## 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 an experienced CE review instructor.

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## MATHalino Now Offers 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.

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## 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.

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**Problem**

The area of a park on a map is 600 mm^{2}. If the scale of the map is 1 to 40,000 determine the true area of the park in hectares (1 hectare = 10^{4} m^{2}).

A. 112 | C. 96 |

B. 84 | D. 120 |

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**Situation**

The three-hinged arch shown below is loaded with symmetrically placed concentrated loads as shown in the figure below.

The loads are as follows:

$$P_1 = 90 ~ \text{kN} \qquad P_2 = 240 ~ \text{kN}$$

The dimensions are:

$$H = 8 ~ \text{m} \qquad S = 4 ~ \text{kN}$$

Calculate the following:

**1.** The horizontal reaction at *A*.

A. 0 | C. 330 kN |

B. 285 kN | D. 436 kN |

**2.** The total reaction at *B*.

A. 0 | C. 330 kN |

B. 285 kN | D. 436 kN |

**3.** The vertical reaction at *C*.

A. 0 | C. 330 kN |

B. 285 kN | D. 436 kN |

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**Problem**

Evaluate $\displaystyle \int_0^1 \dfrac{x \, dx}{x^2 + 2}$.

A. 0.2027 | C. 0.2270 |

B. 0.2207 | D. 0.2072 |

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**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 |

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**Problem**

Calculate the area enclosed by the curve $x^2 + y^2 - 10x + 4y - 196 = 0$.

A. 15π |
C. 169π |

B. 13π |
D. 225π |

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**Problem**

The first three terms of a geometric progression are 2*x*, 4*x* + 14 and 20*x* - 14. Find the sum of the first ten terms.

A. 413,633 | C. 489,335 |

B. 498,533 | D. 431,336 |

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