Artham Resources | Class 12 Mathematics Half-Yearly Sample Paper with Solutions (Set 11)

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 evaluate bijective function verification, elementary transformations, parametric differentiability, and rate-of-change curve analysis 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 establish one-one and onto criteria for multi-variable mappings, evaluate matrix equations to extract inverse matrices without traditional adjoint methods, differentiate functions defined parametrically with respect to another function, and locate critical points and inflection zones along polynomial curves.

• Case-Based & Real-World Optimization: Features real-world contextual models exploring revenue optimization for dynamic pricing algorithms, rate of change of surface water ripples in expanding concentric waves, and production capacity matrices tracking multi-factory supply chains.

• Step-by-Step Marking Scheme: Delivers comprehensive, point-wise solutions detailing explicit algebraic steps, trigonometric identity substitutions, valid branch restrictions for inverse functions, determinant row and column transformations, 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 problems without running out of time.