May 2016

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

 

Situation
Given:

Beam Section, b × h = 300 mm × 450 mm
Effective Depth, d = 380 mm
Compressive Strength, fc' = 30 MPa
Steel Strength, fy = 415 MPa
  1. The beam is simply supported on a span of 5 m, and carries the following loads:
    Superimposed Dead Load = 16 kN/m
    Live Load = 14 kN/m

    What is the maximum moment, Mu (kN·m), at ultimate condition? $U = 1.4D + 1.7L$

    A.   144 C.   104
    B.   158 D.   195
  2. Find the number of 16 mm diameter bars required if the design moment at ultimate loads is 200 kN·m.
    A.   2 C.   6
    B.   4 D.   8
  3. If the beam carries an ultimate concentrated load of 50 kN at midspan, what is the number of 16 mm diameter bars required?
    A.   2 C.   4
    B.   3 D.   5

 

Problem
A rectangular waterfront lot has a perimeter of 1000 feet. To create a sense of privacy, the lot owner decides to fence along three sides excluding the sides that fronts the water. An expensive fencing along the lot’s front length costs Php25 per foot, and an inexpensive fencing along two side widths costs only Php5 per foot. The total cost of the fencing along all three sides comes to Php9500. What is the lot’s dimensions?

A.   300 feet by 100 feet C.   400 feet by 200 feet
B.   400 feet by 100 feet D.   300 feet by 200 feet

 

Problem
A salesperson earns \$600 per month plus a commission of 20% of sales. Find the minimum amount of sales needed to receive a total income of at least \$1500 per month.

A.   \$1500 C.   \$4500
B.   \$3500 D.   \$2500

 

Problem
The tide in Bay of Fundy rises and falls every 13 hours. The depth of the water at a certain point in the bay is modeled by a function d = 5 sin (2π/13)t + 9, where t is time in hours and d is depth in meters. Find the depth at t = 13/4 (high tide) and t = 39/4 (low tide).

  1. The depth of the high tide is 15 meters and the depth of the low tide is 3 meters.
  2. The depth of the high tide is 16 meters and the depth of the low tide is 2 meters.
  3. The depth of the high tide is 14 meters and the depth of the low tide is 4 meters.
  4. The depth of the high tide is 17 meters and the depth of the low tide is 1 meter.

 

Problem
A contractor estimates that he could finish a project in 15 days if he has 20 men. At the start, he hired 10 men then after 6 days, 10 more men are added. How many days was the project delayed?

A.   5 C.   6
B.   3 D.   4

 

Answer Key

Problem
Given the position function x(t) = t4 - 8t2, find the distance that the particle travels at t = 0 to t = 4.

A.   160 C.   140
B.   150 D.   130

 

Problem
A given alloy contains 20% copper and 5% tin. How many pounds of copper and of tin must be melted with 100 lb of the given alloy to produce another alloy analyzing 30% copper and 10% tin? All percentages are by weight.

A.   20.5 lb copper and 4.5 lb tin
B.   17.5 lb copper and 7.5 lb tin
C.   19.5 lb copper and 5.5 lb tin
D.   18.5 lb copper and 6.5 lb tin

 

2016-may-math-mixture-problem-copper-tin-alloy.gif

 

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