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Real numbers Euclid’s division lemma, Fundamental Theorem of Arithmetic - Proofs of results - irrationality of √2, √3, √5, decimal expansions of rational numbers in terms of terminating/non-terminating recurring decimals.
Polynomials Zeros of a polynomial. Relationship between zeros and coefficients of quadratic polynomials. Statement and simple problems on division algorithm for polynomials with real coefficients.
Pair of linear equations in two variables Pair of linear equations in two variables and their graphical solution. Geometric representation of different possibilities of solutions/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.
Triangles Definitions, examples, counter examples of similar triangles.
Introduction to trigonometry Trigonometric ratios of an acute angle of a right-angled triangle. Proof of their existence motivate the ratios whichever are defined at 0° and 90°. Values (with proofs) of the trigonometric ratios of 30°, 45° and 60°.
Statistics Mean, median and mode of grouped data (bimodal situation to be avoided). Cumulative frequency graph.
Quadratic equations Standard form of a quadratic equation ax2 + bx + c = 0, (a ≠ 0). Solution of the 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.
Arithmetic Progressions Derivation of the nth term and sum of the first n terms of A.P. and their application in solving problems.
Circles Tangents to a circle by chords drawn from points.
Trigonometrical Identities: Relationships between the ratios. Proof and applications of the identity sin2A + cos2A = 1. Trigonometric ratios of complementary angles.
Heights and distances: Problems on heights and distances. Angles of elevation / depression.
Probability: Classical definition of probability, problems on single events.
Lines Concepts of coordinate geometry, graphs of linear equations. Distance formula. Section formula (internal division). Area of a triangle.
Areas related to circles: Area of a circle; area of sectors and segments of a circle. Problems based on areas and perimeter / circumference of the plane figures. (Plane figures involving triangles, simple quadrilaterals and circle.)
Surface areas and volumes (i) Problems on finding surface areas and volumes of combinations of the following: cubes, cuboids, spheres, hemispheres and right circular cylinders/cones. Frustum of a cone.
(ii) Problems involving converting one type of metallic solid into another and other mixed problems.
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 of light through a prism, Dispersion of light, scattering of light, applications in daily life.
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. 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. Electromagnetic induction. Induced potential difference, Induced current. Fleming’s Right Hand Rule, Direct current. Alternating current: frequency of AC. Advantage of AC over DC. Domestic electric circuits.
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.
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 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 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, Modern periodic table, gradation in properties, valency, atomic number, metallic and non-metallic properties.
Life processes: "Living being", Basic concept of nutrition, respiration, transport and excretion in plants and animals. Tropic movements in plants, Introduction to plant hormones, control and co-ordination in animals: nervous system; voluntary, involuntary and reflex action, chemical co-ordination: animal hormones.
Reproduction: Reproduction in animal and plants (asexual and sexual) reproductive health-need for 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.
Conservation of natural resources: 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.
The Regional environment and our environment: Big dams: advantages and limitations; alternatives if any, Water harvesting. Sustainability of natural resources. Eco-system, Environmental problems, Ozone depletion, waste production and their solutions. Biodegradable and non-biodegradable substances.
Parts of speech- nouns, pronouns, verbs adjectives, adverb, prepositions conjunctions, articles and interjections.
Tenses- present, past, future, Modal verbs, Determiners and quantifiers.
Vocabulary- antonyms, synonyms, confused words, phrasal verbs.
Sentence correction Sentence completion, Active passive voice, Direct speech.
Clauses- noun clause, adverb clause, relative clause.
Subject-Verb agreement.
Conditionals- zero, first, second and third Short unseen passages with MCQs, Spellings, Idioms and proverbs
Numbers, Percentage, Profit, Loss & Discount, Ratio & Proportion, Simple & Compound Interest, Permutation& Combination & Probability, Time & Distance, Boats & streams, Races & Games, Time & Work, Pipes & Cistern, Calendar & Clocks, Area, Series completion & Coding – Decoding & Alphabet test, Direction sense test & Blood relations &arrangements, Syllogism, Number, Ranking & Time sequence test, Arithmetical reasoning, Inserting the missing character, Data sufficiency, Cubes and dice, Non-verbal reasoning.
Current Affairs, Social Science, Sports, science and Information Technology
Current Affairs: Sports, Economy, International, Science & Technology, Politics and Fashion
Social Science : Democratic Politics, Contemporary India, India and the Contemporary World and Economics:
Sports: Cricket, Football, Tennis and Olympic
Science: World of Living, Chemical Substances-Nature and Behaviour, Natural Phenomena, Effects of Current and Natural Resources.
Information & Technology: Basics of Information Technology, Office Tools
