Problem
Mar wants to make a box with no lid from a rectangular sheet of cardboard that is 18 inches by 24 inches. The box is to be made by cutting a square of side x from each corner of the sheet and folding up the sides. Find the value of x that maximizes the volume of the box.

A.   4.3 inches C.   10.6 inches
B.   5.2 inches D.   3.4 inches

 

Situation
An investment of P250,000 is made at the end of each year with interest of 2.5% compounded annually.

  1. Determine the equal-payment-series compound-amount factor after 10 years.
    A.   11.203 C.   9.632
    B.   10.578 D.   8.736
  2. Determine the total amount of the investment after 10 years.
    A.   P2,800,000.00 C.   P2,400,000.00
    B.   P2,600,000.00 D.   P2,200,000.00
  3. How long (in years) will it take for the investment to amount to P10,000,000.00?
    A.   25 C.   15
    B.   18 D.   28

 

Situation
Given:

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

 

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

2014-dec-design-simple-beam-with-overhang.jpg

 

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

 

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.
 

MATHalino Launches New Online Courses

Jhun Vert
This is not a promotional post. This is about my experience in building the platform for online courses.
online-course.jpg

 

Creating an online course is monumental, especially for a small website like MATHalino. Despite being managed by only one person from the ground up, the development of this functionality has been progressing gradually. I have been conceiving this feature for as long as I can remember, even before online courses became common in the Philippines.

What prevented me from implementing it earlier came down to three factors.