Mathematics 2nd Year ICS book Part 2 (Class 12) is published by the Punjab Curriculum and Textbook Board (PCTB), Lahore. Officially titled Calculus and Analytic Geometry, this is the standard second-year Mathematics textbook for ICS students in Punjab Board colleges. It covers seven units from Functions and Limits to Vectors.
For ICS Part 2 students, Mathematics is the core subject and this book covers the complete board exam syllabus. It goes deeper into calculus, analytic geometry, conic sections, and linear programming. The PDF lets students revise theorems, work through integration and differentiation problems, and prepare step by step before the final board exam.
Book Overview
- Class: 12 (ICS Part 2 / Second Year)
- Subject: Mathematics (Calculus and Analytic Geometry)
- Category: ICS
- Board: Punjab Board (PCTB, Lahore)
- Total Chapters: 7
- Format: PDF
Chapter List
Unit 1 – Functions and Limits
Reviews types of functions and introduces limits of functions rigorously. Covers one-sided limits, continuity, and theorems on limits with worked examples and exercises.
Unit 2 – Differentiation
Covers derivatives from first principles, rules of differentiation, higher-order derivatives, implicit differentiation, and applications including maxima, minima, and related rates.
Unit 3 – Integration
Introduces indefinite and definite integrals, standard integration formulas, techniques (substitution, integration by parts), and applications to area under curves.
Unit 4 – Introduction to Analytic Geometry
Covers the straight line in Cartesian coordinates — slope, equations of lines, distance formulas, angle between lines, and family of lines.
Unit 5 – Linear Inequalities and Linear Programming
Explains systems of linear inequalities, feasible regions, graphical method of solving linear programming problems, and finding optimal solutions.
Unit 6 – Conic Section
Covers the circle, parabola, ellipse, and hyperbola — their standard equations, properties, and geometric interpretations. Includes problem-solving with conics.
Unit 7 – Vectors
Introduces vectors in 2D and 3D space, vector operations, dot and cross products, scalar triple product, and applications in geometry and physics.
Download Mathematics Class 12 ICS Book PDF
Three editions are available below. Click the button for the edition you need — each opens in a new tab and is ready to read or save on any device.
Latest Edition (2020 onwards)
⬇ Download PDF (2020 Edition)E-Learn Punjab Edition
⬇ Download PDF (E-Learn Punjab)Old Edition
⬇ Download PDF (Old Edition)Who Should Read This
This book is for ICS Part 2 (Second Year) students preparing for the Punjab Board annual Mathematics exam. Since Mathematics is the defining subject of ICS, thorough preparation from this book is essential. It is also useful for students planning for ECAT and CS-related entry tests, as calculus, vectors, and linear programming are tested in those exams.
Applicable Boards
This textbook is published by PCTB and is used in Punjab Board colleges. Students from the Federal Board (FBISE) and AJK Board can also use it, as the ICS Part 2 Mathematics syllabus is largely the same. Students from Sindh and KPK boards will find most chapters relevant as well.
FAQs
Is this the Mathematics book for ICS Part 2 Punjab Board?
Yes. It is the official PCTB textbook titled Calculus and Analytic Geometry, used for ICS Part 2 (Class 12) in Punjab Board colleges.
How many chapters are in Mathematics Class 12 ICS?
There are 7 units: Functions and Limits, Differentiation, Integration, Analytic Geometry, Linear Programming, Conic Section, and Vectors.
Is this book the same as the FSC Part 2 Mathematics book?
Yes. ICS and FSC students study the same Mathematics book. The content, chapters, and exercises are identical.
Which edition should I download?
Download the 2020 edition if your college follows the latest PCTB curriculum. The chapter content is the same across all editions — only minor printing updates differ.
Is this book useful for ECAT preparation?
Yes. Calculus, conic sections, vectors, and linear programming from this book are directly tested in ECAT.
Is the PDF free to download?
Yes. All three editions of the Mathematics Class 12 ICS book PDF are completely free to download and read on any device.