These are Multiple Choice Questions (MCQ) from Exams posted before May 2024. These MCQs get orphaned after the system upgrade.
Find the area enclosed by the curve $r^2 = 64 \cos 2\theta$.
A car travels with an initial velocity of 10 m/s or 36 km/hr. If it is decelerating at a rate of 3 m/sec-sec, how far, in meters, does it travel before stopping?
A circle of radius 15 cm is revolved about a line tangent to it. What is the surface area of the resulting by the solid?
A vertical summit curve has tangent grades of +2.6% and -1.5%. Using h1 = 1.37 m and h2 = 0.1 m, calculate the minimum length of curve if the required sight distance is 140 m.
Company A has a fixed expense of P1.5M monthly and each unit is produced at P20.
The area under the curve $y = x^2 between the values $x = 1$ and $x = 7$ is closest to:
A 3-degree simple curve has an external distance of 23 m. What is the length of the long chord?
Find the radius of curvature of the curve $y = x^3 - 2x^2 + 5x - 3$ at $x = 5$.
In how many days will the original gang of pipe layers, under the supervision of foreman B, finish the original pipe-laying job?
To determine the area of a triangular lot ABC, a surveyor set-up a transit at point P inside the lot and recorded the following bearing and distances of each corners of the lot from P.
Find the volume of the tetrahedron bounded by the coordinate planes and the plane $8x + 12y + 4z - 48 = 0$.
At 6:00 A.M., a fighter plane took off at 410 kph from an aircraft carrier, maintaining the direction of N 50° E.
Line AB has point A(4, 5) and point B(-3, -2). Find point C along line AB if distance BC is three times the distance AC.
A dog is tied with a chord 3 m long to the edge of a circular tank 8 m in diameter. The point where the cord is attached to the tank is at the same elevation as the dog’s collar. Determine the total area about which the dog can move, in square meter...
A company invests P10,000 today to be repaid in five years in one lump sum at 12% compounded annually. If the rate of inflation is 3% compounded annually, how much profit in present day pesos is realized over five years?
The map shows 5 cm representing 450 km. What actual distance is represented by a map distance of 2.8 cm?
How far apart are the foci of the curve $9x^2 + 25y^2 - 18x + 100y - 116 = 0$.
There are five harmonic means between 4/3 and 4/11. What is the fourth term?
A contractor bought a concrete mixer at P120,000.00 if paid in cash.
Find $y'$ if $x = 2 \arccos (2t)$ and $y = 4 \arcsin (2t).
A group of dancers consists of x boys and x girls. If two of the boys are replaced by two girls, then 48% of the group members will be boys. Find the original value of the boys.
A and B can finish the job in 8 days and the working speed of A is twice that of B. How many days would it take A to finish the job alone?
If an arc length is 12 m subtends a central angle $\phi$ in a circle of radius 3, find the measure of $\phi$ in terms of radians.
When the population growth of a certain city was first studied, the population was 22,000.
Find the area of a sector of a circle of radius 6 cm and a central angle of 60°.
Convert $5\pi / 6$ into degree measure.
A sector of a circle with radius 10 cm has a central angle of 120°. Find the arc length of the sector.
In the figure, $AB = BC$. The value of $\theta$ is:
In how many ways can 4 couples be seated at a round table with the men and women alternating?
A circle of radius 1 unit is shown. AD is the diameter of the circle and O is the center. Find the length of arc BC.  
Mary was 4 times as old as Ann 4 years ago and if Mary will be twice as old as Ann 4 years hence, how old is Ann?
At what time between 7 and 8 o’clock will the hands of the clock be directly opposite each other?
A man drives from station A to station B 60 km away at an average speed of 30 kph and return to A at an average speed of 20 kph. What was the average speed of the man in the whole journey?
Stations A and B are placed 1000 m apart on a straight road running East and West. From A, the bearing of the tower C is 32° West of North and from B the bearing of C is 26° North of East. Find the shortest distance of the tower from the road.
A strip of 640 m2 is sold from a triangular field whose sides are 96 m, 72 m, and 80 m. The strip is of uniform width h and has one of its sides parallel to the longest side of the field. Find the width of the strip.
Water evaporates at the rate of two liters per hour per one square meter of surface. How long will it take to evaporate 30 liters of water from a cylindrical swimming pool full of water with 6 m in diameter and 2 m depth?
A disease is known to affect 1 in 10,000 people. It can be fatal, but it is treatable if it is detected early.
There are four red, three green and five blue discs in a bag. Find the probability that two discs of the same color are drawn.
Five men and three women are arranged randomly in a row. What is the probability that there are not two women standing together anywhere in the row?
The Department of Health encourages elderly people to have a flu vaccination each year.
Eight books are to be arranged on a bookshelf. Three of the books are by the same author. In how many ways can the book be arranged on the bookshelf if the books by the same author are to stay together?
Pass a plane through a cube so that the section formed will be a regular hexagon. If the edge of the cube is 2 units, find the area of this section.
9. Two cities A and B are 30 km apart. From both of these cities, simultaneously, two hikers start their journeys towards each other.
The box contains 10 tablets of medicine A and 15 tablets of medicine B. N tablets are taken from the box at random. What is the least possible N that ensures that at least two tablets of each kind are among the extracted?
If the power of an engine grows by 10% when the number of its cylinders is increased by one, which of the following is closest to the ratio of the power of a 9-cylinder engine to that of a 12-cylinder engine?
At what angle do the lines $y = 2x + 2$ and $y = x - 4$ intersect?
A furniture manufacturer has two machines, but only one can be used at a time.
The probability that a visitor at the mall buys a pack of candy is 30%. If three visitors come to the mall today, what is the probability that exactly two will buy a pack of candy?
If a certain soccer game ended 3:2, what is the probability that the side that lost scored first? Assume that all scoring scenarios are equiprobable.
Closed right circular cylinder 2 meter in diameter and 2-meter tall is partially filled with water. When lying in a horizontal position, the depth of water is 2/3 the diameter. When the cylinder is in the vertical position, what is the depth of water?