Important topics from Class 12 (2nd PUC) Mathematics, specifically Chapters 1 to 4, based on the 2025–26 Karnataka State Board syllabus and weightage:

 

Chapter-Wise Marks Allocation (2025 Blueprint)

According to the official chapter-wise weightage for the Karnataka 2nd PUC Mathematics exam (out of 80 theory marks):

Chapter Number	Chapter Title	Marks Allocation
1	Relations and Functions	10
2	Inverse Trigonometric Functions	7
3	Matrices	9
4	Determinants	13
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Chapter-Specific Focus Areas

Chapter 1: Relations and Functions (10 marks)

• Types of relations: Understand reflexive, symmetric, transitive, and equivalence relations, including their properties.

• Functions: Master concepts of one-to-one (injective) and onto (surjective) functions, composite functions, and inverses.
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Chapter 2: Inverse Trigonometric Functions (7 marks)

• Key concepts: Grasp definitions, domains and ranges, and principal value branches.

• Applications: Practice drawing and interpreting graphs of inverse trig functions.
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Chapter 3: Matrices (9 marks)

• Matrix operations: Learn various types (zero, identity, symmetric, skew-symmetric), operations (addition, multiplication, scalar multiplication), transpose.

• Special properties: Non-commutativity of matrix multiplication and examples of non-zero matrices whose product is the zero matrix.

• Invertibility: Understand how to find matrix inverses and prove uniqueness.
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Chapter 4: Determinants (13 marks)

• Fundamental concepts: Calculation of determinants (up to 3×3), minors and cofactors.

• Applications: Compute areas of triangles using determinants.

• Advanced concepts: Adjoint and inverse of a square matrix, solving linear systems via inverse method (consistency, number of solutions).
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Why Chapters 1–4 Are Critical

• Together, these first four chapters contribute 39 out of 80 marks, making them essential for scoring well.

• Topics like Determinants, Matrices, and Relations/functions lay the foundation for advanced problem-solving skills in algebra and calculus.

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Study Strategy Recommendations

1. Definitions & Properties

   • Relations/functions: Ensure clarity on types and functional mappings.

   • Matrices/determinants: Be fluent in properties and operational rules.

2. Concrete Examples & Proofs

   • Practice examples that show non-commutativity, invertibility conditions, and solving linear equations using matrices and determinants.

3. Applications

   • Relations/functions: Use composition and inverse function problems.

   • Determinants: Apply to geometry problems like finding triangle areas.

4. Focus on High-Yield Topics

   • Given its highest weight (13 marks), Determinants deserves deeper practice on both computational and applied problems.

5. Blueprint-Based Practice

   • Use model question papers and blueprints (e.g., DPUE’s official model papers) to target different question types—including MCQs, short and long-answer questions.