Prime Numbers

 Prime Numbers are those numbers which can be divided by itself and 1 only for example 1,3,5,7,11,13.......ans so on.

For example, 5 is prime because the only ways of writing it as a product, 1 × 5 or 5 × 1, involve 5 itself. 

Irrational Numbers

 An irrational number can be written as a decimal, but not as a fraction. An irrational number has endless non-repeating digits to the right of the decimal point. All most all real numbers are irrational

Like all real numbers, irrational numbers can be expressed in positional notation, notably as a decimal number. In the case of irrational numbers, the decimal expansion does not terminate, nor end with a repeating sequence . For example, the decimal representation of π starts with 3.14159, but no finite number of digits can represent π exactly, nor does it repeat.

Rational Numbers

Rational numbers: They represents the ratios of two integers. The set of all rational numbers is countable.A rational number is any number that can be expressed as the quotient or fraction p/q of two integers, a numerator p and a non-zero denominator q. Since q may be equal to 1, every integer is a rational number.

For example - 3/4 is a rational number.

24/8 is a rational number.

1.1 is a rational number → 11/10

π is irrational, as it cannot be represented as a fraction of two integers. (Read 22/7 is rational but π is not rational, so what is the ratio for π? for clarification

The digits in pi go on for infinity, but they never repeat. A number whose digits go on for infinity without repeating is irrational.

Any decimal number that terminates is rational because it can be written with a power of ten in the denominator

• 9.2651 = 9265110000$\frac{92651}{10000}$

Any decimal number that ends in repeating digits is rational because the value of those repeating digits can be written as a fraction.

• 6.4212121212121… = 2119330

ational number, in mathematics, a number that can be represented as the quotient p/ q of two integers similar that q ≠ 0. In addition to all the pieces, the set of rational figures includes all the integers, each of which can be written as a quotient with the integer as the numerator and 1 as the denominator. In decimal form, rational figures are moreover terminating or repeating numbers. For illustration,1/7 = 0.142857, where the bar over 142857 indicates a pattern that repeats ever

                                          

                                                  

Even Numbers

Even Numbers are those numbers that can be divided into two equal groups or pairs and are exactly divisible by 2. For example, 2, 4, 6, 8, 10, and so on. 

ODD NUMBERS

 A whole number that is not able to be divided by two into two equal whole numbers The numbers 1, 3, 5, and 7 are odd numbers.

Odd numbers are positive integers that cannot be categorized into groups of two. For example: 1, 3, 5, 7, etc. Let's visualize it using an example of footwear and cherries. Let us assume that we have footwear in counts of 1, 3, 5, and 7. On the other hand, we have cherries in pairs of 2, 4, 6, and 8. Look at the image given below in order to understand how the pairing of these numbers will work.

Properties of Odd Numbers

If you try to carry out a few arithmetic operation the odd numbers, can you come to a common conclusion of all of the numbers? Well yes, there does exist a set of properties that applies not only for the odd numbers given in the list of 1 to 200 but are applicable to any odd number that you may come across. Given below is a list of the properties that will always apply for an odd number. Each of these properties can be explained in a detailed way as given below:

• Addition: The addition of two odd numbers will always give an even number, i.e., the sum of two odd numbers is always an even number. For example, 3 (odd) + 5 (odd) = 8 (even).
• Subtraction: subtract of two odd numbers will always give an even number. For example, 7 (odd) - 1 (odd) = 6 (even).
• Multiplication: it is of two odd numbers will always give an odd number. For example, 3 (odd) × 7 (odd) = 21 (odd).
• Division: division of two odd numbers will always give an odd number. For example, 33 (odd) ÷ 11 (odd) = 3 (odd).

Natural Numbers

A natural number is a number that occurs commonly and obviously in nature. As such, it is a whole, non-negative number. The set of natural numbers, denoted N, can be defined in either of two ways: N = {0, 1, 2, 3, ..} , N = (1, 2, 3, 4, .)

Whole Numbers

Number which are started from 0 are called whole numbers.

For Example: 0, 1, 2, 3, 4, 5, 6, and 7 are all whole numbers. Numbers such as -3, 2.7, or 3 ½ are not whole numbers.

 Let's sing!

Zero, one, two, three and four.

Whole numbers are many more.

Go on! Count on my friend!

Whole numbers just don’t end!

 Fun Facts

• There is no 'largest' whole number. 
• Except 0, every whole number has an immediate predecessor or a number that comes before.
• A decimal number or a fraction lies between two whole numbers, but are not whole numbers. 
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HOW TO GET GOOD MARKS IN MATHS

 Many of us believe that to score high in Mathematics one should have an extraordinary brain. But this is not true. Maths is a subject which develops a rational thinking and a logical approach in a student. It is quite difficult for a student to fall in love with Mathematics overnight but here are a few tips to enhance your Mathematics score.

FOLLOW THESE STEPS

 

1. Maintain a separate register for formulae, theories, and methods

This subject is all about formulae, theories, concepts and you are always suggested to keep them handy. You can read them even when you are on the go. This practice is really useful when you are doing your last minute revision.

2. Find solutions yourself

It is good to go through various types of problems, but at the same time, you should also make sure that you solve them for yourself. It is easy to learn the theories and concepts but to learn their application is not that simple. So, if you want to score full marks in Mathematics, you need to solve each question by yourself, at least 3 to 4 times.

3. Understand the Syllabus

Having a clear understanding of your syllabus and weight to various sections will definitely help you to decide how much time you should dedicate to each section. For example, if you are aware that there will be a 5 mark question from a specific section, then you don’t have to spend too much time on such questions.

4. Determine the areas of Improvement

Realizing the areas where you need to focus more will definitely help you to score better. Solving sample papers, writing tests can help you to find those sections in which you need more practice so that you can improve the scores.

Things to consider during Examination

5. Keep the exam paper clean

You should keep in mind that the examiner has to understand every step of your answer and in most of the cases he would not be having much time to spend on a single answer. Avoid overwriting and cutting clean margins for rough work.

6. Answer in steps

Whenever you go through an answer, ensure to pay special attention to the steps that helped you to reach out to get the answer. You cannot simply write the answer and get full marks in Maths, so simply paying attention to the figures is wastage of time. Instead of all this, learn to keep the steps involved. You will definitely secure some marks for each step.

7. Attempt the Familiar questions

Read the question paper thoroughly before you begin to solve the questions. It is very normal to get stuck on the questions which you are not aware of but simply remember that you have a stipulated time to attend the paper. In order to score high in Maths, you must attend the questions you know and then move on to the unfamiliar ones.