IGCSE Class 12Subject library

IGCSE Class 12 Mathematics

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

13 chapters~143 min read totalFree · printable

Chapters

13 chapters — sequenced for revision and exam prep.

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IGCSE chapters aren't published yet — showing the NCERT equivalent

Cambridge IGCSE runs its own syllabus, not NCERT. Use this for the concepts; check chapter names and order against your own textbook.

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Relations and Functions

This chapter picks up relations and functions where Class 11 left off — reflexive, symmetric, transitive and equivalence relations; one-one and onto functions; composition and invertibility. The book's own introduction and summary still mention "binary operations," but the actual teaching section on it has been removed from the current edition — a leftover reference, not a live topic. CBSE Class 12 Mathematics Chapter 1.

CBSE⏱ 11 minRead chapter

Inverse Trigonometric Functions

Trig functions repeat, so they aren't one-one on their full domain — restrict each one to an interval where it is, and you get an inverse with a well-defined principal value branch. The current book teaches every simplification through one substitution technique (x=sinθ, x=cosθ, x=tanθ, x=secθ) rather than a list of identities to memorise. CBSE Class 12 Mathematics Chapter 2.

CBSE⏱ 9 minRead chapter

Matrices

This chapter builds matrices from notation up through addition, multiplication, transpose, symmetric/skew-symmetric decomposition, and invertibility — but stops at proving an inverse is unique, not computing one. The old "find the inverse using elementary row operations" method has been dropped from the current book entirely, and its exercise shows it: Exercise 3.4 now has exactly one leftover question. CBSE Class 12 Mathematics Chapter 3.

CBSE⏱ 9 minRead chapter

Determinants

This chapter computes determinants, uses them to test for collinearity and invertibility, and solves linear systems — but only by the matrix method X=A⁻¹B, never Cramer's Rule, which the current book never mentions. Its own Miscellaneous Exercise also still points to questions 11-15 and 17-19 that no longer exist after rationalisation trimmed it down to 9. CBSE Class 12 Mathematics Chapter 4.

CBSE⏱ 9 minRead chapter

Continuity and Differentiability

This chapter takes differentiation from Class 11's basic rules to a full toolkit — chain rule, implicit differentiation, logarithmic differentiation, parametric forms, second derivatives — anchored by a precise definition of continuity. What it does not do, despite what older material remembers, is prove Rolle's Theorem or the Mean Value Theorem; neither appears anywhere in the current book. CBSE Class 12 Mathematics Chapter 5.

CBSE⏱ 8 minRead chapter

Applications of Derivatives

This chapter puts the derivative to work — rates of change, monotonicity, and optimisation via the first and second derivative tests. It does not cover tangents and normals, or approximations using differentials, despite the chapter's own introduction promising both; neither exists anywhere in the current book's actual sections. CBSE Class 12 Mathematics Chapter 6.

CBSE⏱ 9 minRead chapter

Integrals

The largest chapter in the book — indefinite integration by substitution, partial fractions and parts, six standard forms, and definite integrals via the Fundamental Theorem of Calculus and its properties. The old "definite integral as a limit of a sum" derivation has been cut to a single passing mention; every question here is solved through the Fundamental Theorem instead. CBSE Class 12 Mathematics Chapter 7.

CBSE⏱ 17 minRead chapter

Application of Integrals

The smallest chapter in the book — just 8 pages, one exercise, and 9 questions total. It teaches only the area under a single curve against an axis (lines, circles, parabolas, ellipses in standard position); "area between two curves," a full section in older editions, is not part of the current syllabus at all. CBSE Class 12 Mathematics Chapter 8.

CBSE⏱ 8 minRead chapter

Differential Equations

Order and degree, general and particular solutions, and three solving techniques — variable separable, homogeneous, and linear. "Formation of a differential equation" from a family of curves, a full section with its own exercise in older editions, does not exist anywhere in the current book. CBSE Class 12 Mathematics Chapter 9.

CBSE⏱ 13 minRead chapter

Vector Algebra

Types of vectors, addition and scalar multiplication, the section formula, and the two products — dot (scalar) and cross (vector). The Scalar Triple Product — volume of a parallelepiped, the coplanarity test [a b c]=0 — does not exist anywhere in the current book. CBSE Class 12 Mathematics Chapter 10.

CBSE⏱ 15 minRead chapter

Three Dimensional Geometry

Direction cosines and ratios, vector and Cartesian equations of a line, angle between two lines, and shortest distance between skew and parallel lines. Planes are entirely absent — despite the chapter's own introduction promising equations of planes, angles between planes, and distance from a point to a plane. CBSE Class 12 Mathematics Chapter 11.

CBSE⏱ 11 minRead chapter

Linear Programming

Formulating and solving optimisation problems in two variables by the graphical Corner Point Method, including the bounded and unbounded cases. The chapter has been cut to a single exercise of 10 questions with no Miscellaneous Exercise — the only chapter in the book without one — and every applied word problem has been removed. CBSE Class 12 Mathematics Chapter 12.

CBSE⏱ 11 minRead chapter

Probability

Conditional probability, the multiplication theorem, independent events, the theorem of total probability and Bayes' theorem. Random variables, probability distributions, mean and variance, and the Binomial distribution are all promised by the chapter's own introduction but taught nowhere in it — the sections carrying them have been removed. CBSE Class 12 Mathematics Chapter 13.

CBSE⏱ 13 minRead chapter

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Not yet. IGCSE Mathematics chapters are still being written, so this page shows the NCERT equivalent — good for the concepts, but chapter names and order will differ from your textbook.

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IGCSE Class 12 Mathematics