ICSE Class 12Subject library

ICSE Class 12 Mathematics

Chapter-wise notes, previous year papers, sample papers and Q&A for ICSE Class 12 mathematics — free, syllabus-aligned, exam-ready.

13 chapters~202 min read totalFree · printable

Chapters

13 chapters — sequenced for revision and exam prep.

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Mathematics — Calculus, Vectors, 3D Geometry, Probability & Linear Programming

ISC Class 12 Mathematics: RELATIONS and FUNCTIONS (advanced). INVERSE TRIGONOMETRY. MATRICES and DETERMINANTS. The CALCULUS sequence — continuity, derivatives, integrals, differential equations. VECTOR ALGEBRA. 3D GEOMETRY. LINEAR PROGRAMMING. And PROBABILITY (Bayes' Theorem, random variables, binomial distribution). ISC Class 12 Mathematics.

ISC⏱ 22 minRead chapter

Relations and Functions

Types of relations — reflexive, symmetric, transitive, equivalence. Types of functions — one-one, onto, bijective. Composition of functions, invertible functions, and binary operations.

ISC⏱ 15 minRead chapter

Inverse Trigonometric Functions

Principal values, domain and range, properties and graphs of inverse trigonometric functions. Key identities and their applications in ISC problems.

ISC⏱ 15 minRead chapter

Matrices

Types of matrices, algebra including addition and multiplication, transpose, symmetric and skew-symmetric matrices, elementary row/column operations, and finding inverse using elementary operations.

ISC⏱ 15 minRead chapter

Determinants

Properties of determinants, minors and cofactors, adjoint and inverse using adjoint, solution of linear equations using Cramers rule and matrix method, area of triangle.

ISC⏱ 15 minRead chapter

Continuity and Differentiability

Continuity of functions, differentiability, chain rule, implicit and parametric differentiation, logarithmic differentiation, second order derivatives, Rolles and Lagranges Mean Value Theorems.

ISC⏱ 15 minRead chapter

Applications of Derivatives

Rate of change, tangents and normals, increasing and decreasing functions, maxima and minima, optimization problems — all essential for ISC exam success.

ISC⏱ 15 minRead chapter

Integrals

Indefinite integrals with standard forms, substitution, partial fractions, integration by parts, special integrals. Definite integrals — properties and evaluation, area under curves.

ISC⏱ 15 minRead chapter

Differential Equations

Order and degree of differential equations, formation of differential equations, solutions using variable separable, homogeneous, linear, and exact equations.

ISC⏱ 15 minRead chapter

Vectors

Magnitude and direction of vectors, types of vectors, addition of vectors, scalar product, vector product, and scalar triple product with applications.

ISC⏱ 15 minRead chapter

Three Dimensional Geometry

Direction cosines and ratios, equations of lines in vector and Cartesian forms, equations of planes, angle between line and plane, distance of point from plane, skew lines.

ISC⏱ 15 minRead chapter

Linear Programming

Formulation of linear programming problems, graphical method for two variables, feasible region, optimal solution, and corner point method.

ISC⏱ 15 minRead chapter

Probability

Conditional probability, multiplication theorem, Bayes theorem, random variables and probability distributions, Bernoulli trials, and binomial distribution.

ISC⏱ 15 minRead chapter