Study Randomness

Introduction to study randomness:

Randomness is a concept of non-order or non-coherence in a sequence of symbols or steps, such that there is no intelligible pattern or combination. Randomness implies a lack of predictability with the concepts of chance, probability, and information entropy. More formally, in statistics, a random process is a repeating process whose outcomes follow no describable deterministic pattern, but follow a probability distribution.


Studying Events on study randomness:

The studying of randomness are as follows:

Event

An outcome of an experiment is called Event. When two or more events occur in connection with each other the joint occurrence is called a compound event. Events are classified into

1) Independent

2) Dependent

3) Mutually Exclusive event.

Independent: An event A is said to be independent of another event B when the actual happening of A does not influence in any degree the probability of the happening of B.

Dependent: If another probability of the happening of B is dependent or influenced by the previous happening, then B is said to be dependent on A.

Mutually Exclusive: Two events B and A are to be mutually exclusive when through the occurrence of one of them, says A, the other event B cannot take place and vice versa, or when two events cannot happen at the same time.


Applications on study randomness


The studying applications of Randomness are as follows:

1) Games: Randomness is used in many games such as gambling, casino games. Randomness is generating unpredictable numbers. Dice, cards use in games of chance because of randomness.

2) Cryptography: Cryptography concept is developed for secure the data from the attacker or unauthorized users. Cryptography has the two events encryption and decryption using algorithms.

3) Music and art: Randomness is used for generating randomness music. We can use randomness for arranging item to exhibit.

4) Simulation: Simulation is used by many engineering field such as neutron transport in nuclear fission

5) Analysis: Many physics experiments are rely on statistical randomness analysis such as analysing x-rays

6) Statistical sampling: Many statistical process based on Randomness concept.

7) Science: Randomness is used in Physics, Operation research and engineering fields

Study Proposition

Definition of proposition:

A proposition is a standpoint that you will create, defend or destroy. It should be worded as a declarative sentence that definitely expresses your position.

A proposition can be the major point of your position. It can also be a single supportive part. It can also be an opposite proposition that you will disprove.

A statement that affirm or denies something.
The meaning expressed in such a statement, as opposite to the way it is expressed.

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Types of proposition


There are three types of proposition that is fact, value and policy.

Proposition of Fact

A proposition of fact is a statement in which you meeting point largely on belief of the listeners in its truth or falsehood. Your arguments are thus expected at getting your listeners to accept the statement as being true or false.

Proposition of Value

In a proposition of values, you make a report where you are asking your listeners to make an evaluative opinion as to whether the report is morally good or bad, right or wrong. This may be done by comparing two things and asking them which is better.

Propositions of Policy

A proportion of policies advocate a course of exploit In this, you ask your listeners to back a policy or to assign themselves to a particular action.

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Example problems


Example 1:

Given:  x/4 = 75 /100

Solution:

Step 1: We need to find x value.

Step 2: Here we are using cross multiplication method to solve x

Step 3: So, when we cross multiply we get 100x= 300

Step 4: Now we divide using 100 on both the sides

Step 5: The value of x= 3.

Example 2:

Given: 15/60 =75/p

Solution:

Step 1:  From this question we need to find p value

Step 2: Using cross multiplication we get, 15x= 4500

Step 3: Now we dived e using 15 on both the sides

Step 4: x= 4500/15

Step 5: x= 300

Study About Trigonometry

Introduction to study about trigonometric

Trigonometry (from Ancient Sanskrit "Trikona" or triangle and "Mati" or measure. Also from Greek trigōnon "triangle" + metron "measure") is a branch of mathematics that studies triangles, particularly right triangles. Trigonometry deals with relationships between the sides and the angles of triangles, and with trigonometric functions, which describe those relationships and angles in general, and the motion of waves such as sound and light waves. Trigonometry is usually taught in secondary schools either as a separate course or as part of a precalculus course. A branch of trigonometry, called spherical trigonometry, studies triangles on spheres, and is important in astronomy and navigation. (Source from Wikipedia)

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Study about basic trigonometry ratios:


There are six basic trigonometric ratios they are following,

sin `theta`= opposite /Hypotenuse

cos `theta`= adjacent / Hypotenuse

tan `theta` = opposite /adjacent

cot `theta` = adjacent / opposite

Sec `theta` = hypotenuse / adjacent

Cosec `theta` = hypotenuse / opposite.


Example problem :


Study about trigonometry word problem:

If the distance of a person from a pyramid is 200 m and the angle subtended by the top of the pyramid with the ground is 30o, what is the height of the pyramid in meters?

Solution:

First we have to plot the diagram to represent the given problem, and mark the date carefully.

Choose which trigonometric function represents the ratio of the side.(200)

Let as assume xy=Distance between man and pyramid.(h)

Similarly yz=Height of the pyramid we have to find

Here we have using the trigonometric function tan x here x=30 degree

Therefore tan x =opposite/adjacent

tan x =yz / xy

tan 30 = h/200

Height=tan 30 degree *200

Tan 30 degree=0.577

=0577*200

Therefore height of the pyramid =115.47

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Study about application of trigonometric:

Trigonometric used large number of application. It is mainly used in astronomy and geography.

Similarly trigonometric used many fields they are,

Electronics
Statics
Number theory
Acoustics
Computer graphics.
Meteorology
Economics
Navigation and aircraft

Study For Patterns Exam

Study for patterns:

A pattern, from the French patron, is a type of theme of recurring events or objects, sometimes referred to as elements of a set. These elements repeat in a predictable manner. It can be a template or model which can be used to generate things or parts of a thing, especially if the things that are created have enough in common for the underlying pattern to be inferred, in which case the things are said to exhibit the unique pattern.

Source: Wikipedia

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More about patterns for exam:


Study for patterns exam, you need to know the numeric patterns. Number patterns in algebra are patterns made from numbers. Study for patterns exam, we need know the basic operations like addition, subtraction, multiplication and division. So you can prepare numbers can be in a list. Any math operation used to make the patterns.

Study for patterns exam, we know about more information about patterns. Many of the patterns in algebra you see will use addition. The same number will be added to each number in the list to make the next number in the list in study for patterns exam.

Example study for patterns exam:

1, 3, 5, 7, 9, 11, 13…

The pattern in algebra is to add 2 every time. The next number is 15, then 17.


Example study for patterns exam:


Example 1:

2,5,8,11,14,17…

Solution:

The pattern in algebra is to add 3 every time. The next number is 20, then 23.

Example 2:

2,4,6,8,9,10,12,14,…

Solution:

If you guessed that the rule is counting by 2 using even numbers, you are correct.

Example 3:

1,1,2,3,5,8,13,21,34,55,…

Solution:

Look carefully and think!!!

If you concluded that the answer to this pattern in algebra is that you need to add number together to get the next number in line, you are correct.

1+1=2,2+1=3,3+2=5,5+3=8,…

This is a famous pattern in algebra or sequence known as the Fibonacci sequence.

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Practice problem study for pattern exam:

Problem 1:

A store gives a door prize to its third customer and to every fifth customer after that. Which of the following customers will get a door prize?

The 62nd

The 71st

The 79th

The 98th

Answer: D

Problem 2:

To find the next two number of pattern with proper explanation                                                                                            1,3,5,6,9,11,13,15,…

Answer: 17,19

Study Calculus Placement Exam

Introduction to Study Calculus Placement Exam

This is for the students who are preparing to take one or two Advance Placement Examinations in Mathematics offered by the College Entrance Examination Board, and for their teachers.

The Courses

Calculus AB and BC are both full-year courses in the calculus of function of a single variable. Both courses emphasize:

Student understanding of concepts and applications of calculus over manipulation and memorization
Developing the student’s ability to express function, concepts problems, and conclusion analytically, graphically, numerically, and verbally, and to understand how these are related.
Using a graphing calculator as a tool for mathematical investigations and problem-solving.

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Studying Topics on Calculus Placement Exam


Both courses are intended for students who have already studied college-preparatory mathematics. The main difference between the two is that BC calculus tests some more theoretical aspects of calculus and it covers a few additional topics. The AB exam usually tests straight forward problems in each topic. The BC asks harder questions but neither is tricky.

The Calculus AB and BC Examinations and the course descriptions are prepared by committees of teachers from colleges or universities and from secondary schools. The examinations are intended to determine the extent to which a student has mastered the subject matter of the course.

Each examination is 3 hours and 15 minutes long.

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The Calculus Placement Exam


First, In Part A there are 28 multiple choice questions for which 55 minutes are allowed. Calculators are not permitted. In Part B there are 17 multiple choice questions for which 50 minutes are allowed and a graphing calculator is permitted.

Second, the free response section ahs twp parts each have three questions each of which requires you to write out the solutions and the steps by which you solved it. You are permitted to use calculators for the first three questions and 45 minutes are allowed for each part.