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.   $x^2 + y^2 + z^2 - 8x - 8y - 8z + 14 = 0$



Beam Section, b × h = 300 mm × 450 mm
Effective Depth, d = 380 mm
Compressive Strength, fc' = 30 MPa
Steel Strength, fy = 415 MPa
  1. The beam is simply supported on a span of 5 m, and carries the following loads:
    Superimposed Dead Load = 16 kN/m
    Live Load = 14 kN/m

    What is the maximum moment, Mu (kN·m), at ultimate condition? $U = 1.4D + 1.7L$

    A.   144 C.   104
    B.   158 D.   195
  2. Find the number of 16 mm diameter bars required if the design moment at ultimate loads is 200 kN·m.
    A.   2 C.   6
    B.   4 D.   8
  3. If the beam carries an ultimate concentrated load of 50 kN at midspan, what is the number of 16 mm diameter bars required?
    A.   2 C.   4
    B.   3 D.   5


The total length of the beam shown below is 10 m and the uniform load $w_o$ is equal to 15 kN/m.



1.   What is the moment at midspan if x = 2 m?

A.   37.5 kN·m C.   -187.5 kN·m
B.   -37.5 kN·m D.   187.5 kN·m

2.   Find the length of overhang x, so that the moment at midspan is zero.

A.   2.5 m C.   2.4 m
B.   2.6 m D.   2.7 m

3.   Find the span L so that the maximum moment in the beam is the least possible value.

A.   5.90 m C.   5.92 m
B.   5.88 m D.   5.86 m


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Conceptual Quiz

Learn or test your concepts and terminology knowledge with this quiz.

Version: 0.5
Number of questions in the bank: 56 (as of June 23, 2021)

High school math questions Engineering math questions Engineering sciences questions Civil engineering questions
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Equations of lines in general form directly from slopes

In this blog, I will discuss the technique will easily allow us to write the equations of lines directly to its general form, without going through the classical methods. All we need is its slope.

MSTE Refresher Lite

MSTE - Mathematics, Surveying and Transportation Engineering
Review Instructor: Jhun Vert
Language: Taglish, more on Tagalog

Get yourself acquainted with the CE board exam problems in MSTE. Experience the level of difficulty you will encounter in the actual board examination and feel the similar time-constraint in solving problems. Learn how to solve the problem in the most efficient way and improve your problem solving strategies from experienced CE review instructor.

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MATHalino Now Offers Online Courses

This is not an announcement or promotional post. This is about my experience in building the platform for online courses.


Creating an online course is monumental specially to a small website like MATHalino. Despite being manned by one person from the ground up, the development of this functionality is actually progressing by degrees. I've been conceiving this feature as far as I can recall, way before online courses become a common thing in the Philippines. What makes me unable to implement it before comes from three factors.

Basic Algebra Review

Is this course right for you?
Although we named this course Basic Algebra Review, this is actually designed for those who already completed their Algebra subject in engineering curriculum, hence, review. Problems presented in later topics are not really for beginners and solutions presented here assumed that you already earned the credits of College Algebra from your university.

Beginners however are also welcome to join, but never consider this course as a substitute to the long standing and thoroughly tested university program. Don't forget that your professor is the one holding the authority of the subject. Whenever contradiction arises between my teaching and that of your professor, do not follow me, listen to your professor. You may consider this course, however, as a supplement material to the already rich Algebra materials handed to you in your school.

The solid pole shown in the figure is loaded with a vertical load P = 25 kN and lateral load H = 0.95 kN. The pole is 3 m high, 300 mm diameter and weighs 22 kN/m3.



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



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