StudyRaah Maharashtra State Board · HSC Commerce · Class 12 (Std XII)
Class 12 Maths and Statistics Notes
Short notes for every chapter of Maharashtra Board Class 12 Maths and Statistics, with key concepts, quick revision points and practice MCQs with answers. Open a chapter below, or practise all chapters with quizzes and mock tests on StudyRaah.
All 16 chapters
- Part 1 Chapter 1: Mathematical Logic
Mathematical logic gives precise rules for reasoning. The chapter defines statements, joins them with logical connectives, uses quantifiers, builds... - Part 1 Chapter 2: Matrices
A matrix is a rectangular array of numbers. The chapter covers types of matrices, matrix algebra, transpose and its properties, elementary... - Part 1 Chapter 3: Differentiation
Building on Std XI, this chapter extends differentiation to composite functions, inverse functions, logarithmic differentiation, implicit and... - Part 1 Chapter 4: Applications of Derivatives
Derivatives describe slopes and rates. The chapter finds equations of tangents and normals, tests whether functions are increasing or decreasing... - Part 1 Chapter 5: Integration
Integration is the reverse process of differentiation. The chapter defines the indefinite integral, lists standard formulas and rules, and integrates... - Part 1 Chapter 6: Definite Integration
A definite integral has limits and gives a number; here ∫[a, b] f(x) dx means the integral of f(x) from x = a to x = b. The chapter states the... - Part 1 Chapter 7: Application of Definite Integration
Definite integrals measure areas. The chapter finds the area under a curve above the X-axis, the area between a curve and the Y-axis, areas of... - Part 1 Chapter 8: Differential Equation and Applications
A differential equation involves derivatives of an unknown function. The chapter defines order and degree, forms differential equations by... - Part 2 Chapter 1: Commission, Brokerage and Discount
Middlemen such as agents, brokers and auctioneers earn commission or brokerage. Sellers allow trade and cash discounts, and bills of exchange are... - Part 2 Chapter 2: Insurance and Annuity
Insurance protects against financial loss from uncertain events, and an annuity is a series of equal payments at regular intervals. The chapter... - Part 2 Chapter 3: Linear Regression
Regression estimates the value of one variable from a known value of another. The chapter explains types of regression, fits simple linear regression... - Part 2 Chapter 4: Time Series
A time series records values of a variable at regular intervals of time. The chapter explains the uses and components of a time series, the additive... - Part 2 Chapter 5: Index Numbers
An index number measures the relative change in prices, quantities or values over time compared with a base period taken as 100. The chapter covers... - Part 2 Chapter 6: Linear Programming
Linear programming finds the best (maximum profit or minimum cost) use of limited resources. The chapter explains the terms of a linear programming... - Part 2 Chapter 7: Assignment Problem and Sequencing
An assignment problem allots jobs to workers or machines one-to-one at minimum cost (or maximum profit); a sequencing problem finds the order of... - Part 2 Chapter 8: Probability Distributions
A random variable assigns a number to each outcome of a random experiment. The chapter covers discrete and continuous random variables, probability...