Mathematics

This is a complete, free study companion for Mathematics — built around what the exam actually asks. The topics examiners repeat most are Relation reflexive-transitive-not symmetric, Principal range of cot^-1 x, and Symmetric and skew-symmetric matrix decomposition. 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 Karnataka Board body, so always confirm the current syllabus and exam dates on the official Karnataka Board website before you rely on them.

Key information

Level: Class 12
Stream: Science
Exam: 2nd Pre-university Course
Conducted by: Karnataka School Examination and Assessment Board (KSEAB)

Most important topics (by past-paper frequency)

#	Topic	Times asked	Likelihood
1	Relation reflexive-transitive-not symmetric	2	100%
2	Principal range of cot^-1 x	2	100%
3	Symmetric and skew-symmetric matrix decomposition	2	100%
4	Solving simultaneous linear equations by matrix method	2	100%
5	2x2 determinant equation and value of x	2	100%
6	Area of triangle using determinants	2	100%
7	Left hand derivative of modulus function	2	100%
8	Implicit differentiation	2	100%
9	Second-order derivative identity for y=3cos(log x)+4sin(log x)	2	100%
10	Continuity of piecewise function at a point	2	100%
11	Local maximum using derivatives	2	100%
12	Integral of e^x(1/x-1/x^2)	2	100%

Based on how often each topic appeared in official previous-year question papers.

What you will study (chapters)

Chapter 1: Relations and Functions
Chapter 2: Inverse Trigonometric Functions
Chapter 3: Matrices
Chapter 4: Determinants
Chapter 5: Continuity and Differentiability
Chapter 6: Applications of Derivatives
Chapter 7: Integrals
Chapter 8: Differential Equations
Chapter 9: Vector and 3-D Geometry
Chapter 10: Linear Programming
Chapter 11: Probability

How to study Mathematics and score well

Start with the highest-frequency topics — In Mathematics, Relation reflexive-transitive-not symmetric, Principal range of cot^-1 x, Symmetric and skew-symmetric matrix decomposition, and Solving simultaneous linear equations by matrix method 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 Karnataka Board 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 Relation reflexive-transitive-not symmetric, Principal range of cot^-1 x, Symmetric and skew-symmetric matrix decomposition. 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 Karnataka Board previous-year question papers are available on the official Karnataka Board 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.