What conic section is described by the equation 4x2 – y2 + 8x + 4y = 15?

Find the maximum area of rectangle which can be inscribed in an ellipse having the

equation x2 + 4y2 = 4.

If the general equation of the conic Ax2 +Bxy + Cy2 + Dx + Ey + F=0. If B2 – 4AC >0, the

equation describes a ______________.

The chord passing through the focus of the parabola and is perpendicular to its axis is

termed as:

What is the equation of the hyperbola with a focus at (-3 - 3sqrt. of 13, 1) asymptotes

intersecting at (-3,1)

Find the ratio of the sides of triangle if its sides form n arithmetic progression and one of

the angles is 90 degrees.

The area enclosed by the ellipse 4x2 + 9y2 = 36 is revolved about the line x=3, what is the

volume generated?

The polynomial x2 + 4x + 4 is the area of a square floor. What is the length of its side?

Given a conic section, if B2 – 4AC =0, it is called?

Find the height of a right circular cylinder of maximum volume which can be inscribed in

a sphere of radius 10 cm.

The length of the latus rectum of the parabola y = 4px2 is:

The area bounded by the curve y2 = 12x and the line x = 3 is revolved about the line x = 3.

What is the volume generated?

. Describe the locus represented by | z − 3| − | z + 3| = 4.

Melissa is 4 times as old as Jim. Pat is 5 years older than Melissa. If Jim is y, how old is

Pat?

A conic section whose eccentricity, is less than one is known as:

Two lines passing through the point (2,3) make an angle of 45 degrees with each other. If

the slope of one of the lines is 2, find the slope of the other.

From the top of a building the angle of depression of the foot of a pole is 48 deg 10 min.

From the foot of a building the angle of elevation of the top of a pole is 18 deg 50 min.

Both building the pole are on a level ground. If the height of a pole is 4 m, how high is

the building?

The locus of a point which moves so that the sum of its distances between two fixed two

points is constant is called?

Totoy is 5 feet 11 inches tall and Nancy is 6 feet 5 inches tall. How much taller is Nancy

than totoy?

If log 64 x = 3/2 , find x.

What is the product of -9p3r and 2p-3r?

Michael’s favourite cake recipe calls for 0.75 pounds of flour: he has a 5 pound bag. He

want to make several cakes of the school bake sale. How many can he make?

Find the minimum amount of tin sheet that can be made into a closed cylinder having a

volume of 108 cu. Inches in square inches.

Carmela and Marian got summer jobs at the ice cream shop and were supposed to work

15 hours per week each for 8 weeks. During that time, Marian was ill for one week and

Carmela took her shifts. How many hours did Carmela work during the 8 weeks?

Manuelita had 75 stuffed animals. Her grandmother gave 15 of them to her. What

percentage of the stuffed animals did her grandmother give her?

. Find the coordinates of an object that has been displaced from the poin (-4, 9) by the

vector 4i – 5j.

A triangle has two congruent sides and the measure of one angle is 40 degrees. Which of

the following types of triangle is it?

48. The parabola defined by the equation 3y2 + 4x = 0 opens ________________

If a place on the earth is 12 degrees south of the equator, find its distance in nautical

miles from the north pole.

If the standard deviation of a population is 9, the population variance is:

Simplify the equation sin2 𝜃 (1 + cos2 𝜃)

What is the complement of a 60-degree angle?

If 2xy - y2 = 3, find y”

The Rotary Club and the Jaycees Club had a joint part, 120 members of the Rotary Club

and 100 members of the Jaycees Club also attended but 30 of those attended are members

of both clubs. How many persons attended the part?

Two numbers have a harmonic mean of 9 and a geometric mean of 6. Determine the

arithmetic mean.

Find the force on one face of a right triangle of sides 4 m and altitude of 3 m. The altitude

is submerged vertically with the 4 m side in the surface.

An airplane flying with wind, took 2 hours to travel 1000 km and 2.5 hours in flying

back. What was the wind velocity in kph?

In how many ways can 6 people be lined up to get on a bus, if a certain 3 persons insist

on following each other?

The line 3x – 4y = 5 is perpendicular to the line

If the plane 3x + 2y – 3z = 0 is perpendicular to the plane 9x – 3ky + 5z -1 = 0, find the

value of k.

A solid has circular base of radius r. Find the volume of the solid if every planar section

perpendicular to a fixed diameter is a semicircle.

Find the y – intercept of the line given by the equation 7 x + 4y = 8.

Find the area inside the cardioid r = 1 + cos 𝜃 and outside the circle r = 1.

A person had a rectangular-shaped garden with sides of lengths 16 feet and 9 feet. The garden was changed into a square design with the same area as the original rectangular shaped garden. How many feet in length are each of the sides of the new square-shaped

garden?

Which of the following rope lengths is longest?

Martin, a motel housekeeper, has finished cleaning about 40% of the 32 room he’s been

assigned. About how many more rooms does he have left to clean?

A horse is tied to a post with a twenty-foot rope. What is the longest part that the horse

can walk?

Doming wants to know the height of the telephone pole. He measures his shadow, which

is 3 feet long, and the pole’s shadow, which is 10 feet ling. Doming’s height is 6 feet.

How tall is the pole?

A weight of 60 pounds rest on the end of an 8-foot lever and is 3 feet from the fulcrum.

What weight must be placed on the other end of the lever to balance the 60-pound

weight?