[PA] Sample Problems 01 | Advanced

Simplify i²⁰¹⁷ + i²⁰¹⁵

Simplify i²⁰¹⁷²⁰¹⁶²⁰¹⁵²⁰¹⁴²⁰¹³¹⁹⁹⁴³

Compute the absolute value of 3 + 4i.

If A = -2 – 13i and B = 3 + 4i, what is A/B?

Solve for x if 9 – 4eˣ = 5

Solve for x if 5³ˣ = 5ˣ⁺⁸

Solve for x if log₈(x – 5) = 2/3

Solve 2/3 + 5/8 – 1/2 = ?

Solve 1 ½ + 2 ¾ = ?

At how many minutes after 3 pm will the hands of a clock be perpendicular to each other for the first time?

In how many minutes after 7 pm will the hands of the clock be together for the first time?

In how many minutes after 3 pm will the hands of the clock be together for the first time?

Six years ago, Jun was 4 times as old as John. In 4 years, he would be twice as old as John. How old is Jun now?

In 5 years, Jose would be twice the age of Ana. Five years ago, Jose was 4 times as old as Ana. Find the sum of their present ages.

A boy is one-third as old as his brother and 8 years younger than his sister. The sum of their ages is 38. How old is his sister?

One number is 5 less than the other. If their sum is 135, what is the product of the numbers?

The sum of the two numbers is 21 and one number is twice the other. Determine the product of the numbers.

The denominator of a certain fraction is 3 more than twice the numerator. If 7 is added to both terms of the fraction, the resulting fraction is 3/5. Find the original fraction.

Express 2763 in Roman Numerals

MCMXCIV is equivalent to

A plumbing supplier bought a faucet for Php 200. At what price should this faucet be sold so that giving a 20% discount, the profit is 30%?

Solve for x if 8ˣ = 2ʸ⁺² and 16³ˣ⁻ʸ = 4ʸ

The value of w varies as the square root of x and is inversely to z. When x = 4, z = 2 and w = 100 Find w if x = 36 and z = 5.

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

2000kg of steel containing 8% nickel is to be made by mixing a steel containing 14% nickel with another containing 6% nickel. How much of the 14% nickel is needed?

A chemist of a distillery experimented on two alcohol solutions of different strength, 35% alcohol and 50% alcohol respectively. How many cubic meters of 35% must he use in order to produce a mixture of 60 cubic meters that contain 40% alcohol.

Find the quotient and remainder when 4y³ + 18y² + 8y – 4 is divided by 2y + 3?

What is the remainder when 3x⁴ + 2x³ – 5x² + x + 7 is divided by x – 3?

Find the 30th term of an Arithmetic Progression 4, 7, 10…

What is the sum of the progression 4, 9, 14… up to the 20th term?

The 5 term of an A.P. is 123 and the 30th term is 245. What is the 12th term?

The 6th term of a harmonic progression is 12, the 10th term is 6, find the 18th term.

Find the value of x if it forms a harmonic progression, 1, 1/3, 1/x, 1/7, …

The 3rd term of a harmonic progression is 15 and the 9th term is 6. Find the 11th term.

The 4th term of a geometric progression is 189 and the 6th term is 1701. What is the 12th term?

If the 3rd term of a GP is 28 and the 5th term is 112, find the sum of the first 10 terms.

Is the most frequently occurring value in the data set.

Factor the expression x² + 6x + 8 completely.

Factor the expression 3x³ + 3x² – 18x.

Factor the expression x⁴ + 9x² + 81.

Find the product of the following algebraic expression: (3x³ + 2x² + x – 2)(x + 4)

(a-b)³ =

The boat travels downstream in 2/3 the time as it does going upstream. If the velocity of the river current is 8kph, determine the velocity of the boat in still water.

The velocity of an airplane in still air is 125 kph. The velocity of the wind due east is 25 kph. If the plane travels east and returns back to its base again after 4 hrs. At what distance does the plane travel due east?

A tank is filled with an intake pipe that will fit it in 4 hours and an outlet pipe that will empty it in 12 hours.in 12hours. If both pipes ate left open, how long will it take to fill the empty tank?

Three pipes are used to fill a pool with water. Pipe A alone can fill the pool in 9 hours. Pipe B can fill it in 6 hours and Pipe C can fil it in only in 3 hours. How many minutes will it take to fill this pool if all three pipes are used simultaneously?

Laborer A can finish pipe laying in 4 days. Laborer B can finish the same job in 6 days. If Laborers A and B plus another Laborer (Laborer C) can finish pipe laying in only 2 days working together, How long will it take for Laborer C to fish the job alone?

48. Two motorists start out from two towns 420 km. apart and travel toward each other at the hourly rate of 30 and 40 km respectively. In how many hours will they meet?

A factor repeated to produce a power is?

Is a branch of mathematics dealing with integers and more generally, numerical computation.

30 ÷ 5 x 3 = _____

In the expression ᵃ√b what do you call “a”

It is defined as the amount of heat required to raise the temperature of one pound of water by one degree Fahrenheit.

5 hp = _____ kW

He conceptualized that the heavier the object, the faster speed it will fall.

If 10 workers are working for 4 hours and complete the work in12 days, in how many days will 8 workers working for 6 hours complete the same work?

A bullet fired at an angle of 45 deg with a velocity of 20 m/s. What is the horizontal range of this flight?

Is an account or record used to store bookkeeping entries for balance-sheet and income-statement transactions.

In liquids and gases, heat transfers takes place by _____.

Is the stored energy in any object or system by virtue of its position or arrangement of parts.