Class 12 Mathematics Half-Yearly Sample Papers with Solutions Set 6| 2026–27

Artham Resources | Class 12 Mathematics Half-Yearly Sample Paper with Solutions (Set 5)

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 inverse function domains, matrix rank and inversion methods, differentiability at boundary points, and curve-sketching optimization under authentic 3-hour examination conditions.

Key Highlights & Academic Features

• Authentic Examination Rigor: Calibrated to mirror official mid-term standards across Relations & Functions, Inverse Trigonometric Functions, Matrices, Determinants, Continuity & Differentiability, and Application of Derivatives, organized into 5 balanced sections (Sections A to E) featuring 20 MCQs/Assertion-Reasoning items, short-answer responses, long-answer proofs, and case-based evaluation scenarios.

• 50% Competency-Focused Mandate: Packed with higher-order thinking skill (HOTS) questions requiring students to evaluate the invertibility and composition of piecewise defined functions, compute minors, cofactors, and adjoint properties to evaluate  verify differentiability of modulus composite functions and apply second derivative tests to solve constrained geometric maximum-volume problems.

• Case-Based & Real-World Optimization: Features practical real-world modeling including finding the maximum carrying capacity of an open-topped trough with trapezoidal cross-section, marginal cost and revenue projections in supply-demand equilibrium, and matrix transformations used to model demographic population shifts between rural and urban centers.

• Step-by-Step Marking Scheme: Delivers comprehensive, point-wise solutions detailing explicit algebraic expansions, standard identity substitutions, domain-range restrictions for inverse trigonometric expressions, determinant factorizations, and structured CBSE mark-distribution rubrics.

• Timed 3-Hour Simulation: Calibrated to train senior secondary mathematics students in pacing across rapid objective calculations, multi-step matrix operations, and multi-tier differential calculus problems without running out of time.