Mathematics

This is a complete, free study companion for Mathematics — built around what the exam actually asks. The topics examiners repeat most are Compound Interest Amount and Interest Calculation, Profit, Loss and Discount Word Problems, and Algebraic Expansions Using Identities. The syllabus runs to 29 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 9
Programme: CL09
Exam: School Based Examination
Conducted by: Council for the Indian School Certificate Examinations (CISCE)

Most frequently examined topics

#	Topic	Times asked
1	Compound Interest Amount and Interest Calculation	4
2	Profit, Loss and Discount Word Problems	4
3	Algebraic Expansions Using Identities	4
4	Factorisation of Quadratic Trinomials	4
5	Simultaneous Linear Equations by Elimination and Word Problems	4
6	Laws of Indices and Exponent Simplification	4
7	Logarithm Laws and Simplification	4
8	Triangle Congruency Proofs and CPCT	4
9	Mid-point Theorem Applications	4
10	Pythagoras Theorem Applications	4
11	Parallelogram and Quadrilateral Proofs	4
12	Circle Chord Theorems	4

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: Rational and Irrational Numbers
Chapter 2: Profit, Loss and Discount
Chapter 3: Compound Interest
Chapter 4: Expansions
Chapter 5: Factorisation
Chapter 6: Changing the Subject of a Formula
Chapter 7: Linear Equations and Simultaneous Linear Equations
Chapter 8: Indices and Exponents
Chapter 9: Logarithms
Chapter 10: Triangles and Congruency
Chapter 11: Inequalities in Triangles
Chapter 12: Mid-point Theorem and Its Converse
Chapter 13: Pythagoras Theorem
Chapter 14: Rectilinear Figures and Quadrilaterals
Chapter 15: Constructions
Chapter 16: Area Theorems
Chapter 17: Circles
Chapter 18: Similarity
Chapter 19: Understanding and Recognition of Data
Chapter 20: Mean and Median for Ungrouped Data
Chapter 21: Area and Perimeter of Plane Figures
Chapter 22: Surface Area and Volume of Solids
Chapter 23: Trigonometrical Ratios
Chapter 24: Trigonometrical Ratios of Standard Angles
Chapter 25: Solution of Right Triangles
Chapter 26: Complementary Angles
Chapter 27: Coordinate System
Chapter 28: Graphical Solution of Simultaneous Linear Equations
Chapter 29: Distance Formula

Official textbook

Mathematics — official textbook / study material — Free download from the official source.

How to study Mathematics and score well

Start with the highest-frequency topics — In Mathematics, Compound Interest Amount and Interest Calculation, Profit, Loss and Discount Word Problems, Algebraic Expansions Using Identities, and Factorisation of Quadratic Trinomials 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 29 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 Compound Interest Amount and Interest Calculation, Profit, Loss and Discount Word Problems, Algebraic Expansions Using Identities. 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.