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

A train, an hour after starting, meets with an accident which detains it an hour, after which it proceeds at 3/5 of its former rate and arrives three hour after the time; but had the accident happened 50 miles farther on the line, it would have arrived one and one-half hour sooner. Find the length of the journey.

A manufacturing firm maintains one product assembly line to produce signal generators. Weekly demand for the generators is 25 units. The line operates for 7 hours per day, 5 days per week. What is the maximum production time per unit in hours required for the line to meet the demand?

A farmer is to plant rice in a rectangular field 30 m by 40 m. He started on the edge and plant around the perimeter. How wide a strip should he plant for each side in order to do half the work?

Think of a number. Double the number. Subtract 6 from the result and divide the answer by 2. The quotient will be 20. What is the number you think?

The volume of the cube is increasing at a rate of 5 cu. m per minute. Determine the rate at which the surface area is increasing in m²/min, when its side is 10 m.

Determine the accumulated value of P2000.00 in 5 years if it is invested at 11% compounded quarterly.

What is the value of k to make the expression kx² − 3kx + 9 a perfect square?

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

How many terms of the sequence −9, −6, −3, … must be taken so that the sum is 66?

There are 6 geometric means between 4 and 8748. Find the sum of all terms.

Find the root mean square of 11, 23 and 35.

A pole cast a shadow 15 m long when the angle of elevation of the sun is 61°. If the pole has lean 15° from the vertical directly toward the sun, what is the length of the pole?

What is the supplement of an angle whose complement is 62°?

A certain angle has a supplementary five times its compliment. What is the angle?

From the top of tower A, the angle of elevation of the top of the tower B is 46°. From the foot of tower B is 28°. Both towers are on a level ground. If the height of tower B is 120 m, how high is tower A?

Determine the absolute value of resultant vector of the following vectors: F1 = 4i + 7j + 6k; F2 = 9i + 2j + 11k; F3 = 5i − 3j − 8k.

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

A man 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 P1950 in cash. Determine the rate of discount.

Find the voltage drop to move 2 C of charge from point A to point B that requires −30 Joules of energy.

If z = √(1 − √(1 − √(1 − ⋯))), what is the value of z?

It is now between 3 and 4 o’clock. In twenty minutes, the minute hand will be as much as the hour hand as it is behind it. What is the time now?

Determine the value of ∫ from −2 to 2 of (x³ + x⁵ + sin x) dx.

Determine the diameter of a circle, x² + y² − 6x + 4y − 12 = 0.

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

Determine the absolute value of the complex number 3 + 4i.

Simplify $$i^{1997} + i^{1999}$$ here i is an imaginary number.

A ball is dropped from a height of 60 meters above the ground. How long does it take to hit the ground?

Determine the outside diameter of a hollow steel tube that will carry a tensile load of 500 kN at a stress of 140 MPa. Assume the wall thickness to be one-tenth of the outside diameter.

This is the process of expressing a polynomial as the product of another polynomial or monomial of lower degree. What is this mathematical process?

Which of the following does not affect owner’s equity?

How do you call an increase in the value of a capital asset?

What is a regular polygon that has 27 diagonals?

What do you think is the output or sales at which income is insufficient to equal operating cost?

The sum of all the cost incurred by the originators of the project up to time that the promoters of the project accept the project is known as:

When a line y = mx + b slope downwards from left to right, the slope m is:

Which of the following is not a theorem on limits?

Which of the following Commonwealth Acts is known as the oldest Mechanical Engineering Law?

How do you call a sequence of numbers where the succeeding term is greater than the preceding term?

This is a series of sequential method for carrying out a desire procedure to solve problems.

This is use for expressing wavelengths of light or ultraviolet radiation with a unit or length equal to 10 – 10 metre.

It is a collection of numbers or letters used to represent a number arrange property in rows and columns.

In complex algebra, we use a diagram to represent a complex plane commonly called as:

The area bounded by two concentric circles is called as

The ratio of annual sales to the average of assets used in producing these sales.

10 to the negative power of 18 is the value of prefix:

Whenever a net force acts on a body, it produces acceleration in the direction of the resultant force, an acceleration which is directly proportional to the resultant force and inversely proportional to the mass of the body. How do you call this theory?

It is defined that the momentum of a moving object is the product of its mass, m and velocity, v. In Newton’s law of motion, what is the rate of change of momentum with respect to time?

The loss of weight of a body submerged in a fluid is:

The amount of company’s profit that the board of directors of the corporation decides to distribute to ordinary shareholders

To be a member of the Board of Mechanical Engineering, he/she must be at least how many years old?

When a homogeneous, flexible cord is held at the two ends and allowed to sag freely on its own weight, it will produce a curve very similar to a parabola opening upwards. How do you call this curve?

How do you call the line passing through the focus and perpendicular to the directrix of a parabola?

What is the ratio of the distance between the foci to the distance between the vertices in either hyperbola or ellipse?

It is a statement that one mathematical expression is greater than or less than another. How do you call this?

What is the artificial expense that spreads the purchase price of an asset or another property over a number of years?

How do you classify this interest rate, which specifies the actual rate of interest on the principal for one year?

What type of curve is generated by a point, which moves in uniform circular motion about an axis, while travelling with a constant speed, v, parallel to the axis.

What do you call the possible outcome of an experiment?

A branch of mathematics which uses the properties of numbers by using symbols or letters to represent numbers in arithmetic operations which usually variables and unknown quantities which usually involves the use and rearranging or equations.

It refers to a straight line, which a curve approaches closely, but never meets or touches the curve.

In a triangle, the length of a line which is equal to the square root of the sides adjacent to the point where this line started minus the product of the segments of the third side is known as:

The whole is greater than any one of its parts. This statement is known as:

A perpendicular segment from a vertex of the triangle to the line containing the opposite side is known as:

An SI unit of area equal to 100 sq. meter.

The angle that the line of sight to the object, makes with the horizontal, which is above the eye of the observer, is called as:

A series of numbers in which each number or term is derived from the preceding number by adding a constant value to it is known as:

A series of equal payments occurring at equal periods of time.

Quick ratio is defined as the ratio of quick assets to the current liabilities, sometimes this is called:

Form of business/company ownership:

It is defined to be any method of repaying a debt, the principal and interest included usually by a series of equal payments at periodic intervals of time.

What is a borrower of a particular loan almost always required to do during repayment?

What is the value of 1 radian in degrees?

How many degrees are 4800 mils?

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

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

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

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?

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?

The sum of P15,000, deposited in an account earning 4% per annum compounded quarterly, will become P18,302.85. Determine the effective rate of interest per year.

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

Find the number of years when P2,500 is compounded to P5,800 if invested at 12% compounded quarterly.

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

A man 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.

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?

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.

A force of 200 lb acts on a block at an angle of $$28^{\circ}$$ with respect to horizontal. The block is pushed $$2\,\text{ft}$$ horizontally. Find the work done by this force.

The atomic weight of hydrogen is $$1\,\text{gram per gram-atom}$$ . What is the mass of a hydrogen atom?

A truck starts from rest and moves with a constant acceleration of $$6\,\text{m/s}^2$$ . Find the speed of the truck after $$4\,\text{s}$$ .

A car starts from rest and has a constant acceleration of $$3\,\text{ft/s}^2$$ . Determine the average velocity during the first $$10\,\text{s}$$ of motion.

A $$5\,\text{m}$$ extension ladder leans against the wall; the bottom is $$3\,\text{m}$$ from the wall. If the bottom stays at the same place, how much should the ladder be extended so that the top would lean against the wall $$1\,\text{m}$$ higher?

If a stone is dropped from a balloon while ascending at the rate of $$7.5\,\text{m/s}$$ and reaches the ground in $$6\,\text{s}$$ , what was the height of the balloon when the stone was dropped?

The salary of an employee’s job has five levels, each one $$5\%$$ greater than the one below it. Due to circumstances, the salary of the employee must be reduced from the top (fifth) level to the second level, which means a reduction of P $$3000$$ per month. What is the employee’s present salary per month?

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

A cubical container that measures $$50.8\,\text{mm}$$ on a side is tightly packed with eight marbles and is filled with water. All eight marbles are in contact with the walls of the container and the adjacent marbles. All of the marbles are the same size. What is the volume of water in the container?

The equation $$y = a_1 + a_2 x$$ is an algebraic expression for which of the following choices?

Given the following vectors: $$A = 3\mathbf{i} + 2\mathbf{j}$$ , $$B = 2\mathbf{i} + 3\mathbf{j} + \mathbf{k}$$ , $$C = 5\mathbf{i} + 2\mathbf{k}$$ . Simplify the expression $$(A \times B) \cdot C$$ .

Determine the slope of the curve $$y = -x^2$$ at the point $$(2, 3)$$ .

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

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

Five years ago the father is three times as old as his son. Ten years from now, the father will be twice as old as his son. How old is the son twelve years from now?

Determine the distance between the foci of a hyperbola if the lengths of the transverse and conjugate axes are $$10\,\text{m}$$ and $$8\,\text{m}$$ , respectively.

An Electrical engineer obtained a loan of P50,000 at the rate of $$6\%$$ compounded annually in order to repair his mistress’s house. How much must the Engineer pay monthly to amortize the loan within a period of ten years?

What is the present value of P5,000 due in 8 years if money is worth $$12\%$$ compounded semi-annually?

How many permutation can be made out of the letters of the word ENGINEERING?

What do you think is the lessening of the value of an asset due to a decrease in the quantity available as a coal, oil and timber in forest?

In the problem of writing the equation of a certain curve with respect to another axes in which the new axes are parallel to the original axes and similarly directed is known as:

Adding more solute to an already saturated solution will cause the excess solute to settle to the bottom of the container. What is this process called?

The length of time at which the original cost of capital used to purchase a unit has already been recovered.

The actual interest earned by a given principal is known as:

How many permutations can be made out of the letters in the word DIEGO taken 3 at a time?

What is the temperature in degrees Celsius of a molecule at absolute zero?

If an angle measures $$x$$ degrees, what is the measure in radians?

This law states, “The voltage, v, across a resistor is directly proportional to the current, I, flowing through the resistor”. How do you call this law?

In electricity, it is an ability of an element to resist the flow of current. What is this?

In electrical circuits, how do you call the reciprocal of resistance?

If $$4y = 3x$$ , then what is the value of $$3x^2/4y^2$$ ?

How do you call a line segment from the center of a regular polygon to the midpoint of a side? It is also called the inradius, the radius of an incircle.

If the daily wage of a CPM and a plumber are in the ratio 2:1. In a day, a CPM has to work 8 hours but the plumber only 6 hours. Determine the ratio of their hour wages.

Which of the following is the equivalent of one circular mil?

How do you call a method of describing a set where the elements are separated by commas and enclosed in braces?

Which of the following is the equivalent of the expression $$2\log_b 6 - \log_b 4$$ ?

A 100-kg salt solution originally 4% by weight salt in water is boiled to reduce water content until the concentration is 5% by weight salt. How much water is evaporated?

Tom can paint a fence 50% faster than Carl and 20% faster than Ted and together they can paint a given fence in 4 hours. How long will it take Tom to paint the same fence if he had to work alone?

This is the amount of property in which a willing buyer will pay to a willing seller for the property when neither one is under the compulsion to buy or sell. What do you call this value?

What is the minimum point of $$y = x + 1/x$$ ?

What is the simple interest rate if an investment of P37,500 accumulates to P45,937.50 in 18 months?

This is a type of bond whose guaranty is in lieu on railroad equipment. What is this type of bond?

A man left Sta. Rosa City to drive to Lopez, Quezon at 6:15 p.m. and arrived at 11:45 p.m. If he averaged 50 kph and stopped 1 hour for dinner, how far is Lopez, Quezon from Sta. Rosa City?

A bag contains 3 white and 5 red balls. If two balls are drawn at random, what is the probability that both are white?

The sum of two interior angles of the triangle is equal to the third angle and the difference of the two angles is equal to $$\tfrac{2}{3}$$ of the third angle. Find the third angle.

Grand total of the assets operational capability of a corporation.

The process of recording all the transactions of the company, which affect any investment of capital so that at any time the results of investments may be known as:

A system of units based on time, length and mass is called:

A US unit capacity used to measure solids equal to 7056 cubic inches (0.1156 m3).

It refers to a statistical distribution having two distinct peaks of frequency distribution.

The straight line or plane that divides a line, a plane, or an angle into two equal parts.

A law, which states that a curvature of the central fiber is proportional to the bending moment in homogeneous bar.

A mathematical method that combines two numbers or quantities to give a third quantity. An example is the multiplication of two numbers in arithmetic.

A logarithm having a base 10 is called:

Any two points along a streamline in an ideal fluid in steady flow, the sum of the pressure, the potential energy per unit volume and the kinetic energy per unit volume has the same value. This concept is known as the:

If the temperature of a confined gas does not change, the product of the pressure and volume is constant. This is known as:

The quantity of heat required to raise the temperature of one pound mass of water through one degree Fahrenheit is known as:

Which statement about a charge placed on a dielectric material is true?

A satellite orbiting the earth passes directly overhead stations in Phoenix and Los Angeles, 340 miles apart. At an instant when the satellite is between these two stations, its angle of elevation is simultaneously observed to be 60° at Phoenix and 75° at Los Angeles. How far is the satellite from Los Angeles?

Given that $$a$$ , $$b$$ , and $$c$$ are real numbers. If $$a = b$$ , then $$a + c = b + c$$ , what property is it?

Simplify $$(x^2 + y - 2)(x^2 - y + 2)$$ .

The expression $$x^4 + ax^3 + 5x^2 + bx + 6$$ when divided by $$(x - 2)$$ leaves a remainder of $$16$$ , and when divided by $$(x - 1)$$ leaves a remainder of $$10$$ . Find the value of $$a$$ and $$b$$ .

Find the middle term of the expansion $$(x^2 - 2y)^{10}$$ .