CBSE Senior Secondary Syllabus 2027 Applied Mathematics

FOR CBSE SENIOR SECONDARY SYLLABUS EXAM PREPARATION

CBSE Senior
Secondary Syllabus
2027
Question Paper ·
Mathematics
EXAM YEAR TYPE SUBJECT

CBSE Senior Secondary Syllabus 2027 Question Paper Mathematics
DETAILS

Applied

Notes · Sample Papers · Previous Year Papers · Mock Tests

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Subject Code – 241 a
Classes XI-XII

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
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has been observed that the syllabus of Mathematics in senior secondary grades meant
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for science subjects may not be appropriate for the students who wish to pursue
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Commerce or Social Science-based subjects in university education. By keeping this in
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mind, one more elective course in the mathematics syllabus is developed for Senior
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Secondary classes with an aim to provide students relevant experience in Mathematics
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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
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mathematical arguments, framing examples, finding counterexamples. It encourages
students to engage in mathematical investigations and to build connections within

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mathematical topics and with other disciplines. The course prepares students to use

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algebraic methods as a means of representation and as a problem-solving tool. It also

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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:
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• To develop an understanding of essential mathematical and

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• To enable students to interpret real-life situations into structured numerical, algebraic
and graphical representations for analysis and decision making.
• To develop ability to organise, analyse and interpret data, and to draw meaningful
conclusions in practical contexts.
• To strengthen logical thinking and reasoning by engaging students in problem-solving
situations that require nuance understanding of qualification and relative change.
• To develop clarity in mathematical communication, including the ability to justify
solutions, examine assumptions and validate results.
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• To help students recognise connections between mathematics and other disciplines,
and to use these connections meaningfully.
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Grade XI (2026-27)

Number of Paper: 1
Time: 3 Hours
Max Marks: 80

No. Units Marks

I Numbers, Quantification and 10
Numerical Applications
II Algebra 18
III Calculus 12
IV Combinatorics and Probability 10
V Descriptive Statistics 10
VI Basics of Financial Mathematics 15
VII Coordinate Geometry 05
Total 80
Internal Assessment 20

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CLASS- XI

Sl. Unit and Details of content Learning Outcomes
No. Chapter

UNIT – 1 NUMBERS, QUANTIFICATION AND NUMERICAL APPLICATIONS

Numbers & Quantification

1.1 Binary ● Introduction to Binary Students will be able to
Numbers Number System ● Understand the relation between
● Conversion of decimal decimal and binary number
numbers to binary system system.
and vice-versa and its ● Able to convert from one system
applications. to another.
● Understand the application of
Binary number system in
programming, coding, machine
learning etc.
1.2 Indices, ● Indices and its properties Students will be able to
Logarithm and ● Common and Natural ● Apply rules of indices to simplify
Antilogarithm logarithm expressions and solve problems
● Laws of logarithms involving powers
● Logarithm and exponential as ● Define logarithms and
inverse operations antilogarithms as inverse
● Procedure of finding operations
logarithm and antilogarithms ● Distinguish between common
of given number logarithms and natural
● Applications of logarithms logarithms
● Apply logarithmic and
antilogarithmic techniques to
simplify complex calculations,
and solve practical problems
1.3 Introduction ● Introduction To Bhartiya Students will be able to
To Bhartiya System of Numeration ● Gain acquaintance with
System of traditional way of expressing
Numeration numbers

Numbers in day-to-day Life

1.4 Clocks ● Evaluate the angular value ofStudents will be able to
a minute • Calculate the angular
● Measure of angle formed displacement of hour and minute
between two hands of clock hands
at given time • Find the exact time when clock
● Calculation of the time for hands coincide, are opposite, or
which hands of clock meet form a specific angle
• Understand the practical utility of
calendar
1.5 Calendar ● Odd days in a month/ year/ Students will be able to
century ● Calculate odd days in any given
● Decode the day for the given month, year, or century
date ● Find the day of the week for any
given date

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c. o1.6 Time s e m
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● Comparison of the work done a
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● Solve time-work problems
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● Represent time-work relationship
by the individual / group graphically
w.r.t. time
1.7 Speed, ● The time taken/ distance Students will be able to
Distance and covered from the given data. ● Represent distance-time
Time relationship graphically

● Creation Students will be able to
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1.8 Seating of seating plan/

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arrangement draft as per given conditions ● Design and create seating plans
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(Linear/circular). in linear and circular

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● Locating the position of a arrangements
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given conditions and applying
logical reasoning
● Apply seating arrangement
concepts to real-life situations

UNIT – 2 ALGEBRA

om will be able to
Sets
2.1 Introduction ● Set as well-defined c. Students
to Sets – collection of objects.
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Sets and ● Representation of a set
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their in Roster form and Set • represent sets accurately using
representati builder form both roster form and set-builder
on ● Different types of sets
form
on the basis of number
• differentiate between the two
of elements in the set
● Differentiate between
methods of expressing the same
equal set and set.
equivalent set
2.2 Subsets, ● Subsets Students will be able to
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Intervals as ● Power set and its ● list all possible subsets of a given set,

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subsets elements calculate the total number of subsets
● Universal Set
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● justify why the empty set is a subset

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of every set through logical reasoning.
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● define power sets, construct the
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all its subsets
● Get an idea about the special sets i.e.,
intervals which have vide utility in the
study of analysis.
2.3
Venn • Concept of Venn Students will be able to
Diagrams and diagram to understand • Use set operations to solve problems
Operations on the relationship in various fields, such as probability,
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• Problems using Venn • Develop problem-solving skills using
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• Operations on sets • Perform operations on sets to solve
practical problems

Relations

2.4 Ordered pairs • Significance of specific Students will be able to
arrangement of • Understand the concept of ordered
Cartesian elements in a pair pairs
product of two • Cartesian product of two • Find the Cartesian product of two finite
sets sets sets
• Calculate the number of elements in a
Cartesian product
2.5 Relations • Expressing relation as a Students will be able to
subset of Cartesian • Identify and express relations as
product subsets of Cartesian products
• Domain and range of a • Determine the domain and range of
relation any relation
• Create and analyse custom relations
from everyday situations
Mathematical Logic

2.6 Mathematical ● Logical problems Students will be able to
Logic involving odd man out, ● Identify patterns and solve odd man
syllogism, blood relation out problems
and coding-decoding ● Draw valid conclusions using
syllogism
● Decode blood relations and solve
coding-decoding problems
● Apply logical reasoning skills to real-
life decision-making situations
Sequences and Series
2.7 Sequence and • Differentiate between Students will be able to
Series sequence and series • Distinguish between sequences and
series
2.8 Arithmetic • Arithmetic mean (AM) of Students will be able to
Progression two positive numbers • Calculate and apply arithmetic mean
(AM) of two positive numbers to find
average values in real-life situations
2.9 Geometric • Introduction of Students will be able to
Progression Geometric Progression • Identify and construct geometric
(GP) progressions
● 𝑛 ℎ term of a GP • Calculate geometric mean (GM) of two
● sum of n terms and sum positive numbers
of infinite terms of a GP • Analyse and prove the AM-GM
● Problems based on inequality relationship
applications of GP • Apply formulas of arithmetic and
● Geometric mean (GM) geometric progressions strategically
of two positive numbers to solve real-world problems
● Relation between AM
and GM and related
problems
● Application problems
based on AP and GP

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UNIT – 3 CALCULUS

Functions
3.1 Functions and • Dependent and Students will be able to
their graphs independent variables ● Define dependent and independent
● Definition of function variables
using dependent and ● Define and differentiate between
independent variable domain, co-domain, and range of
● Domain, range and co- functions
domain of a given ● Classify and define various types of
function functions
• Types of functions ● Determine domain, co-domain, and
● Graphical range of given functions
representation of ● Represent functions graphically on
function coordinate planes
● Apply function concepts to solve
real-life problems involving mapping
relationships like student enrolment
systems, profit-loss calculations,
and designing input-output models
for business.
Limits, Continuity and Derivatives
3.2 Limits and ● Limit of a function Students will be able to
continuity of ● Continuity of a function ● Define and understand the concept of
functions limit of a function by analysing the
behaviour of functions.
● Solve problems based on the algebra
of limits.
● Define continuity of a function at a
point and over an interval
3.3 Differentiation ● Instantaneous rate of Students will be able to
change ● Define the derivative of a function and
● Finding the derivative of relate it to the slope of the tangent to
the functions a curve.
3.4 Algebra of ● Differentiation of Students will be able to
derivatives addition, subtraction, • state and apply the fundamental rules
multiplication and of differentiation for sum, difference,
division of two or more product, and quotient of two or more
functions functions
● Differentiation of a ● understand the chain rule as the
function of a function method for differentiating composite
functions.
UNIT – 4 P E R M U T A T I O N S A N D C O M B I N A T I O N S & PROBABILITY

Combinatorics

4.1 Combinatorics ● Factorial of a number Students will be able to
● Fundamental Principle • Understand and calculate factorials of
of Counting numbers
● Concept of • Appreciate how to count without
Permutation counting
● Simple problems based • Define permutation and apply the
on permutations

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m .co ● Define combination
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• Define combination and differentiate it
from permutation
combination • Apply permutation and combination
● Problems based on formulas strategically
Combinations • Model complex counting situations
using permutation and combination
concepts
Probability

● Random Students will be able to
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4.2 Probability experiment
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● Event and its Types
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● Recognize and differentiate different s e m
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types of events and find their

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probabilities in real life
● Appreciate the use of probability in daily
life situations
situations ● Apply reasoning skills to solve problems
● Concept of conditional based on conditional probability
probability
UNIT- 5 DESCRIPTIVE STATISTICS

Measures of Dispersion and Percentiles

5.1 Measures of ● Meaning of dispersion in om will be able to
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Dispersion a data set ● Understand the meaning of dispersion in
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● Range, mean deviation,
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variance g
standard deviation
a deviation and
between range, mean
standard deviation
● Calculate range, range standard
deviation and variance, and standard
deviation for ungrouped and grouped
data set
● Choose appropriate measure of
dispersion to calculate spread of data
5.2 Percentiles ● Concept of Percentile Students will be able to
rank • Calculate, analyze and interpret
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Percentile rank of scores ungrouped data set.

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● Karl Pearson’s • Analyze relationships between
coefficient of Correlation variables by calculating and
for ungrouped data interpreting Karl Pearson's
● Spearman’s Rank coefficient of correlation and
Correlation for Spearman's rank correlation
ungrouped data coefficient for ungrouped data.
Regression
5.4 Regression
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● Concept of Regression Students will be able to
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● Dependent and regression analysis.
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Independent variables • Compute regression coefficients.
● Regression Coefficients • Solve real-world problems by
● Regression Equations selecting and applying appropriate
● Properties of Regression correlation or regression
Equations techniques.
UNIT – 6 FINANCIAL MATHEMATICS

Interests and Annuities

6.1 Interest and ● Concept Interest Students will be able to
of
Interest Rates Rates • Understand the concept of interest
● Comparison between rates
Nominal Interest Rate, • Differentiate between nominal interest
Effective Rate and rate, effective rate, and real interest
Real Interest Rate rate
● Practical applications of • Calculate and compare simple and
interest rate w.r.t simple compound interest
and compound interest • Apply interest rate concepts to solve
● Concept of effective real-life financial problems
rate of interest • Define with examples the concept of
effective rate of interest
• Analyze and evaluate financial
products and investment schemes
6.2 Annuities ● Meaning of Immediate Students will be able to
Annuity, Annuity due • Understand and differentiate between
and Deferred Annuity immediate annuity, annuity due, and
● Future and present deferred annuity
value of ordinary • Calculate the future and present value
annuity, annuity due (up of regular annuity and annuity due
to 3 period) • Apply annuity concepts to real-life
● Concept of Annuity in financial situations
real life situations
Tax and Utility Bills

6.3 Taxes and • Concept of Income tax Students will be able to
Utility Billsand GST w.r.t. tax new • Understand the concept of income tax
tax guidelines and GST
• Utility bills and its • Calculate income tax and GST
various types – liabilities using applicable tax brackets
Electricity, Water and • Analyse and calculate types of utility
PNG Bills bills – Electricity and Water Bills
• Apply taxation and utility billing
concepts to real-life situations.
UNIT – 7 COORDINATE GEOMETRY

Straight Lines
7.1 Straight lines ● Concept of slope of a Students will be able to
line ● Understand the gradient as the
● Various forms of measure of steepness and calculate it
equation of line using coordinates
● Derive and apply various algebraic
forms to represent lines in a Cartesian
plane.

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• Apply linear equations to model real-
world scenarios like demand and
supply curves in economics.
Circles and Parabola
7.2 Circles and ● Determination of the Students will be able to
Parabola equations of circle and ● Define circles and parabolas as sets
parabola as a locus of of points satisfying specific geometric
a point in a plane under conditions in a plane.
certain conditions ● Formulate and solve equations of
● Different form of circles in standard, central, diameter,
equations of a circle and general forms.
● Solve problems based ● Identify the properties of a parabola
on applications of and express its standard form
circle equation based on its focus and
directrix.
● Utilize the properties of circles to solve
practical and coordinate-based
mathematical problems.

Suggested Practicals using spreadsheet
1. Visualizing Functions and Their Properties: Plotting graphs of functions in GeoGebra
to observe how coefficients change the graph’s shape and to find out their domain and
range graphically.
2. Understanding Derivatives: Constructing a tangent line to a curve in GeoGebra and
observing its slope as the point moves and demonstrating the derivative as the
instantaneous rate of change.
3. Personal Budgeting: Designing a comprehensive monthly budget tracker in a
spreadsheet to manage income and expenditures using summation and percentage
formulas.
4. Comparative Cost-Benefit Analysis: Building a decision-making model to identify the
most economical purchase for a high-value product by comparing cost, shipping
charges, tax and other hidden costs.
5. Descriptive Measures of Data: Using spreadsheet functions (e.g., AVERAGE,
STDEV.P etc.) to compute the mean, median, mode, variance, and standard deviation
of a raw dataset.
6. Interest Growth Analysis: Developing a comparative sheet for Simple vs. Compound
Interest to track the growth of an investment over time.
7. Environmental & Economic Data Modelling: Analysing real-world datasets regarding
local weather, inflation or AQI by generating and interpreting scatter plots, histograms,
bar graphs etc. to identify correlations and seasonal trends.

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Number of Paper: 1

Time: 3 Hours
Max Marks: 80

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No.
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II Algebra 10

III Calculus 15

IV Probability Distributions 10

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V Inferential Statistics 05
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VI Time-based data
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VII
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Financial Mathematics
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15

VIII Linear Programming 08

Total 80

Internal Assessment 20

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CLASS- XII

Sl. Contents Learning Outcomes: Notes / Explanation
No. Students will be able to

UNIT – 1 NUMBERS, QUANTIFICATION AND NUMERICAL APPLICATIONS

Numbers & Quantification

1.1 Modulo Arithmetic • Define modulus of an integer • Definition and meaning
● Apply arithmetic operations • Introduction to modulo
using modular arithmetic operator
rules ● Modular addition and
subtraction

1.2 Congruence Modulo ● Define congruence modulo ● Definition and meaning
● Apply the definition in various ● Solution using congruence
problems modulo
● Equivalence class

1.3 Alligation and ● Understand the rule of ● Meaning and Application of
Mixture alligation to produce a rule of alligation
mixture at a given price ● Mean price of a mixture
● Determine the mean price of
a mixture
● Apply rule of allegation

1.4 Numerical Problems Solve real life problems mathematically

Boats and Streams ● Distinguish between ● Problems based on speed
(upstream and upstream and downstream of stream and the speed of
downstream) ● Express the problem in the boat in still water
form of an equation
Pipes and Cisterns ● Determine the time taken by ● Calculation of the portion of
two or more pipes to fill or the tank filled or drained by
empty the tank the pipe(s) in unit time

Races and Games ● Compare the performance of ● Calculation of the time
two players w.r.t. time, taken/ distance covered /
distance speed of each player

1.5 Numerical ● Describe the basic concepts ● Comparison between two
Inequalities of numerical inequalities statements/situations
● Understand and write which can be compared
numerical inequalities numerically
● Application of the
techniques of numerical
solution of algebraic
inequations

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UNIT-2 ALGEBRA

2.1 Matrices and types ● Define matrix ● The entries, rows and
of matrices ● Identify different kinds of columns of matrices
matrices. Find the size / ● Present a set of data in a
order of matrices matrix form
2.2 Equality of matrices, • Determine equality of two • Examples of transpose of
Transpose of a matrices matrix
matrix, Symmetric • Write transpose of given • A square matrix as a sum of
and Skew symmetric matrix symmetric and skew
matrix • Define symmetric and skew symmetric matrix
symmetric matrix • Observe that diagonal
elements of skew
symmetric matrices are
always zero

2.3 Algebra of Matrices ● Perform operations like ● Addition and Subtraction
addition & subtraction on of matrices
matrices of same order ● Multiplication of matrices
● Perform multiplication of two (It can be shown to the
matrices of appropriate order students that Matrix
● Perform multiplication of a multiplication is similar to
scalar with matrix multiplication of two
polynomials)
● Multiplication of a matrix
with a real number

2.4 Determinants ● Find determinant of a square ● Singular matrix, Non-
matrix singular matrix
● |AB|=|A||B|
● Simple problems to find
determinant value

2.5 Inverse of a matrix • Define the inverse of a • Inverse of a matrix using
square matrix cofactors
● Apply properties of inverse of • If A and B are invertible
matrices square matrices of same
size,
i) (AB)−1 = B −1 A−1
ii) (A−1 )−1 = A
iii) (A′)−1 = (A−1 )′

2.6 Solving system of • Solve the system of • Solution of system of
simultaneous simultaneous equations simultaneous equations
equations using using up to three variables only
matrix method and (non- homogeneous
Cramer’s rule i) Cramer’s Rule equations)
ii) Inverse of coefficient matrix

● Formulate real life problems
into a system of
simultaneous linear
equations and solve it using
these methods

For more Question Papers, Sample Papers, Notes & Syllabus visit Page 12 of 19

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UNIT- 3 CALCULUS
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Differentiation and its Applications

3.1 Derivatives up to • Determine derivatives up to • Simple problems based on
second order second order up to second order
• Understand differentiation of derivatives
parametric functions and • Differentiation of
implicit functions parametric functions and
implicit functions (upto 2nd
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3.2 Application
quantities such as area a
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Derivatives of various quantities
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3.3 Marginal Cost and • Define marginal cost and ● Examples related to
Marginal Revenue marginal revenue marginal cost, marginal
using derivatives ● Find marginal cost and revenue, etc.
marginal revenue
3.4 Increasing • Determine whether a function ● Simple problems related to
/Decreasing is increasing or decreasing increasing and decreasing
Functions • Determine the conditions for
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decreasing
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3.5 Maxima and Minima • Determine
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the function
• Find the point(s) of local
critical point of f if
f is defined at and
maxima and local minima ′( ) = 0 or f is not
and corresponding local differentiable
maximum and local minimum at
values • To find local maxima and
• Find the absolute maximum local minima by:
and absolute minimum value i) First Derivative Test
of a function
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ii) Second Derivative Test

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3.6 Integration • Understand and determine • Integration as a reverse
indefinite integrals of process of differentiation
simple functions as anti- • Vocabulary and Notations
derivative related to Integration

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3.7 Indefinite Integrals as • Evaluate indefinite integrals • Simple integrals based on
family of curves of simple algebraic functions each method (non-
by method of: trigonometric function)
i) substitution
ii) partial fraction
iii) by parts

3.8 Definite Integrals as ● Define definite integral as ● Evaluation of area under
area under the curve area under the curve simple algebraic curves up
● Understand fundamental to 2nd degree.
theorem of Integral calculus
and apply it to evaluate the
definite integral

3.9 Application of ● Identify the region Problems based on finding
Integration representing consumer ● Total cost when Marginal
surplus and producer surplus Cost is given
graphically ● Total Revenue when
● Apply the definite integral to Marginal Revenue is given
find consumer surplus- ● Equilibrium price and
producer surplus equilibrium quantity and
hence consumer and
producer surplus

Differential Equations and Modeling
3.10 Differential Equations ● Recognize a differential ● Definition,order, degree
equation and examples
● Find the order and degree of
a differential equation
3.11 Formulating and ● Formulate differential ● Formation of differential
Solving Differential equation equation by eliminating
Equations ● Verify the solution of arbitrary constants
differential equation ● Solution of simple
● Solve simple differential differential equations
equation using variable (direct integration only)
separable method only

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
Expectation frequency distribution to find discrete random variable as
the expected value of a summation of product of
random variable discrete random variable by
the probability of its
occurrence.
4.3 Variance ● Calculate the Variance and ● Questions based on
S.D. of a random variable variance and standard
deviation

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4.4 Binomial Distribution ● Identify the Bernoulli Trials ● Characteristics of binomial
and apply Binomial distribution
Distribution ● Binomial formula:
( )=𝑛 −
● Evaluate Mean, Variance
and S.D of a binomial Where 𝑛 = number of trials
distribution =probability of success
= probability of failure
Mean = 𝑛
Variance = 𝑛
Standard deviation =
√𝑛

4.5 Poison Distribution ● Understand the Conditions ● Characteristics of Poisson
of Poisson Distribution Probability distribution
● Evaluate the Mean and Poisson formula: ( ) =
−
Variance of Poisson
distribution !
● Mean = Variance =

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

UNIT - 5 INFERENTIAL STATISTICS

5.1 Population and • Define Population and • Population data from
Sample Sample census, economic surveys
• Differentiate between and other contexts from
population and sample practical life
• Define a representative • Examples of drawing more
sample from a population than one sample set from
• Differentiate between a the same population
representative and non- • Examples of representative
representative sample and non-representative
• Draw a representative sample
sample using simple random • Unbiased and biased
sampling sampling
● Draw a representative • Problems based on random
sample using and systematic sampling using simple
random sampling random sampling and
systematic random
sampling (sample size less
than 100)

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of Parameter and
Interferences reference to Sample to Mean and
• Explain the relation between Standard deviation only
Parameter and Statistic • Examples to highlight
• Explain the limitation of limitations of generalizing
Statistic to generalize the results from sample to
estimation for population population
• Interpret the concept of • Only conceptual
Statistical Significance and understanding of Statistical
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Statistical Inferences Significance/Statistical

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• State Central Limit Theorem Inferences

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graphs

5.3 t-Test (one sample ● Define a hypothesis ● Examples and non-
t-test and for a ● Differentiate between Null examples of Null and
small group sample) and Alternate hypothesis Alternate hypothesis (only
● Define and calculate degree non- directional alternate
of freedom hypothesis)
● Test Null hypothesis and ● Framing
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make inferences using t-test Alternate hypothesis
● Testing a Null Hypothesis to
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for small sample size
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UNIT – 6 TIME-BASED DATA

6.1 Time Series ● Identify time series as ● Meaning and Definition
chronological data

Components of Time ● Distinguish between different ● Secular trend
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univariate data
based on statistical data and
interpret the result
and estimating the value

6.4 Secular Trend ● Understand the long-term ● The tendency of the
tendency variable to increase or
decrease over a long period
of time
6.5 Methods of ● Demonstrate the techniques ● Moving Average method
Measuring trend
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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 fund
sinking fund and saving • Advantages of Sinking Fund
account ● Sinking Fund vs. Savings
account

7.2 Valuation of ● Define the concept of ● Meaning of Bond Valuation
Bonds valuation of bond and related ● Terms related to valuation of
terms. bond: Coupon rate, Maturity
● Calculate value of bond rate and Current price.
using present value ● Bond Valuation Method:
approach Present Value Approach

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 Compound • Understand the concept of • Meaning and use of
Annual Growth Compound Annual Growth Compound Annual Growth
Rate Rate Rate
• Differentiate between ● Formula for Compound
Compound Annual Growth Annual Growth Rate
Rate and Annual Growth
Rate
● Calculate Compound Annual
Growth Rate
7.5 Linear method • Define the concept of linear • Meaning and formula for
of Depreciation method of Depreciation Linear Method of
• Interpret cost, residual value Depreciation
and useful life of an asset ● Advantages and
from the given information disadvantages of Linear
● Calculate depreciation Method

UNIT - 8 LINEAR PROGRAMMING

8.1 Introduction and ● Familiarize with terms ● Need for framing linear
related related to Linear programming problem
terminology Programming Problem ● Definition of Decision
Variable, Constraints,
Objective function,
Optimization and Non
negative constraints

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8.2 Mathematical ● Formulate Linear ● Set the problem in terms of
formulation of Programming Problem upto 3 decision variables, identify
Linear non-trivial constraints the objective function,
Programming identify the set of problem
Problem constraints,
● express the problem in
terms of inequations

8.3 Different types of ● Identify and formulate ● Formulate various types of
Linear different types of LPP LPP’s like Manufacturing
Programming Problem, Diet Problem etc.
Problems
8.4 Graphical method of ● Draw the Graph for a system ● Corner Point Method for the
solution for problems of linear inequalities involving Optimal solution of LPP
in two variables and to find its
two variables solution graphically
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, optimal ● Find optimal feasible solution ● Examples of finding the
feasible solutions by graphical
solution method

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

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m .co Investigating Graphs of functions for their properties
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ix)
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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
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xiii) Analysis of population migration data – positive and negative influence on
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urbanization
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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 ag
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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
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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
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