is generally considered to be
a) more accurate than an observation on any star other than
Polaris
b) accurate within plus or minus 3 minutes of arc for an
experienced surveyor
c) less accurate than a meridian observation made with a
good surveyor’s compass
d) poor practice for section line retracement in
mountainous country
110. A profile shows graphically
a) cross sections
b) the grade line along a route
c) contours of the area
d) center-line elevations along a route
GEODETIC ENGINEERING
THEORY AND PRACTICE
111. Given the following cross section notes of an earthwork on a
rolling terrain
STA 5 + 000
 10
31
 14
41
5
0
STA 5 + 020
7
0
3
13.5
 4.5
17.25
The width of the road is 12m and the side slope is 2.5:1.
1
2
3
Compute the volume using End Area Method.
Compute the volume using Prismoidal Formula.
Compute the volume using End Area with Prismoidal
Correction.
112. Given the following cross section notes of an earthwork.
Assume both stations to have the same side slope and width
of the road
STA 10 + 100
6.45
 2.3
0
 1.5
4.5
 1.0
STA 10 + 200
6.0
 2.0
1
2
3
0
x
6.9
 2.6
Compute the side slope of both sections.
Compute the value of x at station 10 + 200 if it has a
cross sectional area of 14.64 m2.
Compute the volume using End Area Method with
Prismoidal Correction.
113. In surveying, the effect of measuring an angle by repetition is
described as:
a) making any mistakes obvious
b) reducing a reading error by spreading it over a multiple
of the angle
c) reducing the effect of several reading errors by
averaging them
d) using a mechanical procedure as a substitute for
mathematical computation
114. The geodimeter is a device which
a) measures slope distance
b) operates on the same electrical principles as radar
c) operates on the same electrical principles as the
tellurometer
d) operates on the same electrical principles as the
electrotape
115. In direct leveling, which of the following is NOT true?
a) a foresight is a rod reading taken on a point whose
elevation is to be found
b) the height of the instrument is the elevation of the line of
sight
c) a backsight relates to the direction in which the sight
was taken
d) to determine the height of instrument involves the
backsight
116. Establishing precise horizontal and vertical control points for
detailed surveys is one of the functions of the:
a) Bureau of Standards
c) Corps of Engineers
b) Coast and Geodetic Survey
d) General Land Office
GEODETIC ENGINEERING
THEORY AND PRACTICE
117. In a certain portion of road to be constructed the following
data were taken:
STA 1 + 040
x
 1.84
0
 1.22
A = 8.3
E = 7.6
I = 7.2
M = 7.2
x
 0.42
STA 1 + 100
x
 1.098
0
 3.05
Base for cut = 9 m
Base for fill = 8 m
x
 0.50
1
Sideslope for cut is 1:1
Sideslope for fill is 1.5:1
What is the volume of cut and fill using end area method?
118. The earthworks data of a proposed highway is shown on the
tabulated data:
Station
2 + 440
2 + 740
3 + 040
Area
Cut
50 m2
0
119. A 90 m x 90 m square lot is to be divided into 9 square
sections. The following data are the elevations of the ground
surface at the corners of the square section of the lot.
Fill
Balancing point
70 m2
Length of economical haul = 450 m
2
B = 7.9
F = 9.2
J = 10.2
N = 6.2
C = 10.8
G = 10.6
K = 9.4
O = 9.6
D = 6.8
H = 8.6
L = 6.9
P = 8.9
What is the volume of the earthworks excavated if the
ground surface is to be leveled to elevation 5 m using
unit area method?
What is the volume of the earthworks excavated if the
ground surface is to be leveled to elevation 5 m using
parallel section method?
120. Maps which represents the earth’s surface in three dimensions
and which usually uses contours to indicate relief is termed as
a) planimeter map
c) nautical map
b) topographic map
d) location map
121. The sun and stars are located by the celestial coordinates
a) right ascension and sidereal hour angle
b) prime vertical and hour angle
c) declination and right ascension
d) hour angle and equation of time
Stationing of limits of economical haul is 2 + 498.03 and 2 + 948.03
Stationing of limits of free haul is 2 + 713.12 and 2 + 763.12
Free haul distance = 50 m
Assume the ground surface to be uniformly sloping.
1
2
3
122. A fathometer is a measuring device which automatically
records measurements of depth taken from
a) an aircraft
c) a nearby shore station
b) a bridge
d) a moving water vessel
What is the overhaul volume?
What is the volume of waste?
What is the volume of borrow?
GEODETIC ENGINEERING
THEORY AND PRACTICE
123. A fracture in the earth’s crust along which slipping or
shearing has occurred.
a) Fault
b) Heave
c) Dip
d) Levels
124. The portion of the vein exposed at the surface of the ground.
a) Outcrop
b) Floor
c) Ore shoot d) Prop
125. The line of intersection of the vein with a horizontal plane;
also the direction of that line expresses as a bearing. It is
always at right angles to the dip.
a) Strike
b) Throw
c) Stull
d) Wall
126. The vertical distance between the planes representing two
parts of the same vein which is divided by a fault. The term is
used only in regard to deposits which are nearly horizontal.
a) Strike
b) Throw
c) Stull
d) Wall
127. A relatively thin deposit of mineral between definite
boundaries. It is a mineral body of flattened shape.
a) Tunnel
b) Vein c) Stull
d) Wall
128. The vertical angle between the plane of the vein and
horizontal plane measured perpendicular to the strike.
a) Drift
b) Dip
c) Strike
d) Vein
129. An inclined passage driven in a particular direction.
a) Drift
b) Dip
c) Strike
d) Vein
130. The rock on each side of the mineral body. The upper wall is
called the hanging wall and the lower the feet wall.
a) Wall
b) Vein c) Stull
d) Winze
131. A vein has a strike of N 22 0 30’ E and a dip of 28 0 10 to the
east. What will be the bearing of the drift if it has a grade of
3%.
132. A vein has a dip of 570 W. A drift is driven N 37 0 W in the
plane of the vein on a grade of 5%. What is the bearing of the
strike?
133. A vein has a strike of N 100 15’ W and a dip of 43 0 40’ W. A
drift in the vein has a grade of 2%.
1 What is the horizontal angle between the strike and the
vertical projection of the drift?
2 What is the bearing of the drift?
3 What is the bearing of the vertical plane containing the
dip?
134. An approximately horizontal under ground passageway
running from the surface into the mine workings and used for
drainage and ventilation.
a) Adit
b) Bed
c) Apex
d) Back
135. The portion of the surface of the undisturbed rock formation
which is included between the walls or sides of the mineral
deposit.
a) Adit
b) Bed
c) Apex
d) Back
136. A passageway which is driven from one accessible part of
the mine to another.
a) Cross-cut
c) Connection
b) Compartment
d) Heading
137. A passage driven into the rock or ore ahead of the main
excavations.
a) Heading
c) Cross-cut
b) Connection
d) Compartment
GEODETIC ENGINEERING
THEORY AND PRACTICE
A vertical summit parabolic curve has a vertical offset of 0.375 m.
from the curve to the grade tangent at sta 10 + 050. The curve has
a slope of + 4% and - 2% grades intersecting at the P.I. The offset
distance of the curve at P.I. is equal to 1.5 m. If the stationing of
the P.C. is at 10 + 000,
1. Compute the required length of curve.
a) 100 m
b) 150 m
c) 200 m
d) 200 m
2. Compute the horizontal distance of the vertical curve turning
point from the point of intersection of the grades.
a) 30.42 m
b) 33.33 m
c) 42.15 m
d) 26.54 m
3. Compute the elevation of the vertical curve turning point if the
elevation of P.T. is 86.42 m.
a) 80.22 m
b) 84.54 m
b) 91.36 m
d) 87.08 m
The perpendicular offset distance from point A 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,
4. Compute the radius of the simple curve.
a) 560.13
b) 557.34
c) 549.25
d) 555.02
5. Compute the length of curve from P.C. to A.
a) 273.04
b) 263.41
c) 267.95
d) 270.31
6. If the angle of intersection of the curve is 64˚, compute the
length of long chord from PC. To PT.
a) 935.12
b) 929.88
c) 932.37
d) 928.74
The following interior angles of a triangle traverse were measured
with the same precision.
Angle
A
B
C
Value
41˚
77˚
63˚
No. of Measurements
5
6
2
7. Determine the most probable value of angle A.
8. Determine the most probable value of angle B.
9. Determine the most probable value of angle C.
A trigonometric leveling conducted by Jereza Surveying Company,
the two points A and B of a certain rough terrain are each distance
2000 m. from a third point C, from which the measured vertical
angles to A is + 3˚30' and to B is + 1˚30'. Elevation at C is known
to be 342.60 m. above sea level. Point C is in between A and B.
10. Compute the difference in elevation between A and B
considering the effect of the earth's curvature and refraction.
a) 66.05
b) 71.35
c) 69.96
d) 62.11
11. Compute the difference in elevation between B and C.
a) 59.136
b) 55.314
c) 49.172
d) 52.638
12. Compute the elevation of A.
a) 475.37
b) 468.18
c) 465.20
d) 472.14
GEODETIC ENGINEERING
MATHEMATICS
1. Solve for x: 3x · 5x + 1 = 6x +2
Ans: 2.153
2. If party “A” can do a survey work in one day more, while party
“B” alone can do the same work in 6 days more and party “C”
alone can do the same work in twice the time, in how many
days would party A, B, C together finish the same work?
Ans: 2/3 days
3. A tower stands 42m from a flagpole on a horizontal plane. At
their bases the angle of elevation of the top of the tower is
twice that of the flagpole but at a point midway between their
bases, the sum of the angle of elevation is complimentary. Find
the height of the tower and the flagpole.
Ans: 31.5 m, 14 m
4. From A, a man is set to travel at a velocity of 4 kph, when he
reaches B, he returned back to A with a velocity of 3 kph. If he
consumed 4 hrs and 5 min, what is the distance between A and
B?
Ans: 7 km
5. Determine the other parts of the spherical triangle.
A = 520 30’ B = 700 15’ C = 1200 15’
Ans: 570 16’ , 870 23’ , 1130 32’
6. A cylindrical tank has a diameter of 5ft and is 8ft long placed
horizontally. If it takes to fill the tank at the rate 15 gpm, how
long will it take to fill the tank up to a depth of 4ft.
Ans: 1.12 hrs
7. An object distance from concave mirror is 15 inches. It made
an image at a distance 7.5 inches, find the focal length. If the
length of object is 10 inches, find the size of the image.
Ans: 5 , 5 in
8. Find the locus of the center of the circle which is tangent to the
y-axis and to the circle of radius one with center at (2,0).
Ans: y2 – 6x + 3 = 0
9. From the given equations, find the points of intersections.
x2 – 6x + 3y + 11 = 0 and 4x2 – 24x + 4y2 – 8y + 15 = 0
Ans: (1.767, -1.174) & (4.233, -1.174)
10. Solve for x: log x2 – log
2x
= 7.58
5
11. Find the equation of the tangent to the parabola x 2 = 6y + 10
through point (7,5).
Ans: 4x -3y – 13 = 0.
12. Find the angle between the given lines.
3x + 4y = 0
5x – 2y = 0
13. A survey party started to walk from their field office to the bus
station at 3:00 o’clock P.M. After walking 16 km, they
increased their speed by 1 kph in order to reach their
destination at 7:36 o’clock P.M. Had they not increased their
first rate, they would have been late by 9 min. What distance
did they walk and what was their first rate? Ans: 19km , 4
kph
14. In the spherical triangle ABC, find the values of A, B and a.
b = 450 48’
c = 1300 41’ C = 900
15. Find the equation of the line passing thru point (-1,3) making
an angle of arctan ¼ from the line x + 3y = 2.
Ans: x + 13y – 38 = 0 , 7x + 11y -26 = 0
If the length of the side of a square is increased by 6m, the area is
multiplied by 4. What is the side of the square?
Ans: 6 m