Question 1

When used in measuring linear distance, the term "station" refers to a point on a line:
A)That was established by continuous chaining from a beginning point.
B)That is a multiple of a full tape length established by continuous chaining from a beginning point.
C)Where a moving vehicle may stop for fuel or to drop off goods or passengers.
D)Where an EDM reading was taken.

Accepted Answer

The term "station," when used in measuring linear distances, refers to a point on a line that was established by continuous chaining from a beginning point. When surveying routes, the term full station is given to each 100 feet of length and is normally staked. The position of any other point is described by its total distance from the beginning point.

Question 2

Examples of common systematic errors encountered when measuring horizontal distances include:
A)Changes in tape length due to variations in atmospheric temperature
B)The difference between a working tape length and a standard tape length
C)Both A and B
D)None of the above

Accepted Answer

Examples of common systematic errors encountered when measuring horizontal distances include changes in the tape length due to variations in atmospheric temperature and the difference between a working tape length and a standard tape length. Corrections for the impact of temperature variations on tape length should be made. If the difference between the working and standard tape lengths becomes significant, the working tape should be replaced.

Question 3

A line is measured as 1,200 ft at 98° F. Using a standard tape, what is the true length of the line?
A)1,197.70 ft
B)1,199.77 ft
C)1200.23 ft
D)1202.30 ft

Accepted Answer

The true length of a line that is measured as 1,200 ft at 98°F is 1,200.23 using a standard tape.
Solution
Correction = (steel tape coefficient of expansion)(outside temperature - standard temperature)(measured length)
Correction = (0.00000645 * 1/°F) (98°F - 68°F) (1,200) = +0.23 ft
True length = distance + correction
True length= 1,200.00 ft + 0.23 ft = 1,200.23 ft

Question 4

A distance of 644.52 chains equals which of the following?
A)189 m
B)42,538.32 ft
C)18,279.44 yd
D)All of the above

Accepted Answer

A distance of 644.52 chains equals 42,538.32 ft.
Solution
(644.52 chains) (66 ft/chain) = 42,538.32 ft

Question 5

A distance of 665.55 chains is equal to:
A)43926.30 yd
B)43926.30 m
C)43926.30 ft
D)None of the above

Accepted Answer

A distance of 665.55 chains is equal to 43926.30 ft.
Solution
One chain = 66 ft
(665.55 chains) (66 ft/chain) = 43,926.30 ft

Question 6

A line that bears N 15°36' E also bears which of the following?
A)N 75°36' W
B)S 15°36' W
C)S 75°24' W
D)None of the above

Accepted Answer

A line that bears N 15°36' E also bears S 15°36'W. The reverse bearing of a line is 180° from the forward bearing.

Question 7

An area was measured to be bounded by 50 chains on one side and 150 chains on the other. The acreage of the area is:
A)200 acres
B)750 acres
C)2,000 acres
D)None of the above

Accepted Answer

The acreage of an area measured to be bounded by 50.00 chains on one side and 150.00 chains on the other is 750 acres.
Solution
One acre = 10 square chains
Area (acres) = (length)(length) / (1 acre/10 square chains)
Area = (50 chains) (150 chains) / (1 acre/10 square chains)
Area = 750 acres

Question 8

A 100' tape was used to measure a horizontal line found to be 1,500 ft. The tape was then compared with a standard and found to be only 99.97 feet in length. The true length of the measured line is:
A)1,499.00
B)1,499.55 ft
C)1,500.00 ft
D)1,500.45 ft

Accepted Answer

The true length of the measured line is 1,499.55.
Solution
True length of horizontal line = (measured distance)(steel tape length / standard tape length)
True length = (1,500 ft)(99.97 ft / 100 ft)
True length = 1,499.55 ft

Question 9

When the direction of zero azimuth is north, a line of 195° azimuth will have a bearing of:
A)S 15° W
B)S 75° W
C)S 15° E
D)S 75° E

Accepted Answer

When the direction of zero azimuth is north, a line of 195° azimuth will have a bearing of S 15° W.
Solution
The bearing angle is 270°-195° = S 15° W (measured clockwise only)

Question 10

For a route surveying project along Interstate 70, the beginning of the project is station 170+00.00. If the end of the project is station 226+45.23, the total length of the project is:
A)22,645.23 ft
B)5,645.23 ft
C)2,645.23 ft
D)56.45 ft

Accepted Answer

For a route surveying project along Interstate 70, where the beginning of the project is station 170+00.00 and the end of the project is station 226+45.23, the total length of the project is 5,645.23 ft.
Solution
End of the project = 226+45.23 = 22,645.23 ft
Beginning of the project = 170+00.00 = 17,000.00 ft
Total length of project = 5,645.23 ft

Question 11

Given a triangle with a base of 42.20 feet and a height of 63.10 feet, find the area of the triangle. A)105.30 ft 2 B)634.3 ft 2 C)1,000 ft 2 D)1,331.41 ft 2

Accepted Answer

The area of the triangle is 1,331.41 ft 2 . Solution Use the formula A = 1/2bh Where A = area b = base h = height A = ½ (42.20 ft) (63.10 ft) = 1,331.41 ft 2

Question 12

Why is trilateration important to the Global Positioning System (GPS)?
A)Trilateration is a method used to calculate the relative location of an object that requires four reference points.
B)The triangulation method was found to be based on incorrect mathematics and has been abandoned in practice.
C)Trilateration is a complex word that confuses many and fulfills the government's desire to make everything as confusing as possible.
D)None of the above

Accepted Answer

Trilateration is important to GPS because it is a method used to calculate the relative location of an object that requires four reference points. Trilateration is the process of determining relative point locations using spherical geometry. The trilateration method is used by GPS technology to determine an object's x, y, and z coordinate location utilizing at least four reference points (satellites).

Question 13

What are the advantages of using the Least Squares Method rather than the Compass Rule adjustment to address traverse closure errors?
A)The least squares method results in a weighted means adjustment.
B)The least squares method may be used to adjust any type of data to meet geometric conditions and reflect statistical considerations.
C)Free computer software programs are readily available to solve complex equations.
D)All of the above

Accepted Answer

The advantages of using the Least Squares Method rather than the Compass Rule adjustment to address traverse closure errors include all of the listed reasons. Using the Compass Rule to adjust traverses results in an even distribution of the error closure throughout the entire traverse, rather than applying an adjustment at a point where the error may have more likely occurred. There are many sources of free software programs that perform least squares adjustment, including Adjust and Utilities (National Geodetic Survey) and Star*Net (MicroSurvey - demonstration software only).

Question 14

The given numbers are daily groundwater elevation readings from a monitoring well taken during a month experiencing snowmelt and extended rainfall events.
7.6 7.7 4.3 5.9 5.0 10.5 7.7 9.5 12.0 12.6 6.5 8.3 8.2 13.2 12.6 13.6 14.1 13.5 11.5 12.0 10.4 10.8 13.1 12.5 10.4 13.0 14.1 15.1
What is the sample variance of these groundwater elevation readings?
A)8.764
B)9.089
C)10.56
D)None of the above

Accepted Answer

The sample variance of the groundwater elevation readings is 9.089. Solution Use the sample variance (s 2 ) equation s 2 = ?(sample value - sample mean)2/(number of samples-1) Where Number of samples = 28 Sample mean = ?(sample values)/number of samples = 295.7/28 = 10.56 ?(sample value - sample mean) 2 = (7.6-10.56)2+(7.7-10.56) 2 + …… = 245.4 s 2 = 245.4/27 = 9.089

Question 15

The given numbers are daily groundwater elevation readings from a monitoring well taken during a month experiencing snowmelt and extended rainfall events.
7.6 7.7 4.3 5.9 5.0 10.5 7.7 9.5 12.0 12.6 6.5 8.3 8.2 13.2 12.6 13.6 14.1 13.5 11.5 12.0 10.4 10.8 13.1 12.5 10.4 13.0 14.1 15.1
What is the standard deviation of these groundwater elevation readings?
A)3.01
B)8.76
C)9.08
D)None of the above.

Accepted Answer

The standard deviation of the groundwater elevation readings is 3.01. Solution Use the standard deviation (s) equation s = square root [ ?(sample value - sample mean) 2 /(number of samples-1)] Where Number of samples = 28 Sample mean = ?(sample values)/number of samples = 295.7/28 = 10.56 ?(sample value - sample mean) 2 = (7.6-10.56) 2 +(7.7-10.56) 2 + …… = 245.4 s 2 = 245.4/27 = 9.089 s = 3.01

Question 16

Which of the following statements correctly describes the law of reflection?
A)The angle between an incident ray of light and the normal to the reflector's surface equals the angle between the reflector's surface and the reflected light ray.
B)The angle between an incident ray of light and the reflector's surface equals the angle between the normal to the reflector's surface and the reflected light ray.
C)The angle between an incident ray of light and the normal to the reflector's surface equals the angle between the normal and the reflected light ray.
D)The angle between an incident ray of light and the normal to the reflector's surface is complementary to the angle between the normal and the reflected light ray.

Accepted Answer

The statement "The angle between an incident ray of light and the normal to the reflector's surface equals the angle between the normal and the reflected light ray" correctly describes the law of reflection. The surface of the reflector is not considered in the law of reflection.

Question 17

Electric force is similar to gravitational force in what way?
A)Electric force decreases in strength as the distance between the charges increases.
B)Electric force is similar in strength to gravitational force.
C)Electric force is both attractive and repulsive.
D)Electric force is proportional to the mass of the object.

Accepted Answer

Electric force is similar to gravitational force in that electric force decreases in strength as the distance between the charges increases. Both electric and gravitational forces are inversely proportional to the square of the distance of separation. Gravitational forces are always attractive. Electric force is significantly stronger than gravitational force and is not proportional to the mass of an object.

Question 18

An airplane that starts from rest at one end of a runway undergoes a uniform acceleration of 16 ft/sec 2 For 15 seconds before takeoff. What is the airplane's speed at takeoff? A)31 ft/sec B)225 ft/sec C)240 ft/sec D)None of the above.

Accepted Answer

The airplane's speed at takeoff is 240 ft/sec.
Solution
Use the equation for velocity of a uniformly accelerated object
vf = vi + a (rt)
Where vf= Final velocity
vi= Initial velocity = 0 ft/sec
a = acceleration = 16 ft/sec2
rt = time interval = 15 sec
vf = 0 ft/sec + (16 ft/sec2 x 15 sec) = 240 ft/sec

Question 19

Angular motion is measured in which of the following units?
A)Radians
B)Degrees
C)Answers A and B
D)None of the above

Accepted Answer

Angular motion is measured in radians and degrees. Although many equations that describe circular motion require angles to be in radians rather than degrees, motion can be measured in either unit. Because there are 2 radians in a full circle, radians are often expressed as a multiple of ?.

Question 20

Dendrology is the study of which of the following?
A)Lakes
B)Trees
C)Teeth
D)Caves

Accepted Answer

Dendrology is a branch of botany that focuses on trees and other woody plants. The study of lakes is called limnology. The study of teeth is odontology. . Speleologists study caves.

Quiz 6: Math Science

When used in measuring linear distance, the term "station" refers to a point on a line:

Examples of common systematic errors encountered when measuring horizontal distances include:

A line is measured as 1,200 ft at 98° F. Using a standard tape, what is the true length of the line?

A distance of 644.52 chains equals which of the following?

A distance of 665.55 chains is equal to:

A line that bears N 15°36' E also bears which of the following?

An area was measured to be bounded by 50 chains on one side and 150 chains on the other. The acreage of the area is:

A 100' tape was used to measure a horizontal line found to be 1,500 ft. The tape was then compared with a standard and found to be only 99.97 feet in length. The true length of the measured line is:

When the direction of zero azimuth is north, a line of 195° azimuth will have a bearing of:

For a route surveying project along Interstate 70, the beginning of the project is station 170+00.00. If the end of the project is station 226+45.23, the total length of the project is:

Given a triangle with a base of 42.20 feet and a height of 63.10 feet, find the area of the triangle.

Why is trilateration important to the Global Positioning System (GPS) ?

What are the advantages of using the Least Squares Method rather than the Compass Rule adjustment to address traverse closure errors?

Which of the following statements correctly describes the law of reflection?

Electric force is similar to gravitational force in what way?

An airplane that starts from rest at one end of a runway undergoes a uniform acceleration of 16 ft/sec< sup> 2< /sup> For 15 seconds before takeoff. What is the airplane's speed at takeoff?

Angular motion is measured in which of the following units?

Dendrology is the study of which of the following?