Class 12 Mathematics Half-Yearly Sample Papers with Solutions Set 4| 2026–27

Artham Resources | Class 12 Mathematics Half-Yearly Sample Paper with Solutions (Set 4)

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 equivalence relation proofs, skew-symmetric determinant properties, logarithmic differentiation, and geometric extrema applications 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 prove equivalence relations on ordered pairs in $\mathbb{N} \times \mathbb{N}$, evaluate determinant factorizations without direct expansion using row/column transformations, differentiate implicit relations involving infinite nested series ($y = \sqrt{\cos x + \sqrt{\cos x + \dots}}$), and determine intervals where trigonometric-polynomial combinations are strictly increasing or decreasing.

• Case-Based & Real-World Optimization: Features applied modeling scenarios analyzing optimal packaging dimensions for cylindrical beverage containers to minimize material costs, rate of change of water levels in conical reservoirs under steady drainage, and multi-variable business investment matrices tracking quarterly revenue yield.

• Step-by-Step Marking Scheme: Delivers comprehensive, point-wise solutions detailing explicit algebraic expansions, standard identity substitutions, domain restrictions for inverse functions, determinant properties, 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 calculus applications without running out of time.