# May 2016

**Problem**

Chords *AB* and *CD* intersect each other at *E* inside the circle. *AE* = 8 cm, *CE* = 12 cm, and *DE* = 20 cm. If *AB* is the diameter of the circle, compute the area of *AEC*.

A. 61.04 cm^{2} |
C. 39.84 cm^{2} |

B. 52.05 cm^{2} |
D. 48.62 cm^{2} |

**Problem**

A point moves in the plane according to equations *x* = *t*^{2} + 2*t* and *y* = 2*t*^{3} - 6*t*. Find *dy*/*dx* when *t* = 0, 2, 5.

A. -3, -3, -12 | C. 3, 3, 12 |

B. 3, -3, 12 | D. -3, 3, 12 |

**Situation**

An open cylindrical vessel 1.3 m in diameter and 2.1 m high is 2/3 full of water. If rotated about the vertical axis at a constant angular speed of 90 rpm,

1. Determine how high is the paraboloid formed of the water surface.

A. 1.26 m | C. 2.46 m |

B. 1.91 m | D. 1.35 m |

2. Determine the amount of water that will be spilled out.

A. 140 L | C. 341 L |

B. 152 L | D. 146 L |

3. What should have been the least height of the vessel so that no water is spilled out?

A. 2.87 m | C. 3.15 m |

B. 2.55 m | D. 2.36 m |

**Problem**

Find the distance from the point *A*(1, 5, -3) to the plane 4*x* + *y* + 8*z* + 33 = 0.

A. 1/2 | C. 2/3 |

B. 2 | D. 1.5 |

**Problem**

Evaluate $\displaystyle \int_0^9 \dfrac{1}{\sqrt{1 + \sqrt{x}}}$

A. 4.667 | C. 5.333 |

B. 3.227 | D. 6.333 |

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