Mathematics

This is a complete, free study companion for Mathematics — built around what the exam actually asks. The topics examiners repeat most are Laws of Exponents and Negative Integral Exponents, Profit, Loss, Discount and Tax Calculations, and Compound Interest and Amount. The syllabus runs to 30 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 8
Programme: CL08
Exam: School Based Examination
Conducted by: Council for the Indian School Certificate Examinations (CISCE)

Most frequently examined topics

#	Topic	Times asked
1	Laws of Exponents and Negative Integral Exponents	9
2	Profit, Loss, Discount and Tax Calculations	9
3	Compound Interest and Amount	8
4	Linear Equations in One Variable and Word Problems	8
5	Surface Area and Volume of Cylinders	8
6	Factorisation Using Identities and Grouping	8
7	Square Roots by Prime Factorisation and Long Division	8
8	Rational Numbers Between Two Rational Numbers	7
9	Direct and Inverse Variation Applications	7
10	Area of Trapezium, Polygon and Semicircle	7
11	Probability of Simple Events	7
12	Algebraic Identities for Expansion and Simplification	7

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 Numbers
Chapter 2: Exponents and Powers
Chapter 3: Squares and Square Roots
Chapter 4: Cubes and Cube Roots
Chapter 5: Playing with Numbers
Chapter 6: Sets
Chapter 7: Percentages, Profit, Loss, Discount and Tax
Chapter 8: Simple and Compound Interest
Chapter 9: Direct and Inverse Variation
Chapter 10: Time and Work
Chapter 11: Algebraic Expressions
Chapter 12: Algebraic Identities
Chapter 13: Properties of Inequalities
Chapter 14: Factorisation
Chapter 15: Linear Equations in One Variable
Chapter 16: Properties of Quadrilaterals
Chapter 17: Properties of Parallelograms, Rectangles, Rhombuses and Squares
Chapter 18: Representing 3-D Shapes in 2-D
Chapter 19: Euler's Relation for 3-D Figures
Chapter 20: Construction of Quadrilaterals
Chapter 21: Reflection Symmetry
Chapter 22: Circles
Chapter 23: Area of Trapeziums, Polygons and Semicircles
Chapter 24: Surface Area of Cubes, Cuboids and Cylinders
Chapter 25: Total Surface Area and Curved Surface Area
Chapter 26: Volume of Cubes, Cuboids and Cylinders
Chapter 27: Volume and Capacity
Chapter 28: Grouped Data and Bar Graphs
Chapter 29: Pie Charts
Chapter 30: Chance and Probability

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, Laws of Exponents and Negative Integral Exponents, Profit, Loss, Discount and Tax Calculations, Compound Interest and Amount, and Linear Equations in One Variable and Word Problems 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 30 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 Laws of Exponents and Negative Integral Exponents, Profit, Loss, Discount and Tax Calculations, Compound Interest and Amount. 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.