Surveying is 6 to 9 questions on the 110-question FE Civil exam, and it rewards bookkeeping more than theory. Latitudes and departures, a closure error, an area by coordinates, an average end area volume: none of the mathematics is hard, but every one of them punishes a sign slip or a bearing read in the wrong quadrant.
These free practice problems use realistic traverse data, station notes, and cross-section areas rather than clean textbook numbers. Each solution shows the full tabulation, so you can see where a departure goes negative, how the compass rule distributes a misclosure, and why the prismoidal correction sometimes matters and often does not.
Exam weight: NCEES lists Surveying at 6-9 questions of the 110-question FE Civil exam. Work each problem below on paper first, then reveal the worked solution — reading a solution you have not attempted builds recognition, not recall.
What NCEES Tests in Surveying
NCEES gives Surveying 6 to 9 of the 110 questions and organizes it around angles, distances, and trigonometry; area computations; earthwork and volume computations; and closure. In practice that is a closed traverse with bearings or azimuths converted to latitudes and departures, a linear misclosure and precision ratio, and a balanced traverse adjusted by the compass rule.
Area problems come as coordinate or double meridian distance computations on an irregular parcel. Earthwork means cut and fill areas at each station turned into volumes by the average end area method, with the prismoidal formula when the sections differ sharply. Elevation work through differential leveling, backsights and foresights, height of instrument, and percent grade also appears regularly.
5 Free Surveying Practice Problems
Each surveying problem below comes from the FEExamClick FE Civil question bank, with worked solutions, and matches the style, difficulty and format of the real exam. Attempt each one under a three-minute limit — roughly the pace the exam demands.
Problem 1 — A. Angles, distances, and trigonometry
A hiker walks \( 100\,\mathrm{m} \) north, then \( 80\,\mathrm{m} \) east. What is the magnitude of the resultant displacement?
Answer: C) \( 128\,\mathrm{m} \)
Step 1 – Identify given information:
| Leg | Direction | Distance |
|---|---|---|
| 1 | North | \( 100\,\text{m} \) |
| 2 | East | \( 80\,\text{m} \) |
Step 2 – Pythagorean theorem for resultant displacement:
Since the two legs are perpendicular:
\( R = \sqrt{\Delta N^2 + \Delta E^2} \)
Step 3 – Substitute and solve:
\( R = \sqrt{100^2 + 80^2} = \sqrt{10{,}000 + 6{,}400} = \sqrt{16{,}400} = 128.1\,\text{m} \)
Step 4 – Answer:
The resultant displacement is approximately \( 128\,\text{m} \).
(A) \( 100\,\text{m} \) reports the longer leg alone, so the 80 m eastward walk never enters the radical.
(B) \( 120\,\text{m} \) is smaller than the hypotenuse of a 100-by-80 right triangle.
(D) \( 140\,\text{m} \) overshoots. Only the arithmetic sum \( 100 + 80 = 180\,\text{m} \) is larger, and the resultant of two perpendicular legs is always less than that sum.
Correct answer: (C)
Problem 2 — A. Angles, distances, and trigonometry
A 4-course traverse has the following (Lat, Dep) in ft: \( (+200, +50) \), \( (-120, +90) \), \( (-60, -100) \), \( (+10, -20) \). What is the linear misclosure?
Answer: A) \( 36\,\mathrm{ft} \)
Step 1 – Identify given information:
| Course | Lat (ft) | Dep (ft) |
|---|---|---|
| 1 | \( +200 \) | \( +50 \) |
| 2 | \( -120 \) | \( +90 \) |
| 3 | \( -60 \) | \( -100 \) |
| 4 | \( +10 \) | \( -20 \) |
Step 2 – Linear misclosure formula (FE Handbook):
For a closed traverse, the sums of latitudes and departures should each be zero. The linear misclosure is:
\( \text{Misclosure} = \sqrt{(\Sigma\text{Lat})^2 + (\Sigma\text{Dep})^2} \)
Step 3 – Substitute and solve:
\( \Sigma\text{Lat} = 200 - 120 - 60 + 10 = +30\,\text{ft} \)
\( \Sigma\text{Dep} = 50 + 90 - 100 - 20 = +20\,\text{ft} \)
\( \text{Misclosure} = \sqrt{30^2 + 20^2} = \sqrt{900 + 400} = \sqrt{1{,}300} = 36.1\,\text{ft} \)
Step 4 – Answer:
The linear misclosure is approximately \( 36\,\text{ft} \).
(B) \( 45\,\text{ft} \) sums only the first three courses, treating the fourth as the closing line instead of as part of the loop.
(C) \( 50\,\text{ft} \) adds the two misclosures arithmetically, \( 30 + 20 \), instead of combining them as a hypotenuse.
(D) \( 70\,\text{ft} \) exceeds even that arithmetic sum, so no combination of these four courses can produce it.
Correct answer: (A)
Problem 3 — B. Area computations
Trapezoidal Rule: \( w = 20\,\mathrm{ft} \), ordinates (ft) are \( 1,\, 3,\, 4,\, 3,\, 2,\, 1 \). What is the area \( (\mathrm{ft}^2) \)?
Answer: D) \( 260\,\mathrm{ft}^2 \)
Step 1 – Identify given information:
| Ordinate | \( h_1 \) | \( h_2 \) | \( h_3 \) | \( h_4 \) | \( h_5 \) | \( h_6 \) |
|---|---|---|---|---|---|---|
| Value (ft) | 1 | 3 | 4 | 3 | 2 | 1 |
Step 2 – Trapezoidal Rule (FE Handbook):
\( A = w\left[\dfrac{h_1 + h_n}{2} + h_2 + h_3 + \cdots + h_{n-1}\right] \)
Step 3 – Substitute and solve:
\( A = 20\left[\dfrac{1 + 1}{2} + (3 + 4 + 3 + 2)\right] = 20\left[1 + 12\right] = 20 \times 13 = 260\,\text{ft}^2 \)
Step 4 – Answer:
The area is \( 260\,\text{ft}^2 \).
(A) \( 140\,\text{ft}^2 \) uses the half-spacing form and never doubles the interior ordinates, so each interior height counts at half its weight: \( (20/2)(1+3+4+3+2+1) \).
(B) \( 200\,\text{ft}^2 \) drops an interior ordinate.
(C) \( 240\,\text{ft}^2 \) follows from an error in summing the interior ordinates.
Correct answer: (D)
Problem 4 — E. Leveling (e.g., differential, elevations, percent grades)
A leveling line is run from BM P (elevation \( 880.00\,\mathrm{ft} \)) to BM Q (known elevation \( 894.15\,\mathrm{ft} \)). One foresight was not recorded (shown as a question mark).
| Station | BS (ft) | FS (ft) |
|---|---|---|
| BM P (880.00) | 12.30 | - |
| TP1 | 9.85 | 5.20 |
| TP2 | 8.20 | 8.90 |
| TP3 | 8.25 | 6.45 |
| BM Q (894.15) | - | ? |
Answer: A) \( 3.90\,\mathrm{ft} \)
Step 1 - Arithmetic check: \( \sum BS-\sum FS=\mathrm{Elev}_{final}-\mathrm{Elev}_{start} \).
Step 2 - Sum the knowns:
\( \sum BS=12.30+9.85+8.20+8.25=38.60 \)
Known foresights: \( 5.20+8.90+6.45=20.55 \)
\( \mathrm{Elev}_{Q}-\mathrm{Elev}_{P}=894.15-880.00=14.15 \)
Step 3 - Solve for the total, then the missing FS:
\( \sum FS=\sum BS-\Delta\mathrm{Elev}=38.60-14.15=24.45 \)
\( FS_{missing}=24.45-20.55=\mathbf{3.90}\,\mathrm{ft} \)
Answer: \( 3.90\,\mathrm{ft} \) (A).
(D) is the required \( \sum FS \); (C) is the sum of the known foresights; (B) is a step slip.
Correct answer: (A)
Problem 5 — C. Earthwork and volume computations
Areas along a roadway are: \( \text{sta } 10+00 \) cut = \( 900 \,\mathrm{ft}^{2} \) fill = \( 0 \); \( \text{sta } 10+60 \) cut = \( 0 \) fill = \( 0 \); \( \text{sta } 11+20 \) cut = \( 0 \) fill = \( 600 \,\mathrm{ft}^{2} \); \( \text{sta } 11+70 \) cut = \( 300 \,\mathrm{ft}^{2} \) fill = \( 200 \,\mathrm{ft}^{2} \); \( \text{sta } 12+20 \) cut = \( 800 \,\mathrm{ft}^{2} \) fill = \( 0 \). Where an area transitions to/from zero, assume triangular cross-sections. What is the net borrow or waste from \( \text{sta } 10+00 \) to \( \text{sta } 12+20 \) (\( \mathrm{ft}^{3} \)), nearest \( 100 \,\mathrm{ft}^{3} \)?
Answer: B) \( 15{,}200\,\mathrm{ft}^{3} \) waste
Step 1\(– Cut=60(900)/3+50(300)/3+50(300+800)/2=50,500 ft^{3}\)
Step 2\(– Fill=60(600)/3+50(600+200)/2+50(200)/3=35,333 ft^{3}\)
Step 3\(– Net waste=50,500−35,333=15,167≈15,200 ft^{3}\)
Correct answer: (B)
Using the FE Reference Handbook for Surveying
The Surveying section gives you latitude and departure definitions, the compass rule, the area by coordinates formula, and the average end area and prismoidal volume equations in a short run of pages. Read that block once so you know its order, because searching for a word like area returns hits across half the handbook. Angle conversions live in the Mathematics tables.
Four Mistakes That Cost Points
- Getting the sign of a latitude or departure wrong A bearing of S 40 E has a negative latitude and a positive departure. Candidates convert the trigonometry correctly and then enter both as positive, which makes the traverse close beautifully around a shape that does not exist. Assign the sign from the quadrant before computing anything.
- Reporting misclosure when the question wants precision Linear misclosure is a distance in feet or meters; precision is that distance divided by the total traverse length, expressed as one over a round number. Questions asking for accuracy want the ratio. Answer choices usually include both, so read the units in the options before selecting.
- Mixing units in earthwork volumes Cross-section areas arrive in square feet and station spacing in feet, but the answer is wanted in cubic yards. Dividing by 27 is the step most often skipped under time pressure, and the unconverted number is typically sitting right there among the four choices.
- Confusing height of instrument with the height of the tripod In differential leveling, height of instrument is the elevation of the line of sight, equal to the known elevation plus the backsight. It is not how high the instrument stands. Foresights subtract from that value to give the new point elevation, and a turning point carries both a foresight and a backsight.
Frequently Asked Questions
How many surveying questions are on the FE Civil exam?
NCEES allocates 6 to 9 of the 110 questions to Surveying. Because the topic is procedural rather than conceptual, it is one of the few areas where consistent practice reliably converts into points. Many candidates last touched a total station in a sophomore lab, so the tabulation habits need rebuilding more than the theory does.
Are horizontal and vertical curves part of the surveying questions?
Curve geometry is listed under Transportation in the current NCEES FE Civil specification, not Surveying, though the two overlap in practice through stationing. Study curves for their own block of questions, and use Surveying practice for traverse, area, earthwork, closure, and leveling work. Knowing stationing notation well helps in both areas.
Do I need a specific calculator for surveying problems?
Any NCEES-approved model works, but you should be fluent with degrees-minutes-seconds entry and conversion on the one you bring. Traverse problems require many sine and cosine evaluations in sequence, and fumbling the angle format on each of them is where the time goes. Practice the keystrokes, not just the method.
How detailed do the traverse problems get on the exam?
Exam items are sized for roughly three minutes, so you will not balance a six-sided traverse from scratch. Expect a partial table with one missing course, a misclosure to compute from given latitudes and departures, or a single adjustment applied to one leg. Practicing the full procedure still matters, because it makes the partial versions obvious.
Keep Going
Done with surveying? Work through the other FE Civil knowledge areas with more free practice problems, review the full FE Civil exam topic breakdown, or plan your preparation with our FE exam study guide and study timeline. Or test yourself against the clock with the free FE Civil practice exam: 20 timed questions in the CBT format.