Class 10

■ NUMBER SYSTEMS

■ ALGEBRA

■ COORDINATE GEOMETRY

UNIT 1: NUMBER SYSTEMS

Real Numbers:

■ GEOMETRY

Fundamental Theorem of Arithmetic - statements after reviewing work done earlier and after illustrating and motivating through examples, Proofs of irrationality of √2, √3, √5.

■ MENSURATION

■ Trigonometry

■ STATISTICS & PROBABILITY

UNIT 2: ALGEBRA

Polynomials:

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

Pair Of Linear Equations In Two Variables:

1. Pair of linear equations in two variables and graphical method of their solution, consistency/inconsistency.

2. Algebraic conditions for number of solutions. Solution of a pair of linear equations in two variables algebraically - by substitution, by elimination. Simple situational problems.

Quadratic Equations:

1. Standard form of a quadratic equation ax2 + bx + c = 0, (a ≠ 0). Solutions of quadratic equations (only real roots) by factorization, and by using quadratic formula.

2. Relationship between discriminant and nature of roots. Situational problems based on quadratic equations related to day to day activities to be incorporated.

Arithmetic Progressions:

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 3: COORDINATE GEOMETRY

Coordinate Geometry:

Review: Concepts of coordinate geometry, graphs of linear equations. Distance formula. Section formula (internal division).

UNIT 4: GEOMETRY

Triangles :

1. Definitions, examples, counter examples of similar triangles.

2. (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.

3. (Motivate) If a line divides two sides of a triangle in the same ratio, the line is parallel to the third side.

4. (Motivate) If in two triangles, the corresponding angles are equal, their corresponding sides are proportional and the triangles are similar.

5. (Motivate) If the corresponding sides of two triangles are proportional, their corresponding angles are equal and the two triangles are similar.

6.(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.

Circles:

1. Tangent to a circle at, point of contact

2. (Prove) The tangent at any point of a circle is perpendicular to the radius through the point of contact.

3. (Prove) The lengths of tangents drawn from an external point to a circle are equal.

UNIT 5: TRIGONOMETRY

Introduction To Trigonometry:

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 of the trigonometric ratios of 300 , 450 and 600. Relationships between the ratios.

Trigonometry Identities:

Proof and applications of the identity sin2A + cos2A = 1. Only simple identities to be given.

HEIGHTS AND DISTANCES: Angle of elevation, Angle of Depression:

Simple problems on heights and distances. Problems should not involve more than two right triangles. Angles of elevation / depression should be only 30°, 45°, and 60°.

UNIT 6: MENSURATION

Areas Related To Circles:

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.

Surface Areas And Volumes:

Surface areas and volumes of combinations of any two of the following: cubes, cuboids, spheres, hemispheres and right circular cylinders/cones.

UNIT 7: STATISTICS AND PROBABILITY

Statistics:

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

Probability:

Classical definition of probability. Simple problems on finding the probability of an event

Advanced Vocabulary:

- Synonyms, antonyms, and idioms

- Academic and technical terms

- Word roots and prefixes

Grammar Refinement:

- Complex sentence structures

- Active and passive voice

- Conditional sentences

Effective Communication:

- Debate and public speaking skills

- Expressing opinions and arguments

- Negotiation and persuasion techniques

Reading and Analysis:

Writing Proficiency:

- Essay writing with clear organization and coherence

- Research skills and citation methods

Cultural & Contextual Understanding:

- Analyzing literature and non-fiction texts

- Interpreting figurative language and symbolism

- Exposure to different cultures and traditions

- Reading and discussing diverse perspectives

■ Chemical Substances-Nature and Behavior

■ World of Living

Unit 1: Chemical Substances - Nature and Behavior

Chemical Reactions:

Chemical equation, Balanced chemical equation, implications of a balanced chemical equation, types of chemical reactions: combination, decomposition, displacement, double displacement, precipitation, endothermic exothermic reactions, oxidation and reduction.

■ Natural Phenomena

■ Effects of Current

■ Natural Resources

Acids, bases and salts:

Their definitions in terms of furnishing of H+ and OH– ions, General properties, examples and uses, neutralization, 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 non-metals:

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 hydro carbons 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.

Unit 2: 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: (topics excluded - evolution; evolution and classification and evolution should not be equated with progress).

Unit 3: 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.

Human eye:

Functioning of a lens in human eye, defects of vision and their corrections, applications of spherical mirrors and lenses.

Refraction of light through a prism, dispersion of light, scattering of light, applications in dailylife (excluding colour of the sun at sunrise and sunset).

Unit 4: Effects of Current

Electricity:

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, Direct current. Alternating current: frequency of AC. Advantage of AC over DC. Domestic electric circuits.

Unit 5: Natural Resources

Our environment:

Eco-system, Environmental problems, Ozone depletion, waste production and their solutions. Biodegradable and non-biodegradable substances.

Advanced concepts of programming using a text-based programming language like Python or Java.

Advanced features of Microsoft Word, PowerPoint, and Excel.

Understanding computer memory, storage, and file management.

Introduction to databases and data management.

Introduction to HTML and website development.

Introduction to cybersecurity and ethical hacking.

Introduction to computer hardware and troubleshooting.

India in the 20th century: Nationalist movements, Indian National Congress, and the role of leaders like Mahatma Gandhi.

Indian freedom struggle: Non-cooperation movement, civil disobedience movement, Quit India movement, and Partition of India.

Post-independence India: Formation of the Indian Constitution, socio-economic development, and major challenges faced by the country.

World history: Major events and movements, such as the French Revolution, Industrial Revolution, World Wars, and the Cold War.

Contemporary world events and their impact on India.