Surveying practice questions

Answer: B) 1,950 m²

The coordinate (shoelace) method gives twice the area as Σ(x_i·y_{i+1} − x_{i+1}·y_i) = 3,900 m², so the parcel area is 1,950 m².

• AIncorrect. This multiplies the average of the two horizontal sides (55 m) by the average of the two vertical sides (35 m). That is not valid for an irregular quadrilateral.
• BCorrect. Σ(x_i·y_{i+1} − x_{i+1}·y_i) = 0 + 2,400 + 1,500 + 0 = 3,900, and A = 3,900/2 = 1,950 m².
• CIncorrect. This is the 60 m × 40 m bounding rectangle. It includes two corner triangles (200 m² and 250 m²) that lie outside the parcel.
• DIncorrect. This is the coordinate cross-product sum before dividing by 2, which equals twice the area.

Answer: B) Horizontal datum

• AIncorrect. That's NAVD 88.
• BCorrect. NAVD 88 is the vertical datum.
• CIncorrect. It's a datum.
• DIncorrect. It's a datum.

Answer: C) 125 m

• AIncorrect. Multiply, don't divide.
• BIncorrect. Multiply by 100.
• CCorrect. D = 100 × rod interval.
• DIncorrect. Recheck the calculation.

Answer: B) 99.62 m

• AIncorrect. That's the vertical component.
• BCorrect. \(100\cos 5^\circ\).
• CIncorrect. The horizontal distance is shorter.
• DIncorrect. Use the cosine of the slope angle.

Answer: A) The national vertical datum that elevations (orthometric heights) are referenced to

NAVD 88 is the North American Vertical Datum of 1988, the U.S. reference for elevations, while NAD 83 is the horizontal datum. NGS plans to replace them with NAPGD2022 and NATRF2022, but the current datums remain official until that transition is complete.

• ACorrect. NAVD 88 is the North American Vertical Datum of 1988, the official U.S. vertical datum within the National Spatial Reference System. NGS plans to replace it with the North American-Pacific Geopotential Datum of 2022 (NAPGD2022), but the current datums remain official until the modernized system is approved.
• BIncorrect. That describes NAD 83 (North American Datum of 1983), which NGS plans to replace with NATRF2022 and related terrestrial reference frames.
• CIncorrect. A geoid model gives the separation between the ellipsoid and the vertical datum surface, so GNSS ellipsoid heights can be converted to NAVD 88 elevations. The model is a conversion tool, not the datum itself.
• DIncorrect. Mean lower low water (MLLW) is a local tidal datum based on observed tides. NAVD 88 is a fixed geodetic vertical datum, not a tidal datum.

Answer: B) 100.0 ft east

• AIncorrect. That's the latitude.
• BCorrect. Departure = \(L\sin\theta = 200\sin 30^\circ\).
• CIncorrect. An east bearing gives positive departure.
• DIncorrect. Use the sine of the bearing.

Answer: B) Permanent point of known elevation

• AIncorrect. That's a turning point.
• BCorrect. Used as a leveling reference.
• CIncorrect. It's a known-elevation point.
• DIncorrect. It's a known-elevation point.

Answer: D) 540°

• AIncorrect. That's for six sides.
• BIncorrect. That's for a quadrilateral.
• CIncorrect. That's for seven sides.
• DCorrect. (n − 2) × 180°.

Answer: D) 106.1 ft east

• AIncorrect. That uses sin 30°.
• BIncorrect. A bearing of S 45° E runs east.
• CIncorrect. Departure is a component.
• DCorrect. \(150 \sin 45°\), east of the meridian.

Answer: A) Line of sight is horizontal when the instrument is leveled

The two-peg test detects collimation error, where the line of sight is not horizontal even though the level is leveled. It compares the elevation difference between two pegs measured from a midway setup with one measured from a setup near one peg.

• ACorrect. The test compares the elevation difference between two pegs from a setup midway between them (which cancels collimation error) with the difference from a setup near one peg. If the two differ, the line of sight is inclined (collimation error).
• BIncorrect. Whether the vertical axis is plumb is checked by adjusting the circular or plate bubble (centering it, rotating the instrument 180° and checking it stays centered), not by the two-peg test.
• CIncorrect. Crosshair orientation is checked by sighting a point at one end of the horizontal hair and turning the instrument to see if the point stays on the hair. It is a separate check from the two-peg test.
• DIncorrect. Rod graduations are checked by calibrating the rod against a standard tape or calibration facility. The two-peg test checks the instrument, not the rod.