CBSE Class 11 Class 12 Syllabus 2023-24 Applied Mathematics

Applied Mathematics (XI-XII)
(Code-241)
Session- 2023-24

Secondary School Education prepares students to explore future career options after
graduating from schools. Mathematics is an important subject that helps students to
choose various fields of their choices. Mathematics is widely used in higher studies as
an allied subject in the field of Economics, Commerce, Social Sciences and many
others. It has been observed that the syllabus of Mathematics in senior secondary
grades meant for Science subjects may not be appropriate for the students who wish to
pursue Commerce or Social Science-based subjects in university education. By keeping
this in mind, one more elective course in the Mathematics syllabus is developed for
Senior Secondary classes with an aim to provide students relevant experience in
Mathematics that can be used in fields other than Physical Sciences.
This course is designed to develop substantial mathematical skills and methods needed
in other subject areas. Topics covered in two years aim to enable students to use
mathematical knowledge in the field of business, economic and social sciences. It aims
to promote appreciation of mathematical power and simplicity for its countless
applications in diverse fields. The course continues to develop mathematical language
and symbolism to communicate and relate everyday experiences mathematically. In
addition, it reinforces the logical reasoning skills of formulating and validating
mathematical arguments, framing examples, finding counterexamples. It encourages
students to engage in mathematical investigations and to build connections within
mathematical topics and with other disciplines. The course prepares students to use
algebraic methods as a means of representation and as a problem-solving tool. It also
enables students to interpret two-dimensional geometrical figures using algebra and to
further deduce properties of geometrical figures in a coordinate system. The course
content will help students to develop a sound understanding of descriptive and
inferential statistics which they can use to describe and analyze a given set of data and
to further make meaningful inferences out of it. Data based case studies from the field
of business, economics, psychology, education, biology and census data will be used to
appreciate the power of data in contemporary society.
It is expected that the subject is taught connecting concepts to the applications in
various fields. The objectives of the course areas are as follows:

Objectives:
a) To develop an understanding of basic mathematical and statistical tools and their
applications in the field of commerce (business/ finance/economics) and social
sciences.
b) To model real-world experiences/problems into mathematical expressions using
numerical/algebraic/graphical representation.
c) To make sense of the data by organizing, representing, interpreting, analysing, and
making meaningful inferences from real-world situations.
d) To develop logical reasoning skills and apply the same in simple problem-solving.
e) To reinforce mathematical communication by formulating conjectures, validating
logical arguments and testing hypothesis.
f) To make connections between Mathematics and other disciplines.

Grade XI (2023-24)

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

No. Units No. of Marks
Periods
I Numbers, Quantification and 25 09
Numerical Applications
II Algebra 45 15
III Mathematical Reasoning 15 06
IV Calculus 35 10
V Probability 25 08
VI Descriptive Statistics 35 12
VII Basics of Financial Mathematics 45 15
VIII Coordinate Geometry 15 05
Total 240 80
Internal Assessment 20

CLASS- XI
Sl. Contents Learning Outcomes: Notes / Explanation
No. Students will be able to
UNIT – 1 NUMBERS, QUANTIFICATION AND NUMERICAL APPLICATIONS
Numbers & Quantification
1.2 Binary Numbers ● Express decimal numbers ● Definition of number system
in binary system (decimal and binary)
● Express binary numbers ● Conversion from decimal to
in decimal system binary system and vice - versa
1.4 Indices, ● Relate indices and ● Applications of rules of indices
Logarithm and logarithm /antilogarithm ● Introduction of logarithm and
Antilogarithm ● Find logarithm and antilogarithm
antilogarithms of given ● Common and Natural logarithm
number
1.5 Laws and ● Enlist the laws and ● Fundamental laws of logarithm
properties of properties of logarithms
logarithms ● Apply laws of logarithm
1.6 Simple ● Use logarithm in different ● Express the problem in the form
applications of applications of an equation and apply
logarithm and logarithm/ antilogarithm
antilogarithm
Numerical Applications
1.7 Averages ● Determine average for a ● Definition and meaning
given data ● Problems on average, weighted
average
1.8 Clock ● Evaluate the angular ● Number of rotations of minute
value of a minute hand / hour hand of a clock in a
● Calculate the angle day
formed between two ● Number of times minute hand and
hands of clock at given hour hand coincides in a day
time
● Calculate the time for
which hands of clock
meet
1.9 Calendar ● Determine Odd days in a ● Definition of odd days
month/ year/ century ● Odd days in a year/ century.
● Decode the day for the ● Day corresponding to a given
given date date
1.10 Time, Work and ● Establish the relationship ● Basic concept of time and work
Distance between work and time ● Problems on time taken / distance
● Compare the work done covered / work done
by the individual / group
w.r.t. time
● Calculate the time taken/
distance covered/ Work
done from the given data
1.11 Mensuration ● Solve problems based on ● Comparison between 2D and 3D
surface area and volume shapes
of 2D and 3D shapes ● Combination of solids
● Calculate the volume/ ● Transforming one solid shape to
surface area for solid another
formed using two or more
shapes

1.12 Seating ● Create suitable seating ● Linear and circular seating
arrangement plan/ draft as per given arrangement
conditions ● Position of a person in a seating
(Linear/circular) arrangement
● Locate the position of a
person in a seating
arrangement
UNIT – 2 ALGEBRA
Sets
2.1 Introduction to ● Define set as well-defined ● Definition of a Set
sets – definition collection of objects ● Examples and Non-examples of
Set
2.2 Representation ● Represent a set in Roster ● Write elements of a set in Set
of sets form and Set builder form Builder form and Roster Form
● Convert a set given in Roster
form into Set builder form and
vice-versa
2.3 Types of sets  Identify different types of  Types of Sets: Finite Set, Infinite
and their sets on the basis of Set, Empty Set, Singleton Set
notations number of elements in the
set
 Differentiate between
equal set and equivalence
set
2.4 Subsets  Enlist all subsets of a set  Subset of a given set
 Find number of subsets of  Familiarity with terms like
a given set Superset, Improper subset,
 Find number of elements Universal set, Power set
of a power set
2.5 Intervals  Express subset of real  Open interval, closed interval,
numbers as intervals semi open interval and semi
closed interval
2.6 Venn diagrams  Apply the concept of  Venn diagrams as the pictorial
Venn diagram to representation of relationship
understand the between sets
relationship between sets  Practical Problems based on
 Solve problems using Venn Diagrams
Venn diagram
2.7 Operations on  Perform operations on  Operations on sets include
sets sets to solve practical i) Union of sets
problems ii) Intersection of sets
iii) Difference of sets
iv) Complement of a set
v) De Morgan’s Laws
Relations
2.8 Ordered pairs  Explain the significance of  Ordered pair, order of elements in
specific arrangement of an ordered pair and equality of
Cartesian elements in a pair ordered pairs
product of two  Write Cartesian product of  Cartesian product of two non-
sets two sets empty sets
 Find the number of

elements in a Cartesian
product of two sets
2.9 Relations  Express relation as a  Definition of Relation, examples
subset of Cartesian pertaining to relations in the real
product number system
 Find domain and range of
a relation
Sequences and Series
2.11 Sequence and ● Differentiate between ● Sequence:𝑎1 , 𝑎2 , 𝑎3, … , 𝑎𝑛
Series sequence and series ● Series: 𝑎1 + 𝑎2 + 𝑎3 + ⋯ + 𝑎𝑛

2.12 Arithmetic ● Identify Arithmetic ● General term of AP:
Progression Progression (AP) 𝑡 𝑛 = 𝑎 + (𝑛 − 1)𝑑
● Establish the formulae of ● Sum of n terms of AP :
𝑛
finding 𝑛𝑡ℎ term and sum Sn = 2 [2𝑎 + (𝑛 − 1)𝑑]
of n terms
● Solve application 𝑎+𝑏
AM of 𝑎 𝑎𝑛𝑑 𝑏= 2
problems based on AP
● Find arithmetic mean
(AM) of two positive
numbers

2.13 Geometric  Identify Geometric ● General term of GP:
Progression Progression (GP) 𝑡𝑛 = 𝑎𝑟 𝑛−1
● Sum of n terms of a GP:
● Derive the 𝑛𝑡ℎ term and 𝑎(𝑟 𝑛 −1)
Sn =
sum of n terms of a given 𝑟−1
GP
 Sum of infinite term of GP =
𝑎
● Solve problems based on 1−𝑟
, where −1 < 𝑟 < 1
applications of GP
● Geometric mean of a and b = √𝑎𝑏
● Find geometric mean ● For two positive numbers a and b,
(GM) of two positive 𝑎+𝑏
AM ≥GM i.e., 2
≥ √𝑎𝑏
numbers
● Solve problems based on
relation between AM and
GM

2.14 Applications of ● Apply appropriate Applications based on
AP and GP formulas of AP and GP to ● Economy Stimulation
solve application ● The Virus spread etc.
problems

Permutations and Combinations
2.15 Factorial ● Define factorial of a ● Definition of factorial:
number n! = n(n-1)(n-2)…3.2.1
● Calculate factorial of a Usage of factorial in counting
number principles
2.16 Fundamental ● Appreciate how to count ● Fundamental Principle of Addition
Principle of without counting ● Fundamental Principle of
Counting Multiplication

2.17 Permutations ● Define permutation ● Permutation as arrangement of
objects in a definite order taken
● Apply the concept of some or all at a time
permutation to solve ● Theorems under different
simple problems 𝑛!
conditions resulting in nPr=(𝑛−𝑟)! or
𝑛𝑟 or
𝑛!
arrangements
𝑛1 !𝑛2 !…𝑛𝑘 !

2.20 Combinations ● Define combination -The number of combinations of
n different objects taken r at a
● Differentiate between 𝑛!
time is given by nCr= 𝑟!.(𝑛−𝑟)!
permutation and
combination Some results on combinations:
n
● C0 = 1 = nCn
● Apply the formula of ●
n
Ca = nCb ⇒ a=b or a+ b=n
combination to solve the ●
n
Cr = nCn-r
related problems ●
n
Cr + nCr-1 = n+1Cr
UNIT -3 MATHEMATICAL REASONING
3.2 Logical ● Solve logical problems ● Odd man out
reasoning involving odd man out, ● Syllogism
syllogism, blood relation ● Blood relations
and coding decoding ● Coding Decoding
UNIT – 4 CALCULUS
4.1 Functions  Identify dependent and ● Dependent variable and
independent variables independent variable
 Define a function using ● Function as a rule or law that
dependent and defines a relationship between
independent variable one variable (the independent
variable) and another variable
(the dependent variable)
4.2 Domain and  Define domain, range ● Domain as a set of all values of
Range of a and co-domain of a given independent variable
function function ● Co-domain as a set of all values
of dependent variable
● Range of a function as set of all
possible resulting values of
dependent variable
4.3 Types of  Define various types of  Following types of functions with
functions functions definitions and characteristics
 Identify domain, co- Constant function, Identity
domain and range of the function, Polynomial function,
function Rational function, Composite
function, Logarithm function,
Exponential function, Modulus
function, Greatest integer
function, Signum function,
Algebraic function
4.4 Graphical ● Representation of ● Graph of some polynomial
representation function graphically functions, Logarithm function,
of functions Exponential Function, Modulus
function, Greatest integer

function, Signum function
4.5 Concepts of ● Define limit of a function ● Left hand limit, Right hand limit,
limits and ● Solve problems based on Limit of a function, Continuity of a
continuity of a the algebra of limits function
function ● Define continuity of a
function
4.6 Instantaneous ● Define instantaneous ∆𝑦 𝑓(𝑥+∆𝑥)−𝑓(𝑥)
● The ratio = as
rate of change rate of change ∆𝑥 ∆𝑥
instantaneous rate of change,
where ∆𝑦 is change in 𝑦 and ∆𝑥
is change in 𝑥 at any instant
4.7 Differentiation ● Find the derivative of the ● Derivatives of functions (non-
as a process of functions trigonometric only)
finding
derivative
4.8 Derivatives of ● Find the derivative of ● If 𝑦 = 𝑓(𝑢) where 𝑢 = 𝑔(𝑥) then
algebraic function of a function differential coefficient of 𝑦 w.r.t x
functions using 𝑑𝑦 𝑑𝑦 𝑑𝑢
is = .
Chain Rule 𝑑𝑥 𝑑𝑢 𝑑𝑥

UNIT – 5 PROBABILITY
5.1 Introduction ● Appreciate the use of ● Probability as quantitative
probability in daily life measure of uncertainty
situations ● Use of probability in determining
the insurance premium, weather
forecasts etc.
5.2 Random ● Define random ● Sample space as set of all
experiment and experiment and sample possible outcomes
sample space space with suitable
examples
5.3 Event  Define an event  Types of Event:
 Recognize and Impossible and sure event,
differentiate different Independent and dependent
types of events and find event, mutually exclusive and
their probabilities exhaustive event
5.4 Conditional  Define the concept of  Conditional Probability of event E
Probability conditional probability given that F has occurred is:
 Apply reasoning skills to 𝑃(𝐸|𝐹) =
𝑃(𝐸∩𝐹)
, 𝑃(𝐹) ≠ 0
solve problems based on 𝑃(𝐹)

conditional probability
5.5 Total Probability  Interpret mathematical  Total Probability:
information and identify Let 𝐸1, 𝐸2 , …,𝐸𝑛 be a partition of the
situations when to apply sample space S, then probability of
total probability an event A associated with S is:
 Solve problems based on 𝑃(𝐴) = ∑𝑛𝑗=1 𝑃(𝐸𝑗 )𝑃(𝐴|𝐸𝐽 )
application of total
probability
5.6 Bayes’  State Bayes’ theorem ● Bayes’ Theorem:
Theorem  Solve practical problems If 𝐸1 , 𝐸2 , … , 𝐸𝑛 be n non empty
based on Bayes’ events which constitute a partition
Theorem of a sample space 𝑆 and 𝐴 be any
event with non zero probability,

then:
𝑃(𝐸𝑖 )𝑃(𝐴|𝐸𝑖 )
𝑃(𝐸𝑖 |𝐴) = ∑𝑛
𝑗=1 𝑃(𝐸𝑗 )𝑃(𝐴|𝐸𝑗 )
UNIT- 6 DESCRIPTIVE STATISTICS
6.4 Data Interpretation
Measure of ● Understand meaning of ● Mean deviation around mean and
Dispersion dispersion in a data set median
● Differentiate between ● Standard deviation and variance
range, quartile deviation, ● Examples of different kinds of data
mean deviation and helping students to choose and
standard deviation compare different measures of
● Calculate range, quartile dispersion
deviation, mean deviation
and standard deviation for
ungrouped and grouped
data set
● Choose appropriate
measure of dispersion to
calculate spread of data
Skewness and ● Define Skewness and ● Examples of symmetrical and
Kurtosis Kurtosis using graphical asymmetrical data
representation of a data set ● Visualization of graphical
● Interpret Skewness and representation of data using Excel
Kurtosis of a frequency Spreadsheet or any other
distribution by plotting the computer assisted tool
graph
● Calculate coefficient of
Skewness and interpret the
results
6.5 Percentile rank ● Define Percentile rank and ● Emphasis on visualizing, analysing
and Quartile Quartile rank and interpreting percentile and
rank ● Calculate and interpret quartile rank scores
Percentile and Quartile
rank of scores in a given
data set
6.6 Correlation ● Define correlation in values ● Emphasis on application, analysis
of two data sets and interpreting the results of
● Calculate Product moment coefficient of correlation using
correlation for ungrouped practical examples
and grouped data
● Calculate Karl Pearson’s
coefficient of correlation
● Calculate Spearman’s rank
correlation
● Interpret the coefficient of
correlation
UNIT – 7 FINANCIAL MATHEMATICS
7.1 Interest and ● Define the concept of ● Impact of high interest rates and
Interest Rates Interest Rates low interest rates on the business
● Compare the difference
between Nominal Interest
Rate, Effective Rate and
Real Interest Rate

● Solve Practical
applications of interest
rate
7.2 Accumulation ● Interpret the concept of ● Meaning and significance of
with simple and simple and compound simple and compound interest
compound interest ● Compound interest rates
interest ● Calculate Simple Interest applications on various financial
and Compound Interest products

7.3 Simple and ● Explain the meaning, ● Concept of Equivalency
compound nature and concept of ● Annual Equivalency Rate
interest rates equivalency
with ● Analyze various
equivalency examples for
understanding annual
equivalency rate
7.4 Effective rate of ● Define with examples the ● Effective Annual Interest Rate
interest concept of effective rate = (1 + i/n)n – 1
of interest where:
i = Nominal Interest Rate
n = No. of Periods
7.5 Present value,  Interpret the concept of  Formula for Present Value:
net present compounding and
value and future discounting along with PV = CF/(1 + r)n
value practical applications Where:
 Compute net present CF = Cash Flow in Future Period
value r = Periodic Rate of return or Interest
(also called the discount rate or the
 Apply net present value in required rate of return)
capital budgeting
n = no. of periods
decisions
 Use of PVAF, FVAF tables for
practical purposes
 Solve problems based on
Application of net present value
7.6 Annuities, ● Explain the concept of ● Definition, Formulae and
Calculating Immediate Annuity, Examples
value of Annuity due and Deferred
Regular Annuity Annuity
● Calculate General Annuity
7.7 Simple ● Calculate the future value ● Examples of regular annuity:
applications of of regular annuity, annuity Mortgage Payment, Car Loan
regular due Payments, Leases, Rent
annuities (upto ● Apply the concept of Payment, Insurance payouts etc.
3 period) Annuity in real life
situations
7.8 Tax, calculation  Explain fundamentals of  Computation of income tax
of tax, simple taxation Add Income from
applications of  Differentiate between Salary, house property,
tax calculation Direct and indirect tax business or profession, capital
in Goods and  Define and explain GST gain, other sources, etc.
service tax, Less deductions
Income Tax
 Calculate GST
PF, PPF, LIC, Housing loan, FD,
 Explain rules under State NSC etc.

Goods and Services Tax  Assess the Individuals under
(SGST) Central Goods Income Tax Act
and Services Tax (CGST)  Formula for GST
and Union Territory Different Tax heads under GST
Goods and Services Tax
(UTGST)
7.9 Bills, tariff rates,  Describe the meaning of  Tariff rates- its basis of
fixed charge, bills and its various types determination
surcharge,  Analyze the meaning and  Concept of fixed charge service
service charge rules determining tariff charge and their applications in
rates various sectors of Indian
 Explain the concept of economy
fixed charge
7.10 Calculation and  To interpret and analyze  Components of electricity
interpretation of electricity bills, water bills bill/water supply and other supply
electricity bill, and other supply bills bills:
water supply bill  Evaluate how to calculate i) overcharging of electricity
and other units consumed under ii) water supply bills
supply bills electricity bills/water bill iii) units consumed in electricity
bills
UNIT – 8 COORDINATE GEOMETRY
8.1 Straight line ● Find the slope and ● Gradient of a line
equation of line in various ● Equation of line:
form Parallel to axes, point-slope form,
● Find angle between the two-points form, slope intercept
two lines form, intercept form
● Find the perpendicular ● Application of the straight line in
from a given point on a demand curve related to
line economics problems
● Find the distance between
two parallel lines
8.2 Circle ● Define a circle ● Circle as a locus of a point in a
● Find different form of plane
equations of a circle ● Equation of a circle in standard
● Solve problems based on form, central form, diameter form
applications of circle and general form

8.3 Parabola ● Define parabola and ● Parabola as a locus of a point in
related terms a plane.
● Define eccentricity of a ● Equation of a parabola in
parabola standard form:
● Derive the equation of ● Focus, Directrix, Axis, Latus
parabola rectum, Eccentricity
● Application in parabolic reflector,
beam supported by wires at the
end of the support, girder of a
railway bridge, etc.

Practical: Use of spreadsheet
Calculating average, interest (simple and compound), creating pictographs, drawing pie
chart, bar graphs, calculating central tendency visualizing graphs (straight line, circles
and parabola using real-time data)

Suggested practical using spreadsheet
1. Plot the graph of functions on excel study the nature of function at various points,
drawing lines of tangents
2. Create a budget of income and spending
3. Create and compare sheet of price & features to buy a product
4. Prepare the best option plan to buy a product by comparing cost, shipping charges,
tax and other hidden costs
5. Smart purchasing during sale season
6. Prepare a report card using scores of the last four exams and compare the
performance
7. Collect the data on weather, price, inflation, and pollution. Sketch different types of
graphs and analyze the results

Grade XII (2023-24)

Number of Paper: 1
Total number of Periods: 240 (35 Minutes Each)
Time: 3 Hours
Max Marks: 80
No. Units No. of Marks
Periods
I Numbers, Quantification and Numerical 30 11
Applications
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

CLASS XII
Sl. No. Contents Learning Outcomes: Notes / Explanation
Students will be able to
UNIT-1 NUMBERS, QUANTIFICATION AND NUMERICAL APPLICATIONS
1.1 Modulo  Define modulus of an integer  Definition and meaning
Arithmetic  Apply arithmetic operations  Introduction to modulo
using modular arithmetic rules operator
 Modular addition and
subtraction
1.2 Congruence ● Define congruence modulo ● Definition and meaning
Modulo ● Apply the definition in various ● Solution using congruence
problems modulo
● Equivalence class
1.4 Alligation and ● Understand the rule of alligation ● Meaning and Application of
Mixture to produce a mixture at a given rule of alligation
price ● Mean price of a mixture
● Determine the mean price of a
mixture
● Apply rule of alligation
1.5 Numerical Solve real life problems mathematically
Problems
Boats and ● Distinguish between upstream ● Problems based on speed of
Streams and downstream stream and the speed of boat
(upstream and ● Express the problem in the form in still water
downstream) of an equation
Pipes and ● Determine the time taken by ● Calculation of the portion of
Cisterns two or more pipes to fill or the tank filled or drained by
empty the tank the pipe(s) in unit time
Races and ● Compare the performance of ● Calculation of the time
Games two players w.r.t. time, taken/ distance covered /
distance speed of each player
1.6 Numerical ● Describe the basic concepts of ● Comparison between two
Inequalities numerical inequalities statements/situations which
● Understand and write numerical can be compared numerically
inequalities ● Application of the techniques
of numerical solution of
algebraic inequations
UNIT-2 ALGEBRA
2.1 Matrices and ● Define matrix ● The entries, rows and
types of ● Identify different kinds of columns of matrices
matrices matrices ● Present a set of data in a
● Find the size / order of matrices matrix form
2.2 Equality of  Determine equality of two  Examples of transpose of
matrices, matrices matrix
Transpose of a  Write transpose of given matrix  A square matrix as a sum of
matrix,  Define symmetric and skew symmetric and skew
Symmetric and symmetric matrix symmetric matrix
Skew  Observe that diagonal
symmetric elements of skew symmetric
matrix matrices are always zero

2.3 Algebra of ● Perform operations like addition ● Addition and Subtraction of
Matrices & subtraction on matrices of matrices
same order ● Multiplication of matrices (It
● Perform multiplication of two can be shown to the students
matrices of appropriate order that Matrix multiplication is
● Perform multiplication of a similar to multiplication of two
scalar with matrix polynomials)
● Multiplication of a matrix with
a real number
2.4 Determinants ● Find determinant of a square ● Singular matrix, Non-singular
matrix matrix
● Use elementary properties of ● |AB|=|A||B|
determinants ● Simple problems to find
determinant value
2.5 Inverse of a  Define the inverse of a square  Inverse of a matrix using:
matrix matrix a) cofactors
 Apply properties of inverse of If A and B are invertible
matrices square matrices of same size,
i) (AB)-1=B -1A –1
ii) (A-1)-1 =A
iii) (AT)-1 = (A-1)T
2.6 Solving system  Solve the system of  Solution of system of
of simultaneous equations using simultaneous equations upto
simultaneous i) Cramer’s Rule three variables only
equations ii) Inverse of coefficient matrix (non- homogeneous
using matrix  Formulate real life problems equations)
method, into a system of simultaneous
Cramer’s rule linear equations and solve it
and using these methods

UNIT- 3 CALCULUS
Differentiation and its Applications
3.1 Higher Order  Determine second and higher  Simple problems based on
Derivatives order derivatives higher order derivatives
 Understand differentiation of  Differentiation of parametric
parametric functions and functions
implicit functions and implicit functions (upto
2nd order)
3.2 Application of  Determine the rate of change of  To find the rate of change of
Derivatives various quantities quantities such as area and
 Understand the gradient of volume with respect to time or
tangent and normal to a curve at its dimension
a given point  Gradient / Slope of tangent
 Write the equation of tangents and normal to the curve
and normal to a curve at a given  The equation of the tangent
point and normal to the curve
(simple problems only)
3.3 Marginal Cost  Define marginal cost and  Examples related to marginal
and Marginal marginal revenue cost, marginal revenue, etc.
Revenue using  Find marginal cost and marginal
derivatives revenue

3.4 Increasing  Determine whether a function is  Simple problems related to
/Decreasing increasing or decreasing increasing and decreasing
Functions  Determine the conditions for a behaviour of a function in the
function to be increasing or given interval
decreasing
3.5 Maxima and  Determine critical points of the  A point x= c is called the
Minima function critical point of f if
 Find the point(s) of local maxima f is defined at c and
and local minima and f ′ (c) =
corresponding local maximum 0 or f is not differentiable
and local minimum values at c
 Find the absolute maximum and  To find local maxima and local
absolute minimum value of a minima by:
function i) First Derivative Test
 Solve applied problems ii) Second Derivative Test
 Contextualized real life
problems

Integration and its Applications
3.6 Integration  Understand and determine  Integration as a reverse
indefinite integrals of simple process of differentiation
functions as anti-derivative  Vocabulary and Notations
related to Integration
3.7 Indefinite  Evaluate indefinite integrals of  Simple integrals based on
Integrals as simple algebraic functions by each method (non-
family of method of: trigonometric function)
curves i) substitution
ii) partial fraction
iii) by parts
3.8 Definite ● Define definite integral as area ● Evaluation of definite integrals
Integrals as under the curve using properties
area under the ● Understand fundamental
curve theorem of Integral calculus and
apply it to evaluate the definite
integral
● Apply properties of definite
integrals to solve the problems
3.9 Application of ● Identify the region representing Problems based on finding
Integration C.S. and P.S. graphically ● Total cost when Marginal Cost
● Apply the definite integral to find is given
consumer surplus-producer ● Total Revenue when Marginal
surplus Revenue is given
● Equilibrium price and
equilibrium quantity and hence
consumer and producer
surplus

Differential Equations and Modeling
3.10 Differential ● Recognize a differential ● Definition, order, degree and
Equations equation examples
● Find the order and degree of a
differential equation

3.11 Formulating ● Formulate differential equation ● Formation of differential
and Solving ● Verify the solution of differential equation by eliminating
Differential equation arbitrary constants
Equations ● Solve simple differential ● Solution of simple differential
equation equations (direct integration
only)
3.12 ● Define Growth and Decay Model
Application of ● Growth and Decay Model in
Differential● Apply the differential equations Biological sciences,
Equations to solve Growth and Decay Economics and business, etc.
Models
UNIT- 4 PROBABILITY DISTRIBUTIONS
4.1 Probability ● Understand the concept of  Definition and example of
Distribution Random Variables and its discrete and continuous
Probability Distributions random variable and their
● Find probability distribution of distribution
discrete random variable
4.2 Mathematical ● Apply arithmetic mean of  The expected value of discrete
Expectation frequency distribution to find the random variable as summation
expected value of a random of product of discrete random
variable variable by the probability of its
occurrence.
4.3 Variance ● Calculate the Variance and S.D.  Questions based on variance
of a random variable and standard deviation
4.4 Binomial ● Identify the Bernoulli Trials and  Characteristics of the binomial
Distribution apply Binomial Distribution distribution
● Evaluate Mean, Variance and  Binomial formula:
S.D of a binomial distribution P(r) = nCr pr qn-r
Where n = number of trials
P = probability of
success
q = probability of
failure
Mean =np
Variance = npq
Standard Deviation = √𝑛𝑝𝑞
4.5 Poison ● Understand the Conditions of  Characteristics of Poisson
Distribution Poisson Distribution Probability distribution
● Evaluate the Mean and Poisson formula:
Variance of Poisson distribution 𝜆𝑥 . 𝑒 −𝜆
P(x) = 𝑥!
 Mean = Variance = 𝜆

4.6 Normal ● Understand normal distribution  Characteristics of a normal
Distribution is a Continuous distribution probability distribution
● Evaluate value of Standard  Total area under the curve =
normal variate total probability = 1
● Area relationship between Mean
 Standard Normal Variate:
and Standard Deviation
𝑥− 𝜇
Z = 𝜎 where
x = value of the random variable
𝜇 = mean
𝜎 = S.D.

UNIT - 5 INFERENTIAL STATISTICS
5.1 Population and  Define Population and Sample  Population data from census,
Sample  Differentiate between population economic surveys and other
and sample contexts from practical life
 Define a representative sample  Examples of drawing more
from a population than one sample set from the
 Differentiate between a same population
representative and non-  Examples of representative
representative sample and non-representative
 Draw a representative sample sample
using simple random sampling  Unbiased and biased sampling
 Draw a representative sample  Problems based on random
using and systematic random sampling using simple random
sampling sampling and systematic
random sampling (sample size
less than 100)

5.2 Parameter and  Define Parameter with reference  Conceptual understanding of
Statistics and to Population Parameter and Statistics
Statistical  Define Statistics with reference  Examples of Parameter and
Interferences to Sample Statistic limited to Mean and
 Explain the relation between Standard deviation only
Parameter and Statistic  Examples to highlight
 Explain the limitation of Statistic limitations of generalizing
to generalize the estimation for results from sample to
population population
 Interpret the concept of  Only conceptual
Statistical Significance and understanding of Statistical
Statistical Inferences Significance/Statistical
 State Central Limit Theorem Inferences
 Explain the relation between  Only conceptual
Population-Sampling understanding of Sampling
Distribution-Sample Distribution through simulation
and graphs

5.3 t-Test (one ● Define a hypothesis ● Examples and non-examples
sample t-test ● Differentiate between Null and of Null and Alternate
and two Alternate hypothesis hypothesis (only non-
independent ● Define and calculate degree of directional alternate
groups t-test) freedom hypothesis)
● Test Null hypothesis and make ● Framing of Null and Alternate
inferences using t-test statistic hypothesis
for one group / two independent ● Testing a Null Hypothesis to
groups make Statistical Inferences for
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 ● Identify time series as ● Meaning and Definition
chronological data

6.5 Components of ● Distinguish between different ● Secular trend
Time Series components of time series ● Seasonal variation
● Cyclical variation
● Irregular variation
6.6 Time Series ● Solve practical problems based ● Fitting a straight line trend and
analysis for on statistical data and Interpret estimating the value
univariate data the result
6.7 Secular Trend ● Understand the long term ● The tendency of the variable to
tendency increase or decrease over a
long period of time
6.8 Methods of ● Demonstrate the techniques of ● Moving Average method
Measuring finding trend by different ● Method of Least Squares
trend methods
UNIT - 7 FINANCIAL MATHEMATICS
7.1 Perpetuity,  Explain the concept of  Meaning of Perpetuity and
Sinking Funds perpetuity and sinking fund Sinking Fund
 Calculate perpetuity  Real life examples of sinking
 Differentiate between sinking fund
fund and saving account  Advantages of Sinking Fund
 Sinking Fund vs. Savings
account
7.3 Calculation of  Explain the concept of EMI  Methods to calculate EMI:
EMI  Calculate EMI using various i) Flat-Rate Method
methods ii) Reducing-Balance Method
 Real life examples to calculate
EMI of various types of loans,
purchase of assets, etc.
7.4 Calculation of  Explain the concept of rate of  Formula for calculation of
Returns, return and nominal rate of Rate of Return, Nominal Rate
Nominal Rate return of Return
of Return  Calculate rate of return and
nominal rate of return
7.5 Compound  Understand the concept of  Meaning and use of
Annual Growth Compound Annual Growth Rate Compound Annual Growth
Rate  Differentiate between Rate
Compound Annual Growth Rate  Formula for Compound Annual
and Annual Growth Rate Growth Rate
 Calculate Compound Annual
Growth Rate
7.7 Linear method  Define the concept of linear  Meaning and formula for
of Depreciation method of Depreciation Linear Method of Depreciation
 Interpret cost, residual value  Advantages and
and useful life of an asset from disadvantages of Linear
the given information Method
 Calculate depreciation
UNIT - 8 LINEAR PROGRAMMING
8.1 Introduction ● Familiarize with terms related to ● Need for framing linear
and related Linear Programming Problem programming problem
terminology ● Definition of Decision Variable,
Constraints, Objective
function, Optimization and Non
Negative conditions

8.2 Mathematical ● Formulate Linear Programming ● Set the problem in terms of
formulation of Problem decision variables, identify the
Linear objective function, identify the
Programming set of problem constraints,
Problem express the problem in terms
of inequations
8.3 Different types ● Identify and formulate different ● Formulate various types of
of Linear types of LPP LPP’s like Manufacturing
Programming Problem, Diet Problem,
Problems Transportation Problem, etc.
8.4 Graphical ● Draw the Graph for a system of ● Corner Point Method for the
method of linear inequalities involving two Optimal solution of LPP
solution for variables and to find its solution ● Iso-cost/ Iso-profit Method
problems in graphically
two variables
8.5 Feasible and ● Identify feasible, infeasible, ● Definition and Examples to
Infeasible bounded and unbounded explain the terms
Regions regions
8.6 Feasible and ● Understand feasible and ● Problems based on
infeasible infeasible solutions optimization
solutions, ● Find optimal feasible solution ● Examples of finding the
optimal solutions by graphical method
feasible
solution

Practical: Use of spreadsheet
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
i) Plot the graphs of functions on excel and study the graph to find out the point of
maxima/minima
ii) Probability and dice roll simulation
iii) Matrix multiplication and the inverse of a matrix
iv) Stock Market data sheet on excel
v) Collect the data on weather, price, inflation, and pollution analyze the data and make
meaningful inferences
vi) Collect data from newspapers on traffic, sports activities and market trends and use
excel to study future trends
List of Suggested projects (Class XI /XII)
i) Use of prime numbers in coding and decoding of messages
ii) Prime numbers and divisibility rules
iii) Logarithms for financial calculations such as interest, present value, future value,
profit/loss etc. with large values)
iv) The cardinality of a set and orders of infinity
v) Comparing sets of Natural numbers, rational numbers, real numbers and others
vi) Use of Venn diagram in solving practical problems

vii) Fibonacci sequence: Its' history and presence in nature
viii) Testing the validity of mathematical statements and framing truth tables
ix) Investigating Graphs of functions for their properties
x) Visit the census site of India
http://www.censusindia.gov.in/Census_Data_2001/Census_Data_Online/Languag
e/State ment3.htm Depict the information given there in a pictorial form
xi) Prepare a questionnaire to collect information about money spent by your friends
in a month on activities like travelling, movies, recharging of the mobiles, etc. and
draw interesting conclusions
xii) 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
xiii) Analysis of population migration data – positive and negative influence on
urbanization
xiv) Each day newspaper tells us about the maximum temperature, minimum
temperature, and 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
xv) Analysis of 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
xvi) Vehicle registration data – correlating with pollution and the number of accidents
xvii) Visit a village near Delhi and collect data of various crops over the 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
xviii) 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 the
amount of rainfall for the current year
xix) Weather prediction (prediction of monsoon from past data)
xx) Visit Kirana shops near your home and collect the data regarding the sales 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
xxi) Stock price movement
xxii) Risk assessments by insurance firms from data
xxiii) Predicting stock market crash
xxiv) Predicting the outcome of an election – exit polls
xxv) Predicting mortality of infants

Assessment Plan
1. Overall Assessment of the course is out of 100 marks.
2. The assessment plan consists of an External Exam and Internal Assessment.
3. External Exam will be of 03 hours duration Pen/ Paper Test consisting of 80 marks.
4. The weightage of the Internal Assessment is 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 a
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:

Sl. Area and Assessment Area Marks
No. Weightage allocated
1 Project work Project work and record 5
(10 marks) Year-end Presentation/ Viva of the Project 5
2 Practical work Performance of practical and record 5
(10 marks) Year-end test of any one practical 5
Total 20