CBSE 12th Maths Book Free PDF Download – NCERT 2026-27

12th Maths Book CBSE NCERT – Free PDF Download 2026-27

12th Maths Book serves as the cornerstone resource for students preparing for their crucial board examinations. Students and parents searching for this essential study material primarily seek authentic, comprehensive NCERT textbooks that align perfectly with CBSE curriculum standards. The latest edition for 2026-27 session addresses their core pain points: accessing official content without expensive purchases, finding chapter-wise organized material, and obtaining reliable preparation resources.

Students specifically want free PDF downloads that cover complete syllabus including Relations and Functions, Matrices, Determinants, and Calculus topics. Parents desire cost-effective solutions that ensure their children receive quality education materials. The commercial intent reflects their readiness to download official NCERT books, while informational needs include understanding chapter structures, exam patterns, and preparation strategies.

These comprehensive resources eliminate exam stress by providing structured learning paths, practice questions, and board-aligned content that guarantees thorough preparation for mathematics board examinations.

Download 12th Maths Book PDF Free – 2026-27 Edition

Mathematics Part-I – Chapter-wise PDF Download for CBSE Students

Mathematics Part-II – Chapter-wise PDF Download for CBSE Students

Ganit-I – Chapter-wise PDF Download for CBSE Students

Ganit-II – Chapter-wise PDF Download for CBSE Students

Riyazi-I – Chapter-wise PDF Download for CBSE Students

Riyazi-II – Chapter-wise PDF Download for CBSE Students

About 12th Maths Book

12th maths book from NCERT provides comprehensive coverage of advanced mathematical concepts essential for CBSE board exam success. This latest edition for 2026-27 session encompasses eight crucial chapters: Relations and Functions, Inverse Trigonometric Functions, Matrices, Determinants, Continuity and Differentiability, Applications of Derivatives, Integrals, and Applications of Integrals. Additionally, each chapter carries specific weightage in board examinations, with Calculus topics (Derivatives and Integrals) contributing approximately 35 marks collectively.

This textbook covers the following chapters:

• Relations and Functions
• Inverse Trigonometric Functions
• Matrices
• Determinants
• Continuity and Differentiability
• Applications of Derivatives
• Integrals
• Applications of Integrals
• Differential Equations
• Vector Algebra
• 3D Geometry
• Linear Programming
• Probability

Moreover, the textbook includes step-by-step theorem proofs, solved examples demonstrating key formulas like integration by parts, and HOTS questions for competitive exam preparation. Furthermore, students can access free PDF downloads chapter-wise, enabling flexible study schedules and revision strategies. The NCERT solutions complement theoretical concepts with practical applications, covering important topics like optimization problems, area calculations, and differential equations. Most importantly, this official resource aligns perfectly with CBSE marking schemes and includes previous year question patterns. Students can download now to access complete study material that bridges the gap between conceptual understanding and board exam requirements, ensuring thorough preparation for grade 12 mathematics.

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Important Points to Remember – Class 12 Maths

• Relations and Functions (Chapter 1) introduces different types of relations including reflexive, symmetric, transitive, and equivalence relations, building on Class XI concepts
• Inverse trigonometric functions exist only when trigonometric functions are restricted to specific domains to make them one-one and onto
• Matrix notation A = [aij] represents elements where ‘i’ denotes row number and ‘j’ denotes column number in the arrangement
• Determinants are associated numbers (real or complex) with square matrices, denoted as |A|, det A, or Δ
• The determinant of a 2×2 matrix [a b; c d] equals ad – bc, which determines if the system has unique solutions
• Composition of functions (f∘g)(x) = f(g(x)) is only defined when range of g is subset of domain of f
• Binary operations on sets follow closure, associativity, commutativity, and existence of identity and inverse properties
• Principal value ranges for inverse trigonometric functions: sin⁻¹ ∈ [-π/2, π/2], cos⁻¹ ∈ [0, π], tan⁻¹ ∈ (-π/2, π/2)
• Matrix multiplication AB is defined only when number of columns in A equals number of rows in B
• Cofactor of element aij in determinant equals (-1)^(i+j) times minor Mij of that element
• System of linear equations AX = B has unique solution when |A| ≠ 0, and solution is X = A⁻¹B
• Adjoint of matrix A is transpose of cofactor matrix, written as adj(A) = [Cij]ᵀ
• For invertible matrices: A⁻¹ = (1/|A|) × adj(A), valid only when |A| ≠ 0
• Area of triangle with vertices (x₁,y₁), (x₂,y₂), (x₃,y₃) = (1/2)|determinant of coordinate matrix|
• CBSE 2025-26 syllabus emphasizes applications of matrices in cryptography, genetics, and industrial management

Quick Revision Notes – Class 12 Maths

• Focus on proving functions are one-one using f(x₁) = f(x₂) ⟹ x₁ = x₂, and onto by showing every element in codomain has preimage
• Remember domain restrictions: sin⁻¹ and cos⁻¹ are defined only for [-1,1], while tan⁻¹ and cot⁻¹ are defined for all real numbers
• Matrix addition and subtraction require same order matrices, while scalar multiplication affects each element individually
• For determinant expansion, choose row/column with maximum zeros to minimize calculations using cofactor method
• Properties of determinants: |AB| = |A||B|, |kA| = kⁿ|A| for n×n matrix, |Aᵀ| = |A|
• Cramer’s rule for solving systems: x = Δx/Δ, y = Δy/Δ, z = Δz/Δ where Δ ≠ 0
• Matrix inverse properties: (AB)⁻¹ = B⁻¹A⁻¹, (Aᵀ)⁻¹ = (A⁻¹)ᵀ, (A⁻¹)⁻¹ = A
• Board exam tip: Always verify your inverse trigonometric function answers lie within principal value ranges
• Important identity for inverse functions: sin⁻¹x + cos⁻¹x = π/2, tan⁻¹x + cot⁻¹x = π/2 for valid domains
• Determinant becomes zero when two rows/columns are identical or proportional, indicating system has infinite or no solutions
• Matrix equation AX = O has non-trivial solutions only when |A| = 0 (homogeneous system)
• Applications chapter includes finding area using determinants – remember to take absolute value for actual area
• For CBSE board exams, practice 3×3 determinant expansion and matrix multiplication as these carry high marks
• Graphical representation of inverse trigonometric functions shows they are reflections of restricted trigonometric functions about y = x line
• Study the historical mathematicians mentioned: Dirichlet (functions), Aryabhata (trigonometry), Laplace (determinants) for potential objective questions

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