Mathematics

This is a complete, free study companion for Mathematics — built around what the exam actually asks. The topics examiners repeat most are Linear inequations and number line solution, Quadratic equations: factorisation, formula and exact roots, and Arithmetic progression nth term and sum. The syllabus runs to 26 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 10
Exam: Indian Certificate of Secondary Education
Conducted by: Council for the Indian School Certificate Examinations (CISCE)

Most frequently examined topics

#	Topic	Times asked
1	Linear inequations and number line solution	5
2	Quadratic equations: factorisation, formula and exact roots	5
3	Arithmetic progression nth term and sum	5
4	Equation of a straight line	5
5	Triangle similarity and proportional sides	5
6	Circle angle and cyclic quadrilateral properties	5
7	Mensuration: cylinder, cone, sphere and hemisphere	5
8	Trigonometrical identities	5
9	Heights and distances	5
10	Mean of grouped data	5
11	Basic probability	5
12	Compound interest and amount	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: Compound Interest
Chapter 2: Goods and Services Tax
Chapter 3: Banking
Chapter 4: Shares and Dividends
Chapter 5: Linear Inequations
Chapter 6: Quadratic Equations
Chapter 7: Problems on Quadratic Equations
Chapter 8: Ratio and Proportion
Chapter 9: Remainder Theorem and Factor Theorem
Chapter 10: Matrices
Chapter 11: Arithmetic Progression
Chapter 12: Geometric Progression
Chapter 13: Reflection
Chapter 14: Section and Mid-Point Formulae
Chapter 15: Equation of a Line
Chapter 16: Similarity
Chapter 17: Loci
Chapter 18: Angle and Cyclic Properties of a Circle
Chapter 19: Tangent Properties of Circles
Chapter 20: Constructions
Chapter 21: Volume and Surface Area of Solids
Chapter 22: Trigonometrical Identities
Chapter 23: Heights and Distances
Chapter 24: Graphical Representation of Statistical Data
Chapter 25: Measures of Central Tendency
Chapter 26: Probability

How to study Mathematics and score well

Start with the highest-frequency topics — In Mathematics, Linear inequations and number line solution, Quadratic equations: factorisation, formula and exact roots, Arithmetic progression nth term and sum, and Equation of a straight line 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 26 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 Linear inequations and number line solution, Quadratic equations: factorisation, formula and exact roots, Arithmetic progression nth term and sum. 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.