Mathematics & Statistics (Arts & Science)

This is a complete, free study companion for Mathematics & Statistics (Arts & Science) — built around what the exam actually asks. The topics examiners repeat most are Definite integrals and properties of definite integrals, Differential equations and applications, and Derivatives of logarithmic, inverse trigonometric and parametric functions. 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 Maharashtra Board body, so always confirm the current syllabus and exam dates on the official Maharashtra Board website before you rely on them.

Key information

Level: Class 12
Programme: CL12
Stream: All
Exam: Higher Secondary Certificate
Conducted by: MSBSHSE

Most frequently examined topics

#	Topic	Times asked
1	Definite integrals and properties of definite integrals	3
2	Differential equations and applications	3
3	Derivatives of logarithmic, inverse trigonometric and parametric functions	3
4	Vector lines, planes and three-dimensional geometry	3
5	Binomial distribution and probability distribution	3
6	Trigonometric identities and inverse trigonometric proofs	2
7	Area under curves by integration	2
8	Applications of derivatives: approximation and optimization	2
9	Lines represented by homogeneous second degree equations	2
10	Logic statements, truth tables and switching circuits	2
11	Vector equation of line and section formula using position vectors	2
12	Triangle trigonometry using sine, cosine and half-angle formulae	2

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: Functions and Graphs
Chapter 2: Polynomials and Rational Functions
Chapter 3: Sequences and Series
Chapter 4: Trigonometric Functions
Chapter 5: Trigonometric Identities and Equations
Chapter 6: Analytic Geometry: Circles and Conic Sections
Chapter 7: Limits and Continuity
Chapter 8: Derivatives and Applications
Chapter 9: Integrals and Applications
Chapter 10: Descriptive Statistics
Chapter 11: Probability and Inference

How to study Mathematics & Statistics (Arts & Science) and score well

Start with the highest-frequency topics — In Mathematics & Statistics (Arts & Science), Definite integrals and properties of definite integrals, Differential equations and applications, Derivatives of logarithmic, inverse trigonometric and parametric functions, and Vector lines, planes and three-dimensional geometry 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 Maharashtra Board Mathematics & Statistics (Arts & Science) 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 & Statistics (Arts & Science)

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 & Statistics (Arts & Science)?

Based on past papers, the most frequently asked topics include Definite integrals and properties of definite integrals, Differential equations and applications, Derivatives of logarithmic, inverse trigonometric and parametric functions. The full ranked list with how often each appears is in the "Most important topics" section above.

Where can I download Mathematics & Statistics (Arts & Science) previous-year question papers?

Official Maharashtra Board previous-year question papers are available on the official Maharashtra 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 & Statistics (Arts & Science) 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 & Statistics (Arts & Science) syllabus and past papers can quiz you on the most-asked topics and show you exactly what to revise.