Math & Engineering Economic Evaluation Exam

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Questions and Answers

Which of the following is the standard acceleration due to gravity in the English unit?

  • 32.2 fps² (correct)
  • 9.8066 fps²
  • 980.66 fps²
  • 32.2 ips²

What is the value of 1 radian in degrees?

57.3°

How many degrees are 4800 mils?

270°

If the density of a gas is 0.003 slug/ft³, what is the specific weight of the gas?

<p>15.2 N/m³ (C)</p> Signup and view all the answers

If the specific weight of a liquid is 58.5 lbf per cubic foot, what is the specific volume of the liquid?

<p>1.0675 cm³/g (A)</p> Signup and view all the answers

From a deck of ordinary cards, what is the probability of drawing a heart or face card?

<p>42.31% (A)</p> Signup and view all the answers

A perfect gas is expanded polytropically with an initial volume and temperature of 0.06 m³ and 147 °C respectively. If the final volume and temperature are 0.21 m³ and 21 °C respectively, what is the index of the expansion?

<p>1.285 (A)</p> Signup and view all the answers

If the loan was for 15 months at 16.8% interest a year and the repayment on a loan was P12,100.00, how much was the principal?

<p>P10,000.00 (B)</p> Signup and view all the answers

Determine the accumulated value of P2,000.00 in 5 years it is invested at 11% compounded quarterly.

<p>P3,440.00 (D)</p> Signup and view all the answers

The sum of P15,000.00, deposited in an account earning 4% per annum compounded quarterly, will become P18,302.85. Determine the effective rate of interest per year.

<p>4.06% (B)</p> Signup and view all the answers

If a machine is purchased on installment and the buyer makes an P80,000.00 down payment and owes a balance of P150,000 in 2 years. Determine the machine cash value if money is worth 14% compounded quarterly.

<p>P193,912.00 (D)</p> Signup and view all the answers

Find the number of years when P2,500.00 is compounded to P5,800.00 if invested at 12% compounded quarterly.

<p>7.12 years (D)</p> Signup and view all the answers

What is the effective rate equivalent of 12% compounded quarterly?

<p>12.55% (D)</p> Signup and view all the answers

What rate compounded-quarterly is equivalent to 14% compounded semi-annually?

<p>13.76% (C)</p> Signup and view all the answers

Celestino owes P500, due in 3 years and P800 due in 7 years. He is allowed to settle these obligations by a single payment on the 6th year. Find how much he has to pay on the 6th year if money is worth 14% compounded semi-annually.

<p>P1,449.12 (D)</p> Signup and view all the answers

Cleofas borrowed P2,000.00 from a bank and agreed to pay the loan at the end of one year. The bank discounted the loan and gave him P1950 in cash. Determine the rate of discount.

<p>2.5% (A)</p> Signup and view all the answers

A machine was purchased under these terms: P30,000 down and P5,000 each month for 5 years. If money is worth 12% compounded monthly, what is the cash price of the machine?

<p>P254,775.19 (D)</p> Signup and view all the answers

Determine the amount that must be deposited every 3 months in a fund paying 12% compounded quarterly in order to have P25,000 in 8 years.

<p>P476.17 (D)</p> Signup and view all the answers

What is the acid test ratio?

<p>The ratio of current assets (exclusive of inventory) to the total current liabilities. (B)</p> Signup and view all the answers

How do call an energy required to move 1 Coulomb of charge through an element?

<p>Voltage (C)</p> Signup and view all the answers

This is a number sequence where the succeeding term is obtained by adding the last pair of preceding terms such as the sequence (1, 1, 2, 3 5, 8 ...). How do you call this number sequence?

<p>Fibonacci number (C)</p> Signup and view all the answers

If the roots of an equation are zero, then, how do you classify the solutions?

<p>Trivial solutions (A)</p> Signup and view all the answers

In electricity, how do you call the rate of charge flow?

<p>Current (B)</p> Signup and view all the answers

This law in electrical circuits states, “The algebraic sum of currents entering a node (or a closed boundary) is zero”. How do you call this law?

<p>Kirrchoff's current law (B)</p> Signup and view all the answers

This law in electrical circuits state, “The algebraic sum of all voltages around a closed path (or loop) is zero”. How do you call this law?

<p>Kirchhoff's voltage law (D)</p> Signup and view all the answers

In electrical, what is the SI unit of conductance?

<p>Mho (A)</p> Signup and view all the answers

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Flashcards

Standard acceleration due to gravity

In English units, the standard acceleration due to gravity is 32.2 fps².

Radian to degrees conversion

1 radian is equal to 57.3 degrees.

Mils to degrees conversion

4800 mils is equal to 270 degrees.

Density and specific weight

Specific weight = density × g; for 0.003 slug/ft³, it's 15.2 N/m³.

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Specific volume of a liquid

If specific weight is 58.5 lbf/ft³, specific volume is 1.0675 cm³/g.

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Probability of drawing a heart or face card

The probability is 42.31%, calculated from card counts.

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Compounding Interest Formula

Future value calculation includes P(1 + i/m)^(mn).

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Effective interest rate

The effective rate of 12% compounded quarterly is 12.55%.

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Determining number of years for investment growth

The time to grow P2,500 to P5,800 at 12% compounded quarterly is 7.12 years.

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Triangle with unequal sides

A triangle with three unequal sides is called scalene.

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Circumference to diameter relationship

In circles, the diameter is derived from the radius or circumference.

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Rate of charge flow

In electricity, it's called current.

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Cubic volume of a solid

Volume of a cylinder = base area × height.

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Adding vectors

Resultant vector = sum of component vectors.

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Rate of depreciation

Depreciation measures asset value reduction over time.

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Type of triangle

A triangle with one angle greater than 90 degrees is obtuse.

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Volume of a pyramid

Volume = (1/3) × base area × height.

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SI unit of conductance

The SI unit of conductance is Siemens.

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The process of factoring

Expressing a polynomial as a product of lower degree polynomials.

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Elliptical Cross-section

A cylinder with elliptical cross-section reflects different geometry.

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Cubic function characterization

A cubic function reflects graph behavior in 3D space.

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Abscissa in a graph

The distance of a point from the y-axis is called the abscissa.

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Diameter of a circle

The diameter is twice the radius.

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Derivatives in calculus

The derivative measures how a function changes.

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Conic sections

Ellipses are formed when a cone intersects a plane.

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Mean value of a data set

The mean is the average of all values in a set.

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Sine law in triangles

The law states that the ratio of a side to sine of opposite angle is constant.

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Study Notes

Math & Engineering Economic Evaluation Exam

  • Standard acceleration due to gravity (English units): 32.2 fps²
  • Value of 1 radian in degrees: 57.3°
  • Degrees in 4800 mils: 270°
  • Specific weight of a gas (density 0.003 slug/ft³): 15.2 N/m³
  • Specific volume of a liquid (specific weight 58.5 lbf/ft³): 1.0675 cm³/g
  • Probability of drawing a heart or face card from a deck of ordinary cards: 42.31%
  • Index of expansion for a perfect gas: 1.285
  • Principal amount of a 15-month loan at 16.8% interest and P12,100 repayment: P10,000
  • Accumulated value of P2,000 in 5 years at 11% compounded quarterly: P3,440
  • Effective rate of interest for P15,000 that becomes P18,302.85 in 4% compounded quarterly: 4.06%
  • Cash value of a machine costing P150,000 after 2 years and P80,000 down payment at 14% quarterly: P193,912
  • Number of years for P2,500 to compound to P5,800 at 12% compounded quarterly: 7.12 years
  • Effective rate equivalent to 12% compounded quarterly: 12.55%
  • Rate compounded quarterly equivalent to 14% compounded semi-annually: 13.76%
  • Determinant of a 2 x 2 matrix with values 2, 1, -1, 1: 3
  • Determniant of a 3 x 3 matrix with values 1 2 -1 1 1 1 1 2 -1 : -7
  • Inverse of a 2 x 2 matrix A cos 0 sin 0/ sin 0 cos 0**:** (cos 0 - sin 0/ sin 0 cos 0)
  • Determinant of a 3 x 3 matrix: -7
  • The sum of the roots of an equation in the form 2x² + 5x + 5 = 0: -2.5
  • Distance traveled by a particle with velocity V = 12t⁴ +7 cm/s between t = 0.2 and 0.3: 2.84 cm
  • Atomic weight of hydrogen: 1 g/gram-atom
  • Mass of a hydrogen atom: 1.66 x 10⁻²⁴ g/atom
  • Specific weight of a gas (density 0.003 slug/ft³): 15.2 N/m³
  • Specific volume of a liquid (specific weight 58.5 lbf/ft³): 1.0675 cm³/g
  • Work done by a force of 200 lbs at 28° angle for 2 feet: 480 J

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