(CODE NO. 041)
The Syllabus in the subject of Mathematics has undergone changes from time to time in accordance with
growth of the subject and emerging needs of the society. The present revised syllabus has been designed in accordance
with National Curriculum Framework 2005 and as per guidelines given in Focus Group on Teaching of Mathematics
which is to meet the emerging needs of all categories of students. Motivating the topics from real life problems and
other subject areas, greater emphasis has been laid on applications of various concepts.
The curriculum at Secondary stage primarily aims at enhancing the capacity of students to employ Mathematics
in solving day-to-day life problems and studying the subject as a separate discipline. It is expected that students should
acquire the ability to solve problems using algebraic methods and apply the knowledge of simple trigonometry to solve
problems of heights and distances. Carrying out experiments with numbers and forms of geometry, framing hypothesis
and verifying these with further observations form inherent part of Mathematics learning at this stage. The proposed
curriculum includes the study of number system, algebra, geometry, trigonometry, mensuration, statistics, graphs and
coordinate geometry etc.
The teaching of Mathematics should be imparted through activities which may involve the use of concrete
materials, models, patterns, charts, pictures posters, games, puzzles and experiments.
The broad objectives of teaching of Mathematics at secondary stage are to help the learners to:
consolidate the Mathematical knowledge and skills acquired at the upper primary stage;
acquire knowledge and understanding, particularly by way of motivation and visualization, of basic concepts,
terms, principles and symbols and underlying processes and skills.
develop mastery of basic algebraic skills;
develop drawing skills;
feel the flow of reasons while proving a result or solving a problem.
apply the knowledge and skills acquired to solve problems and wherever possible, by more than one
to develop positive ability to think, analyze and articulate logically;
to develop awareness of the need for national integration, protection of environment, observance of small
family norms, removal of social barriers, elimination of sex biases;
to develop necessary skills to work with modern technological devices such as calculators, computers
to develop interest in Mathematics as a problem-solving tool in various fields for its beautiful structures
and patterns, etc;
to develop reverence and respect towards great Mathematicians for their contributions to the field of
to develope interest in the subject by participating in related competitions.
to acquaint students with different aspects of mathematics used in daily life.
to develop an interest in students to study mathematics as a discipline.
One Paper Time : 3 Hours Marks : 80
|I. NUMBER SYSTEMS||06|
|III. COORDINATE GEOMETRY||06|
|VI. STATISTICS AND PROBABILITY||22|
UNIT I : NUMBER SYSTEMS
1. REAL NUMBERS (20) Periods
Review of representation of natural numbers, integers, rational numbers on the number line. Representation
of terminating / non-terminating recurring decimals, on the number line through successive magnification.
Rational numbers as recurring/terminating decimals.
Examples of nonrecurring / non terminating decimals such as √2, √3, √5 etc. Existence of non-rational
numbers (irrational numbers) such as √2, √3 and their representation on the number line. Explaining that
every real number is represented by a unique point on the number line and conversely, every point on the
number line represents a unique real number.
Existence of √x for a given positive real number x (visual proof to be emphasized).
Definition of nth root of a real number.
Recall of laws of exponents with integral powers. Rational exponents with positive real bases (to be done by
particular cases, allowing learner to arrive at the general laws.)
Rationalization (with precise meaning) of real numbers of the type (& their combinations)
___1___ & __1___
a + b√x √x + √y
UNIT II : ALGEBRA
1. POLYNOMIALS (25) Periods
Definition of a polynomial in one variable, its coefficients, with examples and counter examples, its terms,
zero polynomial. Degree of a polynomial. Constant, linear, quadratic, cubic polynomials; monomials, binomials,
trinomials. Factors and multiples. Zeros/roots of a polynomial / equation. State and motivate the Remainder
Theorem with examples and analogy to integers. Statement and proof of the Factor Theorem. Factorization
of ax2 + bx + c, a ≠ 0 where a, b, c are real numbers, and of cubic polynomials using the Factor Theorem.
Recall of algebraic expressions and identities. Further identities of the type (x + y + z)2 = x2 + y2 + z2 + 2xy
+ 2yz + 2zx, (x ± y)3 = x3 ± y3 ± 3xy (x ± y).
x3 + y3 + z3 — 3xyz = (x + y + z) (x2 + y2 + z2 — xy — yz — zx) and their use in factorization of
polymonials. Simple expressions reducible to these polynomials.
2. LINEAR EQUATIONS IN TWO VARIABLES (12) Periods
Recall of linear equations in one variable. Introduction to the equation in two variables. Prove that a linear
equation in two variables has infinitely many solutions and justify their being written as ordered pairs of real
numbers, plotting them and showing that they seem to lie on a line. Examples, problems from real life,
including problems on Ratio and Proportion and with algebraic and graphical solutions being done
UNIT III : COORDINATE GEOMETRY
1. COORDINATE GEOMETRY (9) Periods
The Cartesian plane, coordinates of a point, names and terms associated with the coordinate plane, notations,
plotting points in the plane, graph of linear equations as examples; focus on linear equations of the type
ax + by + c = 0 by writing it as y = mx + c and linking with the chapter on linear equations in two variables.
UNIT IV : GEOMETRY
1. INTRODUCTION TO EUCLID'S GEOMETRY (6) Periods
History - Euclid and geometry in India. Euclid's method of formalizing observed phenomenon into rigorous
mathematics with definitions, common/obvious notions, axioms/postulates and theorems. The five postulates
of Euclid. Equivalent versions of the fifth postulate. Showing the relationship between axiom and theorem.
1. Given two distinct points, there exists one and only one line through them.
2. (Prove) two distinct lines cannot have more than one point in common.
2. LINES AND ANGLES (10) Periods
1. (Motivate) If a ray stands on a line, then the sum of the two adjacent angles so formed is 180o and the
2. (Prove) If two lines intersect, the vertically opposite angles are equal.
3. (Motivate) Results on corresponding angles, alternate angles, interior angles when a transversal intersects
two parallel lines.
4. (Motivate) Lines, which are parallel to a given line, are parallel.
5. (Prove) The sum of the angles of a triangle is 180o.
6. (Motivate) If a side of a triangle is produced, the exterior angle so formed is equal to the sum of the two
interiors opposite angles.
3. TRIANGLES (20) Periods
1. (Motivate) Two triangles are congruent if any two sides and the included angle of one triangle is equal
to any two sides and the included angle of the other triangle (SAS Congruence).
2. (Prove) Two triangles are congruent if any two angles and the included side of one triangle is equal to
any two angles and the included side of the other triangle (ASA Congruence).
3. (Motivate) Two triangles are congruent if the three sides of one triangle are equal to three sides of the
other triangle (SSS Congruene).
4. (Motivate) Two right triangles are congruent if the hypotenuse and a side of one triangle are equal
(respectively) to the hypotenuse and a side of the other triangle.
5. (Prove) The angles opposite to equal sides of a triangle are equal.
6. (Motivate) The sides opposite to equal angles of a triangle are equal.
7. (Motivate) Triangle inequalities and relation between 'angle and facing side' inequalities in triangles.
4. QUADRILATERALS (10) Periods
1. (Prove) The diagonal divides a parallelogram into two congruent triangles.
2. (Motivate) In a parallelogram opposite sides are equal, and conversely.
3. (Motivate) In a parallelogram opposite angles are equal, and conversely.
4. (Motivate) A quadrilateral is a parallelogram if a pair of its opposite sides is parallel and equal.
5. (Motivate) In a parallelogram, the diagonals bisect each other and conversely.
6. (Motivate) In a triangle, the line segment joining the mid points of any two sides is parallel to the third
side and (motivate) its converse.
5. AREA (4) Periods
Review concept of area, recall area of a rectangle.
1. (Prove) Parallelograms on the same base and between the same parallels have the same area.
2. (Motivate) Triangles on the same base and between the same parallels are equal in area and its converse.
6. CIRCLES (15) Periods
Through examples, arrive at definitions of circle related concepts, radius, circumference, diameter, chord,
arc, subtended angle.
1. (Prove) Equal chords of a circle subtend equal angles at the center and (motivate) its converse.
2. (Motivate) The perpendicular from the center of a circle to a chord bisects the chord and conversely,
the line drawn through the center of a circle to bisect a chord is perpendicular to the chord.
3. (Motivate) There is one and only one circle passing through three given non-collinear points.
4. (Motivate) Equal chords of a circle (or of congruent circles) are equidistant from the center(s) and
5. (Prove) The angle subtended by an arc at the center is double the angle subtended by it at any point on
the remaining part of the circle.
6. (Motivate) Angles in the same segment of a circle are equal.
7. (Motivate) If a line segment joining two points subtendes equal angle at two other points lying on the
same side of the line containing the segment, the four points lie on a circle.
8. (Motivate) The sum of the either pair of the opposite angles of a cyclic quadrilateral is 180o and its
7. CONSTRUCTIONS (10) Periods
1. Construction of bisectors of line segments & angles, 60 degree, 90o, 45o angles etc., equilateral triangles.
2. Construction of a triangle given its base, sum/difference of the other two sides and one base angle.
3. Construction of a triangle of given perimeter and base angles.
UNIT V : MENSURATION
1. AREAS (4) Periods
Area of a triangle using Hero's formula (without proof) and its application in finding the area of a quadrilateral.
2. SURFACE AREAS AND VOLUMES (10) Periods
Surface areas and volumes of cubes, cuboids, spheres (including hemispheres) and right circular cylinders/
UNIT VI : STATISTICS AND PROBABILITY
1. STATISTICS (13) Periods
Introduction to Statistics : Collection of data, presentation of data — tabular form, ungrouped / grouped,
bar graphs, histograms (with varying base lengths), frequency polygons, qualitative analysis of data to choose
the correct form of presentation for the collected data. Mean, median, mode of ungrouped data.
2. PROBABILITY (12) Periods
History, Repeated experiments and observed frequency approach to probability. Focus is on empirical
probability. (A large amount of time to be devoted to group and to individual activities to motivate the
concept; the experiments to be drawn from real - life situations, and from examples used in the chapter on
INTERNAL ASSESSMENT 20 Marks
Evaluation of activities 10 Marks
Project Work 05 Marks
Continuous Evaluation 05 Marks
(Code No. 086 / 090)
The subject of Science plays an important role in developing in children well-defined abilities in cognitive,
affective and psychomotor domains. It augments the spirit of enquiry, creativity, objectivity and asthetic sensibility.
Whereas the upper primary stage demands that plentiful opportunities should be provided to the students to
engage them with the processes of science like observing, recording observations, drawing, tabulation, plotting
graphs etc., the secondary stage expects abstraction and quantitative reasoning to occupy a more central place in the
teaching and learning of Science. Thus, the idea of atoms and molecules being the building blocks of matter makes
its appearance, as does Newton's law of Gravitation.
The present syllabus has been designed around six broad themes viz. Food, Materials, the world of the
living, how things work, moving things, people and ideas, natural phenomenon and natural reasources. Special care
has been taken to avoid temptation of adding too many concepts than can be comfortably learnt in the given time
frame. No attempt has been made to be comprehensive.
At this stage, while science is still a common subject, the disciplines of Physics, Chemistry and Biology
begin to emerge. The students should be exposed to experiences as well as modes of reasoning that are typical of the
CLASS IX (THEORY)
One Paper Time : 2½ hours. Marks : 60
|II. Matter - Its nature and behaviour||15|
|III. Organisation in living world||13|
|IV. Motion, Force and Work||20|
|V. Our Environment||07|
Theme : Food (10 Periods)
Unit 1 : Food
Plant and animal breeding and selection for quality improvement and management ; use of fertilizers, manures;
protection from pests and diseases; organic farming.
Theme : Materials (50 Periods)
Unit 2 : Matter - Nature and behaviour
Definition of matter; solid, liquid and gas; characteristics - shape, volume, density; change of state-melting
(absorption of heat), freezing, evaporation (Cooling by evaporation), condensation, sublimation.
Nature of matter : Elements, compounds and mixtures. Heterogenous and homogenous mixtures, colloids and
Particle nature, basic units : atoms and molecules. Law of constant proportions. Atomic and molecular masses.
Mole Concept : Relationship of mole to mass of the particles and numbers. Valency. Chemical formula of common
Structure of atom : Electrons, protons and neutrons; Isotopes and isobars.
Theme : The World of the living (45 Periods)
Unit 3 : Organization in the living world.
Biological Diversity : Diversity of plants and animals - basic issues in scientific naming, basis of classification.
Hierarchy of categories / groups, Major groups of plants (salient features) (Bacteria, Thalophyta, Bryo phyta,
Pteridophyta, gymnosperms and Angiosperms). Major groups of animals (salient features) (Non-chordates upto
phyla and chordates upto classes).
Cell - Basic Unit of life : Cell as a basic unit of life; prokaryotic and eukaryotic cells, multicellular organisms; cell
membrane and cell wall, cell organelles; chloroplast, mitochondria, vacuoles, ER, golgi apparatus; nucleus,
chromosomes - basic structure, number.
Tissues, organs, organ systems, organism.
Structure and functions of animal and plant tissues (four types in animals; merismatic and permanent tissues in
Health and diseases : Health and its failure. Infectious and Non-infectious diseases, their causes and manifestation.
Diseases caused by microbes (Virus, Bacteria and protozoans) and their prevention, Principles of treatment and
prevention. Pulse polio programmes.
Theme : Moving things, people and ideas (60 Periods)
Unit 4 : Motion, Force and Work
Motion : Distance and displacement, velocity; uniform and non-uniform motion along a straight line; acceleration,
distance-time and velocity-time graphs for uniform and uniformly accelerated motion, equations of motion by graphical
method; elementary idea of uniform circular motion.
Force and Newton's laws : Force and motion, Newton's laws of motion, inertia of a body, inertia and mass,
momentum, force and acceleration. Elementary idea of conservation of momentum, action and reaction forces.
Gravitation : Gravitation; universal law of gravitation, force of gravitation of the earth (gravity), acceleration due to
gravity; mass and weight; free fall.
Work, Energy and Power : Work done by a force, energy, power; kinetic and potential energy; law of conservation
Floatation : Thrust and pressure. Archimedes' principle, buoyancy, elementary idea of relative density.
Work, Energy and Power : Work done by a force, energy, power; kinetic and potential energy; law of conservation
Sound : Nature of sound and its propagation in various media, speed of sound, range of hearing in humans; ultrasound;
reflection of sound; echo and SONAR.
Structure of the human ear (auditory aspect only).
Theme : Natural Resources (15 Periods)
Unit 5 : Our Environment
Physical resources : Air, Water, Soil.
Air for respiration, for combustion, for moderating temperatures, movements of air and its role in bringing rains
Air, water and soil pollution ( brief introduction). Holes in ozone layer and the probable damages.
Bio-geo chemical cycles in nature : water, oxygen, carbon, nitrogen
LIST OF EXPERIMENTS
Marks : 40 (20 + 20)
1. To prepare
a) a true solution of common salt, sugar and alum
b) a suspension of soil, chalk powder and fine sand in water
c) a colloidal of starch in water and egg albumin in water and distinguish between these on the basis of
ii) filtration criterion
2. To prepare
a) a mixture
b) a compound
using iron filings and sulphur powder and distinguish between these on the basis of :
i) appearance i.e., homogeneity and heterogeneity
ii) behaviour towards a magnet
iii) behaviour towards carbon disulphide as a solvant.
iv) effect of heat.
3. To carry out the following chemical reactions and record observations. Also identify the type of reaction
involved in each case.
i) Iron with copper sulphate solution in water.
ii) Burning of Magnesium in air.
iii) Zinc with dilute sulphuric acid
iv) Heating of Lead Nitrate
v) Sodium sulphate with Barium chloride in the form of their solutions in water.
4. To verify laws of reflection of sound.
5. To determine the density of solid (denser than water) by using a spring balance and a measuring cylinder.
6. To establish the relation between the loss in weight of a solid when fully immersed in
i) tap water
ii) strongly salty water, with the weight of water displaced by it by taking at least two different solids.
7. To measure the temperature of hot water as it cools and plot a temperature-time graph.
8. To determine the velocity of a pulse propagated through a stretched string/slinky.
9. To prepare stained temporary mounts of (a) onion peel and (b) human cheek cells and to record observations
and draw their labeled diagrams.
10. To identify parenchyma and sclerenchyma tissues in plants, striped muscle fibers and nerve cells in animals,
from prepared slides and to draw their labeled diagrams.
11. To separate the components of a mixture of sand, common salt and ammonium chloride (or camphor) by
12. To determine the melting point of ice and the boiling point of water.
13. To test (a) the presence of starch in the given food sample (b) the presence of the adulterant metanil yellow in
14. To study the characteristic of spirogyra/Agaricus, Moss/Fern, Pinus ( either with male or female conre) and an
Angiospermic plant. Draw and give two identifying features of groups they belong to.
15. To observe and draw the given specimens—earthworm, cockroach, bony fish and bird. For each specimen
(a) one specific feature of its phylum
(b) one adaptive feature with reference to its habitat.
SCHEME OF EVALUATION
Multiple choice type question written test (School based) : 20 Marks
Hands-on practicals examination (school based) : 20 Marks
(CODE NO. 087)
Social Sciences is a compulsory subject upto secondary stage of school education. It is an integral component of
general education because it helps the learners in understanding the environment in its totality and developing a broader
perspective and an empirical, reasonable and humane outlook. This is of crucial importance because it helps them
grow into well-informed and responsible citizens with necessary attributes and skills for being able to participate and
contribute effectively in the process of development and nation-building.
The social sciences curriculum draws its content mainly from geography, history, civics and economics. Some elements
of sociology and commerce are also included. Together they provide a comprehensive view of society-over space and
time, and in relation to each other. Each subject’s distinct methods of enquiry help the learners study society from
different angles and form a holistic view.
The main objectives of this syllabus are :
to develop an understanding of the processes of change and development-both in terms of time and space, through
which human societies have evolved.
to make learners realise that the process of change is continuous and any event or phenomenon or issue cannot be
viewed in isolation but in a wider context of time and space.
to develop an understanding of contemporary India with its historical perspective, of the basic framework of the
goals and policies of national development in independent India, and of the process of change with appropriate
connections to world development.
to deepen knowledge about and understanding of India’s freedom struggle and of the values and ideals that it
represented, and to develop an appreciation of the contributions made by people of all sections and regions of the
to help learners understand and cherish the values enshrined in the Indian Constitution and to prepare them for their
roles and responsibilities as effective citizens of a democratic society.
to deepen the knowledge and understanding of India’s environment in its totality, their interactive processes and
effects on the future quality of people's lives
to facilitate the learners to understand and appreciate the diversity in the land and people of the country with its
to develop an appreciation of the richness and variety of India’s heritage-both natural and cultural and the need for
to promote an understanding of the issues and challenges of contemporary India-environmental, economic and
social, as part of the development process.
to help pupils acquire knowledge, skills and understanding to face the challenges of contemporary society as
individuals and groups and learn the art of living a confident and stress-free life as well as participating effectively
in the community
to develop scientific temper by promoting the spirit of enquiry and following a rational and objective approach in
analysing and evaluating data and information as well as views and interpretations
to develop academic and social skills such as critical thinking, communicating effectively both in visual and verbal
forms- cooperating with others, taking initiatives and providing leadership in solving others', problems
to develop qualities clustered around the personal, social, moral, national and spiritual values that make a person
humane and socially effective.
Time : 3 Hrs. Marks : 80 + 20
|Unit 1 : India and the Contemporary World||18||40|
|Unit 2 : India -Land and the People||20||45|
|Unit 3 : Democratic Politics||18||40|
|Unit 4 : Understanding Economics||16||40|
|Unit 5 : Disaster Management||8||25|
|1. Tests (Formative and Summative)||10|
|2. Assignments (School & Home)||05|
|3. Project Work||05|
Unit 1 : India and the Contemporary World - I 40 Periods
Any two themes from each of the first two sub-units and one from the third could be studied.
(c) The different revolutionary groups and ideas of the time.
(d) The legacy.
(b) The nature of social movements between 1905 and 1917.
(c) The First World War and
(d) The legacy.
(c) The ideology of Nazism.
(b) Changes in forest societies under colonialism.
(b) Changes within rural economies in the modern world.
(a) The emergence of cricket as an English sport.
(b) Cricket and colonialism.
(a) A short history of changes in clothing.
(b) Debates over clothing in colonial India.
(c) Swadeshi and the movement
In each of the themes in this unit students would be made familiar with extracts of speeches,
Discuss the critical significance of Nazism in shaping the politics of modern world.
Suggest how sports also have a history and that it is linked up with the politics of power and
Unit 2 : India - Land and the People 45 Periods
1. India : location, relief, structure, major physiographic units.
6. Population : size, distribution, age-sex composition, population change-migration as a determinant of population change, literacy,
To understand the major landform features and the underlying geological structure; their association with various rocks and minerals as well as nature of soil
To identify the various factors influencing the climate and explain the climatic variaton of our country and its impact on the life of the people. Tor explain the importance and unifying role of monsoons;
To analyse the uneven nature of population distribution and show concern about the large size of
Learners may identify songs, dances, festivals and special food preparations associated with certain seasons
in their particular region, and whether they have some commonality with other regions of India.
Collection of material by learners on the flora and fauna of the region in which their school is situated. It
should include a list of endangered species of the region and also information regarding efforts being made to save
Depletion of forests and ecological imbalance.
Unit - 3 : Democratic Politics I 40 Periods
1. What is democracy? Why democracy?
Develop conceptual skills of defining democracy
Develop a historical sense of the choice and nature of democracy in India.
Unit - 4 : Understanding Economics – I 40 Periods
1. The economic story of Palampore: Economic transactions of Palampore and its interaction with the rest of the world through which the concept
Familiarising the children with some basic economic concepts through an imaginary story of a village
Understanding of poverty as a challenge and sensitization of the learner;
Suggested Activities / Instructions :
Theme 1 : Give more examples of activities done by different workers and farmers.
Numerical problems can also be included.
Some of the ways through which description of villages are available in the writings of Prem Chand, MN Srinivas
and RK Narayan. They may have to be referred.
Theme II : Discuss the impact of unemployment
Debate on whether all the activities done by women should be included or not. Why?
Is begging an economic activity? Discuss.
Is it necessary to reduce population growth or family size? Discuss.
Theme IV : Visit a few farms in a village and collect the details of foodgrains cultivated;
Visit a nearby ration shop and collect the details of goods available;
Visit a regulated market yard and observe how goods are transacted and get the details of the places where the
goods come and go.
Unit - 5 : Disaster Management 25 Periods
1. Man made disasters - Nuclear, Biological and Chemical.
2. Common Hazards - Prevention and Mitigation
3. Community Based Disaster Management.
PRESCRIBED TEXTBOOKS :
1. India and the Contemporary World History - Published by NCERT
2. Contemparary India - Geography - Published by NCERT
3. Democratic Politics - Published by NCERT
4. Economics - Published by NCERT
5. Together, Towards a Safer India - Part II, a textbook on Disaster Management for class IX - Published by