 # CBSE Class 12 Applied Mathematics Syllabus: 2020-21

Check the latest CBSE Syllabus for Class 12 Applied Mathematics (Academic Session 2020-21). Students of Class 12 having Applied Mathematics should thoroughly study this syllabus. CBSE Class 12 Applied Mathematics Syllabus: 2020-21

CBSE Class 12 Applied Mathematics Syllabus: 2020-21

 No. Units No. of Periods Marks I. Numbers, Quantification and Numerical Applications 20 06 II. Algebra 20 10 III. Inferential Statistics 10 06 IV. Index Numbers and Time-based data 30 10 V. Calculus 60 15 VI. Financial Mathematics 40 15 VII Linear Programming 25 08 VIII Probability 35 10 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

- Solution of simultaneous linear equations using elimination method (up to 3 variables)

- Matrices and types of matrices

- Algebra of matrices

- Determinants

- Inverse of a matrix

- Cramer’s rule and  its application

- Simple applications of matrices and determinants including Leontiff input output model for two variables

Unit III Calculus

- Application of derivatives

- Increasing/Decreasing functions

- Maxima and Minima

- Marginal cost and marginal revenue using derivatives

- Integration

- Indefinite integral as family of curves

- Definite integral as area under  the curve

- Integration of simple algebraic functions (primitive, by substitution, by parts)

- Application of Integration (consumer surplus-producer surplus)

- Differential equation (definition, order,  degree)

- Formulating and solving linear differential equation

- Application of differential equation (Growth and  Decay  Model)

Unit IV Probability
- Probability Distribution
- Mathematical Expectation
- Variance
- Binomial Distribution
- Poisson distribution
- Normal distribution
- Basic applications and inferences

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
- Index numbers, uses of index numbers
- Construction of index numbers (simple and weighted)
- Tests of adequacy of index numbers (unit test and  time reversal test)
- Trend analysis by moving average method
- Trend analysis by fitting of linear trend  line using least squares

Unit VII Financial Mathematics
- Perpetuity, Sinking funds
- Valuation of Bonds (Present value approach and  Relative price approach)
- Calculation of EMI
- Calculation of returns, nominal rate  of return,  effective rate of interest
- Compound annual growth rate
- Stock, shares and debentures
- Linear method of depreciation

Unit VIII Linear Programming
- Introduction and related terminologies (constraints, objective function, optimization)
- Mathematical formulation of linear programming problems
- Different types of linear programming problems (Transportation and assignment problem)
- Graphical method of solution for problems in two variables
- Feasible and infeasible regions (bounded and unbounded)
- Feasible and infeasible solutions, optimal feasible solutions (up to three  non- trivial constraints)

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

Matrix operations using Excel

1. Plot the graphs of functions on excel and  study the graph  to find out point of maxima/minima;

2. Probability and dice roll simulation;

3. Matrix multiplication and 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  on market  trends and  use excel to study future trends.

List of Suggested projects ( class XI /XII)

Use of prime numbers in coding and decoding of messages; Prime numbers and divisbility rules;

Logrithms  for  financial  calculations  such as  interest,  present  value,  future  vale, profit/loss etc with large values);

Cardinality of a set and orders of infinity;

Comparing sets of Natural numbers, rational numbers, real numbers and others; Use of Venn Diagram in solving practical problems;

Fibonacci Sequence: Its’ history and presence in nature; Testing the validity of mathematical statements and framing truth tables; Investigating graphs of functions for their properties;

Visit the census site of India http://www.censusindia.gov.in/Census_Data_2001/Census_Data_Online/Language/ State ment3.htm

Depict the information given there  in a pictorial form;

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;

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; Analysis   of   population   migration   data    –   positive   and    negative   influence   on urbanization;

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;

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;

Vehicle registration data  – correlating with pollution and number of accidents;

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;

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;

Weather prediction (prediction of monsoon from past data);

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;

Stock price movement ; Risk assessments by insurance firms from data; Predicting stock market  crash;

Predicting outcome of election – exit polls; Predicting mortality of infants.

Assessment Plan
1. Overall Assessment of the course is out of 100 marks.
2. 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. Weightage of Internal Assessment is of 20 marks. Internal Assessment can be  a combination  of activities  spread throughout 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 any one practical 5 Total 20