# CBSE Class 12 Applied Mathematics Syllabus 2022-23

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CBSE Class 12 Applied Mathematics Syllabus 2022-23 includes Numbers, Quantification and Numerical Applications, Probability Distributions, Inferential Statistics, Index Numbers and Time-based data, Financial Mathematics, Linear Programming etc for the session 2022 – 2023. Here is the detailed syllabus. To download class 12 Applied Mathematics CBSE latest sample question papers for the 2023 exams, please install the myCBSEguide App which is the best mobile app for CBSE students. The myCBSEguide app not only provides you the CBSE class 12 Applied Mathematics model question papers but it also provides class 12 Applied Mathematics chapter-wise test papers, class 12 Applied Mathematics best revision notes and other study material for class 12 Applied Mathematics students.

CBSE Class – 12
Applied Mathematics
(Code No. 241)
Syllabus (2022-23)

Number of Paper: 1
Total number of Periods: 240 (35 Minutes Each)
Time: 3 Hours
Max Marks: 80

 No. Units No. of Periods Marks I. Numbers, Quantification and Numerical Applications 30 11 II. Algebra 20 10 III. Calculus 50 15 IV. Probability Distributions 35 10 V. Inferential Statistics 10 05 VI. Index Numbers and Time-based data 30 06 VII Financial Mathematics 50 15 VIII Linear Programming 15 08 Total 240 80 Internal Assessment 20

## Unit I Numbers, Quantification and Numerical Applications

• Modulo Arithmetic
• Congruence modulo
• Simple arithmetic functions
• Allegation or Mixture
• Numerical problems on boats and streams; partnership; pipes and cistern; races and games, scheduling
• Numerical inequalities

## Unit II Algebra

• Matrices and types of matrices
• Equality of matrices, Transpose of a matrix, Symmetric and Skew symmetric matrix
• Algebra of matrices
• Determinants
• Inverse of a matrix
• Solving system of simultaneous equations using matrix method, Cramer’s rule and row reduction method

## Unit III Calculus

Differentiation and its Applications

• High Order Derivatives
• Application of derivatives
• Marginal cost and marginal revenue using derivatives
• Increasing/Decreasing functions
• Maxima and Minima

Integration and its Applications

• Integration
• Indefinite Integrals as family of curves
• Definite Integrals as area under the curve
• Application of Integration

Differential equations and Modeling

• Differential Equations
• Formulating and Solving Differential Equations
• Application of Differential Equations

## Unit IV Probability Distributions

• Probability Distribution
• Mathematical Expectation
• Variance
• Binomial Distribution
• Poisson distribution
• Normal distribution

## Unit V Inferential Statistics

• Population and sample
• Parameter, statistic and statistical inferences
• t-Test (one sample t-test and two independent groups t-test)

## Unit VI Index numbers and Time-based data

• time Series
• Components of Time Series
• Time series analysis for univariant data
• Secular Trend
• Methods of Measuring trend

## Unit VII Financial Mathematics

• Perpetuity, Sinking funds
• Calculation of EMI
• Calculation of returns, nominal rate of return
• Compound annual growth rate
• Linear method of depreciation

## Unit VIII Linear Programming

• Introduction and related terminologies
• Mathematical formulation of linear programming problems
• Different types of linear programming problems
• Graphical method of solution for problems in two variables
• Feasible and infeasible regions
• Feasible and infeasible solutions, optimal feasible solutions

Graphs of an exponential function, demand and supply functions on Excel and study the nature of function at various points, maxima/minima, Matrix operations using Excel

## Suggested practical using the spreadsheet

1. Plot the graphs of functions on excel and study the graph to find out the point of maxima/minima
2. Probability and dice roll simulation
3. Matrix multiplication and the inverse of a matrix
4. Stock Market data sheet on excel
5. Collect the data on weather, price, inflation, and pollution analyze the data and make meaningful inferences
6. Collect data from newspapers on traffic, sports activities and market trends and use excel to study future trends

## List of Suggested projects (class 12)

1. Use of prime numbers in coding and decoding of messages
2. Prime numbers and divisibility rules
3. Logarithms for financial calculations such as interest, present value, future value, profit/loss etc. with large values)
4. The cardinality of a set and orders of infinity
5. Comparing sets of Natural numbers, rational numbers, real numbers and others
6. Use of Venn diagram in solving practical problems
7. Fibonacci Sequence: Its’ history and presence in nature;
8. Testing the validity of mathematical statements and framing truth tables;
9. Investigating graphs of functions for their properties
10. Visit the census site of India
https://www.censusindia.gov.in/Census_Data_2001/Census_Data_Online/Language/Statement3.htm Depict the information given there in a pictorial form;
11. Prepare a questionnaire to collect information about money spent by your friends in a month on activities like traveling, movies, recharging of the mobiles, etc. and draw interesting conclusions;
12. Check out the local newspaper and cut out examples of information depicted by graphs. Draw your own conclusions from the graph and compare it with the analysis given in the report;
13. Analysis of population migration data – positive and negative influence on urbanization;
14. Each day newspaper tells us about the maximum temperature, minimum temperature, humidity. Collect the data for a period of 30 days and represent it graphically. Compare it with the data available for the same time period for the previous year;
15. Analysis career graph of a cricketer (batting average for a batsman and bowling average for a bowler). Conclude the best year of his career. It may be extended for other players also – tennis, badminton, athlete;
16. Vehicle registration data – correlating with pollution and number of accidents;
17. Visit a village near Delhi and collect data of various crops over past few years from the farmers. Also collect data about temperature variation and rain over the period for a particular crop. Try to find the effect of temperature and rain variations on various crops;
18. Choose any week of your ongoing semester. Collect data for the past 10 – 15 years for the amount of rainfall received in Delhi during that week. Predict amount of rainfall for the current year;
19. Weather prediction (prediction of monsoon from past data)
20. Visit Kirana shops near your home and collect the data of sale of certain commodities over a month. Try to figure out the stock of a particular commodity which should be in the store in order to maximize the profit;
21. Stock price movement ;
22. Risk assessments by insurance firms from data;
23. Predicting stock market crash;
24. Predicting outcome of election – exit polls;
25. Predicting mortality of infants.

Assessment Plan

1. Overall Assessment of the course is out of 100 marks.
2. The assessment plan consists of External Exam and Internal Assessment.
3. External Exam will be of 03 hours duration Paper/Pencil Test consisting of 80 marks.
4. The weightage of Internal Assessment is of 20 marks. Internal Assessment can be a combination of activities spread throughout the semester/ academic year. Internal Assessment activities include, projects and excel based practical. Teachers can choose activities from the suggested list of practical or they can plan activities of similar nature. For data-based practical, teachers are encouraged to use data from local sources to make it more relevant for students.
5. Weightage for each area of internal assessment may be as under:
 Sr.No. Area and weightage Assessment Area Marks allocated 1 Project work (10 marks) Project work and record 5 Year-End Presentation/Viva of the Project 5 2 Practical work (10 marks) Performance of practical and record 5 Yearend test of anyone practical 5 Total 20