## Quiz in Basic Mathematics

Evaluate yourself with our basic math problems for engineering. Each problem are carefully selected so that every item in this quiz can be answered by basic principle if not by common sense.

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## MATHalino Now Offers Online Courses

Creating an online course is monumental specially to small websites 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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**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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**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 |

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