MSTE - Mathematics, Surveying and Transportation Engineering
Common name: Math
Algebra, Trigonometry, Statistics, Geometry, Calculus, Differential Equations, Engineering Mechanics, Engineering Economy, Surveying, Transportation Engineering
Problem
Find the equation of a sphere of radius 3 and tangent to all three coordinate planes if the center is on the first octant.
| A. $x^2 + y^2 + z^2 - 9 = 0$ |
| B. $x^2 + y^2 + z^2 - 6x - 6y - 6z + 18 = 0$ |
| C. $x^2 + y^2 + z^2 - 4x - 4y - 4z + 12 = 0$ |
| D. $x^2 + y^2 + z^2 - 8x - 8y - 8z + 14 = 0$ |
Problem
The area of a park on a map is 600 mm2. If the scale of the map is 1 to 40,000 determine the true area of the park in hectares (1 hectare = 104 m2).
| A. 112 | C. 96 |
| B. 84 | D. 120 |
Problem
Evaluate $\displaystyle \int_0^1 \dfrac{x \, dx}{x^2 + 2}$.
| A. 0.2027 | C. 0.2270 |
| B. 0.2207 | D. 0.2072 |
Problem
Determine the radius of curvature of the curve $x = y^3$ at point (1, 1).
| A. 5.27 | C. 5.56 |
| B. 5.65 | D. 5.72 |
Problem
Calculate the area enclosed by the curve $x^2 + y^2 - 10x + 4y - 196 = 0$.
| A. 15π | C. 169π |
| B. 13π | D. 225π |
Problem
The first three terms of a geometric progression are 2x, 4x + 14 and 20x - 14. Find the sum of the first ten terms.
| A. 413,633 | C. 489,335 |
| B. 498,533 | D. 431,336 |
Problem
A 50-m steel tape that is is 0.02 m too long was used to measure the distance between two points A and B. If the measured distance was 160.42 m, calculate the correct distance between A and B.
| A. 160.356 m | C. 160.844 m |
| B. 160.484 m | D. 160.563 m |
Problem
A circle has an equation of $x^2 + y^2 + 2cy = 0$. Find the value of $c$ when the length of the tangent from (5, 4) to the circle is equal to one.
| A. 5 | C. 3 |
| B. -3 | D. -5 |
Problem
Calculate the acute angle between two intersecting surfaces whose equations are as follows:
$$2x - 4y - z = -5$$
$$3x + 4y + 5z = -6$$
| A. 62.4° | C. 42.6° |
| B. 64.2° | D. 46.2° |
Problem
If $\arcsin (3x - 4y) = 1.571$ and $\arccos (x - y) = 1.047$, what is the value of $x$?
| A. 0.5 | C. 1.5 |
| B. 1.0 | D. 2.0 |
