# Mathematics, Surveying and Transportation Engineering

**MSTE - Mathematics, Surveying and Transportation Engineering
Common name: Math**

Algebra, Trigonometry, Statistics, Geometry, Calculus, Differential Equations, Engineering Mechanics, Engineering Economy, Surveying, Transportation Engineering

**Problem**

If the first derivative of the equation of a curve is a constant, the curve is:

A. circle | C. hyperbola |

B. straight line | D. parabola |

**Problem**

A germ population has a growth curve $Ae^{0.4t}$. At what value of $t$ does its original value doubled?

A. t = 7.13 |
C. t = 1.73 |

B. t = 1.37 |
D. t = 3.71 |

**Problem**

The sum and product of three distinct positive integers are 15 and 45, respectively. What is the smallest integer?

A. 1 | C. 5 |

B. 9 | D. 3 |

**Problem**

A contractor can buy a dump trucks for P800,000 each (surplus) or rent them for P1,189 per truck per day. The truck has salvage value of P100,000 at the end of its useful life of 5 years. Annual cost of maintenance is P20,000. If money is worth 14% per annum, determine the number of days per year that a truck must be used to warrant the purchase of the truck.

A. 200 | C. 198 |

B. 199 | D. 197 |

**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.

- Determine the equal-payment-series compound-amount factor after 10 years.
A. 11.203 C. 9.632 B. 10.578 D. 8.736 - 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 - 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

**Problem**

A train is moving at the rate of 8 mi/h along a piece of circular track of radius 2500 ft. Through what angle does it turn in 1 min?

A. 15.18° | C. 13.18° |

B. 13.16° | D. 16.13° |

**Problem**

Find the Cartesian equation of the curve represented by $x = 4t + 3$ and $y = 16t^2 - 9$, -∞ < *t* < +∞.

A. $y = x^2 + 6x$ | C. $y = x^2 + 4x$ |

B. $y = x^2 - 6x$ | D. $y = x^2 - 4x$ |

**Problem**

Find the equation of a sphere of radius 3 and tangent to all three coordinate planes if the center is on the first octant.

A. $x^2 + y^2 + z^2 - 9 = 0$ |

B. $x^2 + y^2 + z^2 - 6x - 6y - 6z + 18 = 0$ |

C. $x^2 + y^2 + z^2 - 4x - 4y - 4z + 12 = 0$ |

D. $x^2 + y^2 + z^2 - 8x - 8y - 8z + 14 = 0$ |