NCERT Class 12 Mathematics Textbook(2026-27) | Download PDF

The Class 12 Mathematics NCERT textbook is the backbone of board exam preparation. It is designed to sharpen logical thinking, strengthen fundamentals, and develop a problem-solving mindset across key areas like calculus, algebra, and probability.

Curated by NCERT and aligned with CBSE guidelines, the book reflects the NEP 2020 focus on conceptual clarity and real-world application.

Download Class 12 NCERT Mathematics I Free PDF 

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Download Class 12 NCERT Mathematics II Free PDF 

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Mathematics Part I 

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Mathematics Part II

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What Makes Class 12 Mathematics Important: Overview 

Mathematics at this level is not just about solving questions - it’s about understanding patterns, building reasoning, and applying concepts to practical scenarios.

Topics like integration, vectors, and probability play a major role not only in CBSE boards but also in competitive exams such as engineering entrances.

Major Pointers for Mathematics: Class 12 NCERT 

• Strictly based on the 2026–27 CBSE curriculum
• Covers all major branches: Calculus, Algebra, and Geometry
• Focuses on application-driven and competency-based learning
• Includes well-graded exercises for concept building to exam-level practice
• Helps in developing accuracy and speed - both crucial for exams

Class 12 Mathematics NCERT Textbook 

NCERT Class 12 Mathematics textbooks include the following chapters, each designed to build strong concepts and problem-solving skills.

NCERT Mathematics Part I 

• Chapter 1: Relations and Functions - Builds the base for understanding mappings and functional relationships
• Chapter 2: Inverse Trigonometric Functions - Deals with principal values and properties
• Chapter 3: Matrices - Essential for solving systems of equations and understanding transformations
• Chapter 4: Determinants 
• Chapter 5: Continuity and Differentiability - Introduces behaviour of functions and derivatives
• Chapter 6: Application of Derivatives - Real-life usage like optimization and rate of change

NCERT Mathematics Part II

• Chapter 7: Integrals - Core concept of calculus with wide application
• Chapter 8: Application of Integrals - Focus on area-related problems
• Chapter 9: Differential Equations - Understanding and solving equations involving derivatives
• Chapter 10: Vector Algebra - Visual and spatial mathematics in three dimensions
• Chapter 11: Three Dimensional Geometry 
• Chapter 12: Linear Programming - Optimization using graphical methods
• Chapter 13: Probability - Logical reasoning with events, distributions, and outcomes

NCERT Class 12 Mathematics 2026-27: Study Resource

For board preparation, NCERT itself acts as the primary and most reliable source. If practiced properly, it eliminates the need for excessive reference books.

Class 12 NCERT Mathematics Textbook: Topics Deleted

As per CBSE’s latest update, there are no changes or deletions in the Class 12 Mathematics syllabus for the academic session 2026–27. Students can follow the same content structure as the previous year.

NCERT Mathematics: Important Questions 

Here are some of the questions from Class 12 NCERT Mathematics which are mostly asked in the CBSE board exams. 

Chapter 1: Relations and Functions 

Q1. Check whether the relation R defined in the set {1, 2, 3, 4, 5, 6} as R = {(a, b) : b=a+1} is reflexive, symmetric or transitive.

Ans. Given:

A={1,2,3,4,5,6}
R={(a,b):b=a+1}

Step 1: Write the relation

R={(1,2),(2,3),(3,4),(4,5),(5,6)}

Step 2: Check Reflexive

A relation is reflexive if (a,a)∈R for all a∈A

Here, no pair of the form (a,a) is present

∴R is not reflexive

Step 3: Check Symmetric

A relation is symmetric if (a,b)∈R⇒(b,a)∈R

Take (1,2)∈R but (2,1)∉R

∴R is not symmetric

Step 4: Check Transitive

A relation is transitive if (a,b) and (b,c) imply (a,c)

(1,2),(2,3)∈R⇒(1,3)

But (1,3)∉R

∴R is not transitive

Chapter 2: Inverse Trigonometric Functions

Q1. Evaluate tan^-1 (√3) -sec^-1 (-2)

Ans. tan^-1(√3) - sec^-1(-2)

We know that:

tan^-1(√3) = π/3

because 

tan π/3 = √3

Also, let 

sec^-1(-2) = θ

Then, 

secθ = −2

which gives

Cosθ = -1/2

The principal value of sec^-1x lies in the interval (0,π), excluding π/2. Therefore, θ = 2π/3

since

cos 2π/3 = -1/2 

Hence,

tan^-1(√3) - sec^-1(-2) = π/3 - 2π/3 = - π/3

Final answer: - π/3

Chapter 10: Vector Algebra

Q1. Find the direction cosines of the vector iˆ+2ˆj+3kˆ

Ans. a=iˆ+2ˆj+3kˆ

Given vector: a=i^+2j^​+3k^

Step 1: Find magnitude of the vector

∣a∣= ​√1²+2²+3² = √1+4+9 = √14

Step 2: Direction cosines

Direction cosines are given by:

l = 1/√14, m=2/√14, n=3/√14
Final Answer:

Direction cosines = (1/√14,2/√14,3/√14)

Chapter 12: Linear Programming 

Q1. 4. A manufacturer produces nuts and bolts. It takes 1 hour of work on machine A and 3 hours on machine B to produce a package of nuts. It takes 3 hours on machine A and 1 hour on machine B to produce a package of bolts. He earns a profit of Rs. 17.50 per package on nuts and Rs. 7.00 per package on bolts. How many packages of each should be produced each day so as to maximize his profit, if he operates his machines for at the most 12 hours a day?

Ans. Let x = number of packages of nuts

Let y = number of packages of bolts

Step 1: Form the constraints

Machine A: x+3y≤12

Machine B: 3x+y≤12

Also, x≥0,y≥0

Step 2: Objective function

Maximise Profit: Z=17.5x+7y

Step 3: Find corner points
From constraints:

1. x+3y=12 → intercepts: (12,0),(0,4)
2. 3x+y=12 → intercepts: (4,0),(0,12)

Feasible region corner points: (0,0),(4,0),(0,4),(3,3)
(Intersection of x+3y = 12 and 3x+y = 12:x = 3,y = 3)

Step 4: Evaluate Z at corner points
Z(0,0)=0
Z(4,0)=17.5×4=70
Z(0,4)=7×4=28
Z(3,3)=17.5×3+7×3=52.5+21=73.5

Step 5: Final Answer
Maximum profit = Rs. 73.50 at (x,y)=(3,3)

Chapter 13: Probability

Q1.Compute P(A|B), if P B 0.5 and P A B 0.32

Ans. P(A∣B) = P(A∩B)​/P(B)

Given: P(B)=0.5,P(A∩B)=0.32

Substitute values: P(A∣B)= 0.32/0.5 = 0.64

Final answer: P(A|B) = 0.64

Smart Preparation Tips for Mathematics

Preparing through the Class 12 NCERT Mathematics textbook can be structured effectively by following these tips:

• Build your base with NCERT: Treat NCERT as your primary source-most questions revolve around its concepts, examples, and exercise patterns.
• Make practice a daily habit: Mathematics improves with consistency; solving questions regularly is key to mastering accuracy and speed.
• Understand the logic behind every step: Focus on why a method works, not just how to solve-it strengthens conceptual clarity in topics like Calculus and Algebra.
• Master formulas through application: Instead of rote learning, apply formulas repeatedly in different questions to retain them effectively.
• Tackle challenging topics head-on: Chapters like Integration, 3D Geometry, and Probability become manageable with gradual and repeated practice.
• Write solutions with proper steps: Stepwise presentation, correct notation, and clarity are crucial for scoring well in board exams. 

FAQs

Q1. Is NCERT Class 12 Mathematics enough for board exam preparation?

Ans. Yes, NCERT Mathematics is sufficient if all examples and exercises are practiced thoroughly, as most board questions are based on it.

Q2. Which chapters are most important in Class 12 Mathematics?

Ans. Calculus (Integrals, Applications of Derivatives), Vector Algebra, and Probability are considered high-weightage chapters.

Q3. How should students start preparing for Class 12 Mathematics?

Ans. Start with understanding concepts from NCERT, solve all examples, and then move on to exercise questions and previous year papers.

Q4. How can students improve speed and accuracy in Mathematics?

Ans. Regular practice, revising formulas, and solving timed mock tests help improve both speed and accuracy

Q5. Why is NCERT Class 12 Mathematics considered the most important book for CBSE boards?

Ans. NCERT forms the base of the CBSE paper pattern, and most questions are either directly taken or conceptually inspired from it.