A collection of distinct and well-defined objects is called a set.
Distinct means the same element should not appear more than once.
If set A is subset of set B and set B is not subset of set A, then set A is called proper subset of set B.
If two sets are equal, then they are improper subsets of each other.
A set having limited number of elements is called a finite set and a set having unlimited number of elements is called an infinite set.
Two sets are called equivalent if and only if one-to-one correspondence can be established between them.
Two sets with same elements are called equal sets.
A set having a single element is called a singleton set.
A set having no element is called an empty set.
The method of establishing one to one correspondence between two sets helps us to find out whether the sets are equivalent or non-equivalent.
If each element of a set A is also an element of a set B then the set A is called the subset of the set B and set B is called the super set of the set A.
The numbers that we use for counting objects are called the counting or natural numbers
The number 0 together with the natural numbers gives us the whole numbers.
According to the commutative law while adding or multiplying the two whole numbers, the result remains unchanged by changing their orders.
According to the associative law while adding or multiplying three whole numbers,any two whole numbers can be added or multiplied first.
The whole numbers can be represented by using a number line.
A number that divides a given number exactly is called a factor of the given number.
The multiples of a number are obtained by multiplying the number with natural numbers.
The numbers which are divisible by 2 are called even numbers and which are not divisible by 2 are called odd numbers.
A number having exactly two factors, 1 and the number itself is called a prime number and a number having more than two factors is called a composite number.
The number 1 is neither prime nor composite number.
The process of writing a number into prime factors is called prime factorization.
The largest common factor of two or more than two numbers is called highest common factor.
The least common multiple is the smallest number which is a multiple of given two or more numbers.
The numerical comparison between two quantities of same kind is called ratio. To find the ratio of two quantities, their units must be the same. A ratio is another form of a common fraction.
When both the elements of a ratio are multiplied or divided by any same number, the value of a ratio is not changed.
The relation of equality of two ratios is called proportion.
In a proportion, the 2nd and 3rd element are called means of a proportion and 1st and 4th elements are called extremes of a proportion.
One ratio is proportional to the other ratio if and only if the product of extremes is equal to the product of means.
Direct proportion is a relation in which one quantity increase or decreases in a same proportion by increasing or decreasing the other quantity.
Inverse proportion is a relation in which one quantity increases by decreasing the other quantity and vice versa.
The geometry is an important branch of Mathematics which deals with the study of points, lines, surfaces and solids.
A line segment is a part of a line which has two distinct end points.
Bisection of a line segment means to divide a line segment into two equal parts.
Aright bisector can be a line, a ray or a line segment which divides another line segment into two equal parts.
A right bisector always crosses the line at a right angle (90°) that can be checked by using a protractor.
The two angles of the same measurements are called congruent angles.
The unit of measuring an angle is the degree which is denoted by “°”.
To construct a triangle with three sides, the sum of the measurements of any two sides is greater than the measurement of 3rd side.
The sum of internal angles in a triangle is always 180°.
A right angled triangle can be constructed if we have the measurement of hypotenuse and its one side.