Class 12 Mathematics Half-Yearly Sample Papers with Solutions Set 2| 2026–27

Artham Resources | Class 12 Mathematics Half-Yearly Sample Paper with Solutions (Set 2)

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 domain-range restrictions, determinant matrix algebra, higher-order derivatives, and differential optimization models 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 questions, 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 simplify composite inverse trigonometric expressions within principal value branches, solve consistent and inconsistent non-homogeneous systems of linear equations using the matrix method ($X = A^{-1}B$), prove logarithmic and parametric second-order derivatives ($d^2y/dx^2$), and verify Rolle’s and Mean Value Theorem analogues in geometric contexts.

• Case-Based & Real-World Optimization: Features practical modeling scenarios analyzing rate of change of volume and surface area in fluid dynamics, cost and marginal profit functions using derivatives, and geometric optimization problems such as finding the dimensions of an open tank or box with maximum volume from fixed sheet metal.

• Step-by-Step Marking Scheme: Delivers comprehensive, point-wise solutions detailing explicit algebraic expansions, identity citations, domain restrictions for inverse functions, matrix inversion steps, and structured CBSE mark-distribution rubrics.

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