Class 12 Mathematics Half-Yearly Sample Papers with Solutions Set 3| 2026–27

Artham Resources | Class 12 Mathematics Half-Yearly Sample Paper with Solutions (Set 3)

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 function mappings, matrix polynomials, implicit differential equations, and tangent-normal 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 analyze injectivity and surjectivity of piecewise and modulus functions, evaluate characteristic equations and matrix polynomials ($A^2 – 5A + 7I = O$) to determine $A^{-1}$, differentiate functions raised to variable powers ($y = x^{\sin x} + (\log x)^x$), and calculate absolute maximum and minimum values on bounded closed intervals.

• Case-Based & Real-World Optimization: Features practical real-world contexts including perimeter-constrained pasture fencing optimization, marginal revenue and cost analysis for manufacturing output, and architectural window design maximizing light transmission through Norman windows.

• Step-by-Step Marking Scheme: Delivers comprehensive, point-wise solutions detailing explicit algebraic expansions, standard identity substitutions, domain restrictions for trigonometric relations, 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, intricate algebraic simplifications, and multi-step differential proofs without running out of time.