MSBSHSE Syllabus for Class 12 Mathematics (Maths)

Class 12 Mathematics and Statistics: Syllabus at a Glance

Your Class 12 textbook is titled Mathematics and Statistics, though almost everyone calls it Maths. The name matters at exam time: a few chapters (Statistics, Probability Distributions, Linear Programming) are statistics-and-applications topics, not pure algebra or calculus, so do not skip them assuming they are "extra". They carry their own questions in the paper.

The subject is worth 100 marks, made up of a theory paper plus internal assessment. The exact split between the written paper and internal marks, and the time allowed for the theory paper, should be confirmed from the current board circular before you plan your revision [verify].

The syllabus is organised into Part I and Part II, matching the two parts of your textbook. Part I covers logic, matrices, trigonometry, pair of straight lines, circles, conics, vectors, three-dimensional geometry and linear programming. Part II moves to differentiation, applications of derivatives, integration, definite integrals and its applications, differential equations, probability distributions, binomial distribution, statistics, mathematical reasoning, complex numbers, permutations and combinations, sequences and series, binomial theorem, sets, relations and functions, limits and continuity.

Use the sections below in this order:

The full chapter list with topic-level points, so you can tick off each sub-topic against your textbook.
Marks weightage, so you know which chapters deserve more practice time [verify].
A study plan that fits the actual writing time you get in the exam.

Every figure on this page marked [verify] is a number you should cross-check in the latest board circular or your school's official handout. Marks distribution and paper pattern details are revised from time to time, and an outdated number can cost you in planning, not in the exam hall, if you catch it early.

Full Chapter List: Part I and Part II

Your Mathematics and Statistics syllabus is split exactly the way your textbook is bound: Part I is one book, Part II is the other. Treat the two parts as separate revision units but one exam. Below, each chapter is given with its topic-level points, so you can open the textbook, find the chapter, and tick off every sub-topic you have actually practised. The "Part" column tells you which book the chapter sits in.

Part I Chapters

Mathematical Logic (Part I): statement and its truth value, logical connectives (and, or, not, if-then, if and only if), truth tables, tautology, contradiction, contingency, duality, negation of a compound statement, converse, inverse, contrapositive, algebra of statements, application to switching circuits.
Matrices (Part I): types of matrices (row, column, square, diagonal, scalar, identity, zero, symmetric, skew-symmetric), equality of matrices, addition, scalar multiplication, matrix multiplication, transpose, determinant of a square matrix, adjoint, inverse of a matrix, solving a system of linear equations by the inverse method and by reduction.
Trigonometric Functions (Part I): inverse trigonometric functions, principal values, domains and ranges, identities involving inverse functions, trigonometric equations and their general solutions.
Pair of Straight Lines (Part I): combined equation of a pair of lines, homogeneous equation of the second degree, angle between the lines, condition for parallel and perpendicular lines, point of intersection, bisectors of the angle between lines.
Circle (Part I): standard and general equation of a circle, centre and radius, tangent to a circle, condition of tangency, normal, director circle, family of circles.
Conics (Part I): parabola, ellipse and hyperbola in standard form, focus, directrix, axis, eccentricity, latus rectum, tangents and normals in standard forms.
Vectors (Part I): types of vectors, addition and subtraction, scalar multiplication, position vector, section formula, scalar (dot) product, vector (cross) product, scalar triple product, applications to area and geometry.
Three-Dimensional Geometry (Part I): direction cosines and direction ratios, equation of a line in space, equation of a plane in various forms, angle between lines, angle between line and plane, shortest distance between skew lines.
Linear Programming (Part I): linear inequations, graphical method, feasible region, corner points, optimisation of a linear objective function, bounded and unbounded regions.

Part II Chapters

Differentiation (Part II): derivative from first principle, derivative of composite functions (chain rule), derivative of inverse functions, logarithmic differentiation, implicit differentiation, derivative of parametric functions, second order derivative.
Applications of Derivatives (Part II): increasing and decreasing functions, maxima and minima (first and second derivative tests), tangents and normals, approximation, Rolle's theorem and mean value theorem [verify the exact scope in your textbook].
Indefinite Integration (Part II): standard integrals, method of substitution, integration by parts, integration by partial fractions, integrals of special forms.
Definite Integration (Part II): definite integral as limit of a sum, properties of definite integrals, evaluation using properties, area under a curve.
Applications of Definite Integration (Part II): area bounded by curves and lines, volume of solids of revolution [verify whether volume is included in the current syllabus].
Differential Equations (Part II): order and degree, formation of a differential equation, general and particular solution, solution by variable separation, homogeneous equations, linear differential equations of first order.
Probability Distributions (Part II): discrete and continuous random variables, probability mass and density functions, cumulative distribution function, expected value (mean) and variance.
Binomial Distribution (Part II): Bernoulli trials, binomial distribution formula, mean and variance of a binomial distribution, simple applications.
Statistics (Part II): measures of dispersion (range, quartile deviation, mean deviation, standard deviation, variance), coefficient of variation, skewness, kurtosis.
Mathematical Reasoning (Part II): statements, logical connectives, validity of a statement, checking validity using truth tables and rules of inference.
Complex Numbers (Part II): algebra of complex numbers, conjugate, modulus and argument, polar form, square root of a complex number, De Moivre's theorem and its applications.
Permutations and Combinations (Part II): fundamental principle of counting, permutations, permutations with repetition, combinations, circular permutations, simple applications.
Sequences and Series (Part II): arithmetic progression, geometric progression, harmonic progression, arithmetic, geometric and harmonic means, sum of special series (sums of n, n², n³).
Binomial Theorem (Part II): expansion for a positive integral index, general term, middle term, particular term, simple applications.
Sets, Relations and Functions (Part II): types of relations (reflexive, symmetric, transitive, equivalence), types of functions (one-one, onto, bijective), composition of functions, inverse of a function.
Limits (Part II): algebra of limits, standard limits, limits of algebraic, trigonometric, exponential and logarithmic functions, indeterminate forms.
Continuity (Part II): definition of continuity at a point and on an interval, algebra of continuous functions, types of discontinuity (removable, jump, infinite).

A practical way to use this list: take one chapter, open the textbook, and read the topic points above as a checklist. If you can write the definition, state the formula, and solve one textbook exercise question for a topic without looking, mark it done. If a topic appears in the list but you have never solved a question on it, that is your gap.

For example, under Matrices, a typical exam question asks you to solve a system of two or three equations using the inverse of the coefficient matrix. The fix for a common mistake here: students compute the adjoint and forget to divide by the determinant, or forget the condition that the inverse exists only when the determinant is non-zero. Write the determinant first, state that it is non-zero, then proceed.

Similarly, under Differentiation, logarithmic differentiation is easy to confuse with implicit differentiation. Use logarithmic differentiation when the function is a product, quotient or power of several terms; use implicit differentiation when y is not given explicitly in terms of x. Knowing which method applies saves time in the exam.

Under Binomial Distribution, remember the formula: P(X = r) = nCr pr qn−r, where q = 1 − p. The mean is np and the variance is npq. A common error is using the wrong value of p, so always write p and q clearly before substituting.

Keep this chapter list beside your study timetable. As you finish each chapter, mark it against the part it belongs to. By the time revision starts, you should have every chapter in both parts marked, and any unmarked chapter tells you exactly where to spend your remaining time.

Frequently Asked Questions

What is the difference between Mathematics and Statistics in Class 12?

Mathematics and Statistics is a single subject that combines pure mathematics topics like algebra, calculus, and geometry with statistics topics like probability distributions and linear programming. The textbook is divided into Part I and Part II, and both parts are equally important for the exam. Do not treat statistics chapters as optional; they carry their own weightage.

How many marks is the Class 12 Mathematics paper worth?

The subject is worth 100 marks, which includes both theory and internal assessment. The exact split between the written exam and internal marks, as well as the exam duration, can change, so confirm from the latest board circular [verify]. Your school's official handout will have the current details.

Which chapters are included in Part I of the Mathematics syllabus?

Part I covers mathematical logic, matrices, trigonometric functions, pair of straight lines, circle, conic sections, vectors, three-dimensional geometry, and linear programming. These chapters form the foundation for many concepts in Part II, so study them thoroughly.

What topics are covered in Part II of the Mathematics syllabus?

Part II includes differentiation, applications of derivatives, integration, definite integrals and their applications, differential equations, probability distributions, binomial distribution, statistics, mathematical reasoning, complex numbers, permutations and combinations, sequences and series, binomial theorem, sets, relations and functions, and limits and continuity.

Is the marks distribution for each chapter available?

The board prescribes a marks distribution, but it is revised periodically. You should check the latest board circular for the current weightage [verify]. Your teacher can also provide an updated handout. Use this to prioritise chapters that carry more marks.

How should I plan my study for the Class 12 Mathematics exam?

First, get the latest syllabus and marks distribution. Allocate more time to high-weightage chapters. Practise writing answers within the actual exam time to improve speed. Revise statistics topics regularly, as they are scoring. Solve previous years' papers to understand the pattern.