Engineering Mathematics and Science Review Practice Problems

Flashcards covering engineering mathematics, physics, and financial calculations based on lecture exam review problems.

If a log has an altitude of $8\,m$, a base diameter of $0.5\,m$, and a right diameter of $0.4\,m$, how many revolutions will it make if it rolls out to the ground covering $1\,hectare$ of land?

796

A salad bowl in the shape of a hemisphere has a diameter of $40\,cm$. If the salad occupies a height of $15\,cm$, what is the volume of the salad and the percentage volume of the salad with respect to the volume of the bowl?

$10,602.88\,cm^3$, $63.28\%$

A train meets with an accident one hour after starting that detains it for one hour, then proceeds at $\frac{3}{5}$ of its former rate and arrives three hours late. If the accident had happened $50\,miles$ farther on, it would have arrived one and one-half hours sooner. What is the length of the journey?

$$800/9\,miles$$

A manufacturing firm with a weekly demand of $25\,units$ operates for $7\,hours$ per day, $5\,days$ per week. What is the maximum production time per unit in hours to meet the demand?

$$1\,hour$$

How wide a strip should a farmer plant on each side of a rectangular field measuring $30\,m$ by $40\,m$ to complete half the work by planting around the perimeter?

$$5\,m$$

If you double a number, subtract 6 from the result, and divide by 2, the quotient is 20. What is the number?

23

If the volume of a cube is increasing at a rate of $5\,m^3/min$, what is the rate at which the surface area is increasing in $m^2/min$ when its side is $10\,m$?

2

What is the accumulated value of $P2000.00$ in $5\,years$ if it is invested at $11\%$ compounded quarterly?

$$P3,440.00$$

What is the value of $k$ that makes the expression $kx^2 - 3kx + 9$ a perfect square?

4

Two times a mother's age is 8 more than six times her daughter's age. Ten years ago, the sum of their ages was 44. How old is the daughter?

15 yrs old

How many terms of the sequence $-9, -6, -3, \dots$ must be taken so that the sum is 66?

11

There are 6 geometric means between 4 and 8748. What is the sum of all terms?

13120

What is the root mean square of 11, 23, and 35?

25

A pole casts a shadow $15\,m$ long when the angle of elevation of the sun is $61^{\circ}$. If the pole leans $15^{\circ}$ from the vertical directly toward the sun, what is the length of the pole?

$$54.23\,m$$

What is the supplement of an angle whose complement is $62^{\circ}$?

$$152^{\circ}$$

What is the angle if its supplementary angle is five times its complement?

$$67.5^{\circ}$$

From the top of tower A, the elevation of the top of tower B is $46^{\circ}$. The distance between the feet of the towers is $28\,m$. If tower B is $120\,m$ high, how high is tower A?

$$40.7\,m$$

Determine the absolute value of the resultant vector of $F_1 = 4i + 7j + 6k$, $F_2 = 9i + 2j + 11k$, and $F_3 = 5i - 3j - 8k$.

21

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

$$12.55\%$$

A man borrowed $P2,000.00$ and received $P1950$ in cash because the bank discounted the loan. What is the rate of discount?

$$2.5\%$$

Find the voltage drop required to move $2\,C$ of charge from point A to point B requiring $-30\,Joules$ of energy.

$$-15\,V$$

What is the diameter of a circle with the equation $x^2 + y^2 - 6x + 4y - 12 = 0$?

$$10\,units$$

If $x$ varies directly as $y$ and inversely as $z$, and $x = 14$ when $y = 7$ and $z = 2$, find $x$ when $z = 4$ and $y = 16$.

16

Find the absolute value of the complex number $3 + 4i$.

5

Simplify the expression $i^{1997} + i^{1999}$ where $i$ is an imaginary number.

0

How long does it take for a ball dropped from a height of $60\,meters$ to hit the ground?

$$3.5\,sec$$

What is the outside diameter of a hollow steel tube carrying a tensile load of $500\,KN$ at a stress of $140\,Mpa$, assuming the wall thickness is one-tenth of the outside diameter?

$$113\,mm$$

How do you call the mathematical process of expressing a polynomial as the product of another polynomial or monomial of lower degree?

Factoring

Which of the following does not affect owner\u2019s equity: expense to get a license, investment capital, license to start business, or dividends paid?

License to start business

What is an increase in the value of a capital asset called?

Capital gain

What regular polygon has 27 diagonals?

Nonagon

What is the term for the output or sales level at which income equals operating cost?

Break-even point

What is the sum of all costs incurred by project originators up to the time the promoters accept the project?

Development cost

When a line $y = mx + b$ slopes downwards from left to right, what is the value of the slope $m$?

Less than zero

What is the name of Commonwealth Act 294?

Mechanical Engineering Law

What is a sequence called where the succeeding term is greater than the preceding term?

Divergent series

What is a series of sequential methods used for carrying out a desired procedure to solve problems?

Algorithm

What unit of length equal to $10^{-10}\,metre$ is used for expressing wavelengths of light or ultraviolet radiation?

Angstrom

What statement describes that the whole is greater than any one of its parts?

Axiom

What is a perpendicular segment from a vertex of a triangle to the line containing the opposite side?

Altitude

What is an SI unit of area equal to $100\,sq. meter$?

Arc

What is the angle that the line of sight to an object makes with the horizontal when the object is above the eye of the observer?

Angle of elevation

What is a series of numbers where each term is derived from the preceding number by adding a constant value?

Arithmetic sequence

What is a series of equal payments occurring at equal periods of time?

Annuity

What is the ratio of quick assets to current liabilities commonly called?

Acid test ratio

Any method of repaying a debt (principal and interest) by a series of equal payments at periodic intervals of time is called:

Amortization

What is the value of $1\,radian$ in degrees?

$$57.3^{\circ}$$

How many degrees are in $4800\,mils$?

$$270^{\circ}$$

If the density of a gas is $0.003\,slug/ft^3$, what is its specific weight?

$$15.2\,N/m^3$$

If the specific weight of a liquid is $58.5\,lbf/ft^3$, what is its specific volume?

$$1.0675\,cm^3/g$$

What is the probability of drawing a heart or a face card from an ordinary deck?

$$42.31\%$$

A gas expands polytropically from $0.06\,m^3$ at $147^{\circ}C$ to $0.21\,m^3$ at $21^{\circ}C$. What is the index of expansion?

1.285

What is the principal of a loan repaid with $P12,100.00$ after $15\,months$ at $16.8\%$ interest a year?

P10,000

Determine the effective rate of interest per year for a deposit of $P15,000$ that becomes $P18,302.85$ at $4\%$ per annum compounded quarterly.

$$4.06\%$$

What is the cash value of a machine if a buyer paid $P80,000$ down and owes $P150,000$ in $2\,years$ with money worth $14\%$ compounded quarterly?

P193,912

Find the number of years for $P2,500$ to compound to $P5,800$ at $12\%$ compounded quarterly.

$$7.12\,years$$

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

$$13.76\%$$

A man owes $P500$ due in $3\,years$ and $P800$ due in $7\,years$. What single payment must he make on the $6th\,year$ if money is worth $14\%$ compounded semi-annually?

P1,449.12

What is the cash price of a machine purchased with $P30,000$ down and $P5,000$ monthly for $5\,years$ at $12\%$ compounded monthly?

P254,775.19

What amount must be deposited every $3\,months$ into a fund paying $12\%$ compounded quarterly to reach $P25,000$ in $8\,years$?

P476.17

Find the work done by a force of $200\,lb$ acting at an angle of $28^{\circ}$ with respect to the horizontal pushed for $2\,ft$.

$$480\,J$$

What is the mass of a hydrogen atom if the atomic weight is $1\,gram$ per gram-atom?

$$1.66 \times 10^{-24}\,g/atom$$

A truck starts from rest with a constant acceleration of $6\,m/s^2$. What is its speed after $4\,seconds$?

$$24\,m/s$$

Find the average velocity during the first $10\,seconds$ of motion for a car starting from rest with a constant acceleration of $3\,fps^2$.

$$15\,fps$$

If a $5\,meter$ ladder is $3\,m$ from a wall at the bottom, how much must it be extended to lean $1\,meter$ higher on the wall from the same base position?

$$0.83095\,m$$

What was the height of a balloon ascending at $7.5\,m/s$ when a stone was dropped from it if the stone hits the ground in $6\,seconds$?

$$131.81\,m$$

Determine the value of each interior angle of a regular pentagon.

$$108^{\circ}$$

What is the volume of water in a cubical container measuring $50.8\,mm$ on a side that is tightly packed with eight equal-sized marbles?

$$62,454.54\,mm^3$$

What is the determinant of the $2 \times 2$ matrix with rows $(8, 5)$ and $(7, 6)$?

33

What is the determinant of the $3 \times 3$ matrix with rows $(2, 3, 1)$, $(0, -1, 2)$, and $(0, 0, 7)$?

-7

What geometric shape is represented by the algebraic expression $y = a_1 + a_2x$?

A straight line

What is the sum of the roots of the equation $2x^2 + 5x + 5 = 0$?

-2.5

Compute the arithmetic mean of the numbers: 18, 24, 27, 30, 35, 42, 50.

32.29

At what rate in GPM is water pouring into a pool at $t = 9\,hours$ if the total volume is $V = \sqrt{t}\,gallons$?

0.0194