Class 12 Mathematics Half-Yearly Sample Papers with Solutions Set 13| 2026–27

Artham Resources | Class 12 Mathematics Half-Yearly Sample Paper with Solutions (Set 13)

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 trigonometric principal branches, singular versus non-singular matrix properties, implicit differentiation techniques, and constrained geometric extrema 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 prove injectivity and surjectivity on piecewise polynomial domains, simplify inverse trigonometric expressions restricted to negative argument branches, differentiate functions with respect to other implicit variables, and identify turning points where the first derivative vanishes while the second derivative changes sign.

• Case-Based & Real-World Optimization: Features applied mathematical modeling including minimizing material consumption for an open-topped cylindrical container, analyzing the instantaneous rate of change of water level inside a draining hemispherical bowl, and applying matrix transformations to optimize multi-tier inventory flow across retail warehouses.

• Step-by-Step Marking Scheme: Delivers comprehensive, point-wise solutions detailing explicit algebraic steps, identity citations, principal value 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 calculations, systematic algebraic proofs, and multi-step differential calculus problems without running out of time.