Mathematics, Surveying and Transportation Engineering

A solid spherical ball remolded into a hollow spherical ball

A 523.6 cm3 solid spherical steel ball was melted and remolded into a hollow steel ball so that the hollow diameter is equal to the diameter of the original steel ball. Find the thickness of the hollow steel ball.

A.   1.3 cm C.   1.2 cm
B.   1.5 cm D.   1.6 cm


Slope of a Curve with Given Parametric Equations

A point moves in the plane according to equations x = t2 + 2t and y = 2t3 - 6t. Find dy/dx when t = 0, 2, 5.

A.   -3, -3, -12 C.   3, 3, 12
B.   3, -3, 12 D.   -3, 3, 12


Distance From a Point to a Plane

Find the distance from the point A(1, 5, -3) to the plane 4x + y + 8z + 33 = 0.

A.   1/2 C.   2/3
B.   2 D.   1.5


Area Bounded by Intersecting Chords in a Circle

Chords AB and CD intersect each other at E inside the circle. AE = 8 cm, CE = 12 cm, and DE = 20 cm. If AB is the diameter of the circle, compute the area of AEC.

A.   61.04 cm2 C.   39.84 cm2
B.   52.05 cm2 D.   48.62 cm2


Amount of Sales Needed to Receive a Specified Income

A salesperson earns P60,000 per month plus a commission of 20% of sales. Find the minimum amount of sales needed to receive a total income of at least P150,000 per month.

A.   P150,000 C.   P450,000
B.   P350,000 D.   P250,000


Fundamental Frequency of Fourier Equation in Cosine Form

Given the Fourier equation:

f(t) = 5 cos (20πt) + 2 cos (40πt) + cos (80πt)

What is the fundamental frequency?

A.   10 C.   40
B.   20 D.   30


Find the Integral of dx / sqrt(1 + sqrt(x))

Evaluate $\displaystyle \int_0^9 \dfrac{1}{\sqrt{1 + \sqrt{x}}}$

A.   4.667 C.   5.333
B.   3.227 D.   6.333


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