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Class VII Maths CBSE Syllabus

Class VIII Science CBSE Syllabus

Class VIII Maths CBSE Syllabus

Class IX Science CBSE Syllabus

Class IX Maths CBSE Syllabus

Class X Science CBSE Syllabus

Class X Maths CBSE Syllabus

Class VI CBSE Syllabus

Class VI Maths Syllabus

Class VI Science Syllabus

1. Food

Sources of food
Plant parts and animal products as sources of food; herbivores, carnivores, omnivores.

Components of food
Carbohydrates, fats, proteins, vitamins, minerals, fibres, their sources and significance for human health; balanced diet; diseases and disabilities due to food deficiencies.

Cleaning food
Threshing, winnowing, hand picking, sedimentation, filtration.

2. Materials

Materials of daily use
Different types of cloth materials –cotton, wool, silk and synthetics. Development of clothing materials. Plant fibre, especially cotton and jute; production of cotton, jute and other locally available plant fibres; types of soil required for the growth of different fibrous plants.

Different kinds of materials
Grouping things on the basis of common properties.

How things change/ react with one another
Some changes can be reversed and others cannot be reversed.Solubility, saturated solutions. Amount of substance dissolving varies with temperature. At the same temperature amounts of different substances that dissolve varies.

3. The World of the Living

Things around us
Living/non-living characteristics; habitat; biotic, abiotic (light, temperature, water, air, soil, fire)

The habitat of the living
Habitat varies aquatic, deserts, mountains etc.plants and animals show adaptation; other plant part modifications like tendrils, thorns etc. Animals in deserts and water.

Plants –form and function
Morphological structure and function of root, stem and leaves. Structure of the flower, differences.

Animals –form and function
Structure and functions of the animal body; Human skeletal system, some other animals e.g. fish, bird, cockroach, snail.

4. Moving Things, People and Ideas

Need to measure distance (length). Measurement of length. Motion as change in position with time.

5. How things work

Electric current and circuits
Electric current: Electric circuit (current flows only when a cell and other components are connected in an unbroken loop) Conductor, Insulator.

Magnet. Poles of a magnet. A freely suspended magnet always aligns in a particular direction. North and South poles. Like poles repel and unlike poles attract each other.

6. Natural Phenomena

Rain, thunder and lightning
Evaporation and condensation, water in different states. Water cycle.

Classification of various materials in terms of transparent, translucent and opaque. A shadow is formed only when there is a source of light and an opaque material obstructs a source it. A shadow is black irrespective of the colour of the object. Reflecting surfaces; images are different from shadows.

7. Natural Resources

Importance of water
Importance of water, dependence of the living on water. Droughts and floods.

Importance of air
Some animals and plants live in water; some live on land and some live in upper layers of soil; but all need air to breath/to respire.

Waste; recycling of waste products; things that rot and things that don’. Rotting is supported by animals/animal and plant products.

Class VI Maths Syllabus

Number System

(i) Knowing our Numbers:
Consolidating the sense of numberness up to 5 digits, Size, estimation of numbers, identifying smaller, larger, etc. Place value (recapitulation and extension), connectives: use of symbols =, <, > and use of brackets, word problems on number operations involving large numbers up to a maximum of 5 digits in the answer after all operations. This would include conversions of units of length & mass (from the larger to the smaller units), estimation of outcome of number operations. Introduction to a sense of the largeness of, and initial familiarity with, large numbers up to 8 digits and approximation of large numbers)

(ii) Playing with Numbers:
Simplification of brackets, Multiples and factors, divisibility rule of 2, 3, 4, 5, 6, 8, 9, 10, 11. (All these through observing patterns. Children would be helped in deducing some and then asked to derive some that are a combination of the basic patterns of divisibility.) Even/odd and prime/composite numbers, Co-prime numbers, prime factorisation, every number can be written as products of prime factors. HCF and LCM, prime factorization and division method for HCF and LCM, the property LCM X HCF = product of two numbers. All this is to be embedded in contexts that bring out the significance and provide motivation to the child for learning these ideas.

(iii) Whole numbers
Natural numbers, whole numbers, properties of numbers (commutative, associative, distributive, additive identity, multiplicative identity), number line. Seeing patterns, identifying and formulating rules to be done by children. (As familiarity with algebra grows, the child can express the generic pattern.)

(iv) Negative Numbers and Integers
How negative numbers arise, models of negative numbers, connection to daily life, ordering of negative numbers, representation of negative numbers on number line. Children to see patterns, identify and formulate rules. What are integers, identification of integers on the number line, operation of addition and subtraction of integers, showing the operations on the number line (addition of negative integer reduces the value of the number) comparison of integers, ordering of integers.

(v) Fractions:
Revision of what a fraction is, Fraction as a part of whole, Representation of fractions (pictorially and on number line), fraction as a division, proper, improper & mixed fractions, equivalent fractions, comparison of fractions, addition and subtraction of fractions (Avoid large and complicated unnecessary tasks). (Moving towards abstraction in fractions) Review of the idea of a decimal fraction, place value in the context of decimal fraction, inter conversion of fractions and decimal fractions (avoid recurring decimals at this stage), word problems involving addition and subtraction of decimals (two operations together on money, mass, length and temperature)


Introduction to Algebra
•Introduction to variable through patterns and through appropriate word problems and generalisations (example 5 X 1 = 5 etc.)
•Generate such patterns with more examples.
•Introduction to unknowns through examples with simple contexts (single perations)

Ratio and Proportion

•Concept of Ratio
•Proportion as equality of two ratios
•Unitary method (with only direct variation implied)
•Word problems


(i) Basic geometrical ideas (2 -D):
Introduction to geometry. Its linkage with and reflection in everyday experience.
•Line, line segment, ray.
•Open and closed figures.
•Interior and exterior of closed figures.
•Curvilinear and linear boundaries
•Angle —Vertex, arm, interior and exterior,
•Triangle —vertices, sides, angles, interior and exterior, altitude and median
•Quadrilateral —Sides, vertices, angles, diagonals, adjacent sides and opposite sides (only convex quadrilateral are to be discussed), interior and exterior of a quadrilateral.
•Circle —Centre, radius, diameter, arc, sector, chord, segment, semicircle, circumference, interior and exterior.

(ii) Understanding Elementary Shapes (2-D and 3-D):
•Measure of Line segment
•Measure of angles
•Pair of lines
- Intersecting and perpendicular lines
- Parallel lines
•Types of angles- acute, obtuse, right, straight, reflex, complete and zero angle
•Classification of triangles (on the basis of sides, and of angles)
•Types of quadrilaterals –Trapezium, parallelogram, rectangle, square, rhombus.
•Simple polygons (introduction) (Upto octagons regulars as well as non regular).
•Identification of 3-D shapes: Cubes, Cuboids, cylinder, sphere, cone,prism (triangular), pyramid (triangular and square)
Identification and locating in the surroundings
•Elements of 3-D figures. (Faces, Edges and vertices)
•Nets for cube, cuboids, cylinders, cones and tetrahedrons.

(iii) Symmetry: (reflection)
•Observation and identification of 2-D symmetrical objects for reflection symmetry
•Operation of reflection (taking mirror images) of simple 2-D objects
•Recognising reflection symmetry (identifying axes)

(iv) Constructions (using Straight edge Scale, protractor, compasses)
•Drawing of a line segment
•Construction of circle
•Perpendicular bisector
•Construction of angles (using protractor)
•Angle 60 degree, 120 degree (Using Compasses)
•Angle bisector- making angles of 30 degree, 45 degree, 90 degree etc. (using compasses)
•Angle equal to a given angle (using compass)
•Drawing a line perpendicular to a given line from a point a) on the line b) outside the line.


Concept of Perimeter and Introduction to area
Introduction and general understanding of perimeter using many shapes. Shapes of different kinds with the same perimeter. Concept of area, Area of a rectangle and a square Counter examples to different misconcepts related to perimeter and area. Perimeter of a rectangle –and its special case –a square. Deducing the formula of the perimeter for a rectangle and then a square through pattern and generalisation.

Data handling
(i) What is data - choosing data to examine a hypothesis?
(ii) Collection and organisation of data - examples of organising it in tally bars and a table.
(iii) Pictograph- Need for scaling in pictographs interpretation & construction.
(iv) Making bar graphs for given data interpreting bar graphs.


Class VII CBSE Syllabus

Class VII Maths Syllabus

Class VII Science Syllabus


Food sources
Autotrophic and heterotrophic nutrition; parasites, saprophytes; photosynthesis.

Utilisation of food
Types of nutrition, nutrition in amoeba and human beings, Digestive system human, ruminants; types of teeth; link with transport and respiration.

2. Materials

Materials of daily use
Wool, silk - animal fibres. Process of extraction of silk; associated health problems. Heat flow; temperature.

Different kinds of materials
Classification of substances into acidic, basic and neutral; indicators.

How things change/react with one another
Chemical substances; in a chemical reaction a new substance is formed. Substances can be separated by crystallisation.

3. The World of the Living

Surroundings affect the living
Climate, soil types, soil profile, absorption of water in soil, suitability for crops, adaptation of animals to different climates.

The breath of life
Respiration in plants and animals.

Movement of substances
Herbs, shrubs, trees; Transport of food and water in plants; circulatory and excretion system in animals; sweating.

Multiplication in plants
Vegetative, asexual and sexual reproduction in plants, pollination - cross, self pollination; pollinators, fertilisation, fruit, seed.

4. Moving Things,People and Ideas

Moving objects
Appreciation of idea of time and need to measure it. Measurement of time using periodic events. Idea of speed of moving objects – slow and fast motion along a straight line.

5. How Things Work

Electric current and circuits
Electric circuit symbols for different elements of circuit. Heating effect of current. Principle of fuse. A current-carrying wire has an effect on a magnet. A current-carrying coil behaves like a magnet. Working of an electric bell.

6. Natural Phenomena

Rain, thunder and lightning
High-speed winds and heavy rainfall have disastrous consequences for human and other life.

Rectilinear propagation of light. Reflection, certain surfaces reflect light. Real and virtual images. White light is composed of many colours.

7. Natural Resources

Scarcity of water
Water exists in various forms in nature. Scarcity of water and its effect on life.

Forest products
Interdependence of plants and animals in forests. Forests contribute to purification of air and water.

Waste Management
Sewage; need for drainage/sewer systems that are closed.


Class VII Maths Syllabus

Number System

(i) Knowing our Numbers:Integers
• Multiplication and division of integers (through patterns). Division by zero is meaningless
• Properties of integers (including identities for addition & multiplication, commutative, associative, distributive) (through patterns).
These would include examples from whole numbers as well. Involve expressing commutative and associative properties in a general form. Construction of counterexamples, including some by children. Counter examples like subtraction is not commutative.
• Word problems including integers (all operations)

(ii) Fractions and rational numbers:
• Multiplication of fractions
• Fraction as an oper • Introduction to rational numbers (with representation on number line)
• Operations on rational numbers (all operations)
• Representation of rational number as a decimal.
• Word problems on rational numbers (all operations)
• Multiplication and division of decimal fractions
• Conversion of units (length & mass)
• Word problems (including all operations)

(iii) Powers:
• Exponents only natural numbers.
• Laws of exponents (through observing patterns to arrive at generalisation.)
(i) am an am+n
(ii) (am)n =amn
(iii) am/an = am-n, where m - n


Algebraic Expressions
• Generate algebraic expressions (simple) involving one or two variables
• Identifying constants, coefficient, powers
• Like and unlike terms, degree of expressions e.g., x²y etc.
• Addition, subtraction of algebraic expressions (coefficients should be integers).
• Simple linear equations in one variable (in contextual problems) with two operations (avoid complicated coefficients)

Ratio and Proportion

• Ratio and proportion (revision)
• Unitary method continued, consolidation, general expression.
• Percentage- an introduction.
• Understanding percentage as a fraction with denominator 100
• Converting fractions and decimals into percentage and vice-versa.
• Application to profit and loss (single transaction only)
• Application to simple interest (time period in complete years).


(i) Understanding shapes:
• Pairs of angles (linear, supplementary, complementary, adjacent, vertically opposite) (verification and simple proof of vertically opposite angles)
• Properties of parallel lines with transversal (alternate,corresponding, interior, exterior angles)

(ii) Properties of triangles:
• Angle sum property (with notions of proof & verification through paper folding, proofs using property of parallel lines, difference between proof and verification.)
• Exterior angle property
• Sum of two sides of a it's third side
• Pythagoras Theorem (Verification only)

(iii) Symmetry
• Recalling reflection symmetry
• Idea of rotational symmetry, observations of rotational symmetry of 2-D objects. (90 degree, 120 degree, 180 degree)
• Operation of rotation through 90 degree and 180 degree of simple figures.
• Examples of figures with both rotation and reflection symmetry (both operations)
• Examples of figures that have reflection and rotation symmetry and vice-versa

(iv) Representing 3-D in 2-D:
• Drawing 3-D figures in 2-D showing hidden faces.
• Identification and counting of vertices, edges, faces, nets (for cubes cuboids, and cylinders, cones).
• Matching pictures with objects (Identifying names)
• Mapping the space around approximately through visual estimation.

(v) Congruence
• Congruence through superposition (examples- blades, stamps, etc.)
• Extend congruence to simple geometrical shapes e.g. triangles, circles.
• Criteria of congruence (by verification) SSS, SAS, ASA, RHS

(vi) Construction (Using scale, protractor, compass)
• Construction of a line parallel to a given line from a point outside it.(Simple proof as remark with the reasoning of alternate angles)
• Construction of simple triangles. Like given three sides, given a side and two angles on it, given two sides and the angle between them.


• Revision of perimeter, Idea of , Circumference of Circle Area Concept of measurement using a basic unit area of a square, rectangle, triangle, parallelogram and circle, area between two rectangles and two concentric circles.

Data handling

(i) Collection and organisation of data – choosing the data to collect for a hypothesis testing.
(ii) Mean, median and mode of ungrouped data – understanding what they represent.
(iii) Constructing bargraphs
(iv) Feel of probability using data through experiments. Notion of chance in events like tossing coins, dice etc. Tabulating and counting occurrences of 1 through 6 in a number of throws. Comparing the observation with that for a coin.Observing strings of throws, notion of randomness.


Class VIII CBSE Syllabus

Class VIII Maths Syllabus

Class VIII Science Syllabus

1. Food

Crop production
Crop production: Soil preparation, selection of seeds, sowing, applying fertilizers, irrigation, weeding, harvesting and storage; nitrogen fixation, nitrogen cycle.

Micro organisms – useful and harmful.

2. Materials

Materials in daily life
Synthetic clothing materials. Other synthetic materials, especially plastics; usefulness of plastics and problems associated with their excessive use.There are a variety of fibrous materials in use. A material is chosen based on desired property.

Different kinds of materials and their reactions
Metals and non-metals.

How things change/ react with one another
Combustion, flame All fuels release heat on burning. Fuels differ in efficiency, cost etc. Natural resources are limited. Burning of fuels leads to harmful by products.

3. The World of the Living

Why conserve
Conservation of biodiversity/wild life/ plants; zoos, sanctuaries, forest reserves etc. flora, fauna endangered species, red data book; endemic species, migration.

The cell
Cell structure, plant and animal cells, use of stain to observe, cell organelles – nucleus, vacuole, chloroplast, cell membrane, cell wall.

How babies are formed
Sexual reproduction and endocrine system in animals, secondary sexual characters, reproductive health; internal and external fertilisation.

4. Moving Things, People and Ideas

Idea of force
Idea of force-push or pull; change in speed, direction of moving objects and shape of objects by applying force; contact and non-contact forces.

Friction – factors affecting friction, sliding and rolling friction, moving; advantages and disadvantages of friction for the movement of automobiles, airplanes and boats/ships; increasing and reducing friction.

Idea of pressure; pressure exerted by air/liquid; atmospheric pressure.

Various types of sound; sources of sound; vibration as a cause of sound; frequency; medium for propagation of sound; idea of noise as unpleasant and unwanted sound and need to minimise noise.

5. How Things Work

Electric current and circuits
Water conducts electricity depending on presence/ absence of salt in it. Other liquids may or may not conduct electricity.
Chemical effects of current. Basic idea of electroplating.

6. Natural Phenomena

Rain, thunder and lightning
Clouds carry electric charge. Positive and negative charges, attraction and repulsion. Principle of lightning conductor.

Laws of reflection. Characteristics of image formed with a plane mirror. Regular and diffused reflection. Reflection of light from an object to the eye. Multiple reflection. Dispersion of light. Structure of the eye. Lens becomes opaque, light not reaching the eye. Visually challenged use other senses to make sense of the world around. Alternative technology available. Role of nutrition in relation to blindness

Night sky
Idea about heavenly bodies/celestial objects and their classification – moon, planets, stars, constellations. Motion of celestial objects in space; the solar system.

Phenomena related to earthquakes.

7. Natural Resources

Man’s intervention in phenomena of nature
Consequences of deforestation: scarcity of products for humans and other living beings, change in physical properties of soil, reduced rainfall. Reforestation; recycling of paper. Formation of coal and petroleum in nature. (fossil fuels). Consequences of over extraction of coal and petroleum.

Pollution of air and water
Water and air are increasingly getting polluted and therefore become scarce for use. Biological and chemical contamination of water; effect of impure water on soil and living beings; effect of soil containing excess of fertilisers and insecticides on water resources. Potable water.


Class VIII Maths Syllabus

Number System

(i) Rational Numbers:
Properties of rational numbers.(including identities). Usinggeneral form of expression to describe properties
Consolidation of operations on rational numbers.
Representation of rational numbers on the number line
Between any two rational numbers there lies another rational number (Making children see that if we take two rational numbers then unlike for whole numbers, in this case you can keep finding more and more numbers that lie between them.)
Word problem (higher logic, two operations, including ideas like area)

(ii) Powers
Integers as exponents.
Laws of exponents with integral powers

(iii) Squares, Square roots, Cubes, Cube roots.
Square and Square roots
Square roots using factor method and division method for numbers containing (a) no more than total 4 digits and (b) no more than 2 decimal places
Cubes and cubes roots (only factor method for numbers containing at most 3 digits)
Estimating square roots and cube roots. Learning the process of moving nearer to the required number.

(iv) Playing with numbers
Writing and understanding a² and 3 digit number in generalized form (100a + 10b + c , where a, b, c can be only digit 0-9) and engaging with various puzzles concerning this. (Like finding the missing numerals represented by alphabets in sums involving any of the four operations.)
Number puzzles and games
Deducing the divisibility test rules of 2, 3, 5, 9, 10 for a two or three-digit number expressed in the general form.


(i) Algebraic Expressions
Multiplication and division of algebraic exp.(Coefficient should be integers)
Some common errors (e.g. 2 + x is not equal to 2x, 7x + y is not equal to 7xy )
Identities (a ± b)² = a² ± 2ab + b², a² - b² = (a - b) (a + b) Factorisation (simple cases only) as examples the following types a(x + y), (x ± y)², a² - b², (x + a).(x + b)
Solving linear equations in one variable in contextual problems involving multiplication and division (word problems) (avoid complex coefficient in the equations)

Ratio and Proportion

Slightly advanced problems involving applications on percentages, profit; loss, overhead expenses, Discount,tax.
Difference between simple and compound interest (compounded yearly up to 3 years or half-yearly up to 3 steps only), Arriving at the formula for compound interest through patterns and using it for simple problems.
Direct variation – Simple and direct word problems
Inverse variation – Simple and direct word problems
Time; work problems– Simple and direct word problems


(i) Understanding shapes:
Properties of quadrilaterals – Sum of angles of a quadrilateral is equal to 360 degrees (By verification)
Properties of parallelogram (By verification)

* Opposite sides of a parallelogram are equal,
* Opposite angles of a parallelogram are equal,
* Diagonals of a parallelogram bisect each other. [Why (iv), (v) and (vi) follow from (ii)]
* Diagonals of a rectangle areequal and bisect each other.
* Diagonals of a rhombus bisect each other at right angles.
* Diagonals of a square are equal and bisect each other at right angles.

(ii) Representing 3-D in 2-D
Identify and Match pictures with objects [more complicated e.g. nested, joint 2-D and 3-D shapes (not more than 2)].
Drawing 2-D representation of 3-D objects (Continued and extended)
Counting vertices, edges; faces ; verifying Euler’s relation for 3-D figures with flat faces (cubes, cuboids, tetrahedrons, prisms and pyramids)

(iii) Construction:

Construction of Quadrilaterals:
- Given four sides and one diagonal
- Three sides and two diagonals
- Three sides and two included angles
- Two adjacent sides and three angles


Area of a trapezium and a polygon.
Concept of volume, measurement of volume using a basic unit, volume of a cube, cuboid and cylinder
Volume and capacity (measurement of capacity)
Surface area of a cube, cuboid, cylinder.

Data handling

Reading bar-graphs, ungrouped data, arranging it into groups, representation of grouped data through bar-graphs, constructing and interpreting bar-graphs.
Simple Pie charts with reasonable data numbers
Consolidating and generalising the notion of chance in events like tossing coins, dice etc. Relating it to chance in life events. Visual representation of frequency outcomes of repeated throws of the same kind of coins or dice. Throwing a large number of identical dice/coins together and aggregating the result of the throws to get large number of individual events. Observing the aggregating numbers over a large number of repeated events. Comparing with the data for a coin. Observing strings of throws, notion of randomness

Introduction to graphs

Axes (Same units), Cartesian Plane
Plotting points for different kind of situations (perimeter vs length for squares, area as a function of side of a square, plotting of multiples of different numbers, simple interest vs number of years etc.)
Reading off from the graphs
- Reading of linear graphs
- Reading of distance vs time graph


Class IX CBSE Syllabus

Class IX Maths Syllabus

Class IX Science Syllabus


Theme : Food

UNIT I : FOOD (10) Periods

Plant and animal breeding and selection for quality improvement and management ; use of fertilizers, manures; protection from pests and diseases; organic farming.

Theme : Materials


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 suspensions.
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 compounds.
Structure of atom : Electrons, protons and neutrons; Isotopes and isobars.

Theme : The World of the living


BiologicalDiversity : 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 plants).
Health and diseases : Health and its failure. Disease and its causes. Diseases caused by microbes and their prevention - Typhoid, diarrhoea, malaria, hepatitis, rabies, AIDS, TB, polio; pulse polio programme.
Transport of materials in the living systems : Diffusion / exchange of substances between cells and their environment and between the cells themselves in the living system; role in nutrition, water and food transport, excretion, gaseous exchange.

Theme : Moving things, people and ideas


Motion: 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 of energy.
Floatation: Thrust and pressure. Archimedes' principle, buoyancy, elementary idea of relative density.
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


Physical resources : Air, Water, Soil. Air for respiration, for combustion, for moderating temperatures, movements of air and its role in bringing rains across India.
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

Class IX Maths Syllabus


Class IX Maths Syllabus


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 non-recurring / non terminating decimals such as v2, v3, v5 etc. Existence of non-rational numbers (irrational numbers) such as v2, v3 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 vx 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. 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, a1 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.

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 simultaneously.


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.


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 180 degrees and the converse.
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 180 degrees.
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.

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 conversely.
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 converse

7. CONSTRUCTIONS (10) Periods
1. Construction of bisectors of line segments & angles, 60 degree, 90 degree, 45 degree angles etc., equilateral triangles.
2. Construction of a trangle 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.


1. AREAS (4) Periods
Area of a triangle using Heros formula(without proof) and its application in finding the area of a quadrilateral

Surface areas and volumes of cubes, cuboids, spheres)including hemispheres) and right circular and right circular cylinders/cones.


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 developed to group and to individual activities to motivate the concept; the experiment to be drawn from real - life situations, and from example used in the chapter on statistics).


Evaluation of activities 10 Marks
Project Work 05 Marks
Continuous Evaluation 05 Marks

Class X CBSE Syllabus

Class X Maths Syllabus

Class X Science Syllabus


Theme : Materials


Acids,bases and salts : General properties, examples and uses.
Chemical reactions : Types of chemical reactions : combination, decomposition, displacement, double displacement, precipitation, neutralization, oxidation and reduction in terms of gain and loss of oxygen and hydrogen.
Metals and non metals : Brief discussion of basic metallurgical processes. Properties of common metals. Elementary idea about bonding.
Carbon Compounds : Carbon compounds, elementary idea about bonding. Saturated hydrocarbons, alcohols, carboxylic acids (no preparation, only properties).
Some Important chemical compounds : Soap-cleansing action of soap.
Periodic classification of elements : Gradations in properties : Mendeleev periodic table.

Theme : The world of the living


Our environment : Environmental problems, their solutions. Biodegradable, non biodegradable, ozone depletion.
Life Processes : "living" things; Basic concept of nutrition, respiration, transport and excretion in plants and animals.
Control and Co-ordination in plants and animals : Tropic movements in plants; Introduction to plant hormones; control and co-ordination in animals : voluntary, involuntary and reflex action, nervous system; chemical co-ordination : animal hormones.
Reproduction: Reproduction in plants and animals. Need for and methods of family planning. Safe sex vs HIV/AIDS. Child bearing and women's health.
Heridity and evolution : Heridity; Origin of life : brief introduction; Basic concepts of evolution.

Theme : How things work.


Potential, Potential difference, Ohm's law; Series combination of resistors, parallel combination of resistors; Power dissipation due to current; Inter relation between P, V, I and R.
Magnets: Magnetic field, field lines, field due to a current carrying wire, field due to current carrying coil or solenoid; Force on current carrying conductor, Fleming's left hand rule. Electro magnetic induction. Induced potential difference, Induced current. Direct current. Alternating current; frequency of AC. Advantage of AC over DC. Domestic electric circuits.

Theme : Natural Phenomena

UNIT 4 :LIGHT (20) Periods

Convergence and divergence of light. Images formed by a concave mirror; related concepts; centre of curvature; principal axis. Optic centre, focus, focal length. Refraction; laws of refraction. Image formed by a convex lens; functioning of a lens in human eye; problems of vision and remedies. Applications of spherical mirrors and lenses. Appreciations of concept of refraction; velocity of light; refractive index; twinkling of stars; dispersion of light. Scattering of light.

Theme : Natural Resources


Conservation of natural resources : Management of natural resources. Conservation and judicious use of natural resources. Forest and wild life, coal and petroleum conservation. People's participation. Chipko movement. Legal perspectives in conservation and international scenario. The Regional environment : Big dams : advantages and limitations; alternatives if any. Water harvesting. Sustainability of natural resources. Sources of energy : Different forms of energy, leading to different sources for human use : fossil fuels, solar energy; biogas; wind, water and tidal energy; nuclear energy. Renewable versus non - renewable sources.

Class X Maths Syllabus



1. REAL NUMBERS (15) Periods

Euclid's division lemma, Fundamental Theorem of Arithmetic - statements after reviewing work done earlier and after illustrating and motivating through examples, Proofs of results - irrationality of root 2, root 3, root 5, decimal expansions of rational numbers in terms of terminating/non-terminating recurring decimals.


1. POLYNOMIALS (6) Periods

Zeros of a polynomial. Relationship between zeros and coefficients of a polynomial with particular reference to quadratic polynomials. Statement and simple problems on division algorithm for polynomials with real coefficients.


Pair of linear equations in two variables. Geometric representation of different possibilities of solutions inconsistency. Algebraic conditions for number of solutions. Solution of pair of linear equations in two variables algebraically- by substitution, by elimination and by cross multiplication. Simple situational problems must be included.
Simple problems on equations reducible to linear equations may be included.


Standard form of a quadratic equation ax² + bx + c = 0, (a1 0). Solution of the quadratic equations (only real roots) by factorization and by completing the square, i.e. by using quadratic formula. Relationship between discriminant and nature of roots.
Problems related today to day activities to be incorporated.


Motivation for studying AP. Derivation of standard results of finding the nth term and sum of first n terms.



Trigonometric ratios of an acute angle of a right-angled triangle. Proof of their existence (well defined); motivate the ratios, whichever are defined at 0 degree & 90 degree. Values (with proofs) of the trigonometric ratios of 30 degree, 45 degree & 60 degree. Relationships between the ratios.


Proof and applications of the identity sin² A + cos² A = 1. Only simple identities to be given. Trigonometric ratios of complementary angles.

3. HEIGHTS AND DISTANCES (8) Periods Simple and believable problems on heights and distances. Problems should not involve more than two right triangles. Angles of elevation / depression should be only 30 degree, 45 degree, 60 degree.


1. LINES (In two-dimensions) (15) Periods

Review the concepts of coordinate geometry done earlier including graphs of linear equations. Awareness of geometrical representation of quadratic polynomials. Distance between two points and section formula (internal). Area of a triangle.


1. TRIANGLES (15) Periods

Definitions, examples, counter examples of similar triangles.

1. (Prove) If a line is drawn parallel to one side of a triangle to intersect the other two sides in distinct points, the other two sides are divided in the same ratio.
2. (Motivate) If a line divides two sides of a triangle in the same ratio, the line is parallel to the third side.
3. (Motivate) If in two triangles, the corresponding angles are equal, their corresponding sides are proportional and the triangles are similar.
4. (Motivate) If the corresponding sides of two triangles are proportional, their corresponding angles are equal and the two triangles are similar.
5. (Motivate) If one angle of a triangle is equal to one angle of another triangle and the sides including these angles are proportional, the two triangles are similar.
6. (Motivate) If a perpendicular is drawn from the vertex of the right angle of a right triangle to the hypotenuse, the triangles on each side of the perpendicular are similar to the whole triangle and to each other.
7. (Prove) The ratio of the areas of two similar triangles is equal to the ratio of the squares on their corresponding sides.
8. (Prove) In a right triangle, the square on the hypotenuse is equal to the sum of the squares on the other two sides.
9. (Prove) In a triangle, if the square on one side is equal to sum of the squares on the other two sides, the angles opposite to the first side is a right traingle.

2. CIRCLES (8) Periods

Tangents to a circle motivated by chords drawn from points coming closer and closer and closer to the point.
1. (Prove) The tangent at any point of a circle is perpendicular to the radius through the point of contact.
2. (Prove) The lengths of tangents drawn from an external point to circle are equal.

3. CONSTRUCTIONS (8) Periods

1. Division of a line segment in a given ratio (internally)
2. Tangent to a circle from a point outside it.
3. Construction of a triangle similar to a given triangle.



Motivate the area of a circle; area of sectors and segments of a circle. Problems based on areas and perimeter / circumference of the above said plane figures. (In calculating area of segment of a circle, problems should be restricted to central angle of 60 degree, 90 degree & 120 degrees only. Plane figures involving triangles, simple quadrilaterals and circle should be taken.)


(i) Problem on finding surface areas and volumes of combinations of any two of the following: cubes, cuboids, spheres, hemispheres and right circular cylinder/cones. Frustum of a cone.
(ii) Problems involving converting one type of metallic solid into another and other mixed problem.(Problems with combination of not more than two different solids be taken.)


1. STATISTICS (15) Periods

Mean, median and mode of grouped data(bimodal situation to be avoided). Cumulative frequency graph.

2. PROBABILITY (10) Periods

Classical definition of probability. Connection with probability as given in class IX. Simple problem on single events, not using set notation.

Evaluation of activities 10 Marks
Project Work 05 Marks
Continuous Evaluation 05 Marks
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