Board of Secondary Education, Madhya Pradesh, Bhopal
Higher Secondary Examination Session 2026-27
Marking Scheme (अंक योजना)
Class: 12th
Subject: Mathematics (गणित)
Maximum Marks: 80
Time: 3:00 Hours
| S.No. | Prescribed Chapters & Topics | Allocated Marks |
|---|---|---|
| 1 | Chapter 1: Relations and Functions Introduction, types of relations, types of functions, composition of functions and invertible functions. | 5 |
| 2 | Chapter 2: Inverse Trigonometric Functions Introduction, basic concepts, properties of inverse trigonometric functions. | 6 |
| 3 | Chapter 3: Matrices Introduction, matrix, types of matrices, operations on matrices, transpose of a matrix, symmetric and skew-symmetric matrices, invertible matrices. | 6 |
| 4 | Chapter 4: Determinants Introduction, determinant, area of a triangle, minors and cofactors, adjoint and inverse of a matrix, applications of determinants and matrices. | 6 |
| 5 | Chapter 5: Continuity and Differentiability Introduction, continuity, differentiability, exponential and logarithmic functions, logarithmic differentiation, derivatives of functions in parametric forms, second-order derivative. | 8 |
| 6 | Chapter 6: Applications of Derivatives Introduction, rate of change of quantities, increasing and decreasing functions, maxima and minima. | 6 |
| 7 | Chapter 7: Integrals Introduction, integration as an inverse process of differentiation, methods of integration, integrals of some particular functions, integration by partial fractions, integration by parts, definite integrals, fundamental theorem of calculus, evaluation of definite integrals by substitution, some properties of definite integrals. | 12 |
| 8 | Chapter 8: Applications of Integrals Introduction, area under simple curves. | 3 |
| 9 | Chapter 9: Differential Equations Introduction, basic concepts, general and particular solutions of a differential equation, methods of solving first-order, first-degree differential equations. | 6 |
| 10 | Chapter 10: Vector Algebra Introduction, some basic concepts, types of vectors, addition of vectors, multiplication of a vector by a scalar, product of two vectors. | 7 |
| 11 | Chapter 11: Three-Dimensional Geometry Introduction, direction cosines and direction ratios of a line, equation of a line in space, angle between two lines, shortest distance between two lines. | 7 |
| 12 | Chapter 12: Linear Programming Introduction, linear programming problem and its mathematical formulation. | 3 |
| 13 | Chapter 13: Probability Introduction, conditional probability, multiplication rule of probability, independent events, Bayes’ theorem. | 5 |
| Total Marks: | 80 |
Examination Guidelines & Blueprint Notes:
Questions 1 to 5 will comprise 32 Objective Type Questions. Each question carries 01 Mark.
Question No. 1 – Multiple Choice Questions (MCQs): 06 Marks
Question No. 2 – Fill in the Blanks: 06 Marks
Question No. 3 – True / False Statements: 06 Marks
Question No. 4 – Match the Following Pairs: 07 Marks
Question No. 5 – Single-word / One-sentence Answers: 07 Marks
Questions 6 to 15: Total 10 short-form evaluation questions. Each question carries 02 Marks.
Questions 16 to 19: Total 04 multi-step evaluation questions. Each question carries 03 Marks.
Questions 20 to 23: Total 04 complex analytical / long-form questions. Each question carries 04 Marks.