**CBSE syllabus for class 10 – Maths and Science** – This course curriculum or syllabus for the class 10th standard for the secondary school certificate examination that students have to study for the fresh exam as well as improvement / compartment exams.

## CBSE syllabus for class 10 – Maths and Science

### Breakup of marks for class 9 mathematics

### Breakup of marks for class 10 mathematics

## CBSE MATHS SYLLABUS FOR CLASS 10

UNIT I: NUMBER SYSTEMS

1. REAL NUMBER (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

irrationality of ? ? ? Decimal representation of rational numbers in terms of

terminating/non-terminating recurring decimals.

UNIT II: ALGEBRA

1. POLYNOMIALS (7) Periods

Zeros of a polynomial. Relationship between zeros and coefficients of quadratic

polynomials. Statement and simple problems on division algorithm for polynomials with

real coefficients.

2. PAIR OF LINEAR EQUATIONS IN TWO VARIABLES (15) Periods

Pair of linear equations in two variables and graphical method of their

solution, consistency/inconsistency.

Algebraic conditions for number of solutions. Solution of a pair of linear equations in two

variables algebraically – by substitution, by elimination and by cross multiplication

method. Simple situational problems. Simple problems on equations reducible to linear

equations.

3. QUADRATIC EQUATIONS (15) Periods

Standard form of a quadratic equation ax2

+ bx + c = 0, (a ? 0). Solutions of quadratic

equations (only real roots) by factorization, by completing the square and by using quadratic

formula. Relationship between discriminant and nature of roots.

Situational problems based on quadratic equations related to day to day activities to be

incorporated.

4. ARITHMETIC PROGRESSIONS (8) Periods

Motivation for studying Arithmetic Progression Derivation of the nth term and sum of the

first n terms of A.P. and their application in solving daily life problems.

UNIT III: COORDINATE GEOMETRY

1. LINES (In two-dimensions) (14) Periods

Review: Concepts of coordinate geometry, graphs of linear equations. Distance formula.

Section formula (internal division). Area of a triangle.

UNIT IV: GEOMETRY

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 of

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 angle.

2. CIRCLES (8) Periods

Tangent to a circle at, point of contact

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 a circle are equal.

3. CONSTRUCTIONS (8) Periods

1. Division of a line segment in a given ratio (internally).

2. Tangents to a circle from a point outside it.

3. Construction of a triangle similar to a given triangle.

UNIT V: TRIGONOMETRY

1. INTRODUCTION TO TRIGONOMETRY (10) Periods

Trigonometric ratios of an acute angle of a right-angled triangle. Proof of their existence

(well defined); motivate the ratios whichever are defined at 0o and 90o. Values (with

proofs) of the trigonometric ratios of 300

, 450

and 600

. Relationships between the ratios.

2. TRIGONOMETRIC IDENTITIES (15) Periods

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: Angle of elevation, Angle of Depression. (8) Periods

Simple problems on heights and distances. Problems should not involve more than two

right triangles. Angles of elevation / depression should be only 30°, 45°, 60°.

UNIT VI: MENSURATION

1. AREAS RELATED TO CIRCLES (12) Periods

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°, 90° and 120°

only. Plane figures involving triangles, simple quadrilaterals and circle should be taken.)

2. SURFACE AREAS AND VOLUMES (12) Periods

1. Surface areas and volumes of combinations of any two of the following: cubes, cuboids,

spheres, hemispheres and right circular cylinders/cones. Frustum of a cone.

2. Problems involving converting one type of metallic solid into another and other mixed

problems. (Problems with combination of not more than two different solids be taken).

UNIT VII: STATISTICS AND PROBABILITY

1. STATISTICS (18) Periods

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

Cumulative frequency graph.

2. PROBABILITY (10) Periods

Classical definition of probability. Simple problems on single events (not using set

notation).

## CBSE SCIENCE SYLLABUS FOR CLASS 10

Theme: Materials (55 Periods)

Unit I: Chemical Substances – Nature and Behaviour

Chemical reactions: Chemical equation, Balanced chemical equation, implications of

a balanced chemical equation, types of chemical reactions: combination,

decomposition, displacement, double displacement, precipitation, neutralization,

oxidation and reduction.

Acids, bases and salts: Their definitions in terms of furnishing of H+ and OH– ions,

General properties, examples and uses, concept of pH scale (Definition relating to

logarithm not required), importance of pH in everyday life; preparation and uses of

Sodium Hydroxide, Bleaching powder, Baking soda, Washing soda and Plaster of Paris.

Metals and nonmetals: Properties of metals and non-metals; Reactivity series;

Formation and properties of ionic compounds; Basic metallurgical processes;

Corrosion and its prevention.

Carbon compounds: Covalent bonding in carbon compounds. Versatile nature of

carbon. Homologous series. Nomenclature of carbon compounds containing functional

groups (halogens, alcohol, ketones, aldehydes, alkanes and alkynes), difference

between saturated hydrocarbons and unsaturated hydrocarbons. Chemical properties of

carbon compounds (combustion, oxidation, addition and substitution reaction).

Ethanol and Ethanoic acid (only properties and uses), soaps and detergents.

Periodic classification of elements: Need for classification, Early attempts at

classification of elements (Dobereiner’s Triads, Newland’s Law of Octaves,

Mendeleev’s Periodic Table), Modern periodic table, gradation in properties, valency,

atomic number, metallic and non-metallic properties.

Theme: The World of the Living (50 Periods)

Unit II: World of Living

Life processes: ‘Living Being’. Basic concept of nutrition, respiration, transport and

excretion in plants and animals.

Control and co-ordination in animals and plants: Tropic movements in plants;

Introduction of plant hormones; Control and co-ordination in animals: Nervous

system; Voluntary, involuntary and reflex action; Chemical co-ordination: animal

hormones.

Reproduction: Reproduction in animals and plants (asexual and sexual) reproductive

health-need and methods of family planning. Safe sex vs HIV/AIDS. Child bearing and

women’s health.

Heredity and Evolution: Heredity; Mendel’s contribution- Laws for inheritance of

traits: Sex determination: brief introduction; Basic concepts of evolution.

Theme: Natural Phenomena (23 Periods)

Unit III: Natural Phenomena

Reflection of light by curved surfaces; Images formed by spherical mirrors, centre of

curvature, principal axis, principal focus, focal length, mirror formula (Derivation not

required), magnification.

Refraction; Laws of refraction, refractive index.

Refraction of light by spherical lens; Image formed by spherical lenses; Lens formula

(Derivation not required); Magnification. Power of a lens.

Functioning of a lens in human eye, defects of vision and their corrections,

applications of spherical mirrors and lenses.

Refraction oflightthrough a prism, dispersion oflight, scattering oflight, applications in

daily life.

Theme: How Things Work (32 Periods)

Unit IV: Effects of Current

Electric current, potential difference and electric current. Ohm’s law; Resistance,

Resistivity, Factors on which the resistance of a conductor depends. Series

combination of resistors, parallel combination of resistors and its applications in daily

life. Heating effect of electric current and its applications in daily life. Electric power,

Interrelation between P, V, I and R.

Magnetic effects of current : Magnetic field, field lines, field due to a current

carrying conductor, field due to current carrying coil or solenoid; Force on current

carrying conductor, Fleming’s Left Hand Rule, Electric Motor, Electromagnetic

induction. Induced potential difference, Induced current. Fleming’s Right Hand Rule,

Electric Generator, Direct current. Alternating current : frequency of AC. Advantage

of AC over DC. Domestic electric circuits.

Theme: Natural Resources (20 Periods)

Unit V: Natural Resources

Sources of energy: Different forms of energy, conventional and non-conventional

sources of energy: Fossil fuels, solar energy; biogas; wind, water and tidal energy;

Nuclear energy. Renewable versus non-renewable sources of Energy.

Our environment: Eco-system, Environmental problems, Ozone depletion, waste

production and their solutions. Biodegradable and non-biodegradable substances.

Management of natural resources: Conservation and judicious use of natural

resources. Forest and wild life; Coal and Petroleum conservation. Examples of

people’s participation for conservation of natural resources. Big dams: advantages

and limitations; alternatives, if any. Water harvesting. Sustainability of natural resources.

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