I85PREP
⌘ K
CT Land Surveyor study materials
CT Land Surveyor study resources

CT Land Surveyor practice questions

One question at a time. Build your CT Land Surveyor understanding.

First 50 of 200 questions. Each one lists the choices, the correct answer, and an explanation. The checker at the top of this page saves progress in this browser when it is available.

Continue in the practice tool above to load more questions, 50 at a time.

Question 1Boundary Surveying and Retracement

Under the U.S. Public Land Survey System, what does a township corner monument control?

  1. The alignment of a meander line along a navigable stream
  2. The boundary of an individual patented lot
  3. The position of the intersection of two township boundary lines Correct answer.
  4. The location of a single section interior quarter-corner

Explanation

A township corner is the intersection of two township boundary lines, so it simultaneously controls the north-south and east-west township lines meeting there. Section corners and quarter-corners are subordinate to it, and lot or meander lines do not define it.

Question 2Boundary Surveying and Retracement

A retracement surveyor finds an original bearing tree stump with visible blaze and scribe marks near a section corner position. How should this evidence be treated?

  1. As irrelevant because the tree is dead
  2. As secondary evidence inferior to a proportioned position
  3. As controlling only if the bark is intact
  4. As direct original evidence of the corner location Correct answer.

Explanation

Original monuments and original bearing trees are direct evidence of the corner as it was established by the original survey. They outrank positions derived by proportionment between other corners. The condition of the bark or the death of the tree does not destroy the evidentiary value of the remaining stump.

Question 3Boundary Surveying and Retracement

Which term describes a boundary line established by the actions and acquiescence of adjoining owners rather than by a recorded deed description?

  1. Centerline
  2. Meander line
  3. Record line
  4. Line of occupation Correct answer.

Explanation

A line of occupation is the line actually recognized and treated as the boundary by the adjoining owners, typically through long acquiescence or practical location. The record line is the deed-described boundary, which may differ from the occupied line. Meander and centerlines describe water boundaries, not acquiescence between upland owners.

Question 4Boundary Surveying and Retracement

In a metes-and-bounds description, the phrase "thence North 45 degrees East, 300 feet" defines what?

  1. A bearing and distance for one course Correct answer.
  2. An area of 300 square feet
  3. A monument call
  4. A radius of curvature

Explanation

The phrase gives a bearing (N 45 E) and a distance (300 feet), which together define one course of the boundary. Area, curvature, and monument calls are expressed differently in a description.

Question 5Boundary Surveying and Retracement

What is the primary purpose of a boundary retracement survey?

  1. To recover and monument the location of an existing boundary as originally established Correct answer.
  2. To create a new boundary where none was recorded
  3. To calculate the market value of the parcel
  4. To redesign the lot layout for subdivision approval

Explanation

A retracement survey seeks to reestablish the position of boundaries as they were originally created, using evidence and record information. It does not create new boundaries or set value; those are different professional activities.

Question 6Boundary Surveying and Retracement

A deed calls for a boundary to run "to a large oak tree," and the tree is found standing. Under the rules of construction, how does the tree call rank against a stated distance?

  1. The call is void because trees are perishable
  2. The distance controls because it is more precise
  3. Neither controls; the line is proportioned
  4. The monument controls over the distance Correct answer.

Explanation

Natural monuments called for in a deed generally control over courses and distances because the monument is the more certain evidence of the parties' intent. Distances yield to the called-for monument when the two conflict.

Question 7Boundary Surveying and Retracement

Which of the following is the best example of a natural monument used in boundary evidence?

  1. A recorded plat
  2. A set aluminum-capped rebar
  3. A stone wall
  4. A river bank Correct answer.

Explanation

A natural monument is a physical feature of the landscape, such as a river bank, ledge, or ancient tree, that the original survey relied upon. Artificial monuments, walls built by people, and written records are classified differently.

Question 8Boundary Surveying and Retracement

In the PLSS, what is a closing corner?

  1. A temporary corner used only during field work
  2. A corner set at the end of every mile of a township line
  3. A corner established where a surveyed line closes on a previously established line without meeting at a standard corner Correct answer.
  4. A corner at the intersection of a base line and principal meridian

Explanation

A closing corner is set where a later survey line intersects an earlier line at a point that is not a standard corner, and the distance to the nearest standard corner is recorded. It is not the initial point or a routine mile corner.

Question 9Boundary Surveying and Retracement

A surveyor must reestablish a lost section corner between two found original section corners 80 chains apart, with no other evidence available. What method applies?

  1. Grant boundary adjustment
  2. Double proportion using lines in both directions Correct answer.
  3. Single proportion along the line only
  4. Meander line extension

Explanation

When a section corner is lost and original evidence is gone, double proportionment uses the surrounding found corners in both north-south and east-west directions to compute the position. Single proportion is used only in limited situations such as certain closing corners.

Question 10Boundary Surveying and Retracement

Two adjoining owners have treated a fence as their boundary for 25 years, and the statutory period for adverse possession is 20 years. What doctrine most directly supports the fence as the boundary?

  1. Eminent domain
  2. Prescriptive easement
  3. Practical location and acquiescence Correct answer.
  4. Dedication

Explanation

Long-recognized occupation of a fence line with acquiescence by both owners supports the doctrine of practical location or boundary by acquiescence. This differs from a prescriptive easement, which grants use rights rather than shifting the fee boundary.

Question 11Boundary Surveying and Retracement

A deed describes a parcel as "Lot 5, Block 2, of Smith's Addition, as recorded in Plat Book 3, Page 12." Which control governs the boundary location?

  1. The current tax assessment map
  2. The recorded plat Correct answer.
  3. The owner's fence
  4. The lot's stated area

Explanation

A lot-and-block description incorporates the recorded plat by reference, and the plat's monuments and lines control the boundary. Stated area and tax maps are secondary, and an owner's fence is occupation evidence, not the record control.

Question 12Boundary Surveying and Retracement

A stream is non-navigable, and a deed conveys land bounded by the stream without specifying the bank. What does the grantee generally receive?

  1. Only to the low water mark
  2. Only to the ordinary high water mark
  3. No riparian rights at all
  4. To the thread (centerline) of the stream Correct answer.

Explanation

For non-navigable streams, the general common-law rule gives the riparian owner title to the thread or centerline of the stream, subject to the water's flow. Navigable waters follow a different rule tied to the high or low water mark depending on state law.

Question 13Boundary Surveying and Retracement

A surveyor finds an original iron pin at a section corner but also finds that the record distance to the next corner is 20 feet longer than measured. What is the proper treatment?

  1. Average the pin position and the record distance
  2. Set a new corner at the record distance
  3. Hold the pin and let the distance yield Correct answer.
  4. Reject the pin as set in error

Explanation

An original monument, such as an original iron pin, is direct evidence of the corner and controls over record distances. Distances in the record are accepted as correct between accepted corners, so the pin is held and the discrepancy is noted.

Question 14Boundary Surveying and Retracement

Which record document most directly establishes the official boundary of a parcel created by a subdivision?

  1. The utility easement atlas
  2. The zoning district map
  3. The recorded subdivision plat Correct answer.
  4. The county road map

Explanation

A subdivision plat, once approved and recorded, establishes the lots, blocks, and monumented lines that define the parcels. Zoning, road, and utility maps serve other regulatory or infrastructure purposes and do not create lot boundaries.

Question 15Boundary Surveying and Retracement

A surveyor retracing a line finds a called-for stone monument at the described position but no bearing tree. What should be recorded about the bearing tree?

  1. That the bearing tree controls the corner
  2. That the bearing tree was destroyed by the surveyor
  3. That the bearing tree was not found Correct answer.
  4. That no bearing tree was ever called for

Explanation

The field record should accurately state that the called-for bearing tree was searched for and not found, preserving the evidentiary status of the corner. The surveyor must not speculate about destruction or claim the tree controls when it is absent.

Question 16Boundary Surveying and Retracement

What does the term "parol evidence" refer to in a boundary dispute?

  1. A court judgment
  2. A recorded survey plat
  3. Written deed language
  4. Testimony about statements and circumstances outside the deed Correct answer.

Explanation

Parol evidence is oral testimony or evidence outside the written instrument, often used to explain ambiguities or establish practical location. It is distinct from the deed, plats, and judgments, which are written records.

Question 17Boundary Surveying and Retracement

In retracement, a surveyor discovers that a monument called for in the deed is a fence post that was not present at the original survey. How should this monument be classified?

  1. An original monument
  2. A controlling record call
  3. A natural monument
  4. A subsequent monument of uncertain weight Correct answer.

Explanation

A monument that postdates the original survey is a subsequent monument and does not carry the weight of original evidence. It may be considered, but it cannot control over original corners or calls.

Question 18Boundary Surveying and Retracement

A deed's calls conflict: it gives a bearing, a distance, and a call to a highway. Which generally controls?

  1. The bearing
  2. The call to the highway as a monument Correct answer.
  3. The distance
  4. All three are averaged

Explanation

A call to a monument, such as a highway, generally controls over courses and distances because the monument is the more certain indicator of intent. Bearings and distances yield when they conflict with the monument call.

Question 19Boundary Surveying and Retracement

What is the significance of the "ordinary high water mark" in a boundary survey along navigable water?

  1. It is a meander line
  2. It marks the limit of private upland title in many states Correct answer.
  3. It is the same as the low water mark
  4. It marks the thread of the stream

Explanation

In many states, the ordinary high water mark defines the boundary between state-owned submerged land and private upland along navigable waters. It is not the thread of the stream, the low water mark, or a meander line, which is only an approximation used in the original survey.

Question 20Boundary Surveying and Retracement

A surveyor finds two original section corners and computes a lost quarter-corner by single proportion between them. What assumption underlies this method?

  1. The original surveyor never set quarter-corners
  2. The original surveyor used a compass only
  3. The original surveyor set the quarter-corner exactly at the midpoint
  4. The original surveyor made uniform errors along the line Correct answer.

Explanation

Proportionment assumes that errors in the original survey were distributed uniformly along the line, so the lost corner is placed proportionally between the found corners. It does not assume exact midpoints or particular instruments.

Question 21Boundary Surveying and Retracement

A parcel is described by metes and bounds that close with a misclosure of 1 in 500. What does this indicate about the description?

  1. The description is mathematically perfect
  2. The description is void
  3. The description has a relatively large relative error and should be checked Correct answer.
  4. The description must be surveyed by double proportion

Explanation

A misclosure of 1 in 500 is a relatively large relative error for a boundary description, suggesting a transcription or measurement problem that warrants checking. It does not void the description, and it is not a perfect closure.

Question 22Boundary Surveying and Retracement

An owner claims a strip of land based on a fence that has been in place for 30 years, but the true owner occasionally used the strip. What effect does the occasional use have on the adverse possession claim?

  1. It strengthens the claim by showing shared use
  2. It has no effect on the claim
  3. It may defeat the exclusivity element Correct answer.
  4. It converts the claim to a prescriptive easement

Explanation

Adverse possession requires exclusive possession, so evidence that the true owner also used the strip may defeat the exclusivity element. Shared use does not strengthen the claim and is not automatically converted to an easement.

Question 23Boundary Surveying and Retracement

A river gradually shifts its channel over decades through accretion, and the boundary between riparian owners follows the movement. What doctrine describes this?

  1. Erosion by avulsion
  2. Accretion Correct answer.
  3. Reliction by avulsion
  4. Avulsion

Explanation

Accretion is the gradual and imperceptible addition of land by water action, and the boundary moves with the water. Avulsion is a sudden change, which generally leaves the boundary where it was.

Question 24Boundary Surveying and Retracement

A surveyor retracing a PLSS line finds that the original surveyor's measured distance between two section corners is 79.50 chains rather than the nominal 80 chains. How should this be handled in a retracement?

  1. Disregard the corners as erroneous
  2. Reset one corner to restore 80 chains
  3. Hold the found corners and accept the record distance between them Correct answer.
  4. Proportion the line to exactly 80 chains

Explanation

In PLSS retracement, the found original corners are held, and the record distance between them is accepted as correct for that line. The surveyor does not reset corners or force the line to the nominal 80 chains.

Question 25Boundary Surveying and Retracement

A deed calls for a boundary along a stone wall that no longer exists, but an old fence line and a line of mature trees follow the same general course. How should the surveyor weigh this evidence?

  1. The tree line controls because trees are natural monuments
  2. The fence line and tree line are secondary evidence that may corroborate the former wall location Correct answer.
  3. The call is void because the wall is gone
  4. The boundary must be set at the record bearing and distance only

Explanation

When a called-for monument is gone, evidence such as an old fence line and a line of trees may corroborate its former location, but such evidence is secondary and must be weighed carefully. The call is not void, and the record bearing and distance are not automatically controlling over better evidence of the monument.

Question 26Boundary Surveying and Retracement

A metes-and-bounds deed calls for a boundary running from a found original concrete monument "to a point on the northerly bank of Mill Creek." In the hierarchy of calls used in retracement, how is the creek bank call best classified?

  1. A call for a natural monument that generally controls over courses and distances Correct answer.
  2. A call for an artificial monument that yields to the recorded bearing
  3. A call for an adjoiner's occupation line that controls only if fenced
  4. A call for area that is disregarded when the deed also states acreage

Explanation

A call to the bank of a natural watercourse is a natural monument call, and in the hierarchy of evidence natural monuments rank above courses, distances, and area. The bank is a physical feature on the ground, not a record quantity, so it governs the location of the terminus when it can be identified with reasonable certainty.

Question 27Boundary Surveying and Retracement

A surveyor retracing a subdivision lot finds the two original plat monuments at the front corners of the lot, but the two rear corners are missing. The plat shows the lot as a rectangle 60 feet wide by 120 feet deep with right-angle corners. Which reestablishment approach is most consistent with accepted retracement practice?

  1. Reject the found monuments because the rear corners cannot be verified and reset all four corners by record
  2. Prorate the record depth between the found front corners and the nearest found monument to the rear
  3. Hold the found front corners as controlling and reestablish the rear corners by record bearing and distance, noting the basis Correct answer.
  4. Set the rear corners by holding the plat dimensions from the found front corners and record the result as the lot corners

Explanation

Found original monuments are the best available evidence of the original survey and are held as controlling. Because the rear corners are lost, they are reestablished by record bearing and distance from the controlling found corners, and the surveyor documents that basis on the plat and in the field notes.

Question 28Boundary Surveying and Retracement

A deed written in 1954 conveys a parcel bounded on the east by "the west line of the right of way of County Road 12 as the same now runs." The road has since been widened and its centerline relocated. In retracing the parcel, which line best represents the deed boundary?

  1. The west right-of-way line of the road as it existed at the date of the deed Correct answer.
  2. The centerline of the road as it exists today
  3. The east right-of-way line of the road as it exists today
  4. The west right-of-way line of the road as it exists today

Explanation

A call to a right-of-way line as it "now runs" refers to the location of that line at the time the deed was executed. Later widening or relocation by the road authority does not move the conveyed boundary, so the historical right-of-way line controls.

Question 29Boundary Surveying and Retracement

In the Public Land Survey System, a surveyor finds the original quarter-section corner monument intact on the north boundary of a section but finds the section corners at both ends of that boundary are lost. What is the proper treatment of the found quarter corner?

  1. Reset the quarter corner at the record midpoint of the computed section line
  2. Hold the found quarter corner as controlling and reestablish the section corners from it and other acceptable evidence Correct answer.
  3. Average the found quarter corner position with the record position to establish the section line
  4. Disregard the quarter corner because the section corners it depends on are lost

Explanation

An original monument, even a single one, is the best evidence of the original survey and controls over record positions. The lost section corners are reestablished from the found corner together with other acceptable evidence such as bearing trees, accessory monuments, and record ties.

Question 30Boundary Surveying and Retracement

A deed conveys a parcel "beginning at the northeast corner of the Jones tract, thence south 200 feet, thence west 150 feet, thence north 200 feet, thence east 150 feet to the point of beginning." The northeast corner of the Jones tract is a well-established monument. What does this description establish about the parcel?

  1. It is an unenforceable description because it lacks a bearing for the first call
  2. It is a lot-and-block description that requires the plat to locate the parcel
  3. It is a metes-and-bounds description whose controlling element is the monument at the point of beginning Correct answer.
  4. It is a description by area only, since the deed closes on itself

Explanation

The description runs by courses and distances from a stated monument, which makes it a metes-and-bounds description. The monument at the point of beginning anchors the parcel, and the courses and distances carry the boundary from that monument.

Question 31Boundary Surveying and Retracement

A surveyor is retracing a boundary and finds that the deed calls for a distance of 500.00 feet between two monuments, but the monuments measure 497.30 feet apart and both appear to be original. Which principle best guides the surveyor?

  1. The record distance controls because the deed is the primary source of the boundary location
  2. The average of the record and measured distances controls to balance the discrepancy
  3. The measured distance controls because monuments, when original, are the best evidence of the boundary Correct answer.
  4. The discrepancy requires the surveyor to reject both monuments and reset the line by record

Explanation

Original monuments are the highest form of boundary evidence, and a discrepancy between the record distance and the monument distance is resolved in favor of the monuments. The surveyor reports the measured relationship and the record discrepancy rather than forcing the line to the deed distance.

Question 32Boundary Surveying and Retracement

A deed describes the southerly boundary of a parcel as running "along the northerly line of the Smith property." The Smith property is described in a separate recorded deed by metes and bounds. What is the surveyor's best course in locating the parcel's southerly boundary?

  1. Establish the line by proportioning between the section corners on either side
  2. Hold the line to the fence currently occupying the ground as the best evidence
  3. Locate the line by the record description of the Smith property as it appears in the Smith deed Correct answer.
  4. Run a straight line between the two nearest found monuments of the subject parcel

Explanation

A call to an adjoiner's line is a call to that line as it is legally established, which requires locating the Smith parcel boundary from its own record description. The subject parcel's line then coincides with the line so established.

Question 33Boundary Surveying and Retracement

A surveyor is asked to retrace a parcel described by a deed that references a recorded survey map, but the deed's written courses differ from the courses shown on the map. Which document generally controls the boundary location?

  1. The newer of the two documents, because it reflects the more recent intent
  2. The written courses in the deed, because they are the direct expression of the grantor Correct answer.
  3. The recorded map, because it is the more detailed representation of the parcel
  4. Neither document controls, and the boundary must be established by litigation

Explanation

The deed is the instrument of conveyance and its written calls generally control over a referenced map, which serves as an aid to locating the described boundary. A surveyor reconciles the two by treating the map as explanatory evidence and reporting any conflict.

Question 34Boundary Surveying and Retracement

A surveyor is retracing a line along a non-navigable stream where the deed conveys land bounded by the stream. The stream has gradually eroded its bank over many years, moving the water's edge several feet. How is the boundary between the riparian owners generally treated?

  1. The boundary is fixed at the ordinary high water mark as it exists today
  2. The boundary remains fixed at the location of the stream as it existed when the deed was written
  3. The boundary is fixed at the thread of the stream as it exists today
  4. The boundary follows the stream as it gradually shifts through erosion and accretion Correct answer.

Explanation

For non-navigable streams, gradual changes by erosion and accretion move the boundary with the water, so riparian owners gain or lose land slowly. This differs from avulsion, where a sudden channel change does not move the boundary.

Question 35Boundary Surveying and Retracement

A surveyor retracing a subdivision boundary finds that the plat shows a curve with a radius of 300.00 feet, a central angle of 40 degrees, and an arc length of 209.44 feet, while the chord distance shown is 205.21 feet. Which relationship should the surveyor verify first?

  1. That the tangent length equals the radius times the sine of the central angle
  2. That the arc length equals the radius times the central angle in radians Correct answer.
  3. That the external distance equals the radius times the cosine of the central angle
  4. That the chord length equals the radius times the central angle in radians

Explanation

Arc length is computed as radius multiplied by the central angle expressed in radians, so 300 feet times 0.6981 radians gives 209.44 feet, matching the plat. Checking this relationship confirms the curve data before the surveyor uses the chord for field layout.

Question 36Boundary Surveying and Retracement

A surveyor finds a stone monument at a section corner with markings consistent with the original government survey, and also finds a bearing tree stump nearby. A later survey map shows the section corner at a location 12 feet away. How should the surveyor treat the conflict?

  1. Hold the original stone monument as controlling and note the bearing tree as corroborating evidence Correct answer.
  2. Disregard both the monument and the map and reestablish the corner by proportioning
  3. Hold the later survey map position because it is a more recent professional opinion
  4. Hold a position halfway between the monument and the map location to balance the evidence

Explanation

Original government monuments are the best evidence of the original survey and control over later survey maps or remonumentation. The bearing tree stump provides corroborating accessory evidence that supports the original monument's authenticity.

Question 37Boundary Surveying and Retracement

A deed describes a parcel by lot and block in a recorded subdivision plat, and the plat shows the lot abutting a dedicated street. The deed is silent about the street. What is the general rule regarding the lot's boundary along the dedicated street?

  1. The lot boundary is determined solely by the area stated in the deed
  2. The lot boundary extends to the far right-of-way line of the street
  3. The lot boundary extends to the centerline of the dedicated street, subject to the public easement Correct answer.
  4. The lot boundary stops at the street right-of-way line, and the fee in the street remains with the subdivider

Explanation

When a platded lot abuts a dedicated street and the deed does not expressly limit the conveyance, the lot is generally presumed to extend to the centerline of the street, subject to the public easement. The subdivider is presumed not to have retained the fee in the street.

Question 38Boundary Surveying and Retracement

A surveyor retracing a metes-and-bounds parcel discovers that the deed's courses and distances do not close by 0.8 foot over a perimeter of about 2,600 feet. What is the most appropriate professional response?

  1. Adjust the bearings and distances to force a perfect closure and record the adjusted values as the deed line
  2. Ignore the misclosure because deeds are not required to close mathematically
  3. Report the misclosure, hold the found monument control, and disclose the discrepancy in the survey record Correct answer.
  4. Reset all corners to the record positions to eliminate the misclosure

Explanation

A misclosure in the deed is a record discrepancy, not a license to alter the deed's calls. The surveyor holds the found monument control, reports the misclosure, and discloses the discrepancy so that the client and any reviewing professional can evaluate it.

Question 39Boundary Surveying and Retracement

A parcel is bounded on the north by a line described as "the south line of the Brown tract, now or formerly owned by Brown." The Brown tract has been subdivided, and the original south line is no longer marked on the ground. What evidence should the surveyor seek first?

  1. The record description of the Brown tract as it existed before subdivision Correct answer.
  2. The nearest section corner and the bearing to the subject parcel
  3. The current occupation lines of the lots created from the Brown tract
  4. The area of the subject parcel as stated in its deed

Explanation

A call to an adjoiner's line refers to that line as legally established, so the surveyor first obtains the record description of the Brown tract before subdivision. That record, together with any found monuments of the Brown tract, establishes the line called for.

Question 40Boundary Surveying and Retracement

A surveyor retracing a boundary finds a called-for iron pipe that is clearly not the original monument because it is a modern type set by a later surveyor at a location inconsistent with the deed. What weight should the surveyor give this pipe?

  1. It is evidence to be evaluated and reported, but it does not control over original monument evidence Correct answer.
  2. It must be removed because it is not an original monument
  3. It controls only if the later surveyor recorded it on a plat
  4. It controls because any monument found on the line is treated as original

Explanation

A monument that is demonstrably not original is not controlling evidence of the original boundary; it is a later surveyor's opinion expressed on the ground. The surveyor evaluates it, reports its location and character, and gives controlling weight to original monuments and other acceptable evidence.

Question 41Mathematics, Measurement and Computations

A boundary bearing is recorded as N 42°17'35" E. Expressed as an azimuth measured clockwise from north, what is the bearing?

  1. 137°42'25"
  2. 317°42'25"
  3. 47°42'25"
  4. 42°17'35" Correct answer.

Explanation

In the northeast quadrant, the azimuth equals the bearing angle measured clockwise from north, so the azimuth is simply 42°17'35". Quadrant conversions change the value only when the bearing lies in another quadrant.

Question 42Mathematics, Measurement and Computations

A closed traverse has interior angles measured as 118°24'10", 92°15'50", 104°38'40", 121°07'20", and 103°34'00". What is the angular misclosure for a five-sided closed loop?

  1. 0°00'20"
  2. 0°01'20"
  3. 0°00'40" Correct answer.
  4. 0°00'00"

Explanation

The sum of interior angles in a closed polygon equals (n−2)×180°, which for n = 5 is 540°00'00". Summing the five measured angles gives 540°00'40", so the misclosure is 40 seconds.

Question 43Mathematics, Measurement and Computations

A rectangular parcel measures 250.00 m by 400.00 m. How many hectares does it contain?

  1. 1.000 ha
  2. 100.0 ha
  3. 0.1000 ha
  4. 10.00 ha Correct answer.

Explanation

Area equals 250.00 m × 400.00 m = 100,000 m². Since one hectare equals 10,000 m², the parcel contains 10.00 hectares.

Question 44Mathematics, Measurement and Computations

A slope distance of 325.00 m is measured between two points whose elevation difference is 18.00 m. What is the horizontal distance?

  1. 324.00 m
  2. 307.00 m
  3. 325.50 m
  4. 324.50 m Correct answer.

Explanation

Horizontal distance equals the square root of (slope distance squared minus elevation difference squared): √(325.00² − 18.00²) = √(105,625 − 324) = √105,301 ≈ 324.50 m.

Question 45Mathematics, Measurement and Computations

A total station occupies a point with elevation 152.30 m. The instrument height is 1.52 m, the rod reading is 2.85 m, and the zenith angle to the target is 90°00'00". What is the elevation of the target point?

  1. 155.15 m
  2. 151.00 m
  3. 150.97 m Correct answer.
  4. 153.82 m

Explanation

With a zenith angle of 90°, the line of sight is horizontal, so the elevation difference equals the instrument height minus the rod reading. Thus 152.30 + 1.52 − 2.85 = 150.97 m.

Question 46Mathematics, Measurement and Computations

A map is drawn at a scale of 1:24,000. A line measures 3.75 inches on the map. What is the equivalent ground distance in feet?

  1. 9,000 ft
  2. 7,500 ft Correct answer.
  3. 3,000 ft
  4. 6,000 ft

Explanation

Ground distance equals map distance times the scale factor: 3.75 in × 24,000 = 90,000 in. Dividing by 12 in/ft gives 7,500 ft.

Question 47Mathematics, Measurement and Computations

The coordinates of point A are (E 5,000.00, N 4,000.00) and of point B are (E 5,300.00, N 4,400.00). What is the bearing from A to B?

  1. N 36°52'12" W
  2. S 36°52'12" W
  3. N 36°52'12" E
  4. N 53°07'48" E Correct answer.

Explanation

The change in northing is 400.00 and the change in easting is 300.00, giving a tangent of 400/300 = 1.3333. The arctangent is 53°07'48", and since both differences are positive the bearing is N 53°07'48" E.

Question 48Mathematics, Measurement and Computations

A parcel is described as a triangle with a base of 160.00 m and a perpendicular height of 95.00 m. What is its area?

  1. 7,600 m² Correct answer.
  2. 30,400 m²
  3. 15,200 m²
  4. 1,520 m²

Explanation

The area of a triangle equals one-half base times height: 0.5 × 160.00 × 95.00 = 7,600 m².

Question 49Mathematics, Measurement and Computations

A distance measured repeatedly gives values of 100.02, 100.00, 99.98, and 100.00 m. What is the standard deviation of this sample (using n−1)?

  1. 0.020 m
  2. 0.016 m Correct answer.
  3. 0.010 m
  4. 0.000 m

Explanation

The mean is 100.00 m; the squared residuals are 0.0004, 0, 0.0004, and 0. The sum is 0.0008, divided by n−1 = 3 gives 0.000267, and the square root is about 0.0163 m.

Question 50Mathematics, Measurement and Computations

In a level loop, backsight and foresight readings are recorded as BS 1.245, FS 1.860, BS 1.105, FS 0.980. Starting elevation at the first point is 200.000 m. What is the elevation of the final point?

  1. 200.510 m
  2. 199.490 m Correct answer.
  3. 200.490 m
  4. 201.510 m

Explanation

The change in elevation equals the sum of backsights minus the sum of foresights: (1.245 + 1.105) − (1.860 + 0.980) = 2.350 − 2.840 = −0.490 m. Adding that to 200.000 m gives 199.490 m.