Steps in problem solving

Previously we have discussed about verifying trigonometric identities worksheet and In today's session we are going to discuss about Steps in problem solving which is the most important part of secondary school education andhra pradesh, The problems that looks very complex initially are not solve directly so there are basically some Steps in problem solving that are use in solve math problems as follows:
Step no (1): Problem understanding – In this step first states the problem in your own words then find the main problem or thing you want to solve.
Then find the all unknown variable into the given problem and check the other information you need to find the solution for main problem.
Step no (2): After writing the problem into own understanding way make a plan to solve the problem – There are some steps or strategies that helps in making a plan:
First of all check the pattern of the problem then research for the other problems that are solved before having the same pattern .After getting the all results then make the tables and diagram according to the given problem and at last make the suitable expression for the problem that have the same pattern as before solved problems
Step no (3) : act according to the plan – After making a useful plan implement according to the plan means perform the necessary actions and computations that are helping us in solving problem .when getting the answer check them that these are according to the expected answer or not and if these are not according to them then apply other plan for problem solving .Maintain the record for each and every calculations .
Step no (4) : Back track :Check the Result by putting in the original problem and find another method to cross check the answer and also find the other related problem that are in more general form by solve with the existing technique or method .
In the next session we are going to discuss about Mathematics in daily life and You can visit our website for getting information about online math help.

equally likely events

Hello students,Previously we have discussed about inverse function worksheet and In today's session we are going to discuss about equally likely events which is a part of board of intermediate education andhra pradesh, In the mathematics we deals with the probability and their events such as exhaustive, dependent, independent, mutually exclusive, favorable and many more. Equally likely events are one of them. Let’s talk about the equally likely events definition : - In some experiments we know the results in advance but actually do not know the exact result, this type of results are called the random experiments and the result of random experiments are called equally likely events if the different outcomes have the same chance of occurrence.
For example when a die is thrown, each of the faces bearing one, two, three, four, five or six dots is equally like to appear.
Another example when we toss a coin then we have a chance to get either a Head or Tail.
Means it includes all those experiments in which we know the all results but we do not know the actual or exact results.
Let’s take examples -
Which of the following experiments have equally likely outcomes or events.
I) A driver attempts to start a car. The car start or does not start.
II) A players attempts to shot a basketball. she/he shoots or misses the shot.
III) A trial is made to answer a true false question. The answer is right or wrong.
IV) A baby is born. It is a boy or girl
Solutions : - (I) A driver attempts to start a car. The car starts or does not start, is not equally like events.
(II) A players attempts to shot a basketball. she/he shoots or misses the shot are not equally like events.
(III) A trial is made to answer a true false question. The answer is right or wrong is an equally like to occur.
(IV) A baby is born. It is a boy or girl is an equally like occur event.


In the next session we are going to discuss Grade VI, Steps in problem solving and You can visit our website for getting information about free math tutor.

Mathematical Reasoning

Previously we have discussed about difference between rational and irrational numbers and In today's session we are going to discuss about Mathematical Reasoning which is a part of ap secondary education board, Mathematical reasoning explained by solving the problem without knowing that what is to be done but when you know how to solve the problem then it is not consider as mathematical reasoning .For the question about what is mathematical reasoning the answer is that collection of the problems that are not in routine life and they are not solved by using any normal procedure and these problems are solved by making own strategies and by making own methods , also these are not based on the single strategy but based on the variety of strategies are known as the mathematical
There are some mathematical reasoning examples to understand the way of solving the problems of mathematical reasoning: Example: If Jon have 23 chocolates and he put equal number of chocolates in two bags and after putting seven chocolates are left then how many chocolates he put into each bag? The problems will need only little bit of attention to solve are considered as mathematical reasoning problems.
These types of problems are helping the students to make their mathematical concept strong as well as they helps the student to save their extra time that is spend in problem solving as for example If we want to multiple the number 36 * 18 then it will solved in more easy way as add 4 to 36 that is equal to 40 (36 + 4) and add 2 in 18 to make it 20 as (18 + 2) and multiply them that is much easier then multiply 36 * 18 and answer for multiplication 40 * 20 = 800 and subtract 4 and 2 that is totally 6 from 800 that is 794 that is the actual answer for multiplication of 36 * 18 .
In the next session we are going to discuss Grade VI, equally likely events and You can visit our website for getting information about free online tutor.

Informal and mathematical language

Hello students, in daily to daily life we use language to telling something to anyone not only we use but everyone use the language for the communication. The language may be anyone like English, Hindi, Latin and many more. But have you ever think about the language of Maths.  Here we are going to discuss the language of maths especially for the informal and mathematical language. In mathematics we use so many types of methods, theorems, expressions, symbols, proofs and many things, the all are comes in mathematical language. It is true that mathematics language is not used for the communication but without this we can nothing understand in math. Like algebra which is totally written in symbolic form.
We assumes math as a language and generally mathematical language is used for the better understanding, to represents the mathematical theorems more clearly, give their reason very logically so that everyone can easily understand. Mathematical language have own grammar, syntax, symbols and conventions. Like we use x for expressing theorems. The vocabulary words for the logic are ‘and’, ‘or’, ‘not’, ‘if…then’, ‘for all’, and ‘if and only if’. Symbols for operation are +, -, *, /, ∏, ∟, ∞, √, ∑, and ⌠ many more. Mathematical language is only used by the mathematicians for the communicating mathematical thoughts among themselves. (know more about cbse books for class 11, here)
Mathematical language also gives precise information for English like statements like we write a is equal to b in English language but the same statement in mathematical form will be a = b. The informal language in math is only used for understanding the concepts and proofs. Generally this language is not written; usually it is used for spoken and used according to the situations or conditions. In the next session we will discuss about Mathematical Reasoning. 

dependent

Probability can be considered as a branch of mathematics that deals with the calculation of likelihood of a given event’s occurrence. The occurrence of an event can be described in terms of number between the 1 and o. In the terms of probability, an event with a probability of 1 can be describe as certain or in the same aspect the probability of .5 can be specify as a half odd or half even. In the probability, an event is word which can be defined as a particular work which is performed in continues time period. When an event is performed in a particular time period then to estimate the outcome of that event, we use the concept of probability.
In the simple form we can say that when the number of occurring events is divide by the total number of events plus the number of failure of occurrence are known as probability. In the probability, some of the cases occur which has the two events. It means that in the probability some time two events are performed together at a time. On the basis of probability we can categorized the events in two ways, which are given below:
A)      Dependent event
B)      Independent event
Dependent events = Dependents are those events in which outcome of the one event affects the outcome of another event. It means to say that the output of the one event depends on the output of another event.
Independent events: independents events are those events which are independent to each other. It means that the outcome of one event not affect the outcome of another event. (know more about cbse sample papers for class 10, here)

Example: Suppose there is pack of playing card. If in case we pick card of king of heart. In the next time if we pick the card then it is obvious that card is not same to the king of heart. So, we can say that here both events are dependent to each other because in a Dependent Events Probability of the pack of card, there is only one king of heart exists.  In the next session we will discuss about Informal and mathematical language. 

Tools to solve problems

In mathematics, we know that various types of tools are provided to solve the problem that is related to calculation. Problem solving is the logical process which includes the process of finding the problem and estimate there solution. In the process of solving problem, mathematics provides lots of tools like addition, subtraction, multiplication, division, various types of concept like equation and various types of formulas and theorems. Here we are going to discussing about the most popular Problem Solving Model that are used to solving problem.
Addition: addition is the most basic tool of the mathematics which is used to perform the sum of the different objects like total money in the account, total amount of bill etc.
Example: 4 + 3 = 7
Subtraction: this operation is also a most basic tool to perform the difference between two given objects like how money was left after spending in the market and so on.
Example 15 – 5 = 10
Multiplication and division: these are the most popular that helps in to overcome form the problem of repetitive calculation.
The above are the most basic tools that are used in our daily routine life without applying any concept or rule. But in mathematics, sometime we need to solve to solve those types of problem, where we need to find the value of the unknown variable. On the basis of unknown variable the solution of the problem depends. To solve that kind of problem we required the concept of mathematics that is known as algebra. Algebra is the mathematical concept, which is used to change the problem into equation then by finding the value of variable to solve the problem. (know more about cbse sample paper for class x, here)
Example: a + 5 = 9
In the above we can say that there is an example of equation, where we need to fill the value of a by the appropriate number which satisfy the given equation true. In the various field of science mathematical Tools To Solve Problems, are most widely. In the next session we will discuss about dependent.