COMPUTER SCIENCE

Subject Code – 083

Class XII (2025-26)

1. Prerequisites
Computer Science- Class XI

2. Learning Outcomes

Student should be able to

a) apply the concept of function.
b) explain and use the concept of file handling.
c) use basic data structure: Stacks
d) explain basics of computer networks.
e) use Database concepts, SQL along with connectivity between Python and SQL.

3. Distribution of Marks:

Unit No. Unit Name Marks

Computational Thinking and

1 40
Programming – 2

2 Computer Networks 10

3 Database Management 20

Total 70

4. Unit wise Syllabus

Unit 1: Computational Thinking and Programming – 2
● Revision of Python topics covered in Class XI.
● Functions: types of function (built-in functions, functions defined in module, user
defined functions), creating user defined function, arguments and parameters,
default parameters, positional parameters, function returning value(s), flow of
execution, scope of a variable (global scope, local scope)
● Exception Handling: Introduction, handling exceptions using try-except-finally
blocks
● Introduction to files, types of files (Text file, Binary file, CSV file), relative
and absolute paths
 ● Text file: opening a text file, text file open modes (r, r+, w, w+, a, a+), closing a text
file, opening a file using with clause, writing/appending data to a text file using
write() and writelines(), reading from a text file using read(), readline() and
readlines(), seek and tell methods, manipulation of data in a text file
● Binary file: basic operations on a binary file: open using file open modes (rb, rb+,
wb, wb+, ab, ab+), close a binary file, import pickle module, dump() and load()
method, read, write/create, search, append and update operations in a binary file
● CSV file: import csv module, open / close csv file, write into a csv file using
writer(),writerow(),writerows() and read from a csv file using reader()
● Data Structure: Stack, operations on stack (push & pop), implementation of stack
using list.

Unit 2: Computer Networks

● Evolution of networking: introduction to computer networks, evolution of networking

(ARPANET, NSFNET, INTERNET)
● Data communication terminologies: concept of communication, components of
data communication (sender,receiver, message, communication media,
protocols), measuring capacity of communication media (bandwidth, data
transfer rate), IP address, switching techniques (Circuit switching, Packet
switching)
● Transmission media: Wired communication media (Twisted pair cable, Co-axial
cable, Fiber-optic cable), Wireless media (Radio waves, Micro waves, Infrared
waves)
● Network devices (Modem, Ethernet card, RJ45, Repeater, Hub, Switch, Router,
Gateway, WIFI card)
● Network topologies and Network types: types of networks (PAN, LAN, MAN,
WAN), networking topologies (Bus, Star, Tree)
● Network protocol: HTTP, FTP, PPP, SMTP, TCP/IP, POP3, HTTPS, TELNET,
VoIP
● Introduction to web services: WWW, Hyper Text Markup Language (HTML),
Extensible Markup Language (XML), domain names, URL, website, web
browser, web servers, web hosting
Unit 3: Database Management
● Database concepts: introduction to database concepts and its need
● Relational data model: relation, attribute, tuple, domain, degree, cardinality, keys
(candidate key, primary key, alternate key, foreign key)
● Structured Query Language: introduction, Data Definition Language and Data
Manipulation Language, data type (char(n), varchar(n), int, float, date), constraints
(not null, unique, primary key), create database, use database, show databases,
drop database, show tables, create table, describe table, alter table (add and
remove an attribute, add and remove primary key), drop table, insert, delete, select,
operators (mathematical, relational and logical), aliasing, distinct clause, where
clause, in, between, order by, meaning of null, is null, is not null, like, update
command, delete command, aggregate functions (max, min, avg, sum, count),
group by, having clause, joins: cartesian product on two tables, equi-join and
natural join
● Interface of python with an SQL database: connecting SQL with Python, performing
 insert, update, delete queries using cursor, display data by using connect(),
cursor(), execute(), commit(), fetchone(), fetchall(), rowcount, creating database
connectivity applications, use of %s format specifier or format() to perform queries

5. Practical

Marks
S.No Unit Name
(Total=30)

Lab Test:
1 1. Python program (60% logic + 20% 8
documentation + 20% code quality)

2. SQL queries (4 queries based on one

4
or two tables)

Report file:
 Minimum 15 Python programs.
 SQL Queries – Minimum 5 sets using
2 7
one table / two tables.
 Minimum 4 programs based on
Python – SQL connectivity

Project (using concepts learnt in Classes 11

3 8
and 12)

4 Viva voce 3

6. Suggested Practical List:

Python Programming

● Read a text file line by line and display each word separated by a #.
● Read a text file and display the number of vowels/consonants/uppercase/lowercase
characters in the file.
● Remove all the lines that contain the character 'a' in a file and write it to another
file.
● Create a binary file with name and roll number. Search for a given roll number and
display the name, if not found display appropriate message.
● Create a binary file with roll number, name and marks. Input a roll number and
update the marks.
● Write a random number generator that generates random numbers between 1 and
6 (simulates a dice).
● Write a Python program to implement a stack using list.
● Create a CSV file by entering user-id and password, read and search the password
for given userid.
Database Management

● Create a student table and insert data. Implement the following SQL commands on
the student table:
o ALTER table to add new attributes / modify data type / drop attribute
o UPDATE table to modify data
o ORDER By to display data in ascending / descending order
o DELETE to remove tuple(s)
o GROUP BY and find the min, max, sum, count and average
● Similar exercise may be framed for other cases.
● Integrate SQL with Python by importing suitable module.

7. Suggested Reading Material

● NCERT Textbook for COMPUTER SCIENCE (Class XII)

● Support Materials on the CBSE website.

8. Project

The aim of the class project is to create something that is tangible and useful using
Python file handling/ Python-SQL connectivity. This should be done in groups of two to
three students and should be started by students at least 6 months before the
submission deadline. The aim here is to find a real world problem that is worthwhile to
solve.
Students are encouraged to visit local businesses and ask them about the problems that
they are facing. For example, if a business is finding it hard to create invoices for filing
GST claims, then students can do a project that takes the raw data (list of transactions),
groups the transactions by category, accounts for the GST tax rates, and creates
invoices in the appropriate format. Students can be extremely creative here. They can
use a wide variety of Python libraries to create user friendly applications such as games,
software for their school, software for their disabled fellow students, and mobile
applications, of course to do some of these projects, some additional learning is required;
this should be encouraged. Students should know how to teach themselves.
The students should be sensitized to avoid plagiarism and violations of copyright issues
while working on projects. Teachers should take necessary measures for this.
 ENGLISH CORE
CLASS – XII (2025-26)

Section A
Reading Skills-22 Marks

I. Reading Comprehension through Unseen Passage 12+10 = 22 Marks

1. One unseen passage to assess comprehension, interpretation, analysis and inference.

Vocabulary assessment will also be assessed via inference. The passage may be factual,
descriptive or literary.
2. One unseen case-based factual passage with verbal/visual inputs like statistical data, charts
etc. to assess comprehension, interpretation, analysis, inference and evaluation.

Note: The combined word limit for both the passages will be 700-750 words.

Multiple Choice Questions / Objective Type Questions and Short Answer Type Questions (to
be answered in 40-50 words) will be asked.

Section B
Creative Writing Skills-18 Marks
3. Notice, up to 50 words. One out of the two given questions to be answered.
(4 Marks: Format :1 / Content: 2 / Accuracy of Spelling and Grammar: 1).

4. Formal/Informal Invitation and Reply, up to 50 words. One out of the two given questions to
be answered. (4 Marks: Format: 1 / Content: 2 / Accuracy of Spelling and Grammar :1).

5. Letters based on verbal/visual input, to be answered in approximately 120-150 words. Letter

types include application for a job with bio data or resume. Letters to the editor (giving
suggestions or opinion on issues of public interest). One out of the two given questions to be
answered. (5 Marks: Format: 1/Organisation of Ideas:1/Content:2/ Accuracy of Spelling and
Grammar :1).

6. Article/ Report Writing, descriptive and analytical in nature, based on verbal inputs, to be
answered in 120-150 words. One out of the two given questions to be answered.
(5 Marks:Format:1/Organisation of Ideas:1/Content:2/Accuracy of Spelling and Grammar:1).

10
 Section C

Literature Text Book and Supplementary Reading Text- 40 Marks

This section will have variety of assessment items including Multiple Choice Questions,
Objective Type Questions, Short Answer Type Questions and Long Answer Type Questions to
assess comprehension, interpretation, analysis, evaluation and extrapolation beyond the text.
7. One Poetry extract out of two, from the book Flamingo, to assess comprehension,
interpretation, analysis, inference and appreciation. (6x1=6 Marks)

8. One Prose extract out of two, from the book Vistas, to assess comprehension,
interpretation, analysis, evaluation and appreciation. (4x1=4 Marks)

9. One prose extract out of two from the book Flamingo, to assess comprehension,
interpretation, analysis, inference and evaluation. (6x1=6Marks)

10. Short answer type questions (from Prose and Poetry from the book Flamingo), to be
answered in 40-50 words each. Questions should elicit inferential responses through critical
thinking. Five questions out of the six given, are to be answered. (5x2=10 Marks)

11. Short answer type questions, from Prose (Vistas), to be answered in 40- 50 words each.
Questions should elicit inferential responses through critical thinking. Any two out of three
questions to be done. (2x2=4 Marks)

12. One Long answer type question, from Prose/Poetry (Flamingo), to be answered in 120-
150 words. Questions can be based on incident / theme / passage / extract / event as
reference points to assess extrapolation beyond and across the text. The question will elicit
analytical and evaluative response from the student. Any one out of two questions to be
done. (1x5=5 Marks)

13. One Long answer type question, based on the chapters from the book Vistas, to be
answered in 120-150 words, to assess global comprehension and extrapolation beyond the
text. Questions to provide analytical and evaluative responses using incidents, events,
themes, as reference points. Any one out of two questions to be done. (1x5=5 Marks)

11
 Prescribed Books

1. Flamingo: English Reader published by National Council of Education Research and

Training, New Delhi
Prose
 The Last Lesson
 Lost Spring
 Deep Water
 The Rattrap
 Indigo
 Poets and Pancakes
 The Interview
 Going Places

Poetry
 My Mother at Sixty-Six
 Keeping Quiet
 A Thing of Beauty
 A Roadside Stand
 Aunt Jennifer’s Tigers

2. Vistas: Supplementary Reader published by National Council of Education Research and

Training, New Delhi
 The Third Level
 The Tiger King
 Journey to the End of the Earth
 The Enemy
 On the Face of It
 Memories of Childhood
- The Cutting of My Long Hair
- We Too are Human Beings

INTERNAL ASSESSMENT

Assessment of Listening Skills 05 marks.

Assessment of Speaking Skills 05 Marks
Project Work 10 Marks

12
 CLASSXII
CLASS XII(2023-24)
(2025-26)
PHYSICS (THEORY)

Time: 3 hrs. Max Marks: 70

UNIT CHAPTERS MARKS

Unit–I Electrostatics
Chapter–1: Electric Charges and Fields

Chapter–2: Electrostatic Potential and Capacitance 16

Unit-II Current Electricity

Chapter–3: Current Electricity

Unit-III Magnetic Effects of Current and Magnetism

Chapter–4: Moving Charges and Magnetism

Chapter–5: Magnetism and Matter 17

Unit-IV Electromagnetic Induction and Alternating Currents

Chapter–6: Electromagnetic Induction

Chapter–7: Alternating Current

Unit–V Electromagnetic Waves

Chapter–8: Electromagnetic Waves

Unit–VI Optics 18
Chapter–9: Ray Optics and Optical Instruments

Chapter–10: Wave Optics

Unit–VII Dual Nature of Radiation and Matter

Chapter–11: Dual Nature of Radiation and Matter

Unit–VIII Atoms and Nuclei 12

Chapter–12: Atoms

Chapter–13: Nuclei

Unit–IX Electronic Devices

Chapter–14: Semiconductor Electronics: Materials, Devices 7

and Simple Circuits

Total 70
Unit I: Electrostatics

Chapter–1: Electric Charges and Fields

Electric charges, Conservation of charge, Coulomb's law-force between two- point charges,
forces between multiple charges; superposition principle and continuous charge distribution.

Electric field, electric field due to a point charge, electric field lines, electric dipole, electric
field due to a dipole, torque on a dipole in uniform electric field.

Electric flux, statement of Gauss's theorem and its applications to find field due to infinitely
long straight wire, uniformly charged infinite plane sheet and uniformly charged thin spherical
shell (field inside and outside).

Chapter–2: Electrostatic Potential and Capacitance

Electric potential, potential difference, electric potential due to a point charge, a dipole and
system of charges; equipotential surfaces, electrical potential energy of a system of two-point
charges and of electric dipole in an electrostatic field.

Conductors and insulators, free charges and bound charges inside a conductor. Dielectrics
and electric polarization, capacitors and capacitance, combination of capacitors in series and
in parallel, capacitance of a parallel plate capacitor with and without dielectric medium
between the plates, energy stored in a capacitor (no derivation, formulae only).

Unit II: Current Electricity

Chapter–3: Current Electricity

Electric current, flow of electric charges in a metallic conductor, drift velocity, mobility and
their relation with electric current; Ohm's law, V-I characteristics (linear and non-linear),
electrical energy and power, electrical resistivity and conductivity, temperature dependence
of resistance, Internal resistance of a cell, potential difference and emf of a cell, combination
of cells in series and in parallel, Kirchhoff's rules, Wheatstone bridge.

Unit III: Magnetic Effects of Current and Magnetism

Chapter–4: Moving Charges and Magnetism

Concept of magnetic field, Oersted's experiment.

Biot - Savart law and its application to current carrying circular loop.

Ampere's law and its applications to infinitely long straight wire. Straight solenoid (only
qualitative treatment), force on a moving charge in uniform magnetic and electric fields.
Force on a current-carrying conductor in a uniform magnetic field, force between two parallel
current-carrying conductors-definition of ampere, torque experienced by a current loop in
uniform magnetic field; Current loop as a magnetic dipole and its magnetic dipole moment,
moving coil galvanometer- its current sensitivity and conversion to ammeter and voltmeter.

Chapter–5: Magnetism and Matter

Bar magnet, bar magnet as an equivalent solenoid (qualitative treatment only), magnetic field
intensity due to a magnetic dipole (bar magnet) along its axis and perpendicular to its axis
(qualitative treatment only), torque on a magnetic dipole (bar magnet) in a uniform magnetic
field (qualitative treatment only), magnetic field lines.

Magnetic properties of materials- Para-, dia- and ferro – magnetic substances with examples,
Magnetization of materials, effect of temperature on magnetic properties.

Unit IV: Electromagnetic Induction and Alternating Currents

Chapter–6: Electromagnetic Induction

Electromagnetic induction; Faraday's laws, induced EMF and current; Lenz's Law, Self and
mutual induction.

Chapter–7: Alternating Current

Alternating currents, peak and RMS value of alternating current/voltage; reactance and
impedance; LCR series circuit (phasors only), resonance, power in AC circuits, power factor,
wattless current. AC generator, Transformer.

Unit V: Electromagnetic waves

Chapter–8: Electromagnetic Waves

Basic idea of displacement current, Electromagnetic waves, their characteristics, their

transverse nature (qualitative idea only).

Electromagnetic spectrum (radio waves, microwaves, infrared, visible, ultraviolet, X-rays,

gamma rays) including elementary facts about their uses.
Unit VI: Optics

Chapter–9: Ray Optics and Optical Instruments

Ray Optics: Reflection of light, spherical mirrors, mirror formula, refraction of light, total
internal reflection and optical fibers, refraction at spherical surfaces, lenses, thin lens formula,
lens maker’s formula, magnification, power of a lens, combination of thin lenses in contact,
refraction of light through a prism.

Optical instruments: Microscopes and astronomical telescopes (reflecting and refracting)

and their magnifying powers.

Chapter–10: Wave Optics

Wave optics: Wave front and Huygen’s principle, reflection and refraction of plane wave at
a plane surface using wave fronts. Proof of laws of reflection and refraction using Huygen’s
principle. Interference, Young's double slit experiment and expression for fringe width (No
derivation final expression only), coherent sources and sustained interference of light,
diffraction due to a single slit, width of central maxima (qualitative treatment only).

Unit VII: Dual Nature of Radiation and Matter

Chapter–11: Dual Nature of Radiation and Matter

Dual nature of radiation, Photoelectric effect, Hertz and Lenard's observations; Einstein's
photoelectric equation-particle nature of light.
Experimental study of photoelectric effect
Matter waves-wave nature of particles, de-Broglie relation.

Unit VIII: Atoms and Nuclei

Chapter–12: Atoms

Alpha-particle scattering experiment; Rutherford's model of atom; Bohr model of hydrogen

atom, Expression for radius of nth possible orbit, velocity and energy of electron in nth orbit,
hydrogen line spectra (qualitative treatment only).

Chapter–13: Nuclei

Composition and size of nucleus, nuclear force

Mass-energy relation, mass defect; binding energy per nucleon and its variation with mass
number; nuclear fission, nuclear fusion.
Unit IX: Electronic Devices

Chapter–14: Semiconductor Electronics: Materials, Devices and Simple Circuits

Energy bands in conductors, semiconductors and insulators (qualitative ideas only) Intrinsic
and extrinsic semiconductors- p and n type, p-n junction

Semiconductor diode - I-V characteristics in forward and reverse bias, application of junction
diode -diode as a rectifier.
 COURSE STRUCTURE
CLASS XII
THEORY
Time: 3 Hours Total Marks: 70

S. No. Title Marks

1 Solutions 7
2 Electrochemistry 9
3 Chemical Kinetics 7
4 d -and f -Block Elements 7
5 Coordination Compounds 7
6 Haloalkanes and Haloarenes 6
7 Alcohols, Phenols and Ethers 6
8 Aldehydes, Ketones and Carboxylic Acids 8
9 Amines 6
10 Biomolecules 7
Total 70

Unit 1: Solutions

Types of solutions, expression of concentration of solutions of solids in liquids, solubility

of gases in liquids, solid solutions, Raoult’s law, colligative properties - relative lowering
of vapor pressure, elevation of boiling point, depression of freezing point, osmotic
pressure, determination of molecular masses using colligative properties, abnormal
molecular mass, Van't Hoff factor

Unit 2: Electrochemistry

Redox reactions, EMF of a cell, standard electrode potential, Nernst equation and its
application to chemical cells, Relation between Gibbs energy change and EMF of a cell,
conductance in electrolytic solutions, specific and molar conductivity, variations of
conductivity with concentration, Kohlrausch's Law, electrolysis and law of electrolysis
(elementary idea), dry cell-electrolytic cells and Galvanic cells, lead accumulator, fuel
cells, corrosion.

Unit 3: Chemical Kinetics

Rate of a reaction (Average and instantaneous), factors affecting rate of reaction:

concentration, temperature, catalyst; order and molecularity of a reaction, rate law and
specific rate constant, integrated rate equations and half-life (only for zero and first order

9
reactions), concept of collision theory (elementary idea, no mathematical treatment),
activation energy, Arrhenius equation.
Unit 4: d and f Block Elements

General introduction, electronic configuration, occurrence and characteristics of

transition metals, general trends in properties of the first row transition metals – metallic
character, ionization enthalpy, oxidation states, ionic radii, colour, catalytic property,
magnetic properties, interstitial compounds, alloy formation, preparation and properties
of K2Cr2O7 and KMnO4.
Lanthanides - Electronic configuration, oxidation states, chemical reactivity and
lanthanide contraction and its consequences.
Actinides - Electronic configuration, oxidation states and comparison with lanthanides
Unit 5: Coordination Compounds

Coordination compounds - Introduction, ligands, coordination number, colour, magnetic

properties and shapes, IUPAC nomenclature of mononuclear coordination compounds.
Bonding, Werner's theory, VBT, and CFT; structure and stereoisomerism, importance
of coordination compounds (in qualitative analysis, extraction of metals and biological
system).

Unit 6: Haloalkanes and Haloarenes

Haloalkanes: Nomenclature, nature of C–X bond, physical and chemical properties,

optical rotation mechanism of substitution reactions.
Haloarenes: Nature of C–X bond, substitution reactions (Directive influence of halogen
in monosubstituted compounds only).
Uses and environmental effects of - dichloromethane, trichloromethane,
tetrachloromethane, iodoform, freons, DDT.
Unit 7: Alcohols, Phenols and Ethers

Alcohols: Nomenclature, methods of preparation, physical and chemical properties (of

primary alcohols only), identification of primary, secondary and tertiary alcohols,
mechanism of dehydration, uses with special reference to methanol and ethanol.
Phenols: Nomenclature, methods of preparation, physical and chemical properties,
acidic nature of phenol, electrophilic substitution reactions, uses of phenols.
Ethers: Nomenclature, methods of preparation, physical and chemical properties, uses

Unit 8: Aldehydes, Ketones and Carboxylic Acids

Aldehydes and Ketones: Nomenclature, nature of carbonyl group, methods of

preparation, physical and chemical properties, mechanism of nucleophilic addition,
reactivity of alpha hydrogen in aldehydes, uses.

10
Carboxylic Acids: Nomenclature, acidic nature, methods of preparation, physical and
chemical properties; uses.

Unit 9: Amines
Amines: Nomenclature, classification, structure, methods of preparation, physical and
chemical properties, uses, identification of primary, secondary and tertiary amines.
Diazonium salts: Preparation, chemical reactions and importance in synthetic organic
chemistry.

Unit 10: Biomolecules

Carbohydrates - Classification (aldoses and ketoses), monosaccahrides (glucose and

fructose), D-L configuration oligosaccharides (sucrose, lactose, maltose),
polysaccharides (starch, cellulose, glycogen); Importance of carbohydrates.

Proteins -Elementary idea of - amino acids, peptide bond, polypeptides, proteins,

structure of proteins - primary, secondary, tertiary structure and quaternary structures
(qualitative idea only), denaturation of proteins; enzymes. Hormones - Elementary idea
excluding structure.

Vitamins - Classification and functions.

Nucleic Acids: DNA and RNA.

PRACTICAL

Evaluation Scheme for Examination Marks

Volumetric Analysis 08
Salt Analysis 08
Content Based Experiment 06
Project Work 04
Class record and viva 04
Total 30

PRACTICAL SYLLABUS

Micro-chemical methods are available for several of the practical experiments,

wherever possible such techniques should be used.

A. Surface Chemistry
1. Preparation of one lyophilic and one lyophobic sol

11
 MATHEMATICS QUESTION PAPER DESIGN

CLASS – XI (2025-26)

Time: 3 hours Max. Marks: 80

%
S. Typology of Questions Total Weight
No. Marks age

Remembering: Exhibit memory of previously learned material

by recalling facts, terms, basic concepts, and answers.
1 55
44
Understanding: Demonstrate understanding of facts and ideas
by organizing, comparing, translating, interpreting, giving
descriptions, and stating main ideas

Applying: Solve problems to new situations by applying

2 20 25
acquired knowledge, facts, techniques and rules in a different
way.

Analysing:
Examine and break information into parts by identifying motives
or causes. Make inferences and find evidence to support
generalizations

Evaluating:
3 Present and defend opinions by making judgments about 16 20
information, validity of ideas, or quality of work based on a set
of criteria.

Creating:
Compile information together in a different way by combining
elements in a new pattern or proposing alternative solutions

Total 80 100

1. No chapter wise weightage. Care to be taken to cover all the chapters

2. Suitable internal variations may be made for generating various templates keeping the
overall weightage to different form of questions and typology of questions same.
Choice(s):
There will be no overall choice in the question paper. However, 33% internal choices will be
given in all the sections

INTERNAL ASSESSMENT 20 MARKS

Periodic Tests (Best 2 out of 3 tests conducted) 10 Marks
Mathematics Activities 10 Marks

Note: Please refer the guidelines given under XII Mathematics Syllabus.
 CLASS – XI (2025-26)
The following topics are included in the syllabus but will be assessed only formatively to reinforce
understanding without adding to summative assessments. This reduces academic stress while
ensuring meaningful learning. Schools can integrate these with existing chapters as they align well.
Relevant NCERT textual material is enclosed for reference.

S.No. Content
Unit-I: Sets and Functions
1. Sets
Practical problems on Union and Intersection of two sets.
2. Relations and Functions
Composition of Functions
3. Trigonometric Functions
General solution of trigonometric equations of the type sin 𝑦 = sin 𝑎 , cos 𝑦 = cos 𝑎 and
tan 𝑦 = tan 𝑎.
Unit-II: Algebra
1. Principle of Mathematical Induction
Process of the proof by induction, motivating the application of the method by looking at
natural numbers as the least inductive subset of real numbers. The principle of
mathematical induction and simple applications.
2. (Complex Numbers and) Quadratic Equations
Polar representation of complex numbers. Statement of Fundamental Theorem of
Algebra, solution of quadratic equations (with real coefficients) in the complex number
system.
3. Linear Inequalities
Graphical solution of linear inequalities in two variables. Graphical method of finding a
solution of system of linear inequalities in two variables.
4. Binomial Theorem
General and middle term in binomial expansion.
5. Sequence and Series
Formulae for the following special sums
𝑛 𝑛 𝑛

∑ 𝑘 , ∑ 𝑘2 , ∑ 𝑘3
𝑘=1 𝑘=1 𝑘=1
Unit-III: Coordinate Geometry
1. Straight Lines
Normal form. General equation of a line.
2. Introduction to Three-dimensional Geometry
Section formula.
Unit-IV: Calculus
1. Limits and Derivatives
Derivatives of composite functions (Chain rule).
Unit-V Statistics and Probability
1. Probability
Random experiments; outcomes, sample space (set representation).
 COURSE STRUCTURE
CLASS – XII
(2025-26)
One Paper Max. Marks: 80
No. Units Marks
I. Relations and Functions 08
II. Algebra
10
III. Calculus
35
IV. Vectors and Three - Dimensional Geometry
14
V. Linear Programming 05
VI. Probability
08
Total
80
Internal Assessment
20

Unit-I: Relations and Functions

1. Relations and Functions

Types of relations: reflexive, symmetric, transitive and equivalence relations. One to one and
onto functions.

2. Inverse Trigonometric Functions

Definition, range, domain, principal value branch. Graphs of inverse trigonometric functions.

Unit-II: Algebra

1. Matrices
Concept, notation, order, equality, types of matrices, zero and identity matrix, transpose of a
matrix, symmetric and skew symmetric matrices. Operations on matrices: Addition and
multiplication and multiplication with a scalar. Simple properties of addition, multiplication and
scalar multiplication. Non- commutativity of multiplication of matrices and existence of non-
zero matrices whose product is the zero matrix (restrict to square matrices of order 2).
Invertible matrices and proof of the uniqueness of inverse, if it exists; (Here all matrices will
have real entries).
2. Determinants
Determinant of a square matrix (up to 3 x 3 matrices), minors, co-factors and applications of
determinants in finding the area of a triangle. Adjoint and inverse of a square matrix.
Consistency, inconsistency and number of solutions of system of linear equations by
examples, solving system of linear equations in two or three variables (having unique solution)
using inverse of a matrix.
Unit-III: Calculus

1. Continuity and Differentiability

Continuity and differentiability, chain rule, derivative of composite functions, derivatives of

inverse trigonometric functions like sin−1 𝑥, cos−1 𝑥 and tan−1 𝑥, derivative of implicit functions.
Concept of exponential and logarithmic functions. Derivatives of logarithmic and exponential
functions. Logarithmic differentiation, derivative of functions expressed in parametric forms.
Second order derivatives.

2. Applications of Derivatives

Applications of derivatives: rate of change of quantities, increasing/decreasing functions,

maxima and minima (first derivative test motivated geometrically and second derivative test
given as a provable tool). Simple problems (that illustrate basic principles and understanding
of the subject as well as real- life situations).

3. Integrals

Integration as inverse process of differentiation. Integration of a variety of functions by

substitution, by partial fractions and by parts, Evaluation of simple integrals of the following
types and problems based on them.

𝒅𝒙 𝒅𝒙 𝒅𝒙 𝒅𝒙 𝒅𝒙 𝒑𝒙+𝒒
∫ 𝒙𝟐 ±𝒂𝟐 , ∫ √ ,∫ ,∫
𝒂𝒙𝟐 +𝒃𝒙+𝒄
,∫ ,∫
𝒂𝒙𝟐 +𝒃𝒙+𝒄
𝒅𝒙,
𝒙𝟐 ±𝒂𝟐 √𝒂𝟐 −𝒙𝟐 √𝒂𝒙𝟐 +𝒃𝒙+𝒄
𝒑𝒙+𝒒
∫√ 𝒅𝒙, ∫ √𝒂𝟐 ± 𝒙𝟐 𝒅𝒙 , ∫ √𝒙𝟐 − 𝒂𝟐 𝒅𝒙 , ∫ √𝒂𝒙𝟐 + 𝒃𝒙 + 𝒄 𝒅𝒙
𝒂𝒙𝟐 +𝒃𝒙+𝒄

Fundamental Theorem of Calculus (without proof). Basic properties of definite integrals and
evaluation of definite integrals.

4. Application of the Integrals

Applications in finding the area under simple curves, especially lines, circles/ parabolas/ellipses
(in standard form only)

5. Differential Equations

Definition, order and degree, general and particular solutions of a differential equation. Solution
of differential equations by method of separation of variables, solutions of homogeneous
differential equations of first order and first degree. Solutions of linear differential equation of the
type:
𝑑𝑦
+ 𝑝𝑦 = 𝑞, where 𝑝 and 𝑞 are functions of 𝑥 or constants.
𝑑𝑥

𝑑𝑥
+ 𝑝𝑥 = 𝑞, where 𝑝 and 𝑞 are functions of 𝑦 or constants.
𝑑𝑦