## CBSE CLASS 12 APPLIED MATHS SYLLABUS

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## Unit 1 - Numbers Theory

* Modulo Arithmetic

* Congruence Modulo

* Simple Arithmetic Functions

* Allegation & Mixture

* Numerical Problems on :

Boats & Streams, Pipes & Cisterns, Partnership, Races, Games, Scheduling.

* Numerical Inequalities

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## Unit 2 - Algebra

* Solution of simultaneous linear equation using elimination method upto 3 variables.

* Matrices and types of Matrices

* Algebra of Matrices

* Determinants

* Inverse of a Matrix

* Cramer's rule and its application

* Simple application of Matrices and determinants including Leontiff input output model for two variables

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## Unit 3 - Calculus

* Application of Derivatives

* Increasing/ Decreasing Functions

* Maxima & Minima

* Marginal cost & Marginal revenue using derivatives

* Integration

* Indefinite integral as a family of curves

* Definite integral as area under one curve

* Integration of Simple algebraic functions

* Application of Integration

* Differential equation

* Formulating and solving linear differential equation

* Application of Differential equation

## Unit 4 - Probability

* Probability distribution

* Mathematical expectation

* Variance

* Binomial distribution

* Poission distribution

* Normal distribution

* Basic application and inferences

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## Unit 5 - Inferential Statistics

* Population and sample

* Parameter, statistic and statistical inferences

* T-test

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## Unit 6 - Index Numbers & Time Based Data

* Index numbers, uses of index numbers

## * Construction of index numbers

## * Tests of adequacy of index numbers

## * Time series, its analysis for univariant data sets

## * Trend analysis by moving average

## * Trend analysis by fitting of linear trend line using least squares

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## Unit 7 - Financial Mathematics

* Perpetuity, sinking funds

* Valuation of Bonds

* Calculation of EMI

* Calculation of returns, nominal rate of return, effective rate of interest

* Compound annual growth rate

* Stocks, shares and debentures