Term 2 CBSE Class 12 Applied Mathematics Syllabus: CBSE Exam 2022

One Paper - Time: 2 Hours Max. Marks: 40

No.

Units

Marks

I

Calculus (Continued)

9

V

Inferential Statistics

5

VI

Index Numbers and Time-series (Continued)

5

VII

Financial Mathematics

15

VIII

Linear Programming

6

Total

40

Sl. No.

Contents

Notes / Explanation

3.5

Integration

Integration as a reverse process of differentiation Vocabulary and Notations related to Integration

3.6

Indefinite Integrals as the family of curves

Simple integrals based on each method (nontrigonometric function)

3.7

Definite Integrals as the area under the curve

Evaluation of definite integrals using properties

3.9

Application of Integration

Problems based on finding

Total cost when Marginal Cost is given

Total Revenue when Marginal Revenue is given

Equilibrium price and equilibrium quantity and hence consumer and producer surplus

Differential Equations and Modeling

3.10

Differential Equations

Definition, order, degree and examples

3.12

Application of Differential Equations

Growth and Decay Model in Biological Sciences, Economics and business, etc

Unit- 5 Inferential Statistics

5.1

Population and Sample

Population data from the census, economic surveys and other contexts from practical life

Examples of drawing more than one sample set from the same population

Examples of a representative and non-representative sample

Unbiased and biased sampling

Problems based on random sampling using simple random sampling and systematic random sampling (sample size less than 100)

5.2

t-Test (one-sample t-test and two independent groups t-test)

Examples and non-examples of Null and Alternate hypotheses (only nondirectional alternate hypotheses)

Framing of Null and Alternate hypothesis

Testing a Null Hypothesis to make Statistical Inferences for a small sample size

(for small sample size: t-test for one group and two independent groups

Use of t-table

Unit – 6 Index Numbers And Time-Based Data

6.4

Time Series

Meaning and Definition

6.5

Components of

Time Series

Secular trend

Seasonal variation

Cyclical variation

Irregular variation

6.6

Time Series analysis for univariate data

Fitting a straight line trend and estimating the value

6.7

Secular Trend

The tendency of the variable to increase or decrease over a long period of time

6.8

Methods of Measuring trend

Moving Average method

Method of Least Squares

Unit 7- Financial Mathematics

7.1

Perpetuity, Sinking Funds

Meaning of Perpetuity and Sinking Fund

Real life examples of sinking fund

Advantages of Sinking Fund

Sinking Fund vs. Savings account

7.2

Valuation of Bonds

Meaning of Bond Valuation

Terms related to valuation of bond:

Coupon rate, Maturity rate and

Current price

Bond Valuation Methods:

i) Present Value Approach

ii) Relative Price Approach

7.3

Calculation of EMI

Methods to calculate EMI:

i) Flat-Rate Method

ii) Reducing-Balance Method

Real life examples to calculate EMI of various types of loans, purchase of assets, etc.

7.4

Calculation of Returns, Nominal Rate of Return

Formula for calculation of Rate of Return, Nominal Rate of Return

7.5

Compound Annual Growth Rate

Meaning and use of Compound Annual Growth Rate

The formula for Compound Annual Growth Rate

7.7

Linear method of Depreciation

Meaning and formula for Linear Method of Depreciation

Advantages and disadvantages of Linear Method

Unit 8- Linear Programming

8.1

Introduction and related terminology

Need for framing linear programming problem

Definition of Decision Variable, Constraints, Objective function, Optimization and Non Negative conditions

8.2

The mathematical formulation of Linear Programming Problem

Set the problem in terms of decision variables, identify the objective function, identify the set of problem constraints, express the problem in terms of inequations

8.3

Different types of Linear Programming Problems

Formulate various types of LPP’s like Manufacturing Problem, Diet Problem, Transportation Problem, etc

8.4

Graphical method of solution for problems in two variables

Corner Point Method for the Optimal solution of LPP

8.5

Feasible and Infeasible Regions

Definition and Examples to explain the terms

8.6

Feasible and infeasible solutions, optimal feasible solution

Problems based on optimization

Examples of finding the solutions by graphical method

Term

Area and Weightage

Assessment Area

Marks allocated

Term 2

Practical

Performance of practical and record

5

Term-end test of anyone practical + Viva

5

Total

10