These free Mathematics Class 12 (2nd Year) notes are prepared for ICS students studying under the PECTAA Board (Punjab Education, Curriculum, Training and Assessment Authority), 2026-27 edition, following the Updated/Revised National Curriculum of Pakistan 2023. The complete book covers all 11 units of the syllabus, from differentiation and integration through analytical geometry, conic sections, kinematics, numerical methods, inverse trigonometric functions, and vector-valued functions.
Every unit follows the same structure: an overview and learning objectives, key concepts explained in plain language, definitions, formulas, diagrams, worked solved examples (so students can see exactly how each method is applied step by step), short and long question-answers, multiple choice questions, a revision summary, and exam tips. Each unit is available as its own downloadable PDF, and the complete book is also available as one combined PDF below.
What’s Covered in This Book
- Unit 1: Graphical Representation of Functions
- Unit 2: Further Differentiation
- Unit 3: Integration
- Unit 4: Differential Equations
- Unit 5: Analytical Geometry
- Unit 6: Conic Section
- Unit 7: Kinematics of Motion in a Straight Line
- Unit 8: Numerical Solutions of Nonlinear Equations
- Unit 9: Inverse Trigonometric Functions and Their Graphs
- Unit 10: Solution of Trigonometric Equations
- Unit 11: Vector Valued Functions and Their Differentiations
Who These Notes Are For
These notes are designed for ICS (Intermediate in Computer Science) Part-II students preparing for their Mathematics Class 12 board exams under the PECTAA Board syllabus. They are equally useful for FSc Part-II students following the same PECTAA Mathematics curriculum, for quick revision before tests, and for building a strong step-by-step understanding of each topic through the worked solved examples in every unit.
How to Use This Book
- Start with the unit matching your current classroom topic, or work through units 1 to 11 in order for a full first pass.
- Read the overview and key concepts first, then work through the solved examples to see each method applied step by step.
- Use the definitions, formulas, and key facts table as a quick-reference sheet while solving your own textbook exercises.
- Attempt the short questions, long questions, and MCQs at the end of each unit to test your understanding before checking the answers.
- Use the revision summary and exam tips in the final days before your exam for fast recall of every unit’s key points.
Frequently Asked Questions
Are these Mathematics Class 12 notes free to download?
Yes, all 11 units of these Mathematics Class 12 (2nd Year, ICS, PECTAA Board) notes, along with the combined full-book PDF, are completely free to download from freebooks.pk.
Which board and curriculum do these notes follow?
These notes follow the PECTAA Board (Punjab Education, Curriculum, Training and Assessment Authority) syllabus for the 2026-27 edition, based on the Updated/Revised National Curriculum of Pakistan 2023.
Do these notes include solved examples?
Yes, every unit includes multiple fully worked solved examples showing each method step by step, so students can clearly see how to apply the concepts and formulas covered in that unit.
Can FSc students use these ICS Mathematics notes?
Yes, FSc Part-II students following the same PECTAA Board Mathematics Class 12 curriculum can use these notes as well, since the syllabus content is shared between the ICS and FSc Mathematics streams.
Is there a single PDF with all 11 units combined?
Yes, a complete combined PDF containing all 11 units, a cover page, and a full table of contents is available to download from this page.