These are Multiple Choice Questions (MCQ) from Exams posted before May 2024. These MCQs get orphaned after the system upgrade.
How many three-digit numbers are not divisible by 3?
A semi-elliptical arch in a stone bridge has a span of 6 meters and a central height of 2 meters. Find the height of the arch at a distance of 1.5 m from the center of the arch.
For triangle BOA, B is on the y-axis, O is the origin, and A is on the x-axis. Point C(5, 2) is on the line AB. Find the length of AB if the area of the triangle is 36 unit2.
Find the approximate amount of material in an open rectangular box whose inside measurements are 1.60 m long, 1.00 m wide and 0.60 m deep, if the box is made of lumber which is 1.75 cm thick.
The pilot of an airplane left A and flew 200 miles in the direction S 20° 20' W. He then turned and flew 148 miles in the direction S 69° 40' E. If he now heads back to A, in what direction should he fly?
A right cylindrical tank 2 m in diameter and 5 m long has its axis horizontal. It is filled with fuel to a depth of 1.5 m. Find the volume of fuel in the tank in liters.
By the conditions of a will, the sum of P25,000 is left to a girl to be held in a trust fund by her guardian until it amounts to P45,000. When will the girl receive the money if the fund is invested at 8% compounded quarterly?
A company purchased an equipment for a total of P960M including its freight and installation charges. What is its annual depreciation charge if salvage value is zero and the sinking fund deposit factor is 0.0430?
Find the point in the parabola y2 = 4x at which the rate of change of the ordinate and abscissa are equal.
Find the distance between foci of the conic 8x^2 + 9y^2 = 288.
Determine the equation of an open upward parabola with (2, 1) and (-4, 1) as ends of latus rectum.
The median of a right triangle drawn to the hypotenuse is 3 cm long and makes an angle of 60° with it. Find the area of the triangle.
Three forces 20 N, 30 N, and 40 N are in equilibrium. Find the angle between the 20 N and 40 N forces.
A circle with radius 6 has half its area removed by cutting off a border of uniform width. Find the width of the border.
A rectangle ABCD which measures 18 by 24 units is folded once, perpendicular to diagonal AC, so that the opposite vertices A and C coincide. Find the length of the fold.
The distance between the centers of the three circles which are mutually tangent to each other externally are 10, 12, and 14 units. Find the area of the smallest circle.
Calculate $\sqrt{2 + \sqrt{2 + \sqrt{2 + \dots}}}$
Find the product of roots of $\dfrac{x^{2002} + 4x^{2001}}{4x^{2000}} = 8$.
Aedan opened his Science book and noticed that the product of the two pages in front of him was equal to 1122. What were the sum of the numbers of those pages?
Find the term that is independent of x in the expansion of $\left( 2 + \dfrac{3}{x^2} \right)\left( x - \dfrac{2}{x} \right)^6$.
If one root of the quadratic equation with integer coefficients is $3 + 4i$, what is the constant term of the equation?
A boy playing under the street-light noticed that the length of shadow of his 5-foot stick erected vertically on the pavement, is 20 inches.
w varies jointly with x and y and inversely with the square of z. If w = 12 when x = 3, y = 8, and z = 2, find the constant of proportionality k.
At what price will a businessman mark a digital camera for sale that cost P6,000 in order that 20% discount can be offered on the marked price and still makes a profit of 25% of the selling price.
If x + y = 5 and xy = 6, find the value of x^3 + y^3.
From a tank filled with 240 gallons of alcohol, 60 gallons are drawn off and the tank is filled up with water. Then 60 gallons of the mixture are removed and replaced with water, and so on. How many gallons of alcohol remain in the tank after 5 drawings
Determine the amplitude of $y = 4 \cos 2x$.
A cube is 6 inches in edge. A cutting plane is passed through the midpoint of three adjacent edges. Find the volume of the smaller solid.
A slope of 20 degrees in percent is most nearly equal to:
The magnetic bearing of a line was recorded as S 80° 15' W in 2000 at Mactan Island which had a declination of 16° E in that year. Compute the present magnetic bearing of the same line in 2006 if the declination in 2006 is 4° 30' E.
A trapezoid has an area of 360 m2 and altitude of 20 m. Its two bases have ratio of 4:5. One of the bases i
A non-square rectangle is inscribed in a square so that each vertex of the rectangle is at the trisection point of the different sides of the square. Find the ratio of the area of the rectangle to the area of the square.
The area bounded by the waterline of a reservoir is determined by using planimeter and the following are the results: A1 = 20,000 m2; A2 = 18,000 m2; A3 = 14,000 m2; A4 = 10,000 m2; and A5 = 8,000 m2. If the contour interval is 2 m, find the capacity of
Two regular pentagons are concentric to each other. One of which has sides of 20 m and the other has sides of 10 m. If their corresponding vertices are in the same direction, find the area inside the larger pentagon but outside the smaller pentagon.
A boy is 25 years younger than his father. In 10 years, his father will be twice his age. Find the age of the boy.
A hole 10 inches in diameter is to be punched out from a sphere having a diameter of 16 inches. Determine the volume punched out if the center of the hole is along the diameter of the sphere.
A circle 8 cm in radius is tangent to a line at A. Another circle 3 cm in radius is tangent also to the same line at B. Find the distance AB if the two circles are tangent externally to each other.
Chords AB and AC are drawn on a circle of radius 10 inches. Find the angle between the chords if the arc BAC is 28 inches long.
If one third of the air in the tank is removed by each stroke of an air pump, what part of the total air will be removed in 6 strokes?
The sum of the digits of a 3-digit number is 17. The hundred’s digit is twice the unit’s digit. If 396 be subtracted from the number, the order of the digits will be reversed. Find the number.
Find the sum of the first terms of the progression 2, 4, 8, 16,…
In how many ways can you line up 5 persons if two persons refuse to follow each other?
Two triangles have equal bases. The altitude of one triangle is 3 units more than its base while the altitude of the other is 3 units less than its base. If the areas of the triangles differ by 21 square units, find the altitude of the smaller triangle.
Find the maximum and minimum values of $$ 3^{\sin x} for 0^\circ \le x \le 360ˆ\circ $$
At what value of x will the function $f(x) = \dfrac{x - 4}{x + 2}$ is discontinuous?
z1UpedR-2 the numbers are even and repetition of digit is not allowed.
Find the capacity of a conical vessel that is made from a semi-circular tin of radius 2.5 m.
Determine the volume of a regular tetrahedron of edge 2 ft.
A man invested P100,000 at an interest rate of 10% compounded annually. What will be the final amount of his investment, in terms of today’s peso, after 5 years, if inflation remains the same at the rate of 8% per year?
Through a given cone of altitude h and base A, two planes are passed parallel to the base, cutting the altitude $\frac{1}{3}h$ and $\frac{2}{3}h$ units from the base. Find the ratio of the volumes of the two frustums thus formed.