NIOS Mathematics Book Class 12 (Course 311) – Complete 2025 Student Guide

NIOS Mathematics Book Class 12 (Course 311) – Complete 2025 Student Guide

Mathematical precision is a universal language. It helps us to analyze and solve real problems.

The NIOS Mathematics Book Class 12 is a course 311 developed by the National Institute of Open Schooling. It helps learners build a strong base in algebra, geometry, and trigonometry.

This course does not focus on rote learning, but rather on conceptual understanding of mathematics and practical problem-solving. Each unit moves from simple to more complex concepts so that students can master their mathematical reasoning independently.

The NIOS Books for Class 12 Math are available in both English and Hindi, making them easily accessible to students across India. This course will improve your quantitative reasoning, whether you are a science student or someone returning to the academic world through an open school system.

Unnati Education offers a premium version of the NIOS Mathematics Book for Class 12 in PDF format. This book includes detailed questions and answers, chapter-by-chapter explanations, exercises, and examples. These resources are designed for systematic preparation and are exam-ready.

Quick Course Overview

Course Title	It is a good way to start learning
Course Code	311
You can also find out more about Level	Senior Secondary (12th class)
The medium-sized apprehension	English & Hindi
Syllabus Year	2025 (Revised & Updated)
Duration	One Academic year (Flexible Education)
Mode of study	Distance / Online
Eligibility	Pass Class 10 or Equivalent
The Right to Certification	Recognized by NIOS, under the Ministry of Education of the Govt. India

The mathematics course helps students improve their accuracy, consistency, and clarity in their mathematical work.

About NIOS Mathematical Book Class 12 (Course 311

The NIOS Mathematics Book Class 12 (311) follows a module structure that combines theoretical knowledge with practical application. Every module begins by presenting real-life scenarios to make abstract ideas relatable.

The book helps students understand how mathematical patterns are used to describe our world. From understanding number systems, calculating areas, interpreting algebraic relationships, and applying trigonometric ratios.

Each chapter is organized as follows:

• Formulas and definitions are easy to understand
• Examples for self-study with answers
• Worksheets (WSs) for practice
• Real-life applications and problems

The course will be a natural upgrade for students who previously studied with the NIOS Hindi Book, Class 10 PDF.

Students who are pursuing a higher education in Science or Commerce, Engineering, or Business Management should take this course. It can be used for exams such as JEE and NDA.

Key Highlights by 2025

1. Revised according to the 2025 Syllabus. Topics updated to reflect accuracy and modern applications
2. Balanced Learning – Equal emphasis is placed on both theoretical understanding and practical examples
3. Dual Medium advantage - Available in English as well as Hindi for nationwide accessibility
4. Self-learning Design - Simple explanations and stepwise derivations. Practice problems
5. Exam-Oriented questions - exercises aligned with NIOS boards' patterns and TMAs
6. Commercial Application Integration – Chapters on percentages of interest, installments, and interest
7. Digital Access - You can access the NIOS Mathematics Book Class 12 in PDF format on your mobile device, laptop, or tablet
8. Unnati Education's Paid Verified Content - Professionally edited to eliminate errors and provide expert-level clarity

Topics covered

The syllabus is divided into five main modules. Each module has detailed chapters with conceptual explanations, solved examples, and worksheets.

MATHEMATICS 311	Module / Topic
Module–I: Sets, Relations and Functions	1. Sets 2. Relations and Functions–I 3. Trigonometric Functions–I 4. Trigonometric Functions–II 5. Relation between Sides and Angles of a Triangle
Module–II: Sequences and Series	6. Sequences and Series 7. Some Special Sequences
Module–III: Algebra–I	8. Complex Numbers 9. Quadratic Equations and Linear Inequalities 10. Principle of Mathematical Induction 11. Permutations and Combinations 12. Binomial Theorem
Module–IV: Co-ordinate Geometry	13. Cartesian System of Rectangular Co-ordinates 14. Straight Lines 15. Circles 16. Conic Sections
Module–V: Statistics and Probability	17. Measures of Dispersion 18. Random Experiments and Events 19. Probability
Module–VI: Algebra–II	20. Matrices 21. Determinants 22. Inverse of a Matrix and its Applications
Module–VII: Relations and Functions	23. Relations and Functions–II 24. Inverse Trigonometric Functions
Module–VIII: Calculus	25. Limits and Continuity 26. Differentiation 27. Differentiation of Trigonometric Functions 28. Differentiation of Exponential and Logarithmic Functions 29. Application of Derivatives 30. Integration 31. Definite Integrals 32. Differential Equations
Module–IX: Vectors and Three Dimensional Geometry	33. Introduction to Three Dimensional Geometry 34. Vectors 35. Plane 36. Straight Line
Module–X: Linear Programming and Mathematical Reasoning	37. Linear Programming 38. Mathematical Reasoning

Module I: Algebra
1. Number Systems
The chapter discusses the different types of numbers (natural, whole numbers, integers, rational, irrational, and real), their representation, and operations on a number line. This chapter provides the basis for algebraic thinking.
2. Exponents and Radicals
The book also covers the basic operations, laws of exponents, rational powers, and simplification of radicals. The mastery of this skill improves algebraic manipulation.
3. Algebraic Expressions & Polynomials
Students learn to simplify expressions and multiply, divide, add, subtract, and multiply polynomials. Students learn about polynomials and their degrees.
4. Special Products & Factorization
Introduces algebraic identities like \((a+b)^2\), \((a-b)^2\), \((a+b)(a-b)\), and their uses in factorizing complex expressions.
5. Linear Equations
The course teaches single and pairs of linear equations as well as graph plotting. It also teaches solutions using substitution and elimination methods.
6. Quadratic Equations
The book covers standard forms and how to solve them through factorization. It also explains the quadratic formula, completing the square, the factorization method, and how to solve the problem by factoring. Included are the nature of roots and how they relate to coefficients.
7. Arithmetic Progressions
The formula for the nth term and the sum of the nth terms is covered. Salary growth, installment payments, and population trends are all examples from real life.

Module II - Commercial Mathematics
8. Percentage and Its Applications
This book explains how to calculate profit, loss, and compound interest. This book helps to connect math with financial literacy.
9. Installment Buying
It explains how to calculate the total amount of payments and interest. Included are practical examples, such as buying a car or a product on EMI.

Module 3: Geometry
10. Lines and Angles
Defines line, ray, and angle, as well as their relationship (vertical opposite, complementary, supplementary). Transversal lines, parallel line theorems, and their relationships are covered.
11. Congruence between Triangles
The book explains the SSS congruence criteria and also SAS, ASA, and RHS, allowing students to confidently demonstrate geometric properties.
12. Concurrent Lines
Explains the medians of altitudes as well as perpendicular bisectors meeting at one point. Introduces concurrency as a concept in triangles.
13. Quadrilaterals
Details different quadrilateral types--parallelogram, rectangle, square, rhombus, and trapezium--and their properties.
14. Triangles that look similar
This course focuses on theorems that are based on proportionality, their applications in real life, such as design, architecture, and mapping.
15. Circles
Defines the circle components (radius, diameter, chords, tangents, and arcs). Teaches chord properties and tangent theorems.
16. Angles within a Circle, and Cyclic Quadrilaterals
Explains the relationship between chords and angles, cyclic property, and inscribed angles.
17. Secants and Tangents: Their Properties
This book teaches properties of secants, chord-tangents, and tangent-chord theorems that are useful for problem solving and proofs.
18. Constructions
The chapter is a practical guide to geometric constructions that can be taught using a ruler and compass. It includes the use of tangents and bisectors.
19. Coordinate Geometry
Introduces plotting onto the Cartesian plane, distance formulae, midpoint, and section formulae. It is the basis of trigonometry and calculus.

Module IV - Mensuration
20. Perimeters, Areas, and Plane Figures
This book includes formulas that calculate the perimeter and area of circles, rectangles, triangles, and trapezoids. Included are composite figures, as well as real-world issues like fencing costs and land area.
21. Surface Area of Solid Figures
Calculates surface areas, volumes, and surfaces of 3D forms--cuboid, Cube, Cylinder, Cone, Sphere. This program provides visualizations and practical solutions for packaging, construction, and other problems.

Module V - Trigonometry
22. Trigonometry: An Introduction
Defines trigonometric ratios (sin, cos, tan, etc. The reciprocal identities of right-angled triangles, as well as the relation between their sides and angles, are discussed.
23. Trigonometric Ratios Special Angles
The book includes standard angles (0°, 30°, 45°, 60°, 90°), their ratios as well as applications to geometry and physics.

How to download a PDF

Unnati Education offers a professionally designed paid version of the NIOS Mathematics Book Class 12 Pdf (Course 311 - not a download for free). It contains detailed explanations, illustrations, and complete coverage of topics according to the syllabus for 2025.

Get Your Book:

1. Unnati Education's official website
2. To send a message directly through WhatsApp, click on the "View Response" button
3. Mention your subject - "NIOS Mathematics Book Class 12 (Course 311)"
4. Select between PDF and Printed Copy
5. Confirm the payment securely
6. Get your verified study materials within 24-48 hours

This edition includes all modules required and provides a structure for complete board prep.

How to Study NIOS Maths Effectively

1. Refresh your arithmetic identity and algebraic identities
2. Create Formula Notes. Maintain separate notebooks of formulas, theorems, and other information for quick reference
3. Solve daily: Try to answer at least 15 questions per day from each subject
4. Visual Learning: Draw geometrical diagrams and figures to help you remember
5. Revise by Example: Review the examples you have already solved
6. Examine past papers: Familiarize with the NIOS examination pattern and timing
7. Unnati Education's weekly tests allow you to track your progress and take mini-tests at the end of each chapter

NIOS exam success is assured by regular practice combined with conceptual clarity.

Exam Pattern and Study Strategy

The NIOS Class 12 mathematics exam assesses conceptual understanding, calculation accuracy, and application ability.

Examining Format:

• Duration: 3 hours
• Total marks: 100
  • Theory: 80
  • TMA (Assignments ): 20

Question Distribution:

• Very Short Answer (1 point): Conceptual memory
• Short Answer (2-4 marks): Application-based
• Long Answer (5-8 Marks): Analytical thinking and problem solving

Preparation tips:

• Focus on chapters that are high-weight, like Algebra and Geometry
• Revise formulas daily
• Unnati Education has model worksheets that you can use to learn
• Solve the TMAs during an exam

Career Options After Studying Math (311)

Mathematics opens doors to many different industries: science, commerce, and technology.

Pathways for Academics:

• B.Sc. B.Sc
• B.Tech / Engineering Programs
• BCA / Computer Sciences Degrees
• B.Com / Economics / Actuarial Studies
• Graduate Diploma in Applied Mathematics, Analytics, or Analytics

Careers for Professionals:

• Engineer / Data Analyst / Statistician
• Financial Consultant / Investment Banking
• Maths Educators and Lecturers
• Software Developer/Data Scientist
• Civil Service or Defense Candidate

The ability to think quantitatively and make decisions is a skill that all professions require.

Unnati Education: What are the Benefits?

Our Expertise:

Unnati Education is a leading provider of structured, clear NIOS study resources.

What We Provide:

• Updated NIOS Books Class 12 Mathematics (2025 edition)
• Download the PDF Formats and print them
• For full preparation, you can use Assignments, Test Measurements, and Sample Papers
• Expert Faculty - Live and Recorded Class Instruction
• One-on-One Doubt sessions
• Get instant help with 24/7 WhatsApp support

Why Students Choose Us:

Our materials are written by professionals, checked for errors, and aligned 100% with the official NIOS curriculum. We simplify complex concepts to build understanding and not just memorization.

Unnati students consistently achieve higher scores in board exams as we teach them using purposeful training, not shortcuts.

FAQ

Q1. What is the NIOS Mathematics Book Class 12 Course 311?

Ans. It is an official mathematics textbook published by NIOS, which covers Algebra, Geometry, and Mensuration.

Q2. Can I download it as a PDF?

Ans. Yes. Unnati Education provides the NIOS Mathematics Book Class 12 in PDF format (2025 edition) to paid students.

Q.3 Do you have Hindi Medium?

Ans. Yes. We have NIOS Books available in Hindi and English for Class 12.

Q4. Is Unnati Education free or paid?

No. Unnati Education is a provider of paid, enhanced, and verified study material designed by professionals to ensure maximum accuracy.

Q5. Do you include TMAs, solutions, and TMAs?

Yes.

Q6. What if my Maths is not up to scratch?

The materials we provide start from the basics and progress step-by-step. Join live sessions to get additional help.

Q7. How do I start?

To contact us via WhatsApp, simply click on "View answer" or give us a call. Our team will guide you through the enrolment process and deliver your books within two business days.

📞 Contact Unnati Education

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🗣️ Mediums: English & Hindi

Take the first step toward mastering mathematics. Get your NIOS Mathematics Book Class 12 (Course 311) from Unnati Education and transform how you understand numbers, logic, and problem-solving.