Class 10 Important Topics for Real no Mathematics

For the academic year 2025–2026, the important topics for Class 10 Maths Chapter 1 (Real Numbers) focus on

the Fundamental Theorem of Arithmetic, proving the irrationality of numbers, and rational numbers with terminating or non-terminating decimal expansions. 

Fundamental Theorem of Arithmetic 

• Prime factorization: This theorem states that every composite number can be uniquely expressed as a product of prime numbers, regardless of the order.
• HCF and LCM: Using the prime factorization method to find the HCF and LCM of two or more numbers is a key application of the theorem.
• Relationship between HCF and LCM: You should be able to solve problems using the relationship: HCF(a,b)×LCM(a,b)=a×bcap H cap C cap F open paren a comma b close paren cross cap L cap C cap M open paren a comma b close paren equals a cross b𝐻𝐶𝐹(𝑎,𝑏)×𝐿𝐶𝑀(𝑎,𝑏)=𝑎×𝑏.
• Applications: Practice real-world problems that require finding the HCF or LCM, such as determining the maximum number of columns in a parade or finding when people running on a circular track will meet again.
• Ending digits: Understand why a number of the form 6n6 to the n-th power6𝑛 or 4n4 to the n-th power4𝑛 can never end with the digit 0. 

Irrational numbers 

• Proof of irrationality: A crucial topic is proving that numbers like 2the square root of 2 end-root2√, 3the square root of 3 end-root3√, and 5the square root of 5 end-root5√ are irrational. This is a standard question type in the board exams.
• Operations with irrational numbers: Be prepared to prove the irrationality of expressions involving sums, differences, products, and quotients with irrational numbers, such as 5+325 plus 3 the square root of 2 end-root5+32√ or 3+5the square root of 3 end-root plus the square root of 5 end-root3√+5√. 

Terminating and non-terminating decimals 

• Decimal expansions: Revise the conditions under which the decimal expansion of a rational number terminates or is non-terminating and repeating.
• Predicting decimal behavior: You should be able to determine whether a given rational number’s decimal expansion will terminate without performing the actual division, by analyzing the prime factors of the denominator.
• Questions: Expect multiple-choice questions (MCQs) that ask you to identify whether a given decimal expansion is rational or irrational. 

Removed topic for 2025–2026 

• Euclid’s Division Lemma: This lemma, which was previously used to find the HCF of two numbers, is no longer part of the official CBSE syllabus for the 2025–2026 academic year. While related concepts of divisibility are still relevant, questions specifically asking for the HCF using this algorithm are not expected