Mathematics

This is a complete, free study companion for Mathematics — built around what the exam actually asks. The topics examiners repeat most are Differentiation of inverse trigonometric, exponential, logarithmic, implicit and parametric functions, Indefinite integration by substitution, partial fractions and integration by parts, and Maxima and minima with first and second derivative tests. The syllabus runs to 11 chapters. Below you'll find the full topic-frequency ranking, the exam paper pattern, every chapter, a step-by-step study plan, and the official downloads — everything in one place.

Everything here is free. We're an independent student resource, not the official ICSE & ISC body, so always confirm the current syllabus and exam dates on the official ICSE & ISC website before you rely on them.

Key information

Level: Class 12
Exam: Indian School Certificate
Conducted by: Council for the Indian School Certificate Examinations (CISCE)

Most frequently examined topics

#	Topic	Times asked
1	Differentiation of inverse trigonometric, exponential, logarithmic, implicit and parametric functions	5
2	Indefinite integration by substitution, partial fractions and integration by parts	5
3	Maxima and minima with first and second derivative tests	4
4	Definite integrals and properties of definite integrals	4
5	Differential equations: variable separable and linear form dy/dx + Py = Q	4
6	Inverse trigonometric functions: principal values and identities	4
7	Linear programming graphical method and corner point optimization	4
8	Relations: reflexive, symmetric, transitive and equivalence relation	3
9	Matrices and determinants for solving simultaneous linear equations	3
10	Properties and evaluation of determinants	3
11	Continuity and differentiability from algebraic functions and graphs	3
12	Increasing and decreasing functions using derivative sign	3

Counted across the official previous-year question papers we have analysed for this subject. It shows what has been asked before — it does not predict what will appear in your exam. Always confirm the current syllabus on the official portal.

What you will study (chapters)

Chapter 1: Relations and Functions
Chapter 2: Algebra
Chapter 3: Calculus
Chapter 4: Probability
Chapter 5: Vectors
Chapter 6: Three-Dimensional Geometry
Chapter 7: Applications of Integrals
Chapter 8: Application of Calculus
Chapter 9: Linear Regression
Chapter 10: Linear Programming
Chapter 11: Mathematics Project Work

How to study Mathematics and score well

Start with the highest-frequency topics — In Mathematics, Differentiation of inverse trigonometric, exponential, logarithmic, implicit and parametric functions, Indefinite integration by substitution, partial fractions and integration by parts, Maxima and minima with first and second derivative tests, and Definite integrals and properties of definite integrals appear again and again in past papers. Master these first — they return the most marks for the time you put in.
Practise with previous-year papers — Solve the last 5–10 years of ICSE & ISC Mathematics papers under timed, exam-like conditions. Past papers show exactly which topics repeat and how questions are worded.
Revise actively, not passively — Write a one-page summary for each of the 11 chapters — key definitions, formulas and the points examiners reward — then re-test yourself instead of re-reading.
Mark your answers with the official scheme — After each practice paper, score yourself against the official marking scheme. It shows how marks are awarded step-by-step, so you learn to present answers the way examiners expect.

Exam tips: how to score higher in Mathematics

Where students lose marks: rushing the high-weightage questions, skipping the steps the marking scheme rewards, and saving easy sections for last. Read the whole paper first, attempt your strongest section early to bank marks, and always show your working.

Manage your time: split your time in proportion to the marks each section carries, keep a few minutes at the end to check, and never leave a question blank — a partial, structured answer still earns partial marks.

Frequently asked questions

What are the most important topics in Mathematics?

Based on past papers, the most frequently asked topics include Differentiation of inverse trigonometric, exponential, logarithmic, implicit and parametric functions, Indefinite integration by substitution, partial fractions and integration by parts, Maxima and minima with first and second derivative tests. The full ranked list with how often each appears is in the "Most important topics" section above.

Where can I download Mathematics previous-year question papers?

Official ICSE & ISC previous-year question papers are available on the official ICSE & ISC website. Open the Question Papers section for the direct link, plus the exam pattern and the topics that repeat most.

How can I prepare for Mathematics faster?

Start with the highest-frequency topics, learn the exam pattern so you know how each section is marked, and practise with past papers. A subject-aware study tutor can quiz you on exactly these topics.

A Gyani AI tutor trained on the Mathematics syllabus and past papers can quiz you on the most-asked topics and show you exactly what to revise.