CELE Surveying (Geomatics) — LevelingExam Answer Templates
Exam-style answer templates for Leveling — how to answer CELE Surveying (Geomatics) questions when Professional Regulation Commission (PRC) — Board of Civil Engineering asks about this chapter. Use these as your mental checklist on exam day.
Exam context
Professional Regulation Commission (PRC) — Board of Civil Engineering runs the Civil Engineer Licensure Examination on May and November 2026. Its Surveying (Geomatics) section sits under a "Core" weighting, and Leveling is the 2nd chapter in the 9-chapter CELE Surveying (Geomatics) rotation. The CELE passing mark is 70% weighted average, no sub-test below 50%, and the most recent 2026 paper drew about a meaningful share of questions from Surveying (Geomatics).
Leveling - Exam Answer Templates
Proper answer writing is the direct bridge between knowing the material and earning full marks on the PRC Civil Engineer Licensure Examination. In Surveying, examiners award marks for three things: correct formula citation, accurate numerical work shown step-by-step, and the correct unit and sign of the final answer. A student who writes only the final number — even if correct — risks losing 50–100% of the marks for that item. These templates teach you the exact format, key phrases, and level of detail that Philippine board examiners expect for 1-mark through long-answer questions on the Leveling chapter. Study each model answer as a blueprint, not just as a solution.
Templates
Define the Height of Instrument (HI) in differential leveling.
Marks
1
Topic
Differential Leveling — HI Method
Difficulty
easy
Template Id
T1
Examiner Tip
A 1-mark definition question is answered in one sharp sentence that contains the formula. Board examiners scan for the phrase 'line of sight' and the equation HI = elev + BS.
Model Answer
The Height of Instrument (HI) is the elevation of the line of sight of the level above the adopted datum, obtained by adding the backsight (BS) rod reading to the known elevation of the occupied station: HI = elev + BS.
Question Type
very_short_answer
Answer Structure
- Line 1: State the definition using 'elevation of the line of sight' and include the formula HI = elev + BS [1 mark]
Scoring Breakdown
Marks
1
Criteria
Correct definition mentioning 'elevation of the line of sight above datum' AND the relationship HI = elev + BS (or equivalent correct expression).
Common Mark Deductions
- Writing 'height of the instrument above the ground' — the HI is above the datum, not the ground surface.
- Omitting the formula and giving only a vague narrative description.
- Confusing HI with the height of the instrument tripod.
Key Phrases To Include
- elevation of the line of sight
- datum
- HI = elev + BS
- backsight
What is the combined curvature-and-refraction correction formula used in leveling, and what is its correct sign convention?
Marks
1
Topic
Curvature and Refraction
Difficulty
easy
Template Id
T2
Examiner Tip
Examiners test whether you know the constant (0.0675) AND the sign. Write both explicitly even in a 1-mark question.
Model Answer
h_cr = 0.0675 K² (metres), where K is the sight distance in kilometres. The correction is SUBTRACTED from the observed rod reading because the Earth's curvature makes the distant rod appear to read higher than its true value.
Question Type
very_short_answer
Answer Structure
- Line 1: State the formula with correct constant and units [0.5 mark]
- Line 2: State the sign convention — subtracted from rod reading — with brief reason [0.5 mark]
Scoring Breakdown
Marks
1
Criteria
Correct formula h_cr = 0.0675K² (m, K in km) AND correct statement that the correction is subtracted from the rod reading.
Common Mark Deductions
- Using K in metres instead of kilometres in the formula.
- Stating the correction is added — reversing the sign convention.
- Omitting the unit statement for h_cr (metres).
Key Phrases To Include
- h_cr = 0.0675K²
- K in kilometres
- subtracted from the rod reading
- curvature dominates
Differentiate a turning point (TP) from an intermediate foresight (IF) in profile leveling.
Marks
2
Topic
Profile Leveling — Intermediate Foresight vs. Turning Point
Difficulty
medium
Template Id
T3
Examiner Tip
The key discriminator is the new HI — say it explicitly for TP and explicitly deny it for IF. That single phrase earns the mark for each.
Model Answer
A turning point (TP) is a temporary, stable point where BOTH a foresight (FS) and a subsequent backsight (BS) are taken, thereby transferring the level to a new instrument position and establishing a new Height of Instrument. An intermediate foresight (IF) is a rod reading taken on a station along the profile whose elevation is computed from the current HI only; no backsight is taken on it, so it does NOT establish a new HI. Errors in an IF affect only that station's elevation, whereas errors at a TP propagate through all subsequent elevations.
Question Type
short_answer
Answer Structure
- Sentence 1: Define TP — both FS and BS taken, transfers instrument, establishes new HI [1 mark]
- Sentence 2: Define IF — rod reading only, no new HI, error is localised [1 mark]
Scoring Breakdown
Marks
1
Criteria
Correct definition of TP — temporary stable point that receives both a FS and a BS, allowing the level to be moved and a new HI computed.
Marks
1
Criteria
Correct definition of IF — single rod reading under the existing HI, does NOT produce a new HI, error confined to that point.
Common Mark Deductions
- Stating that an IF establishes a new HI — this is the most critical conceptual error.
- Omitting the fact that a TP receives BOTH a FS and a subsequent BS.
- Confusing IF with a check shot on a benchmark.
Key Phrases To Include
- turning point
- backsight and foresight
- new HI
- intermediate foresight
- does not establish a new HI
- error propagation
A benchmark (BM-A) has an elevation of 100.000 m. A backsight of 1.525 m is read on BM-A, and a foresight of 2.310 m is read on the next point (TP-1). Compute the HI and the elevation of TP-1.
Marks
2
Topic
Differential Leveling — HI Method
Difficulty
easy
Template Id
T4
Examiner Tip
Write both formulas explicitly before substituting. Even if you get the arithmetic wrong, you earn the formula mark — that is often the difference between passing and failing a numerical question.
Model Answer
Given: Elevation of BM-A = 100.000 m BS on BM-A = 1.525 m FS on TP-1 = 2.310 m Step 1 — Height of Instrument: HI = elev(BM-A) + BS HI = 100.000 + 1.525 HI = 101.525 m Step 2 — Elevation of TP-1: elev(TP-1) = HI − FS elev(TP-1) = 101.525 − 2.310 elev(TP-1) = 99.215 m
Question Type
numerical
Answer Structure
- Step 1: Write formula HI = elev + BS and substitute — answer 101.525 m [1 mark]
- Step 2: Write formula elev = HI − FS and substitute — answer 99.215 m [1 mark]
Scoring Breakdown
Marks
1
Criteria
Correct formula and computation of HI = 101.525 m.
Marks
1
Criteria
Correct formula and computation of elev(TP-1) = 99.215 m.
Common Mark Deductions
- Subtracting BS instead of adding it to get HI.
- Adding FS to HI instead of subtracting it.
- Missing units (m) on the final answers.
- Rounding to fewer than 3 decimal places when the problem data has 3 decimal places.
Key Phrases To Include
- HI = elev + BS
- elev = HI − FS
- 101.525 m
- 99.215 m
A level loop starts and ends at BM-1 (elevation = 50.000 m). The sum of all backsights recorded is 8.540 m, and the sum of all foresights is 6.210 m. (a) Find the computed final elevation of BM-1. (b) Verify the loop closure using the arithmetic check.
Marks
2
Topic
Arithmetic Check and Loop Closure
Difficulty
medium
Template Id
T5
Examiner Tip
For a closed loop, always state 'If the loop closed perfectly, Δelev = 0.' Then give the actual value and call it the misclosure. This two-step reasoning earns both marks.
Model Answer
Given: elev(BM-1) = 50.000 m (starting elevation) ΣBS = 8.540 m, ΣFS = 6.210 m (a) Net elevation change and computed final elevation: Δelev = ΣBS − ΣFS = 8.540 − 6.210 = +2.330 m elev_final = 50.000 + 2.330 = 52.330 m (b) Arithmetic check (loop returns to BM-1, true Δelev = 0): Misclosure = elev_final − elev_initial = 52.330 − 50.000 = +2.330 m Since misclosure ≠ 0, the loop does NOT close — there is a 2.330-m error in the run.
Question Type
numerical
Answer Structure
- Part (a): Apply Δelev = ΣBS − ΣFS and add to starting elevation [1 mark]
- Part (b): Compare computed final elevation with the true elevation of BM-1; state misclosure with correct sign [1 mark]
Scoring Breakdown
Marks
1
Criteria
Correct Δelev = +2.330 m and final elevation = 52.330 m.
Marks
1
Criteria
Correct arithmetic check statement and identification of a 2.330-m misclosure (loop does not close).
Common Mark Deductions
- Computing ΣFS − ΣBS (wrong sign) and getting a negative Δelev.
- Failing to state whether the loop closes — just computing a number without interpreting it.
- Forgetting that a closed loop must have Δelev = 0 for perfect closure.
Key Phrases To Include
- ΣBS − ΣFS
- arithmetic check
- misclosure
- Δelev
- loop closure
Compute the combined curvature-and-refraction correction for a line-of-sight distance of 3.5 km. Should this correction be added to or subtracted from the rod reading? Explain.
Marks
3
Topic
Curvature and Refraction
Difficulty
medium
Template Id
T6
Examiner Tip
Board examiners always look for the unit declaration for K. Write 'K = 3.5 km' boldly before substituting — it shows you know the formula's domain and prevents the most common error.
Model Answer
Given: K = 3.5 km Formula: h_cr = 0.0675 K² (h_cr in metres, K in kilometres) Substitution: h_cr = 0.0675 × (3.5)² h_cr = 0.0675 × 12.25 h_cr = 0.827 m (rounded to 3 decimal places) Sign convention: The correction is SUBTRACTED from the observed rod reading. Reason: The Earth's curvature causes the far rod to appear higher than its true position (the horizontal line of sight rises above the curved Earth surface). Atmospheric refraction partially offsets this effect, but curvature dominates. Therefore, the net apparent rod reading is too large by h_cr, and the correction is subtracted to obtain the true reading.
Question Type
numerical
Answer Structure
- Step 1: State the formula h_cr = 0.0675K² with units [1 mark]
- Step 2: Substitute K = 3.5 km and compute h_cr = 0.827 m [1 mark]
- Step 3: State 'subtracted' and explain why — curvature makes rod read too high, refraction partially offsets [1 mark]
Scoring Breakdown
Marks
1
Criteria
Correct formula h_cr = 0.0675K² with explicit statement that K is in km and h_cr is in m.
Marks
1
Criteria
Correct numerical result h_cr = 0.827 m with working shown.
Marks
1
Criteria
Correct sign convention (subtracted) with a clear physical explanation referencing Earth's curvature and atmospheric refraction.
Common Mark Deductions
- Using K = 3500 m (metres) instead of K = 3.5 km — gives a wildly incorrect answer.
- Stating the correction is added instead of subtracted.
- Giving the sign convention without any physical justification — examiners require the 'why'.
- Rounding to only 1 decimal place when input data precision warrants 3.
Key Phrases To Include
- h_cr = 0.0675K²
- K in kilometres
- 0.827 m
- subtracted
- curvature
- atmospheric refraction
- rod reads too high
Explain the purpose of profile leveling and cross-section leveling in route-survey projects. How does each contribute to engineering design?
Marks
3
Topic
Profile and Cross-Section Leveling
Difficulty
medium
Template Id
T7
Examiner Tip
Use the words 'longitudinal' for profile and 'transverse/perpendicular' for cross-section — these contrasting terms immediately signal conceptual clarity to the examiner.
Model Answer
Profile Leveling Profile leveling determines ground elevations at regular intervals (stations) along a route's centerline. The results are plotted as a longitudinal section (profile) showing the existing ground line. Engineers use this profile to design the vertical alignment — computing cut and fill depths at each station, setting grade elevations, and ensuring proper drainage slopes. Cross-Section Leveling Cross-section leveling measures ground elevations at points perpendicular to the centerline at each station, typically at fixed offsets (e.g., 5 m, 10 m left and right). The resulting cross-sectional shapes are used to compute earthwork volumes (cut or fill) by the end-area method or prismoidal formula, which directly determines the cost of grading operations. Design Contribution Together, the profile provides the vertical control for alignment design, while cross-sections provide the data for earthwork quantity estimates — both essential inputs to road, railway, and canal design.
Question Type
short_answer
Answer Structure
- Paragraph 1: Define profile leveling, state it is along the centerline, and link to vertical alignment / longitudinal section design [1 mark]
- Paragraph 2: Define cross-section leveling, state it is perpendicular to centerline at offsets, and link to earthwork volume computation [1 mark]
- Paragraph 3: Synthesise both — how they complement each other in route engineering design [1 mark]
Scoring Breakdown
Marks
1
Criteria
Correct definition of profile leveling (centerline stations, longitudinal section) and its use in vertical alignment and drainage design.
Marks
1
Criteria
Correct definition of cross-section leveling (perpendicular offsets) and its use in earthwork volume estimation.
Marks
1
Criteria
Clear synthesis or comparison of the two methods showing complementary roles in route-survey design.
Common Mark Deductions
- Describing profile and cross-section leveling as identical — missing the perpendicular vs. longitudinal distinction.
- Failing to connect each method to its engineering application (design or earthwork).
- Treating profile leveling as a plan-view survey rather than an elevation survey along the centerline.
Key Phrases To Include
- centerline
- stations
- longitudinal section
- vertical alignment
- perpendicular offsets
- earthwork volumes
- cut and fill
- end-area method
During a differential leveling run, the following data were recorded starting from BM-1 at elevation 215.400 m: Station | BS (m) | FS (m) BM-1 | 1.345 | — TP-1 | 2.120 | 0.875 TP-2 | 1.560 | 1.985 BM-2 | — | 0.660 Compute: (a) the HI at each setup, (b) the elevation of each TP and BM-2, and (c) verify the result using the arithmetic check.
Marks
5
Topic
Differential Leveling — Multi-Setup Run with Arithmetic Check
Difficulty
hard
Template Id
T8
Examiner Tip
Draw a vertical rod-and-level sketch or at minimum a ruled table before calculating. Board examiners for this type of question explicitly allocate 1 mark for a correct, complete table. A messy or unorganised solution loses that mark regardless of numerical accuracy.
Model Answer
Given starting elevation: elev(BM-1) = 215.400 m ───────────────────────────────────────────────────────── STATION | BS (m) | HI (m) | FS (m) | ELEVATION (m) ───────────────────────────────────────────────────────── BM-1 | 1.345 | 216.745 | — | 215.400 TP-1 | 2.120 | 218.110 | 0.875 | 215.870 TP-2 | 1.560 | 217.685 | 1.985 | 216.125 ← wait — recalculate BM-2 | — | — | 0.660 | 217.025 ───────────────────────────────────────────────────────── Step-by-step calculations: Setup 1 (instrument over BM-1): HI₁ = 215.400 + 1.345 = 216.745 m elev(TP-1) = HI₁ − FS(TP-1) = 216.745 − 0.875 = 215.870 m Setup 2 (instrument over TP-1): HI₂ = 215.870 + 2.120 = 217.990 m elev(TP-2) = HI₂ − FS(TP-2) = 217.990 − 1.985 = 216.005 m Setup 3 (instrument over TP-2): HI₃ = 216.005 + 1.560 = 217.565 m elev(BM-2) = HI₃ − FS(BM-2) = 217.565 − 0.660 = 216.905 m (Corrected table:) ───────────────────────────────────────────────────────── STATION | BS (m) | HI (m) | FS (m) | ELEVATION (m) ───────────────────────────────────────────────────────── BM-1 | 1.345 | 216.745 | — | 215.400 TP-1 | 2.120 | 217.990 | 0.875 | 215.870 TP-2 | 1.560 | 217.565 | 1.985 | 216.005 BM-2 | — | — | 0.660 | 216.905 ───────────────────────────────────────────────────────── (c) Arithmetic check: ΣBS = 1.345 + 2.120 + 1.560 = 5.025 m ΣFS = 0.875 + 1.985 + 0.660 = 3.520 m Δelev = ΣBS − ΣFS = 5.025 − 3.520 = +1.505 m Independent check: elev(BM-2) − elev(BM-1) = 216.905 − 215.400 = +1.505 m ✓ The arithmetic check closes — the computations are consistent.
Question Type
numerical
Answer Structure
- Setup layout: Neatly tabulated BS, HI, FS, Elevation columns [1 mark]
- HI₁ = 216.745 m; elev(TP-1) = 215.870 m [1 mark]
- HI₂ = 217.990 m; elev(TP-2) = 216.005 m [1 mark]
- HI₃ = 217.565 m; elev(BM-2) = 216.905 m [1 mark]
- Arithmetic check: ΣBS − ΣFS = +1.505 m = Δelev ✓ [1 mark]
Scoring Breakdown
Marks
1
Criteria
Correct table format with proper column headings and organisation of data.
Marks
1
Criteria
Correct HI₁ = 216.745 m and elev(TP-1) = 215.870 m, with working shown.
Marks
1
Criteria
Correct HI₂ = 217.990 m and elev(TP-2) = 216.005 m, with working shown.
Marks
1
Criteria
Correct HI₃ = 217.565 m and elev(BM-2) = 216.905 m, with working shown.
Marks
1
Criteria
Complete arithmetic check: ΣBS = 5.025, ΣFS = 3.520, Δelev = +1.505 m, verified against direct elevation difference.
Common Mark Deductions
- Reusing HI₁ for all subsequent setups instead of recomputing HI after each TP.
- Adding FS instead of subtracting it when computing an elevation.
- Omitting the arithmetic check entirely — this costs a guaranteed mark.
- Carrying 3 or more errors silently with only a final answer — examiners cannot award method marks without shown work.
- Confusing which BS belongs to which HI (a TP's BS is used for the NEXT setup, not the current one).
Key Phrases To Include
- HI = elev + BS
- elev = HI − FS
- ΣBS − ΣFS = Δelev
- arithmetic check
- turning point
- 216.905 m
- 1.505 m
State the arithmetic check equation for a differential leveling run and explain what each term represents.
Marks
1
Topic
Arithmetic Check
Difficulty
easy
Template Id
T9
Examiner Tip
Memorise the equation in the form shown — 'BS sums first, FS sums second, then elevation difference.' That order matches the mnemonic 'BS adds, FS subtracts.'
Model Answer
ΣBS − ΣFS = elev_last − elev_first ΣBS = sum of all backsight readings; ΣFS = sum of all foresight readings; elev_last and elev_first are the elevations of the final and initial benchmark, respectively. The equation is satisfied when all HI and elevation computations are arithmetically consistent.
Question Type
very_short_answer
Answer Structure
- Write the equation ΣBS − ΣFS = Δelev [0.5 mark]
- Define each term correctly [0.5 mark]
Scoring Breakdown
Marks
1
Criteria
Correct equation ΣBS − ΣFS = elev_last − elev_first (or Δelev) with all four terms correctly identified.
Common Mark Deductions
- Writing ΣFS − ΣBS (reversed sign).
- Stating the check as ΣBS = ΣFS — valid only for a closed loop returning to the same benchmark, not a general open-ended run.
Key Phrases To Include
- ΣBS − ΣFS
- elev_last − elev_first
- arithmetic check
- backsight
- foresight
A surveyor observes a rod reading of 3.750 m at a distance of 4.0 km. Compute the corrected rod reading after applying the combined curvature-and-refraction correction.
Marks
2
Topic
Curvature and Refraction
Difficulty
medium
Template Id
T10
Examiner Tip
Always write 'K = 4.0 km' in your solution header — it signals unit awareness. Then the computation is mechanical and full marks follow.
Model Answer
Given: Observed rod reading = 3.750 m Distance K = 4.0 km Step 1 — Curvature-and-refraction correction: h_cr = 0.0675 K² h_cr = 0.0675 × (4.0)² h_cr = 0.0675 × 16 = 1.080 m Step 2 — Apply correction (subtract, since curvature makes rod appear too high): Corrected rod reading = observed reading − h_cr Corrected rod reading = 3.750 − 1.080 = 2.670 m
Question Type
numerical
Answer Structure
- Step 1: Compute h_cr = 0.0675(4.0)² = 1.080 m [1 mark]
- Step 2: Subtract correction — corrected reading = 2.670 m [1 mark]
Scoring Breakdown
Marks
1
Criteria
Correct computation of h_cr = 1.080 m with formula and K in km explicitly shown.
Marks
1
Criteria
Correct application: corrected reading = 3.750 − 1.080 = 2.670 m, with subtraction justified.
Common Mark Deductions
- Adding 1.080 m instead of subtracting.
- Using K = 4000 m — gives h_cr = 1,080,000 m, an obviously absurd answer not flagged by the student.
- Computing the correction but failing to apply it to the rod reading (stopping after Step 1).
Key Phrases To Include
- h_cr = 0.0675K²
- 1.080 m
- subtract
- corrected rod reading = 2.670 m
A surveyor finds HI = 215.400 m and reads an intermediate foresight (IF) of 1.850 m on Station 1+060. Compute the ground elevation at Station 1+060. Does this IF establish a new HI? Explain.
Marks
3
Topic
Profile Leveling — Intermediate Foresight
Difficulty
medium
Template Id
T11
Examiner Tip
Part 2 of this question is worth 2 marks — the 'No' answer earns only 1. The second mark comes from the reason. Always write: 'Because no backsight is taken on the IF, the HI is NOT changed.'
Model Answer
Given: HI = 215.400 m IF on Sta. 1+060 = 1.850 m Step 1 — Ground elevation at Sta. 1+060: elev = HI − IF elev = 215.400 − 1.850 elev = 213.550 m Step 2 — Does this IF establish a new HI? No. An intermediate foresight is a rod reading taken on a profile station under the CURRENT instrument setup. Because no backsight is subsequently taken on Station 1+060, the level is not moved, and no new HI is computed. The HI remains 215.400 m for all subsequent IF and FS readings in this setup. Rule: Only turning points (TP) — where both a foresight AND a subsequent backsight are taken — establish a new Height of Instrument.
Question Type
numerical
Answer Structure
- Step 1: Apply elev = HI − IF; compute 213.550 m [1 mark]
- Step 2: State 'No' and explain — no BS taken, HI unchanged, only TPs establish new HI [2 marks]
Scoring Breakdown
Marks
1
Criteria
Correct elevation computation: elev = 215.400 − 1.850 = 213.550 m.
Marks
1
Criteria
Clear statement that the IF does NOT establish a new HI, with the reason that no backsight is taken on it.
Marks
1
Criteria
Correct general rule articulated — only turning points, where both FS and BS are taken, produce a new HI.
Common Mark Deductions
- Adding IF to HI instead of subtracting — a direct formula error.
- Saying the IF does establish a new HI — fundamental conceptual error.
- Failing to state the general rule about turning points in Part 2 — loses the third mark.
Key Phrases To Include
- elev = HI − IF
- 213.550 m
- does not establish a new HI
- no backsight taken
- turning point
- HI remains unchanged
Describe the two-peg test for checking the collimation error of a dumpy level. How is the collimation error computed?
Marks
3
Topic
Collimation Error — Two-Peg Test
Difficulty
hard
Template Id
T12
Examiner Tip
Board examiners for the two-peg test question want to see: (1) midpoint = true difference, (2) near-peg = apparent difference, (3) the correction formula. Write all three components clearly, one per paragraph.
Model Answer
Purpose of the Two-Peg Test The two-peg test determines whether the line of collimation of a level is truly horizontal when the bubble is centred — i.e., it checks for collimation (line-of-sight) error. Procedure 1. Set up the level at the midpoint M between two pegs A and B, placed approximately 60–80 m apart. Read rods at A (r₁) and B (r₂). The difference in rod readings (r₁ − r₂) gives the TRUE difference in elevation Δh, because equal sight lengths cancel the collimation error: Δh_true = r₁ − r₂ (from midpoint setup) 2. Move the level close to peg A (within 1–3 m). Read the rod at A again (r₃, short sight — nearly free of error) and at B again (r₄, long sight — full collimation error ε present). 3. The APPARENT elevation difference from the near-A setup: Δh_apparent = r₃ − r₄ Computing the Collimation Error Collimation error per unit length: e = (Δh_apparent − Δh_true) / D_AB where D_AB is the full peg-to-peg distance. If e ≠ 0, the level needs adjustment. The correct rod reading at B (from the near-A position) should be: r₄_correct = r₃ − Δh_true
Question Type
short_answer
Answer Structure
- Para 1: State purpose — check if collimation is horizontal [0.5 mark]
- Para 2 Step 1: Level at midpoint — reads cancel collimation error, gives true Δh [1 mark]
- Para 2 Step 2: Level near one peg — long sight carries full error [0.5 mark]
- Para 3: Formula for collimation error e = (Δh_apparent − Δh_true) / D_AB [1 mark]
Scoring Breakdown
Marks
1
Criteria
Correct explanation of midpoint setup — equal sight lengths eliminate collimation error, giving true Δh.
Marks
1
Criteria
Correct explanation of the near-peg setup — short sight has negligible error, long sight carries full collimation error.
Marks
1
Criteria
Correct formula or method for computing collimation error and identifying the required rod-reading correction.
Common Mark Deductions
- Describing only one setup position — the two-peg test requires TWO specific instrument positions.
- Failing to explain WHY equal sight lengths eliminate the error (the mathematical reasoning earns marks).
- Not providing the correction formula — the 'compute' part of the question is left unanswered.
Key Phrases To Include
- collimation error
- midpoint setup
- equal sight lengths cancel error
- true elevation difference
- near-peg setup
- long sight
- r₄_correct = r₃ − Δh_true
A complete differential level run is conducted from BM-A (elev = 75.000 m) to BM-B. The field notes show: Station | BS (m) | FS (m) BM-A | 2.135 | — TP-1 | 1.820 | 3.015 TP-2 | 2.560 | 1.440 BM-B | — | 2.085 (a) Compute the elevation of BM-B. (b) Apply the arithmetic check. (c) If the published elevation of BM-B is 74.800 m, find the misclosure and express the allowable misclosure for a third-order level line over this distance using the formula: Misclosure_allow = ±12√K mm, where K is the total leveled distance in km. Assume four instrument setups, each with an average sight distance of 60 m.
Marks
5
Topic
Differential Leveling — Complete Run with Accuracy Assessment
Difficulty
hard
Template Id
T13
Examiner Tip
Five-mark questions in Surveying almost always have exactly five scorable elements. Identify them from the question parts and ensure each has a clearly labelled, complete response. Never merge parts — write (a), (b), (c) as separate sections.
Model Answer
Given: elev(BM-A) = 75.000 m Field notes as tabulated. ────────────────────────────────────────────────────────────────── STATION | BS (m) | HI (m) | FS (m) | ELEVATION (m) ────────────────────────────────────────────────────────────────── BM-A | 2.135 | 77.135 | — | 75.000 TP-1 | 1.820 | 75.940 | 3.015 | 74.120 TP-2 | 2.560 | 77.060 | 1.440 | 74.500 ← wait, recalc BM-B | — | — | 2.085 | 74.975 ────────────────────────────────────────────────────────────────── (a) Step-by-step: Setup 1: HI₁ = 75.000 + 2.135 = 77.135 m elev(TP-1) = 77.135 − 3.015 = 74.120 m Setup 2: HI₂ = 74.120 + 1.820 = 75.940 m elev(TP-2) = 75.940 − 1.440 = 74.500 m Setup 3: HI₃ = 74.500 + 2.560 = 77.060 m elev(BM-B) = 77.060 − 2.085 = 74.975 m (b) Arithmetic check: ΣBS = 2.135 + 1.820 + 2.560 = 6.515 m ΣFS = 3.015 + 1.440 + 2.085 = 6.540 m Δelev = ΣBS − ΣFS = 6.515 − 6.540 = −0.025 m Check: elev(BM-B) − elev(BM-A) = 74.975 − 75.000 = −0.025 m ✓ Arithmetic check closes. (c) Misclosure vs. published elevation: Misclosure = computed elev(BM-B) − published elev(BM-B) Misclosure = 74.975 − 74.800 = +0.175 m = +175 mm Total leveled distance: K = (number of setups × 2 sides × avg sight) / 1000 K = (3 setups × 2 × 60 m) / 1000 = 360 m / 1000 = 0.36 km (Note: 3 instrument positions cover 3 forward sights + 2 backsights forward = ~360 m total run) Allowable misclosure (third-order): Misclosure_allow = ±12√K mm = ±12√0.36 = ±12 × 0.6 = ±7.2 mm Since |misclosure| = 175 mm >> 7.2 mm, the leveling does NOT meet third-order accuracy requirements. The survey must be repeated or checked for blunders.
Question Type
numerical
Answer Structure
- Table: Correct HI and elevation columns [1 mark]
- Part (a): elev(BM-B) = 74.975 m with all intermediate values [1 mark]
- Part (b): ΣBS = 6.515, ΣFS = 6.540, Δelev = −0.025 m, arithmetic check confirms ✓ [1 mark]
- Part (c): Misclosure = +175 mm computed and compared with allowable ±7.2 mm [1 mark]
- Conclusion: Does not meet third-order accuracy, survey must be redone [1 mark]
Scoring Breakdown
Marks
1
Criteria
Correct table setup with proper HI computations for all three setups.
Marks
1
Criteria
Correct final elevation BM-B = 74.975 m with all intermediate TP elevations shown.
Marks
1
Criteria
Complete arithmetic check with ΣBS, ΣFS, Δelev computed and confirmed against elevation difference.
Marks
1
Criteria
Correct misclosure = +175 mm and correct allowable misclosure = ±7.2 mm with formula application.
Marks
1
Criteria
Correct engineering conclusion — survey fails third-order accuracy and must be redone.
Common Mark Deductions
- Failing to include a conclusion about whether the survey meets accuracy requirements — the question explicitly asks for this.
- Using K in metres instead of kilometres in the misclosure formula.
- Mixing up misclosure (vs. published BM) with the internal arithmetic check — these are two separate checks.
- Not showing the arithmetic check (Part b) separately from the elevation computation (Part a).
Key Phrases To Include
- HI = elev + BS
- elev = HI − FS
- ΣBS − ΣFS
- arithmetic check
- misclosure
- ±12√K mm
- third-order accuracy
- 74.975 m
- 175 mm
State three sources of error in differential leveling and classify each as systematic or accidental.
Marks
3
Topic
Errors in Leveling
Difficulty
medium
Template Id
T14
Examiner Tip
For a 3-mark enumeration question, give exactly 3 points, each with: name, one-sentence description, and classification. Do not write a paragraph — bullet or numbered format is fastest and clearest.
Model Answer
1. Collimation error (line-of-sight not horizontal when bubble is centred) — SYSTEMATIC. The error accumulates in the same direction with each setup; minimised by balancing BS and FS distances. 2. Rod not held vertically (rod lean) — ACCIDENTAL. The rod may lean in any direction, causing the observed reading to be larger than the true vertical reading; error magnitude and direction vary randomly. 3. Atmospheric refraction variation — SYSTEMATIC (for a single survey session) / ACCIDENTAL (session to session). Refraction bends the line of sight by an amount dependent on atmospheric conditions, generally overestimated by long sights; partially accounted for in the curvature-refraction correction h_cr = 0.0675K².
Question Type
short_answer
Answer Structure
- Error 1: Name + brief description + classification with minimisation note [1 mark]
- Error 2: Name + brief description + classification with minimisation note [1 mark]
- Error 3: Name + brief description + classification with reason [1 mark]
Scoring Breakdown
Marks
1
Criteria
Correctly named and classified first error with a brief description.
Marks
1
Criteria
Correctly named and classified second error with a brief description.
Marks
1
Criteria
Correctly named and classified third error with a brief description.
Common Mark Deductions
- Listing only instrument errors and no human or environmental errors — examiners expect variety across error categories.
- Confusing systematic with accidental — a blunder (e.g., misread rod) is neither; it is a gross error.
- Describing an error without classifying it — the question explicitly asks for classification.
Key Phrases To Include
- collimation error
- systematic
- accidental
- rod lean
- refraction
- balancing backsight and foresight distances
Define a benchmark (BM) as used in leveling surveys and state two characteristics that make a structure suitable for use as a benchmark.
Marks
2
Topic
Benchmarks and Datum Reference
Difficulty
easy
Template Id
T15
Examiner Tip
Mention NAMRIA or mean sea level as the datum reference for Philippine surveys — this contextual detail signals awareness of local practice and earns the definition mark.
Model Answer
A benchmark (BM) is a permanent, stable physical object of known elevation above an adopted datum (in the Philippines, mean sea level as established by the National Mapping and Resource Information Authority, NAMRIA) from which leveling surveys originate or are referenced. Two characteristics required of a suitable benchmark: 1. Permanence — the structure must be stable and resistant to movement, settlement, or destruction over the long term (e.g., concrete monument, brass disc set in bedrock, or a stable building foundation). 2. Accessibility and identifiability — the BM must be easily found and precisely described so that any surveyor can re-occupy the exact point; an ambiguous or hidden mark is not useful as a reference.
Question Type
short_answer
Answer Structure
- Sentence 1: Define benchmark — permanent, stable, known elevation, referenced to datum [1 mark]
- Points 1 and 2: Two correct characteristics with brief justification [1 mark]
Scoring Breakdown
Marks
1
Criteria
Correct definition of benchmark mentioning permanence, known elevation, and datum reference.
Marks
1
Criteria
Two distinct, valid characteristics stated with brief justification (any two of: permanence/stability, accessibility/identifiability, physical durability, official recognition/publication).
Common Mark Deductions
- Defining BM as merely 'a known point' without mentioning permanence and elevation above datum.
- Listing 'high accuracy' as a characteristic — this is a property of the elevation value, not of the physical structure.
- Mentioning the same characteristic twice in different words (e.g., 'stable' and 'unmovable').
Key Phrases To Include
- permanent
- stable
- known elevation
- datum
- mean sea level
- NAMRIA
- permanence
- accessibility
Mark Wise Strategy
Dos
- State the formula and its domain (e.g., 'K in km') in one line.
- Use correct engineering notation and units.
- Answer exactly what is asked — definition, formula, or term.
- Write legibly — a smudged formula earns zero.
Donts
- Do not write introductory sentences ('In surveying, leveling is the process of...').
- Do not leave any blank — a formula attempt earns partial credit even if wrong.
- Do not use abbreviations the examiner might not recognise without defining them.
Marks
1
Strategy
Write the formula or key definition immediately. Do not pad with background information. Examiners scan for the correct equation or the critical phrase — deliver it in the first line.
Expected Length
1–2 lines (one sharp sentence or one equation with brief identification of terms)
Time Allocation
1–2 minutes
Dos
- Label each given quantity at the start (e.g., 'BS = 1.50 m').
- Write the formula before substituting.
- Box or underline the final numerical answer with its unit.
- For two-part questions, clearly label Part (a) and Part (b).
Donts
- Do not merge two separate ideas into one run-on sentence — each idea needs its own line to earn its own mark.
- Do not skip unit conversion steps — write 'K = 2.0 km' explicitly.
- Do not omit the unit from the final answer.
Marks
2
Strategy
Allocate one mark per step or per idea. Write the formula, substitute values with labelled quantities, compute, and state the answer with units. For conceptual questions, write two distinct, clearly separated points.
Expected Length
3–6 lines; for numericals, show formula + substitution + boxed answer
Time Allocation
3–5 minutes
Dos
- Draw a ruled table for multi-setup leveling problems — it forces correct organisation.
- Show all intermediate values (HI for each setup, each TP elevation).
- Apply the arithmetic check as a final step — it shows professional completeness.
- For classification/explanation questions, name → describe → classify, in that order.
Donts
- Do not leave the arithmetic check out — it is worth a dedicated mark.
- Do not write large paragraphs when a table or numbered list communicates more clearly.
- Do not guess and leave errors uncorrected — cross out and rewrite; do not over-write.
Marks
3
Strategy
Structure the answer in clearly numbered steps. For leveling problems, use an HI-method table. For descriptive questions, use three distinct, well-developed paragraphs or a numbered list. Every sentence should earn a mark — avoid redundancy.
Expected Length
8–15 lines; tabular format preferred for leveling calculations
Time Allocation
6–8 minutes
Dos
- List all given data in a 'Given:' block at the top.
- Set up a complete HI-method table with all columns before computing.
- Write each formula before substituting values.
- State an engineering conclusion — especially for accuracy-assessment questions.
- Show the complete arithmetic check with ΣBS, ΣFS, Δelev, and confirmation statement.
Donts
- Do not start computing before organising given data — wasted time and column errors result.
- Do not omit the engineering conclusion for questions that compare computed vs. allowable misclosure.
- Do not cram everything into a single column — board examiners penalise unreadable solutions.
- Do not use pencil smudges or illegible handwriting — marks cannot be awarded for answers that cannot be read.
Marks
5
Strategy
Treat the 5-mark question as five separate 1-mark items. Identify all five scorable elements from the question parts before writing. Use headings, tables, and clearly labelled steps. Reserve 2 minutes at the end to verify the arithmetic check and re-read your answer for missing units or sign errors.
Expected Length
Full tabulated solution plus arithmetic check plus conclusion/interpretation; 20–35 lines
Time Allocation
12–15 minutes
General Answer Writing Tips
- Always write the governing formula first before substituting numbers — examiners award a formula mark even if your arithmetic is wrong.
- Label every quantity with its symbol and unit (e.g., BS = 1.50 m, not just '1.50'). Missing units is the single most common deduction in numerical surveying questions.
- Show the arithmetic check (ΣBS − ΣFS = Δelev) explicitly whenever a level-run table is given — it signals professional rigor and earns a dedicated mark.
- State whether K is in kilometres when using h_cr = 0.0675K² — examiners flag unit confusion as a conceptual error worth a full mark deduction.
- For differential-leveling table questions, set up a neat HI–FS table with columns BM/TP, BS, HI, FS, and Elevation. A disorganised table is hard to follow and loses presentation marks.
- Distinguish intermediate foresight (IF) from turning-point foresight (FS) in your answer — IF readings do NOT establish a new HI; confusing the two is a classic board-exam error.
- After computing a final elevation, verify it using the arithmetic check. Write 'Check: ΣBS − ΣFS = Δelev ✓' to demonstrate self-verification — examiners reward this habit.
- Round only at the final step, carrying at least four decimal places through intermediate calculations, then express the answer to the precision stated in the problem (usually 3 decimal places for elevations in metres).
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