Mathematics Formula For your Exams.!

Important Notes and Formulas

Numbers

Type	Definition
Natural numbers	All whole numbers except 0 eg: 1, 2, 3, 4, 5...
Even numbers	0, 2, 4, 6, 8, 10...
Odd numbers	1, 3, 5, 7, 9...
Integers	whole numbers that can be positive, negative, or zero eg: -1, -2, -3, 1, 2, 3...
Prime number	a natural number which has only 2 different factors eg: 2, 3, 5, 7, 11, 13...
Composite number	a natural number that has more than 2 different factors eg: 4, 6, 8, 9...
Real number	Include rational and irrational numbers, fractions, and integers
Rational number	a number that can be expressed as a fraction or as a ratio
Irrational number	a number that cannot be expressed as a fraction or a ratio of 2 integers. eg: pi and roots

Mathematics Formula For your Exams.!

Important Notes and Formulas

Numbers

Type	Definition
Natural numbers	All whole numbers except 0 eg: 1, 2, 3, 4, 5...
Even numbers	0, 2, 4, 6, 8, 10...
Odd numbers	1, 3, 5, 7, 9...
Integers	whole numbers that can be positive, negative, or zero eg: -1, -2, -3, 1, 2, 3...
Prime number	a natural number which has only 2 different factors eg: 2, 3, 5, 7, 11, 13...
Composite number	a natural number that has more than 2 different factors eg: 4, 6, 8, 9...
Real number	Include rational and irrational numbers, fractions, and integers
Rational number	a number that can be expressed as a fraction or as a ratio
Irrational number	a number that cannot be expressed as a fraction or a ratio of 2 integers. eg: pi and roots

Numbers

The numbers are used for counting and measuring. In mathematics, number is a mathematical object used to count and measure. There are so many numbers like negative numbers, zero, positive numbers, real numbers and they are said to be the main source of mathematics. All numbers are classified into sets and every number represented a unique representation. Mathematical operations are only possible if one have the knowledge of numbers..

The general format of the counting number is {1, 2, 3, 4, 5…}. The counting number is known as the positive integer or non negative integer. The counting number should not use the zero, negative number, fraction number and decimal numbers. The examples of the negative numbers are -86, -97 and -56 etc.

Operations for counting numbers

The counting numbers are performing the many operations. Those operations are

• Add the counting numbers
• Subtract the counting numbers
• Multiple the counting numbers
• Divide the counting numbers

Add the counting number operator is +, subtracting the counting number operator is -, the multiple the counting number operator is * and divide the counting number operator is /. 

Numbers for Kids

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A number is a mathematical object used in counting and measuring. A notational symbol which represents a number is called a numeral, but in common usage the word number is used for both the abstract object and the symbol, as well as for the word for the number. In addition to their use in counting and measuring, numerals are often used for labels.

Below you could see some examples

Solved Examples

Question 1: How many apples are there in the picture?

Solution:

There are 5 apples in the picture.

Question 2: In the following picture, which is more? Number of parrots or number of flowers?

Solution:

Number of parrots = 4

Number of flowers = 3



Therefore, number of parrots are more than number of flowers in the given picture.

Number Chart

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Let us learn about number chart. Here number chart is one of the most important manipulative devices, that is available for teaching mathematics. We can certainly count a numbers from a number chart. The number chart is used in mathematics for teaching a number patterns, number relationships, operations and problem solving.

Below you could see the number chart 1-100

The numbers will not be over within 3 digits, 4 digits, or......N digit numbers. But we cannot keep counting them till N digit numbers hence, they go on forever till ∞ (infinity).

Number Line

A number line is a line on which real numbers are placed according to their value. For example, the number 3.5 or 3 12 corresponds with the point on a number line that is halfway between the numbers 3 and 4. Each point on a number line corresponds to a real number, and each real number has a unique point on the Number line that corresponds only to that number. Number lines are valuable tools which are easily used to illustrate the mathematical concepts such as subtraction, addition and positive and negative numbers. In number line, right side of zero are positive numbers and left side of zero are negative numbers.


The number line is usually represented as a horizontal line.

Types of Numbers

There are several types of numbers, which can be given below :-

1. Natural Numbers
In learning algebra numbers, it is necessary to learn about Natural numbers. That can be represented by all Whole numbers except ' 0 '. And all these numbers are positive numbers only.
Example: (1, 2, 3, 4, 5, . . . )

2. Whole Numbers
In algebra numbers, the whole numbers can be represented by the set of numbers which is starting from 0 to infinity.
Example: (0, 1, 2, 3, . . . )

3. Integers
The integers are the set of numbers which contains all negative, positive numbers and also zero. There is no decimal numbers.
Example: (. . . . . . . . -4, -3, -2, -1, 0, 1, 2, 3, 4, . . . . . . . . . . . )

4. Rational Numbers and Irrational Numbers
The rational numbers and are the set of all numbers which can be written in fraction form. As a fraction ab, where a and b are integers(b≠0). Irrational is used only when a number which cannot be written in the form of simple fraction.

Example: 3√ Irrational
4√ = 2 Rational
5√, 6√, 7√, 8√ Irrational
94−−√ Rational
2√ Irrational

5. Real Numbers
The real numbers are the set all numbers which contains both rational numbers and irrational numbers.


6. Odd Numbers
A number which is not divisible by 2 is called an odd number.

Example: (3, 5, 7, 9, 11, . . . . . . . )
⇒ Find out the all Odd numbers from (7, 2, 5, 3, 9, 22, 49, 18, 29, 36)
Answer : Odd Numbers: 3, 5, 7, 9, 29, 49

7. Even Numbers
A number which is divisible by 2 is called an even number.

Example: (2, 4, 6, 8, 10, . . . . . . . )
⇒ Find out the all Even numbers from (7, 2, 5, 3, 9, 22, 49, 18, 29, 36)
Answer : Even Numbers: 2, 18, 22, 36

8. Prime Numbers
A number which is divisible by it self and it's not divisible by any numbers.

Example: (2, 5, 7, 11, . . . . . . . . . .)
⇒ Find out the all prime numbers from the given below. (9, 2, 4, 7, 11, 29, 17, 49, 101)
Answer : Prime numbers: 2, 7, 11, 17, 29, 101

Number System

Number system is defined as the proper understanding and usage of the numbers in the various places. Numbers are the basic building stones of mathematics.Number system is a way of counting using a particular base.There are different types of numbers exist, we will learn about them in brief at number system.
It includes:

• Ability to find the relative values of a number.
• How to use a number in different arithmetic operations like addition, subtraction, multiplication and division
• Finding the problem solving strategies

Numbers system covers various topics. They are,

• Estimating and rounding
• Rounding and addition
• Rounding and product
• Rounding and division

  Estimating and Rounding

  The rounded number value will be same as the original number value but it will less exact. It is an approximate value of the original number.
  Rules:
  

  • If the number we are rounding is followed by number greater than or equal to 5, then round the number up.
  • If the number we are rounding is followed by number less than 5, then round number down.

  Example 1:
  Round the number 46 to nearest ten
  Solution:
  Here 6 is greater than 5, so it is rounded up
  46 is rounded to near ten digit 50
  Example 2:
  Round the number 43 nearest ten
  Solution:
  Here 3 is less than 5, so it is rounded down
  43 is rounded down to near ten digit 40
  Example 3:
  Round the number 1975 to nearest thousand
  Solution:
  Here it is rounded to 2000
  

  Rounding and Product

  Here, the numbers are rounded and then multiplication operation is carried on.
  Example1:
  62 x 56
  solution :
  Rounded value of 62 is 60
  Rounded value of 56 is 60
  Product = 60 x 60
  Product = 3600
  Example 2:
  25 x 9
  solution:
  Rounded value of 25 is 30
  Rounded value of 9 is 10
  Product = 30 x 10
  Product is 300
  The same procedure is also carried out in decimals.
  

  Rounding and Division

  Here, first round up the given numbers and then division of numbers are performed.
  Example 1:
  4218
  Solution:
  Rounded value of 42 is 40
  Rounded value of 18 is 20
  Now dividing the rounded numbers
  4020
  = 2
  Example 2:
  496
  Solution:
  Rounded value of 49 is 50
  Rounded value of 6 is 10
  Now dividing the rounded numbers
  5010
  = 5
  The same procedure is carried out for decimal rounding also.
  Number system is a wide topic in mathematics and new research has been held based on number system frequently.
  

  Rounding and Addition

  Here, we have to round the number and we have to perform the addition.
  Example 1:
  33 + 56
  Solution:
  Rounded value of 33 is 30
  Rounded value of 56 is 60
  Sum of the numbers = 30 + 60 = 90
  Example 2:
  23+34
  Solution:
  Rounded value of 23 is 20
  Rounded value of 34 is 30
  Sum = 20 +30 = 50
  

Types of Lines

Lines are infinitely long and thin straight geometrical object. Lines are classified in to different types based on their properties. The different types of lines are:

• Straight Line
• Vertical line
• Horizontal line
• Skew Lines
• Parallel Lines
• Perpendicular Lines

  Vertical Line

  
  
  
  Vertical Line is one of the types of lines with an undefined slope. Slope of the vertical line is undefined. We can draw a graph for vertical line by plotting x=n. Here, n equals to any type of real numbers. In simple words, we can say that all points in the straight line have the same x coordinate. It is parallel to the y axis of the co-ordinate plane.
  The equation of the vertical line is, x=a. Here x is any point in the line of coordinate x and a is the x - intercept.
  

  Horizontal Line

  Horizontal Line is one of the types of lines in which all points has the same y - coordinate. It is parallel to the x-axis of the plane. The slope of the horizontal line is zero.
  The horizontal line equation is Y=b. Here y is any point in the line of x coordinates and b is the y - intercept. It is independent on x.
  

  Parallel Lines

  
  If the distance between two straight lines is same at all points, then these types of lines are said to be parallel lines. In the two dimensional Euclidean space are said to be parallel if they do not intercept the two lines.
  

  Skew lines:

  

  When two non parallel lines are not intersecting in a space, they are called as skew lines. These types of lines are also known as agonic lines. It exists in three or more dimensions.
  

  Perpendicular lines:

  Perpendicular lines are one of the types of lines which is formed when a horizontal and a vertical lines meet each other. In other words, when the two lines form congruent adjacent angles to each other, they are said to be perpendicular lines.
  
  
  
  

Coordinate Geometry

The coordinate geometry is an important branch of mathematics. It mainly helps us to locate the points in a plane. Its uses are spread in all fields like trigonometry, calculus ,dimensional geometry etc. And the subject have obvious applications in statistics ,physics also. Here we will see some applications through examples. First we will see the coordinate plane, which is made up of x and y axes. The horizontal line is the x axis and the vertical line is the y axis.

We can see in the figure two intersecting lines, that is the x and y axis,and they meet at the origin (0,0). We are marking the coordinates using x and y ordinates respectively ,with a seperating comma. We can see the numbers marked in the plane ,at a unit difference. This will help us to locate the points easily.
For example: We can mark the point (1,1) directly up to the point 1 in x axis and directly straight to 1 in y axis to the right side. And for drawing graphs we have to plot the points like this and have to join them.

Coordinate Geometry Help

Suppose we have to find the distance between 2 points, we can use the help of coordinate geometry for this. For calculating the distance we have the distance formula in coordinate geometry. Distance d= √ [(x₂-x₁)² +(y ₂-y₁)² ]. To find the angle between 2 lines, we can use tan ^-1m, where m is the slope of the line with respect to the origin.

Coordinate Geometry in Real Life

In real life for the construction field we are mainly using the coordinate geometry. The sketch of the building is pure geometry. and for printing pdf files we are using this geometry help. For finding the distance between the places we are using coordinate geometry and in geography also it have many applications . In astrophysics to find the distance between the planets,coordinate geometry helps.