FUNDAMENTAL SURVEYING Mathematics and Statistics 1 — Questions and Answers
Question 1: What is the sum of interior angles of a closed traverse with 5 sides?
- 360°
- 540° (Correct answer)
- 720°
- 900°
Correct answer: 540°
The sum of interior angles of a closed polygon is (n-2) × 180°, so (5-2) × 180° = 540°.
Question 2: A slope distance of 500 ft is measured at a vertical angle of 10°. What is the horizontal distance?
- 492.4 ft (Correct answer)
- 500.0 ft
- 507.6 ft
- 485.2 ft
Correct answer: 492.4 ft
Horizontal distance = slope distance × cos(vertical angle) = 500 × cos(10°) ≈ 492.4 ft.
Question 3: What is the standard deviation of a series of measurements: 10.1, 9.9, 10.0, 10.2, 9.8?
- 0.158 (Correct answer)
- 0.141
- 0.200
- 0.100
Correct answer: 0.158
The standard deviation of this data set (mean = 10.0) is approximately 0.158.
Question 4: In surveying, the propagation of random errors follows which law?
- Law of sines
- Law of cosines
- Law of error propagation (Correct answer)
- Gaussian elimination
Correct answer: Law of error propagation
The law of error propagation states that the variance of a function equals the sum of squared partial derivatives times the respective variances.
Question 5: What does a 90% confidence interval mean in surveying measurements?
- 90% of observations fall within the interval
- There is a 90% probability the true value lies within the interval (Correct answer)
- Only 10% of measurements are incorrect
- The measurement error is less than 10%
Correct answer: There is a 90% probability the true value lies within the interval
A 90% confidence interval means there is a 90% probability that the true value falls within the stated range.
Question 6: A line has a bearing of N 45° E. What is its azimuth from north?
- 45° (Correct answer)
- 135°
- 315°
- 225°
Correct answer: 45°
An azimuth is measured clockwise from north, so N 45° E converts directly to an azimuth of 45°.
FUNDAMENTAL SURVEYING Mathematics and Statistics 1
What is the sum of interior angles of a closed traverse with 5 sides?