Algebra and Complex Numbers Flashcards

Flashcards for Algebra and Complex Numbers supplementary problems.

Algebra

A line or expression characteristic.

Complex Numbers

Numbers that includes a real and imaginary part.

h = 17/2

In the equation 3x² + 4x + (2h-5) = 0, if the product of the roots is 4, what is h?

k = 4

What value of k makes the expression kx² - 3kx + 9 = 0 a perfect square?

m/n = 2 or 6

In the equation m² - 8mn + 12n² = 0, what is the ratio of m to n?

k = 5

Determine the value of k so that the equation x² + (k-5)x + 2 =0 is a perfect trinomial square.

Remainder = 652

Find the remainder when (x^12 + 2) is divided by (x-√3).

Fifth term = 3240x^4y

Find the fifth term in the expansion of (2x-3y)^5

Sum of areas = 180 sq ft

The area of two squares differs by 108 sq ft and their perimeters differ by 24. Find the sum of their area.

Least amount = P2.4M

Three electrical engineers divide their company profit of P18M in the ratio 2:5:8. Find the amount of the one who will receive the least.

Time to fill = 1.92 hours

One pipe can fill a tank in 5 hours and another pipe can fill the same tank in 4 hours. A drain pipe can empty the full content of the tank in 20 hours. With all the three pipes open, how long will it take to fill the tank?

y = 2xz/(x+z)

If 1/x, 1/y, 1/z are in arithmetic progression, then y in terms of x and z is equal to:

Roots are 1/u and 1/v

If the roots of ax² + bx + c = 0 are u and v, then the roots of cx² + bx + a = 0 are:

Original men = 20

A group of men can do a job in as many days as there are men in the group. If the number of men is reduced by 4, the job will be delayed by 5 days. How many men were there originally in the group?

Terms = 50

How many terms in the progression 3, 5, 7, 9, … must be taken in order that the sum is 2,600?

10th term = 55

Find the 10th term of the sequence 1, 1, 2, 3, 5, …

Theorem

An idea formed from something that is already proved.

Fibonacci Numbers

A series of numbers which are perfect square numbers (i.e. 1, 4, 9, 16, …) is called

Rational

The number 0.123123123… is

Loss P200

A man sold his two cellphones at P9900 each. He gained 10% on one and loss 10% on the other. Did he gain or lose on this transaction?

$80

John started his egg farm business. His chicken's produce 480 eggs per week. If he sells it at $2 a dozen (let 1 week = 7 days). How much does his chicken produce per week?

23,700

The sum of the integers between 288 and 887 that are exactly divisible by 15 is

41

The sum of the prime numbers between 1 and 15 is:

3/4

What is the sum to infinity of the sequence 1/2, 1/6, 1/18…?

x² - 12x + 32 = 0

Two students were solving a problem that would reduce it to a quadratic equation. The first student committed an error in the constant term and found the roots to be 5 and 7 while the second student made an error in the first-degree term and gave the roots as 2 and 16. If you were to check their solutions, the right equation is?

80

What is the sum of the first 80 positive odd integers subtracted from the sum of the first 80 positive even integers?

P3.70

Ana bought ballpens for P90. Then she sold it all with a profit of P2 each ballpen. If after selling the ballpens, she will buy with additional 15 ballpens, what is the cost of each ballpen?

1

What is the sum of the coefficients of the expansion of (2x-1)^20?

16 & 32

A father is twice as old as his son and the sum of their ages is 48. How old is each?

18 & 27

I am three times as old as you were when I was as old as you are now. When you got to be my age together our ages will be 84. How old are we now?

C = 1

4(abcde4) = 4abcde, where a, b, c, d, and e are digits of the number. Find c?

16 kg, 14 kg

How much silver and how much copper must be added to 20 kg of an alloy containing 10% silver and 25% copper to obtain an alloy containing 36% silver and 38% copper?

64/729

A tank full of alcohol is emptied of one third of its content and then filled up with water and mixed. If this is done six times, what fraction of the volume (original) of alcohol remains?

76 kilos

If 19 kilos of gold lose 1 kilo; and 10 kilos of silver loses 1 kilo when weighed in water, find the weight of gold in a bar of gold and silver weighing 106 kilos in air and 99 kilos in water?

20 km

A man travels in a motorized banca at the rate of 15 kph from his barrio to the población and come back to his barrio at the rate of 12 kph. If his total time of travel back and forth is 3 hours, the distance from the barrio to the población is

6 km

March: 1978. A troop of soldiers marched 15 km, going to the concentration camp after they were forced to surrender, while the victorious general who is supervising the "march" rode from the rear of the troop to the front and back at once to the rear. If the distance covered by the victorious general is 25 km. and both the troop and general traveled at uniform rate, how long is the troop?

81, 121

Two numbers differ by 40 and their arithmetic mean exceeds their positive geometric mean by 2. The numbers are

4.7461

A 20-liter container is filled with pure acid. Five liters are drawn off and replaced with water; then 5 liters of the mixture are drawn off and replaced with water, and so on until 5 drawings and 5 replacements have been made. Find the amount of acid in the final mixture.

10 kg

A certain amount of 80% sugar solution added to another amount of 40% sugar solution yields a solution that contains 14 kg of sugar. Had the amount been reversed, the solution would have contained 16 kg sugar. How much of the 80% solution was there?

2.36

Find the harmonic mean 7, 1, 5, 2, 6 and 3.

0.03

Find the 100th term of the sequence 1.01, 1.00, 0.99,…

2

A can do a job in 4 days, B can do the job in 6 days and C can do the job in 8 days. How long will it take to do the job if A and B work for 1 day then B and C finish the job?

60

A father and his son can dig a well if the father works 6 hours and his son works for 12 hours or they can do the job if the father works 9 hours and the son works for 8 hours. How long will it take for the son to dig the well alone?

45 days

A man and a boy can dig a trench in 20 days. It would take the boy 9 days longer to dig it alone than it would take the man. How long would it take the boy to dig alone?

6:21.82

What time between 6 and 7 o'clock will the minute and hour hands of the clock form 60° for the first time?

22

How many times in one complete day will the hour and the minute hands coincide with each other?

500

If 500 cats can catch 500 rats in 500 hours how many cats are needed to catch 3 rats in 3 hours?

43251

Numbers like 12345, 13542, 53412 and 21435 are some of the 120 different arrangements that can be made from the digits 1, 2, 3, 4 and 5. If all 120 arrangements are placed in numerical order, what will be the 87th number?

88% C

If A is 10% greater than B and B is 20% less than C, then A in terms of percentage of C is

40 hectares

One proposal in the Agrarian Reform Program is to have a retention limit of 10 hectares. If a landowner was left with 10 hectares fewer than 40% of his land after selling 6 hectares more than 70% of his land, what size of land did he initially own?

12

Find the greatest common factor of 108 and 60.

19%

When the side of a square is decreased by 10%, its area decreases by?

21%

When the diameter of a circle is increased by 10%, its area increases by?

71

Find the 10th term of the sequence 2, 4, 7, 12, 21,..

1

Which of the following cannot be the base of a logarithm?

Pyramidal Number

A sequence of numbers where every term is obtained by adding all the preceding terms such as (1, 5, 14, 30…) is called:

Harmonic Progression

A sequence of terms whose reciprocals form an arithmetic progression.

Naperian Logarithm

The logarithm of a number to the base e (2.718281828…) is called

Solution Set

Two or more equations are equal if and only if they have the same:

8

Compute the sum of all the coefficients in the expansion of (x + 2y - z)^3

Zero

Any number divided by infinity is?

Probability

The number of favorable outcomes divided by the number of possible outcomes is:

24.3 cm

A figure 30 cm high is reduced by