This is the National Council of Educational Research and Training (NCERT) mathematics textbook for Class XII, Mathematics Part I — the first of the two-volume Class 12 mathematics set. It is an English medium (Roman script) book — the complete text, theorems, worked examples, exercises and answers are in English, and there is no Hindi content in it. It is prescribed for CBSE schools and for state boards that follow the NCERT curriculum.
Part I carries algebra and the first half of calculus. It opens with relations and functions — types of relations, one-one and onto functions, composition and invertibility — followed by inverse trigonometric functions, their domains, ranges and principal values. Matrices covers types of matrices, operations, transpose, symmetric and skew-symmetric matrices and the inverse by elementary operations. Determinants takes up properties, minors and cofactors, adjoint and inverse, area of a triangle, and the solution of a system of linear equations. Continuity and differentiability then moves into calculus proper — continuity, differentiability, chain rule, implicit and logarithmic differentiation, derivatives of inverse trigonometric and exponential functions, second order derivatives, and the mean value theorems. The volume closes with application of derivatives: rate of change, increasing and decreasing functions, tangents and normals, and maxima and minima.
These are the chapters that carry the most marks in the Class 12 mathematics paper and the most difficulty. The reason to work from the prescribed text is that the board sets its questions on these exercises directly, often with only the numbers changed, and expects the standard method as shown here. For JEE candidates the same chapters are among the highest-yielding in the syllabus — matrices, determinants, continuity and differentiability, and maxima and minima recur every year — and the miscellaneous exercise at the end of each chapter is consistently pitched at a harder level than the main sets and is worth doing in full.
The text is supported by worked examples set out step by step, graded exercises within each chapter, a miscellaneous exercise at the end, summary points and historical notes, with answers provided at the back. Note that this is Part I — integrals, application of integrals, differential equations, vector algebra, three-dimensional geometry, linear programming and probability are in Part II, and both volumes are needed for the complete Class 12 syllabus.
Key Features:
English medium book — complete content written in English (Roman script), no Hindi content
Published by NCERT (National Council of Educational Research and Training)
Mathematics Part I — Textbook for Class XII (Class 12)
Prescribed for CBSE schools and state boards following the NCERT curriculum
Covers Relations and Functions — types, composition and invertibility
Covers Inverse Trigonometric Functions — domain, range and principal values
Covers Matrices — operations, transpose, symmetric matrices and inverse
Covers Determinants — properties, minors, cofactors, adjoint and system of linear equations
Covers Continuity and Differentiability — chain rule, implicit and logarithmic differentiation
Covers Application of Derivatives — rate of change, tangents and normals, maxima and minima
Worked examples set out step by step
Graded exercises with a harder miscellaneous exercise at the end of each chapter
Summary points and historical notes with each chapter
Answers provided at the back for independent checking
Base textbook for the CBSE Class 12 mathematics board examination
Standard source text for JEE Main and JEE Advanced
Part I of a two-volume set — Part II carries integrals, vectors, 3D geometry and probability
यह पुस्तक राष्ट्रीय शैक्षिक अनुसंधान और प्रशिक्षण परिषद (NCERT) द्वारा कक्षा XII (कक्षा 12) के लिए निर्धारित गणित की पाठ्यपुस्तक Mathematics Part I है। ध्यान दें: यह पुस्तक पूर्णतः अंग्रेज़ी भाषा एवं रोमन लिपि में है — इसमें हिन्दी भाषा का प्रयोग नहीं है। इस भाग में संबंध एवं फलन, प्रतिलोम त्रिकोणमितीय फलन, आव्यूह, सारणिक, सांतत्य तथा अवकलनीयता एवं अवकलज के अनुप्रयोग — ये अध्याय सम्मिलित हैं। हल किए गए उदाहरण चरणबद्ध रूप में दिए गए हैं, प्रत्येक अध्याय में क्रमबद्ध प्रश्नावलियाँ तथा अंत में विविध प्रश्नावली (miscellaneous exercise) दी गई है, और उत्तर पुस्तक के अंत में हैं। बोर्ड परीक्षा के प्रश्न प्रायः इन्हीं अभ्यासों से पूछे जाते हैं तथा वही मानक विधि अपेक्षित होती है जो इस पुस्तक में दी गई है। JEE की तैयारी में भी आव्यूह, सारणिक, सांतत्य-अवकलनीयता तथा उच्चिष्ठ-निम्निष्ठ सर्वाधिक महत्त्वपूर्ण अध्याय माने जाते हैं। ध्यान दें कि यह भाग-I है; समाकलन, अवकल समीकरण, सदिश बीजगणित, त्रिविमीय ज्यामिति, रैखिक प्रोग्रामन एवं प्रायिकता भाग-II में हैं — सम्पूर्ण पाठ्यक्रम हेतु दोनों भाग आवश्यक हैं।
