NCERT Solutions for Class 10 Maths Chapter 1

Class 10 Maths Chapter 1 NCERT Solutions 2021-22 and study material related to 10th Maths chapter 1 is modified according to latest CBSE Syllabus 2021-2022. UP Board students also use this solution for their exams. The fundamental theorem of arithmetic and Euclid’s division lemma are the main topics of this chapter (Real Numbers). The Fundamental Theorem of Arithmetic and Euclid’s division lemma has many applications, both within mathematics and in other fields. NCERT Solutions of all other subjects are also available in PDF form.

Changes in CBSE Syllabus 2021-2022 Class 10 Maths Chapter 1

Get the latest CBSE syllabus to observe the changes due to corona-virus with full detail for class 10 Maths Chapter 1. CBSE has issued a new syllabus for session 2021-2022 educational session. See all the changes made for Class 10 Maths Syllabus for 2021-2022.

Class 10 Maths Chapter 1: Real Numbers

Class 10 Maths Exercise 1.1

In Exercise 1.1 of Class 10 Maths Chapter 1, there are only five questions. All the questions are based on Euclid’s Division Lemma and its applications. In Questions number 1 we have to find HCF applying Euclid’s Division Lemma. In Questions number 2, 4 and 5 also apply step by step Euclid’s Division Algorithms to prove the questions. In Questions 3, we have to find out the maximum number of columns in which they can march, that is, HCF of the two numbers.

Class 10 Maths Exercise 1.2

In Exercise 1.2 of Class 10 Maths, the Fundamental Theorem of Arithmetic is main to solve the questions. Question number 1, 2, 3 are based on the prime factorisation method of LCM and HCF. In Question 4, we can use direct formula a × b = LCM × HCF. Question number 6 is an important question as per exams point of view and based on Example Number 5. One can solve Question 6 by taking common or directly solving each number and showing that it has more than two factors. At last in Question 7, we have to find out a number which is divisible by both 12 and 18 that is LCM of the two numbers.

Class 10 Maths Exercise 1.3

In Exercise 1.2 of Class 10 Maths, only three questions are there. We know that the square root of a non-perfect square number is an irrational number. Here, we have to prove the same fact with a various set of numbers. In each of these questions, first of all, we assume that the given number is a rational number with numerator and denominator as coprime integers. Later on, we receive a false result due to the wrong assumption, so we conclude that the given number is irrational.

Class 10 Maths Exercise 1.4

Class 10 Maths Exercise 1.4 deals with that decimal representation of rational numbers. Questions of Exercise 1.4 are based on Theorem 1.5, Theorem 1.6 and Theorem 1.7 given in NCERT Book of Class 10 Maths Chapter 1. Using these theorems, we can find whether the given rational number is either terminating or non-terminating repeating or non-terminating non-repeating. Most often, one mark questions are asked in CBSE Board exams or school tests also from Exercise 1.4 of Class 10 Maths.

Euclid’s division algorithm

The step by step way to find the HCF of two positive integers, say c and d, with c > d.

• Step 1: Apply Euclid’s division lemma, to c and d. So, we find whole numbers, q and r such that c = dq + r, 0 £ r < d.
• Step 2: If r = 0, d is the HCF of c and d. If r ≠ 0, apply the division lemma to d and r.
• Step 3: Continue the process till the remainder is zero. The divisor at this stage will be the required HCF.

Download the practice test series with answers. Level 1 Test 1 contains basic questions for practicing the chapter Real Numbers. Most of the questions of Level 1 Test 2 are easy to understand and provides good practice. Answers of these test series will be available on website free to use.

The word algorithm come from the name of the name of the 9th century Persian mathematician al-Khwarizmi. The word ‘algebra’ is derived from a book, he wrote, called Hisab al-jabr w’al-muqabala.
An equivalent version of Fundamental theorem of Arithmetic was probably first recorded as Proposition 14 of Book IX in Euclid’s Elements, before it came to be known as the Fundamental Theorem of Arithmetic.
However, the first correct proof was given by Carl Friedrich Gauss in his al-Khwarizmi.
Carl Friedrich Gauss is often referred to as the ‘Prince of Mathematicians’ and is considered one of the three greatest mathematicians of all time, along with Archimedes and Newton. He has made fundamental contributions to both mathematics and science.