[PA] Sample Problems 02 | Advanced

Find the value of Tan (8x + 1) = Cot 17°.

Find the value of Tan 4x = Cot 6x.

Find the value of Sin 2x = Cos x.

The sides of triangle ABC have sides AB = 22, BC = 15, and AC = 8. What is the area of the triangle?

If 4y = 3x, then, what is the value of (3x²/4y²)?

In triangle ABC, BC = 40 m and AB = 50 m, and angle A = 53°. Determine the area of the triangle.

If Cos 65° + Cos 55° = Cos X, what is X in radians?

What is the area of a trapezoid with bases of 9 cm and 7 cm, and a height of 3 centimeters?

A triangular prism has a base dimension of AB = 24 m, BC = 20 m, and CA = 16 m. Determine the volume of the prism if its height is 12 m.

In number 4, what is the value of angle CAB?

What is the travel distance of the pipe if the offset angle is 60° and the offset length is 30 cm?

What is the area of the cross-section of a pipe with the inside diameter of 22 mm and an outside diameter of 25.4 mm?

Find the diameter of a circle whose area is equal to the difference between the area of a 8″ circle and the area of a 4″ circle?

A spherical steel ball is placed into a vertical circular cylinder containing water, causing the water level to rise by 12 cm. If the radius of the cylinder is 15 cm. What is the radius of the ball in cm?

What is the surface area of a sphere whose volume is 36 cu. m?

Find the volume of a cone to be constructed from a sector having a diameter of 72cm and a central angle of 210 deg.

Find the distance between the points A(-2, -5) and B(7, -2).

In number 17, what is the slope of the Line AB?

What is the volume of regular hexagonal pyramid with the length of one side of its base is 6 cm and its altitude measured to be 8 cm.

If the length of a rectangle is increased by 20% and the width is decreased by 20%, what percent change occurs in the area?

If product of 1/4 and 1/5 of a number is 500. What is the number?

Point (-2, 6) is the center of a Circle that is tangent to the x-axis. The coordinates of the point of tangency is _____.

The width of a rectangle is 4/5 its length. If its perimeter is 72, what is its area?

What is a regular polygon that has 27 diagonals?

What is the volume of a cylindrical tank with a diameter of 1 m and a height of 2 m?

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

Which of the following numbers will give a maximum difference when subtracted by its cube?

The bases of a right prism are pentagons with each side 6 cm long. The bases are 12 cm apart. What is the volume of the prism?

Find the area or a pentagon that is inscribed in a circle if the area of the circle is 314 sq. m.

An area of 25.6 cm² on the map represents a lot having an area of 640 m². If the scale on the map is 1:x, what is x?

Solve for the value of x from the following equation: ᵪxˣ˙˙˙ = 10

Find the distance from point (5, -3) to the line 7x – 4y – 28 = 0.

How many 4 digit numbers can be formed by the use of digits 1, 2, 3, 4, 6 and 7 if one digit is used only once in one number?

In how many ways can 4 persons be seated in a room where there are 9 seats?

How many combinations can be made out of the letters ABCD and E taken two at a time.

In how many ways can you choose 3 desserts from a menu of 10?

There are 50 tickets in a lottery in which there is a first and second prize. What is the probability of a man drawing a prize if he owns 5 tickets?

One card from the pack is drawn at random from 52 cards. What is the probability of getting a king or a queen?

A bag contains 3 white and 5 black balls. If two balls are drawn in succession without replacement, what is the probability that both balls are black?

A bag contains 3 yellow and 5 black balls. If two ball are drawn in succession without replacement, find the probability that the balls drawn is one yellow and one black ball.

A person draws 3 balls in succession from a box containing 5 red balls, 6 yellow balls, and 7 green balls. Find the probability of drawing balls in the order red, yellow and green.

Terms of Sales: Php 90,000 payable in 120 days or Php 85,500 payable in 45 days. Find the equivalent annual rate of simple interest if paid in 120 days.

A plumbing tool vendor borrowed Php 2,400 and agreed to pay Php 3,000 after 30 days. What is the simple interest rate per annum?

In 1940, the average value of a house is Php 290,000. In 1990, the average value of a house of the same model is Php 7,910,000. What was the rate of inflation for the house?

The amount of Php 12,800 in 4 yrs at 5% compounded quarterly is _____.

If P5,000 shall accumulate for 10 years at 8% compounded quarterly, find the compounded interest at the end of 10 years.

Php 500,000 was deposited at an interest of 6% compounded quarterly. Compute the compound interest after 4 years and 9 months.

A man purchased a monthly installment a P100,000 worth of land. The interest rate is 12% nominal and payable in 20 years. What is the monthly amortization?

If the nominal interest rate is 3%, how much is Php 5,000 worth in 10 years in a continuously compounded account?

The initial cost of pumping equipment including installation is Php 800,000 and the approved life of this equipment is 10 years for depreciation. The estimated salvage value of the mill is Php 50,000 and the cost of dismantling is estimated to be Php l5,000. Using Straight Line depreciation, what is the annual deprecation charge and what is the book value of the machine at the end of the 6th year?

A machine cost Php 7,350 has a life of 8 years and has a salvage value of Php 350 at the end of 8 years. Determine its book value at the end of 4 years using Sum of Years Digit Method.

A machine cost Php 7,350 has a life of 8 years and has a salvage value of Php 350 at the end of 8 years. Determine its book value at the end of 4 years using Declining Balance Method.

A machine cost Php 7,350 has a life of 8 years and has a salvage value of Php 350 at the end of 8 years. Determine its book value at the end of 4 years using Double Declining Balance Method.

Engr. Aldrei borrowed Php 50,000 from a Business Loan with an interest rate of 8% compounded quarterly payable in equal quarterly installments for 10 years. Find the quarterly payments.

The _____ of an asset is the difference between its cost and the accumulated depreciation.

A temperature of 180 °F is approximately equal to _____.

What is the number or horsepower required to raise 25,000 lbs of water for a height of 30 meters within 10 mins?

What is the pressure in pounds per square inch at the base of a 10 foot water cylinder?

A man bought plumbing tools worth Php 2,100. The sales tax was 8%. How much did he pay?

How many gallons of water can a 75 hp engine raise 150 ft in 5 hours? Assume 1 gal = 8.35 lbs

2 gallons is equal to _____.

What is the Fahrenheit equivalent of 26.50 °C?

1 rev = _____ mils.

The specific gravity of Cast Iron is 7.20. Find its weight density in lbs/ft³.

In a class of 40 students, 27 like Calculus and 25 like Chemistry. How many like both Calculus and Chemistry?

A polygon with 10 sides.

Dudong sold 100 boxes of A4 paper. Eighty of them were sold at a profit of 30% while the rest were sold at a loss of 40%. What is the percentage gain or loss on the whole stock?

Decrease in the value of a physical property due to the passage of time.

We may classify an interest rate which specifies the actual rate of interest on the principal for one year as _____.

An index of short term paying ability is called _____.

Direct labor cost incurred in the factory and direct materials costs are the cost of all materials that go into production. The sum of these two direct cost is known as:

A market whereby there is only one buyer of an item for which there are no goods substitute.

The paper currency issued by the Central Bank which forms part of the country’s money supply.

The total income equal to the total operating cost

The place where buyers and sellers come.

Work-in process is classified as _____.

These are product or services that are required to support human life and activities that will be purchased in somewhat the same quantity even though the price varies considerably.

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

What do you call the area bounded by two concentric circles?

The amount of heat needed to raise the temperature one pound of that substance one degree Fahrenheit is _____.