Syllabus: Applied Mathematics for Class 12

 Page 1


 
Applied Mathematics  
Subject Code – 241 
Classes XI-XII (2025 – 26) 
 
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. 
 
 
Page 2


 
Applied Mathematics  
Subject Code – 241 
Classes XI-XII (2025 – 26) 
 
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 (2025-26) 
 
Number of Paper: 1 
Time: 3 Hours 
Max Marks: 80 
 
 
 
No. Units Marks 
I Numbers, Quantification and 
Numerical Applications 
09 
II Algebra 15 
III Mathematical Reasoning 06 
IV Calculus 10 
V Probability 08 
VI Descriptive Statistics 12 
VII Basics of Financial Mathematics 15 
VIII Coordinate Geometry 05 
Total 80 
Internal Assessment       20 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
Page 3


 
Applied Mathematics  
Subject Code – 241 
Classes XI-XII (2025 – 26) 
 
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 (2025-26) 
 
Number of Paper: 1 
Time: 3 Hours 
Max Marks: 80 
 
 
 
No. Units Marks 
I Numbers, Quantification and 
Numerical Applications 
09 
II Algebra 15 
III Mathematical Reasoning 06 
IV Calculus 10 
V Probability 08 
VI Descriptive Statistics 12 
VII Basics of Financial Mathematics 15 
VIII Coordinate Geometry 05 
Total 80 
Internal Assessment       20 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
CLASS- XI 
 
Sl. 
No. 
Contents Learning Outcomes: 
Students will be able to 
 
Notes / Explanation 
 
UNIT – 1 NUMBERS, QUANTIFICATION AND NUMERICAL APPLICATIONS 
 
Numbers & Quantification 
 
1.1 Binary 
Numbers 
? Express decimal numbers 
in binary system 
? Express binary numbers 
in decimal system 
 
? Definition of number system 
(decimal and binary) 
? Conversion from decimal to 
binary system and vice - versa 
1.2 Indices, 
Logarithm and 
Antilogarithm 
? Relate indices and 
logarithm /antilogarithm 
? Find logarithm and 
antilogarithms of given 
Number 
 
? Applications of rules of indices 
? Introduction of logarithm and 
antilogarithm 
? Common and Natural logarithm 
1.3 Laws and 
properties 
of 
logarithms 
? Enlist the laws and 
properties of logarithms 
? Apply laws of logarithm 
? Fundamental laws of logarithm 
1.4 Simple 
applications 
of logarithm 
and 
Antilogarithm 
 
? Use logarithm in different 
applications 
? Express the problem in the form 
of an equation and apply 
logarithm/ antilogarithm 
Numerical Applications 
 
1.5 Clock ? Evaluate the angular 
value of a minute 
? Calculate the angle 
formed between two 
hands of clock at given 
time 
? Calculate the time for 
which hands of clock 
Meet 
 
? Number of rotations of minute 
hand / hour hand of a clock in a 
day 
? Number of times minute hand 
and hour hand coincides in a 
day 
1.6 Calendar ? Determine Odd days in a 
month/ year/ century 
? Decode the day for the 
given date 
 
? Definition of odd days 
? Odd days in a year/ century. 
? Day corresponding to a given 
date 
1.7 Time, Work 
and Distance 
? Establish the relationship 
between work and time 
? Compare the work done 
by the individual / group 
w.r.t. time 
? Calculate the time taken/ 
distance covered/ Work 
done from the given data 
? Basic concept of time and work 
? Problems on time taken / 
distance covered / work done 
Page 4


 
Applied Mathematics  
Subject Code – 241 
Classes XI-XII (2025 – 26) 
 
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 (2025-26) 
 
Number of Paper: 1 
Time: 3 Hours 
Max Marks: 80 
 
 
 
No. Units Marks 
I Numbers, Quantification and 
Numerical Applications 
09 
II Algebra 15 
III Mathematical Reasoning 06 
IV Calculus 10 
V Probability 08 
VI Descriptive Statistics 12 
VII Basics of Financial Mathematics 15 
VIII Coordinate Geometry 05 
Total 80 
Internal Assessment       20 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
CLASS- XI 
 
Sl. 
No. 
Contents Learning Outcomes: 
Students will be able to 
 
Notes / Explanation 
 
UNIT – 1 NUMBERS, QUANTIFICATION AND NUMERICAL APPLICATIONS 
 
Numbers & Quantification 
 
1.1 Binary 
Numbers 
? Express decimal numbers 
in binary system 
? Express binary numbers 
in decimal system 
 
? Definition of number system 
(decimal and binary) 
? Conversion from decimal to 
binary system and vice - versa 
1.2 Indices, 
Logarithm and 
Antilogarithm 
? Relate indices and 
logarithm /antilogarithm 
? Find logarithm and 
antilogarithms of given 
Number 
 
? Applications of rules of indices 
? Introduction of logarithm and 
antilogarithm 
? Common and Natural logarithm 
1.3 Laws and 
properties 
of 
logarithms 
? Enlist the laws and 
properties of logarithms 
? Apply laws of logarithm 
? Fundamental laws of logarithm 
1.4 Simple 
applications 
of logarithm 
and 
Antilogarithm 
 
? Use logarithm in different 
applications 
? Express the problem in the form 
of an equation and apply 
logarithm/ antilogarithm 
Numerical Applications 
 
1.5 Clock ? Evaluate the angular 
value of a minute 
? Calculate the angle 
formed between two 
hands of clock at given 
time 
? Calculate the time for 
which hands of clock 
Meet 
 
? Number of rotations of minute 
hand / hour hand of a clock in a 
day 
? Number of times minute hand 
and hour hand coincides in a 
day 
1.6 Calendar ? Determine Odd days in a 
month/ year/ century 
? Decode the day for the 
given date 
 
? Definition of odd days 
? Odd days in a year/ century. 
? Day corresponding to a given 
date 
1.7 Time, Work 
and Distance 
? Establish the relationship 
between work and time 
? Compare the work done 
by the individual / group 
w.r.t. time 
? Calculate the time taken/ 
distance covered/ Work 
done from the given data 
? Basic concept of time and work 
? Problems on time taken / 
distance covered / work done 
1.8 Seating 
arrangement 
? Create suitable seating 
plan/ draft as per given 
conditions (Linear/circular) 
? Locate the position of a 
person in a seating 
arrangement 
? Linear and circular seating 
arrangement 
? Position of a person in a seating 
arrangement 
 
UNIT – 2 ALGEBRA 
 
 
Sets 
 
2.1 Introduction 
to sets – 
definition 
? Define set as well-
defined collection of 
objects 
? Definition of a Set 
? Examples and Non-examples of 
Set 
 
2.2 Representation 
of sets 
? Represent a set in 
Roster form and Set 
builder form 
? Write elements of a set in Set 
Builder form and Roster Form 
? Convert a set given in Roster 
form into Set builder form and 
vice-versa 
 
2.3 Types of sets 
and their 
notations 
? Identify different types 
of sets on the basis of 
number of elements in 
the set 
? Differentiate between 
equal set and 
equivalence set 
 
? Types of Sets: Finite Set, Infinite 
Set, Empty Set, Singleton Set 
2.4 Subsets ? Enlist all subsets of a 
set 
? Find number of subsets 
of a given set 
? Find number of 
elements of a power 
set 
 
? Subset of a given set 
? Familiarity with terms like 
Superset, Improper subset, 
Universal set, Power set 
2.5 Intervals ? Express subset of real 
numbers as intervals 
? Open interval, closed interval, 
semi open interval and semi 
closed interval 
 
2.6 Venn diagrams ? Apply the concept of 
Venn diagram to 
understand the 
relationship between 
sets 
? Solve problems using 
Venn diagram 
 
? Venn diagrams as the pictorial 
representation of relationship 
between sets 
? Practical Problems based on 
Venn Diagrams 
Page 5


 
Applied Mathematics  
Subject Code – 241 
Classes XI-XII (2025 – 26) 
 
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 (2025-26) 
 
Number of Paper: 1 
Time: 3 Hours 
Max Marks: 80 
 
 
 
No. Units Marks 
I Numbers, Quantification and 
Numerical Applications 
09 
II Algebra 15 
III Mathematical Reasoning 06 
IV Calculus 10 
V Probability 08 
VI Descriptive Statistics 12 
VII Basics of Financial Mathematics 15 
VIII Coordinate Geometry 05 
Total 80 
Internal Assessment       20 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
CLASS- XI 
 
Sl. 
No. 
Contents Learning Outcomes: 
Students will be able to 
 
Notes / Explanation 
 
UNIT – 1 NUMBERS, QUANTIFICATION AND NUMERICAL APPLICATIONS 
 
Numbers & Quantification 
 
1.1 Binary 
Numbers 
? Express decimal numbers 
in binary system 
? Express binary numbers 
in decimal system 
 
? Definition of number system 
(decimal and binary) 
? Conversion from decimal to 
binary system and vice - versa 
1.2 Indices, 
Logarithm and 
Antilogarithm 
? Relate indices and 
logarithm /antilogarithm 
? Find logarithm and 
antilogarithms of given 
Number 
 
? Applications of rules of indices 
? Introduction of logarithm and 
antilogarithm 
? Common and Natural logarithm 
1.3 Laws and 
properties 
of 
logarithms 
? Enlist the laws and 
properties of logarithms 
? Apply laws of logarithm 
? Fundamental laws of logarithm 
1.4 Simple 
applications 
of logarithm 
and 
Antilogarithm 
 
? Use logarithm in different 
applications 
? Express the problem in the form 
of an equation and apply 
logarithm/ antilogarithm 
Numerical Applications 
 
1.5 Clock ? Evaluate the angular 
value of a minute 
? Calculate the angle 
formed between two 
hands of clock at given 
time 
? Calculate the time for 
which hands of clock 
Meet 
 
? Number of rotations of minute 
hand / hour hand of a clock in a 
day 
? Number of times minute hand 
and hour hand coincides in a 
day 
1.6 Calendar ? Determine Odd days in a 
month/ year/ century 
? Decode the day for the 
given date 
 
? Definition of odd days 
? Odd days in a year/ century. 
? Day corresponding to a given 
date 
1.7 Time, Work 
and Distance 
? Establish the relationship 
between work and time 
? Compare the work done 
by the individual / group 
w.r.t. time 
? Calculate the time taken/ 
distance covered/ Work 
done from the given data 
? Basic concept of time and work 
? Problems on time taken / 
distance covered / work done 
1.8 Seating 
arrangement 
? Create suitable seating 
plan/ draft as per given 
conditions (Linear/circular) 
? Locate the position of a 
person in a seating 
arrangement 
? Linear and circular seating 
arrangement 
? Position of a person in a seating 
arrangement 
 
UNIT – 2 ALGEBRA 
 
 
Sets 
 
2.1 Introduction 
to sets – 
definition 
? Define set as well-
defined collection of 
objects 
? Definition of a Set 
? Examples and Non-examples of 
Set 
 
2.2 Representation 
of sets 
? Represent a set in 
Roster form and Set 
builder form 
? Write elements of a set in Set 
Builder form and Roster Form 
? Convert a set given in Roster 
form into Set builder form and 
vice-versa 
 
2.3 Types of sets 
and their 
notations 
? Identify different types 
of sets on the basis of 
number of elements in 
the set 
? Differentiate between 
equal set and 
equivalence set 
 
? Types of Sets: Finite Set, Infinite 
Set, Empty Set, Singleton Set 
2.4 Subsets ? Enlist all subsets of a 
set 
? Find number of subsets 
of a given set 
? Find number of 
elements of a power 
set 
 
? Subset of a given set 
? Familiarity with terms like 
Superset, Improper subset, 
Universal set, Power set 
2.5 Intervals ? Express subset of real 
numbers as intervals 
? Open interval, closed interval, 
semi open interval and semi 
closed interval 
 
2.6 Venn diagrams ? Apply the concept of 
Venn diagram to 
understand the 
relationship between 
sets 
? Solve problems using 
Venn diagram 
 
? Venn diagrams as the pictorial 
representation of relationship 
between sets 
? Practical Problems based on 
Venn Diagrams 
2.7 Operations on 
sets 
? Perform operations on 
sets to solve practical 
problems 
? Operations on sets include 
i) Union of sets 
ii) Intersection of sets 
iii) Difference of sets 
iv) Complement of a set 
v) De Morgan’s Laws 
 
Relations 
 
2.8 Ordered pairs 
 
Cartesian 
product of two 
sets 
? Explain the significance 
of specific arrangement 
of elements in a pair 
? Write Cartesian product 
of two sets 
? Find the number of 
elements in a Cartesian 
product of two sets  
 
? Ordered pair, order of elements in 
an ordered pair and equality of 
ordered pairs 
? Cartesian product of two non- 
empty sets 
2.9 Relations ? Express relation as a 
subset of Cartesian 
product 
? Find domain and range 
of a relation 
 
? Definition of Relation, examples 
pertaining to relations in the real 
number system 
Sequences and Series 
 
2.10 Sequence and 
Series 
? Differentiate between 
sequence and series 
? Sequence: ?? 1
, ?? 2
, ?? 3
, … , ?? ?? 
? Series: ?? 1
+ ?? 2
+ ?? 3
+ … + ?? ?? 
2.11 Arithmetic 
Progression 
? Identify Arithmetic 
Progression (AP) 
? Establish the formulae 
of finding ?? ?? h 
term and 
sum of n terms 
? Solve application 
problems based on AP 
? Find arithmetic mean 
(AM) of two positive 
numbers 
 
? General term of A P: 
?? ?? = ?? + (?? - 1)?? 
? Sum of ?? terms of A P: 
?? ?? =
?? 2
[2?? + (?? - 1)?? ] 
? AM of ?? and ?? =
?? +?? 2
  
2.12 Geometric 
Progression 
 
 
 
 
 
 
 
 
 
 
 
 
? Identify Geometric 
Progression (GP) 
? Derive the ?? ?? h 
term and 
sum of n terms of a 
given GP 
? Solve problems based 
on applications of GP 
? Find geometric mean 
(GM) of two positive 
numbers 
? Solve problems based 
on relation between AM 
and GM 
? General term of GP: 
?? ?? = ?? ?? ?? -1
 
 
? Sum of ?? terms of A P: 
?? ?? =
?? (?? ?? - 1)
?? - 1
 
 
? Sum of infinite terms of GP =
 
?? 1-?? , where -1 < ?? < 1 
 
? Geometric mean of ?? and ?? =
v???? 
 
? For two positive numbers a and b, 
AM =GM i.e., 
?? +?? 2
= v????