NCERT Class 10 Mathematics Formula CBSE Board Sample Problems Part 1

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CBSE Class 10 Math’s Summary

This pdf list all the Class 10 CBSE math’s formula in a concise manner to help the students in revision and examination as per NCERT syllabus

Real Numbers

Real Numbers

S.no

Type of Numbers

Description

1

Natural Numbers

It is the counting numbers

2

Whole number

W

It is the counting numbers + zero

3

Integers

4

Positive integers

5

Negative integers

6

Rational Number

A number is called rational if it can be expressed in the form p/q where p and q are integers (q>0).

Example: etc.

7

Irrational Number

A number is called rational if it cannot be expressed in the form p/q where p and q are integers (q> 0).

Example: etc.

8

Real Numbers

All rational and all irrational number makes the collection of real number. It is denoted by the letter R

S.no Type of Numbers Description

S.no

Type of Numbers

Description

1

Euclid’s Division Lemma

For a and b any two positive integer, we can always find unique integer q and r such that

,

If r =0, then b is divisor of a.

2

HCF (Highest common factor)

HCF of two positive integers can be find using the Euclid’s Division Lemma algorithm

We know that for any two integers a, b. we can write following expression

,

If r=0, then

HCF (a, b) = b

If ,then

HCF (a, b) = HCF (b, r)

Again expressing the integer b, r in Euclid’s Division

Lemma, we get

Similarly successive Euclid ‘s division can be written

until we get the remainder zero, the divisor at that

point is called the HCF of the a and b

3

HCF (a, b) =1

Then a and b are co primes.

4

Fundamental Theorem of Arithmetic

Composite number = Product of primes

5

HCF and LCM by prime factorization method

HCF = Product of the smallest power of each common factor in the numbers

LCM = Product of the greatest power of each prime factor involved in the number

6

Important Formula

Important concept for rational Number

Terminating decimal expression can be written in

the form