**Problem**

Which of the following is the derivative with respect to *x* of $(x + 1)^3 - x^3$?

A. 6x + 3 |
C. 1 + 2x - 3x^{2} |

B. 3x^{2} + 2x + 1 |
D. 6x - 3 |

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**Problem**

How many terms from the progression 3, 5, 7, 9, ... must be taken in order that their sum will be 2600?

A. 80 | C. 50 |

B. 60 | D. 70 |

## Find the probability that somebody is healthy given that they have positive test result?

**Problem**

A disease is known to affect 1 in 10,000 people. A screening test for the disease shows a positive result for 99% of the people with the disease. The test also shows positive for 2% of people who do not have the disease. Find the probability that somebody is healthy given that they have positive test result?

A. 99.51% | C. 46.32% |

B. 12.32% | D. 78.36% |

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## What is the probability that 4 depth charges will sink the submarine?

**Problem**

Assume that a single depth charge has a probability of 1/2 of sinking a submarine, 1/4 of damage and 1/4 of missing. Assume also that two damaging explosions sink the sub. What is the probability that 4 depth charges will sink the sub?

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**Problem**

Find the equation of the curve passing through the point (3, 2) and having s slope 5*x*^{2} - *x* + 1 at every point (*x*, *y*).

A. $y = \frac{5}{3}x^3 - \frac{1}{2}x^2 + x - \frac{31}{3}$ | C. $y = 5x^3 - 2x^2 + x - 118$ |

B. $y = 5x^3 - 2x^2 + x - 31$ | D. $y = \frac{5}{3}x^3 - \frac{1}{2}x^2 + x - \frac{83}{2}$ |

**Problem**

A coin is so unbalanced that you are likely to get two heads in two successive throws as you are to get tails in one. What is the probability of getting heads in a single throw?

A. 0.168 | C. 0.681 |

B. 0.618 | D. 0.816 |

## Probability Problems Involving Coins

When you toss a coin, the outcome can either be *head* or *tail*. If the coin is so balanced that these two outcomes are equally likely to occur, then the probability that the outcome is head is 1/2, and the probability that the outcome is tail is also 1/2.

**Example**

A coin is tossed three times. What is the probability that the head will appear only once?

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## Civil Engineering Board Exam Subjects

**Philippines' CE Board Subjects**

- Mathematics, Surveying and Transportation Engineering
- Hydraulics and Geotechnical Engineering
- Structural Engineering and Construction

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## 01 Area of a right triangle of known median bisecting the hypotenuse

**Problem**

The median of a right triangle drawn to the hypotenuse is 3 cm long and makes an angle of 60° with it. Find the area of the triangle.

A. 7.97 cm^{2} |
C. 8.79 cm^{2} |

B. 8.97 cm^{2} |
D. 7.79 cm^{2} |

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