Artham Resources | Class 12 Mathematics Half-Yearly Sample Paper with Solutions (Set 12)

Strictly Aligned with CBSE Board Pattern & New NCERT Curriculum 2026–27

A full-length, board-calibrated 80-mark practice examination for Class 12 Mathematics designed to test composite relation properties, non-singular matrix transformations, logarithmic differentiation methods, and bounded optimization problems under authentic 3-hour examination conditions.

Key Highlights & Academic Features

• Authentic Examination Rigor: Calibrated to mirror official mid-term standards across Relations and Functions, Inverse Trigonometric Functions, Matrices, Determinants, Continuity and Differentiability, and Application of Derivatives, organized into 5 balanced sections featuring multiple-choice questions, assertion-reasoning items, short-answer responses, long descriptive proofs, and case-based evaluation scenarios.

• 50% Competency-Focused Mandate: Packed with higher-order thinking skill questions requiring students to analyze equivalence classes across modular relations, compute matrix adjoints to establish consistency in non-homogeneous linear systems, verify differentiability for absolute value functions across boundary points, and evaluate points of inflection using higher-order derivatives.

• Case-Based & Real-World Optimization: Features applied modeling scenarios examining optimal cylindrical packaging dimensions to minimize manufacturing sheet cost, velocity and acceleration analysis for moving bodies using rate of change derivatives, and matrix multiplication frameworks modeling multi-product distribution costs across retail networks.

• Step-by-Step Marking Scheme: Delivers comprehensive, point-wise solutions detailing explicit algebraic steps, identity citations, domain restrictions for inverse functions, determinant row and column operations without direct expansion, and structured CBSE mark-distribution rubrics.

• Timed 3-Hour Simulation: Calibrated to train senior secondary mathematics students in pacing across rapid objective evaluations, systematic algebraic proofs, and multi-tier differential calculus applications without running out of time.