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Tag: 2023
TGT | Physical Sciences | Telangana | Syllabus
TGT | General Sciences | Telangana | Syllabus
TGT | Biological Sciences | Telangana | Syllabus
TGT | Mathematics | Telangana | Syllabus
TGT | Physical Sciences | Telangana | Syllabus
Free | Teaching & Learning | Material
CBSE 6 | Science | E-Tools
No Matter Where You Start Among Study, Assess & Interact. But Your Course Will Be Completed Successfully.
Written Examination Syllabus for the post of Trained Graduate Teacher in Residential Educational Institutions Societies.
Paper- 1 | General Studies, General Abilities, & Basic Proficiency In English
General Studies, General Abilities, & Basic Proficiency In English
Section-I: General Studies
Current Affairs – Regional, National & International.
Indian Constitution: Indian Political System; Governance and Public Policy.
Social Exclusion: Rights issues such as Gender, Caste, Tribe, Disability etc.and inclusive policies.
Society Culture, Civilization Heritage, Arts and Literature of India and Telangana.
General Science: India’s Achievements in Science and Technology
Environmental Issues: Disaster Management – Prevention and Mitigation Strategies and Sustainable Development.
Economic and Social Development of India and Telangana.
Socio-economic, Political and Cultural History of Telangana with special emphasis on Telangana Statehood Movement and formation of Telangana state.
Section-II: General AbilitiesAnalytical Abilities: Logical Reasoning and Data Interpretation.
Moral Values and Professional Ethics in Education.
Teaching Aptitude Section – III: Basic Proficiency in English
i) School Level English Grammar:
Articles; Tense; Noun & Pronouns; Adjectives; Adverbs; Verbs; Modals;
Subject-Verb Agreement; Non-Finites; reported speech; Degrees of
Comparison; Active and Passive Voice; Prepositions; Conjunctions;
Conditionals.
ii) Vocabulary:
Synonyms and Antonyms; Phrasal Verbs; Related Pair of Words; Idioms and Phrases; Proverbs.
iii) Words and Sentences :
Use of Words; Choosing Appropriate words and Words often Confused;
Sentence Arrangement, Completion, Fillers and Improvement;
Transformation of Sentences; Comprehension; Punctuation; Spelling Test; Spotting of Errors.Paper-2 | Pedgogy Of Physical Sciences
Pedgogy Of Physical Sciences
Syllabus for the post of Trained Graduate Teacher in Residential Educational Institutions Societies.
1) The Nature of Physical Sciences and its Historical Development including the contributions of important Physicists and Chemists given in the school textbooks. Importance of Physical Sciences in School Curriculum.
2) Values, Aims and Objectives of Teaching Physical Sciences.
3) Child Development; Psychology of Teaching and Learning Physical Sciences.
4) Physical Sciences Curriculum: Construction ,Organization and Development.
5) Approaches, Methods and Techniques of Teaching Physical Sciences with special reference to Measurement, units and dimensions; Natural Resources, Our Universe; Natural Phenomenon (Light; Heat; and Sound); Mechanics; Magnetism; Electricity and Electro Magnetism; Modern Physics; Electronics and Communication; Matter; Chemical Reactions; Acids and Bases; Atomic Structure; Periodic Classification of Elements; Chemical Bonding; Carbon and its Compounds; and Metallurgy; Environmental Chemistry.
6) Planning for Effective Instruction in Physical Sciences: Different Plans and Designing Learning Experiences.
7) Learning Resources and Designing Instructional Material in Physical Sciences; Physical Science Labs; Teaching Aids ; Textbooks; ICT in Physical Sciences.
8) Measurement and Evaluation in Physical Sciences; Continuous and Comprehensive Evaluation (CCE); Tools and Techniques of Evaluation; chievement and Diagnostic
Tests.9) Learning Disabilities/Difficulties and Education of Exceptional/ Disabled Children in Physical Sciences.
10) Physical Sciences and Everyday Life; Non-formal Physical Sciences Education.
Paper-3 | Physics Subject Contents
Subject Contents – Physics
I. Measurements, Units and Dimensions: Need of measurement in daily life. Systems of units. Units and dimentions, Significance of accuracy in measurement. Measuring instruments; Types of errors in measurements – mean absolute relative percentage errors; Fundamental and derived physical quantities. Rules for writing units in SI, derived units SI, Multiples and submultiples of SI units; Dimensional formulae and dimensional equations, dimensionless quantities; principle of homogeneity of dimensions. Application of dimensional analysis.
II. Natural Resources – Air and Water: Composition of air, atmospheric pressure, the consequences of air pollution, ways to reduce air pollution. Winds, cyclones, natural calamities and management of their bad consequences, Composition of water, water cycle, change of phase, Latent Heat. Forms of water in atmosphere, boiling, melting, water pollution and hardness of water. How to handle the shortage of drinking water? Methods of increasing ground water levels.
III. Our Universe: Need to develop the Habit of Night sky observation, How to differentiate constellations with zodiac signs, study of solar system, different laws pertaining to the motion of celestial bodies and ways of measuring the distances in space. Principles of launching of satellites and their applications in day to day life.
IV Natural Phenomenon:
i. Light: Nature of light, Theories of light, Fermat principle, Reflection – its laws. Image formation in plane and spherical mirrors.Rules for Ray diagrams and Formula for spherical
mirrors – focal length and sign convention.Application of mirrors. Properties of Light and Laws; Electro Magnetic spectra.
ii. Heat: Heat as energy- sources of heat, Transmission of heat, Expansion of solids, liquids and gases. Temperature (based on thermal equilibrium), Different Scales of Temperaturemeasurement Different type of Thermometers and their construction. Calorimetry, Applications of Specific heat, Latent heat. Anomalous expansion of water and it significance in nature. Combustion, Calorific value, specific heat of gases.
iii. Sound: Sources of sound. Noise and music. Musical instruments. Propagation of sound. Velocity of sound in different media / substances. Characteristics of sound. Structure of human ear – in Auditory aspect. Reflection of sound, echo, Resonance, Sonar and Doppler effect. Simple Harmonic Motion.V. Mechanics: Application of Simple Machines in daily life situations. Scalars and Vectors. Free Body Diagram. All types of motion. Different types of Forces. Different types of frictions and effects of friction. Newton’s laws of motion. Momentum. Equations of motion (under gravity and freely falling), projectile. Range. Laws of Floatation. Different laws of fluids. Different types of Energies. Conservation of energy, Work and Power. Work energy theorem. Center of mass. Centre of gravity for regular and irregular objects. Stability and
Equilibrium. Universal law of Gravitation. Relation between ‘g’ and ‘G’.Circular motion, Frame of reference, Kepler’s Laws. Elasticity and Hooke’s LawVI. Magnetism: Types of Magnets, Identification of Magnetic and Non-magnetic substances, magnetic field, Uniform and non uniform magnetic fields. Magnetic induction. Magnetic lines of force. Terrestrial magnetism–Terrestrial magnetic field. Geo magnetism. Uses of Magnetism; Dip, Declination Magnetic pole strength, Magnetic moment. Inverse square law of magnetism. Magnetic properties of materials and their classification. Domine theory.
VII. Electricity & Electro Magnetism:
Electric charge, field, electric intensity, electric potential, potential difference. Simple Electric Circuits and precautionary measures. House hold circuits. Conductors, Non conductors / Insulators, Coulomb’s inverse square law. Primary and secondary Cells. Ohm’s Law – its limitations.Resistances in series and parallel, Emf of a circuit; Specific resistance.Kirchhoff’s laws. Relation between electric potential and Electric energy, electric Power (wattage), House hold and Industrial power saving. Heating effect of electric current, and Joule’s law. Lighting and Working of lightning conductor, Prevention and control of damage due to lightning. Earthing in electrical appliances. Magnetic field due to currents carrying wire, Ampere’s law, circular loop and Solenoid. Magnetic force on moving charged particle and long straight conductors.Fleming’s left hand rule, Electric motor. Electromagnetic induction – Faraday’s law Electromagnetic flux. Lentz law, Generators and Alternating Currents. Inductance – self, mutual inductance and principles of transformer.VIII. Modern Physics: Discharge of Electricity through gases, Discharge tube phenomena, Cathode rays, Properties of Cathode rays, Anode rays and their properties; X-rays; Atomic models: JJ Thomson, Rutherford and Bohr’s models. Atomic nucleus and its structure. Atomic models: Mass defect; Radio Activity- Discovery, properties of alpha, beta, and gamma radiations. Applications of alpha, beta, and gamma radiations, Radioactive transformations, alpha, beta decays, Half life period, Isotopes, Isobars, and Isotones. Radioactive transmutation-artificial radioactivity; radio isotopes and their uses in different fields; radioactive series; Chain and controlled nuclear reactions; Fission and fusion of nuclei – atomic bomb and hydrogen bomb.
IX. Electronics and Communications: Semi conductors – intrinsic and extrinsic; band theory; diode, p-n junction characteristics. Transistor – pnp & npn characteristics and uses. Ziner Diode characteristics. Simple electronic circuits, Logic gates – applications. Importance of ICT Block diagram of
computer and its parts Input devices, process and output devices, applications of computers Communication: components of Communication. Basic terminology used in electronic communication system. Band width of transmission medium, propagation, modulation and demodulation.Paper-3 | Chemistry Subject Contents
Chemistry Subject Contents
X. Matter: States of matter.Elements, Compounds and Mixtures. Methods of separation of mixtures.Chromatography. Behavior of gases; measurable properties of gases; gas laws. Mole concept. Dolton, Avogadro, Berzelius laws.
XI. Chemical Reactions: Physical and chemical changes. Types of Chemical reactions; daily applications.Laboratory preparation of different gases. Physical and Chemical properties various compounds. Chemical calculations. Sources of common salt. Common salt – as a raw material for other chemicals (NaOH, Bleaching powder, baking soda, washing soda, and their uses, Plaster of Paris)
XII. Acids and Bases, Salts: Preparation, properties, Strength and uses of Acids & Bases. Neutralization. Preparation, properties, nature and uses of different Salts.Water of crystallization.Complex, Neutral and double salts.Oxidation and Reduction, Rancidity. Identification of Acids, Bases–Indicators: Natural, Chemical. PHScale – Role of PH in daily life-agriculture, medicine. Classification of salts based on affinity to water Examples of Acidic, Basic, Mixed, Complex, Neutral and double salts. Solutions – Types of solutions; solubility, ionization, Concentration; Oxidation number concept. Balancing of Redox reactions, Calculation of Concentrations. Titration and volumetric analysis. Stoichiometry.
XIII. Atomic Structure: Electromagnetic spectrum, Atomic spectrum, Characteristics of electron, proton and neutron, Rutherford’s model of an atom, nature of electromagnetic radiation, Plank’s quantum mechanics, explanation of photo electric effect, features of atomic spectra, characteristics of hydrogen spectrum, Bohr’s theory of structure of atom, Bohr’s explanation of spectral lines, failure of Bohr’s theory, wave particle nature of electrons, de Broglie’s hypothesis, Heisenberg’s uncertainty principle, important features of the Quantum mechanical model of an atom, Quantum numbers, concept of orbitals, define an atomic orbital in terms of quantum numbers-shapes of s, p and d orbitals, n l x rule, Energies of electronic energy levels (n+l) rule state Auffbau principle, Pauli’s exclusive principle and Hund’s rule of maximum multiplicity, electronic configuration of atom, explanation of stability of half filled and completely filled orbital.
XIV. Periodic Classification of Elements: Need for arrangement of elements in an organized manner. Historical background of classification of elements Doberiener’s Triads, Newland’s law of Octaves. Mendeleev’s Periodic Table (Achievements & Limitations).Mosley periodic table – based on electronic configuration. Characteristics of elements in groups and periods. The concept of grouping elements in accordance to their properties; the periodic law the signification of atomic number and electronic configuration as the basis per periodic classification. Classification of elements into s-block, p-block, d-block, f-block. and their main characteristics. Periodic trends in physical and chemical properties of elements. Study of different Groups of periodic table.
XV. Chemical Bonding: Why do atoms combine? Electronic theory of Valence by Lewis and Kossel Octet Rule, Ionic and Covalent bonds: examples with Lewis Dot formulae Introduction of chemical bonding. Electronic Configuration of Noble gases. sigma, pi bond with examples. Shapes of molecules bond lengths and bond angles in molecules. Hybridization and explanation of H2O, BF3, CH4, NH3 etc. molecules. Hydrogen bonding and types of H-bonds.
XVI. Carbon and its Compounds: Need to study of carbon compounds separately. Classification of Organic compounds Hydro carbons – Alkanes, alkenes, alkynes aromatic and aliphatic compounds with examples. Bonding in Carbon including Hybridization. Allotropes of Carbon. Versatile nature of carbon. Tetravalency, Chains, branches and rings. Catenation, Multiple bonding, Isomerism. Saturated and Unsaturated carbon compounds. Bonding of carbon with other elements. Functional groups in carbon compounds. Homologous series. Chemical properties of carbon compounds Combustion and Oxidation. Addition reactions. Substitution reaction. Important carbon compounds. Nomenclature organic compounds.
Carbohydrates and their classification. Proteins-examples, Oils and fats examples Polythene – Nylon, PVC, Polyvinyl alcohol; Rubber – uses in daily life. Polymers, and other important organic compounds.XVII. Environmental Chemistry and Metallurgy
Different types of pollutions, acid rains, green chemistry, strategies to control environmental pollution. Occurrence of Metals. Minerals, Ores – Examples. Metallurgy – Processes involved in metallurgy. Extractions of metals – activity series and related metallurgy, flow chart of steps involved in the extraction of metals from ore. Refining metals, Electrolytic refining, Corrosion – Prevention of Corrosion. Alloys and their uses.TGT | General Sciences | Telangana | Syllabus
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General Sciences = Physical Sciences + Biological Sciences.
0 votes, 0 avg50 votes, 0 avg0TGT | Biological Sciences | Telangana | Syllabus
Free | Teaching & Learning | Material
CBSE 6 | Science | E-Tools
No Matter Where You Start Among Study, Assess & Interact. But Your Course Will Be Completed Successfully.
Written Examination Syllabus for the post of Trained Graduate Teacher in Residential Educational Institutions Societies.
Paper- 1 | General Studies, General Abilities, & Basic Proficiency In English
General Studies, General Abilities, & Basic Proficiency In English
Section-I: General Studies
Current Affairs – Regional, National & International.
Indian Constitution: Indian Political System; Governance and Public Policy.
Social Exclusion: Rights issues such as Gender, Caste, Tribe, Disability etc.and inclusive policies.
Society Culture, Civilization Heritage, Arts and Literature of India and Telangana.
General Science: India’s Achievements in Science and Technology
Environmental Issues: Disaster Management – Prevention and Mitigation Strategies and Sustainable Development.
Economic and Social Development of India and Telangana.
Socio-economic, Political and Cultural History of Telangana with special emphasis on Telangana Statehood Movement and formation of Telangana state.
Section-II: General AbilitiesAnalytical Abilities: Logical Reasoning and Data Interpretation.
Moral Values and Professional Ethics in Education.
Teaching Aptitude Section – III: Basic Proficiency in English
i) School Level English Grammar:
Articles; Tense; Noun & Pronouns; Adjectives; Adverbs; Verbs; Modals;
Subject-Verb Agreement; Non-Finites; reported speech; Degrees of
Comparison; Active and Passive Voice; Prepositions; Conjunctions;
Conditionals.
ii) Vocabulary:
Synonyms and Antonyms; Phrasal Verbs; Related Pair of Words; Idioms and Phrases; Proverbs.
iii) Words and Sentences :
Use of Words; Choosing Appropriate words and Words often Confused;
Sentence Arrangement, Completion, Fillers and Improvement;
Transformation of Sentences; Comprehension; Punctuation; Spelling Test; Spotting of Errors.Paper-2 | Pedgogy Of Biological Sciences
Teaching Methodology Of Biological Sciences
1. The Nature of Biological Sciences and its Historical Development including the
contributions of important Biologists given in the school textbooks. Importance of Biological Sciences in School Curriculum
2. Values, Aims and Objectives of Teaching Biological Sciences
3. Child Development; Psychology of Teaching and Learning Biological Sciences
4. Biological Sciences Curriculum : Construction ,Organization and Development
5. Approaches, Methods and Techniques of Teaching Biological Sciences with special reference to Living World; Cell &Tissues; Plant World; Animal World; Our Environment ; Heredity &Genetics ; Evolution and Applied Biology
6. Planning for Effective Instruction in Biological Sciences: Different Plans and Designing Learning Experiences.
7. Learning Resources and Designing Instructional Material in Biological Sciences; Biological Science Labs; Teaching Aids ; Textbooks; ICT in Biological Sciences
8. Measurement and Evaluation in Biological Sciences: Continuous and Comprehensive Evaluation (CCE); Tools and Techniques of Evaluation; Achievement and Diagnostic Tests.
9. Learning Disabilities/Difficulties and Education of Exceptional/ Disabled Children in Biological Sciences
10. Biological Sciences and Everyday Life; Non-formal Biological Sciences Education.
Paper-3 | Discipline Knowledge In Biological Sciences
Biological Sciences Subject Contents
1. Biological Sciences: Its importance and human welfare, Branches of Biology, Biologists, Reputed Biological Institutions in India.
2. Living World: Life and its Characteristics, Classification of Living Organisms Microbial World : Virus, Bacteria, Algae, Fungi and Protozoan, Useful and Harmful Micro-organisms.
3. Cell &Tissues: Cell – Structural and Functional unit of life. Prokaryotic and Eukaryotic Cell, Structure of Eukaryotic Cell, Cell Organelles, Biomolecules, Differences between Plant Cell and Animal Cell, Cell Division – Mitosis and Meiosis, Tissues – Structure, Functions and Types of Plant and Animal tissues.
4. Plant World: Morphology of a Typical Plant – Root, Stem, Leaf, Flower, Inflorescence, Fruit – their Structure, Types and Functions, Parts of a Flower,
Modifications of Root, Stem and Leaf, Photosynthesis, Transpiration, Transportation (Ascent of Sap), Respiration, Excretion and Reproduction in Plants, Plant Hormones, Economic importance of Plants, Wild and Cultivated Plants, Agricultural Operations, Crop diseases and Control measures, Improvement in Crop yield,
Storage, Preservation and Protection of Food and Plant Products.
5. Animal World: Organs and Organ Systems including man – Their Structure and Functions Digestive, Respiratory, Circulatory, Excretory, Nervous, Control and Coordination, Sensory perception and Reproduction, Need for reproductive health and prevention of STD, birth control- Need and methods of contraception and MTP, Amniocentesis, infertility and assisted reproductive technologies – IVF –ET – ZIFT, GIFT.
6. Sense Organs: Structure and Functions of Eye, Ear, Nose, Tongue and Skin. Nutrition in man – Digestion and absorption – Breathing and Respiration in humans – Nutrients and their functions, Balanced Diet, Deficiency diseases, Tropical diseases, Skin diseases, Blindness in man: Causes, Prevention and Control, Health agencies, First Aid – Bites: Insect, Scorpion and Snakes. Wild and Domesticated Animals.
7. Our Environment: Abiotic and Biotic factors and Ecosystems, Natural Resources – Classification, Judicial use of Renewable, Non-renewable and Alternative Resources, Forests, Wild Life – Conservation, Sanctuaries, National Parks in India, Bio-Geochemical Cycles, Pollution – Air, Water, Soil and Sound, Global Environmental issues – Global Warming (Green House Effect), Acid Rains, Depletion of Ozone layer and scarcity of water.
8. Heredity and Genetics:- Mendel’s laws of inheritance, Pleiotropy, Multiple alleles: Inheritance of blood groups and Rh-factor, dominance (Blood groups as example), Elementary idea of polygenic inheritance; Skin colour in humans (refer Sinnott, Dunn and Dobzhansky); Sex determination – in humans – Sex linked inheritance – Haemophilia, Color blindness; Mendalian disorders in humans: Thalassemia, Haemophilia, Sickle celled anemia, cystiefibrosis PKU, Alkaptonuria; Chromosomal disorders – Down’s syndrome, Turner’s syndrome and Kilnefelter syndrome; Genome, Human Genome Project and DNA Finger Printing. Gene Bank, Gene flow and genetic drift; Variations (mutations and genetic recombination).
9. Evolution: Origin of Life, Biological evolution and Evidences for biological evolution (paleontological, comparative anatomical, embryological and molecular evidences); Theories of evolution: Lamarckism, Darwin’s theory of Evolution – Natural Selection, Mutation Theory of Hugo De Vries; Modern synthetic theory of Evolution – Hardy-Weinberg Law; Types of Natural Selection; Adaptive radiation – Human evolution; Speciation – Allopatric, sympatric; Reproductive isolation.
10. Applied Biology: Animal Husbandry: Apiculture, Pisciculture, Poultry management, Dairy management; Animal breeding; Bio-medical Technology: Diagnostic Imaging
(X-ray, CT scan, MRI), ECG, EEG; Biotechnology – its importance for human welfare – Human insulin and vaccine production; Gene Therapy; Transgenic animals; ELISA: vaccines, MABs, Cancer biology, Stem Cells.
TGT | Mathematics | Telangana | Syllabus
Free | Teaching & Learning | Material
CBSE 6 | Science | E-Tools
No Matter Where You Start Among Study, Assess & Interact. But Your Course Will Be Completed Successfully.
Written Examination Syllabus for the post of Trained Graduate Teacher in Residential Educational Institutions Societies.
Paper- 1 | General Studies, General Abilities, & Basic Proficiency In English
General Studies, General Abilities, & Basic Proficiency In English
Section-I: General Studies
Current Affairs – Regional, National & International.
Indian Constitution: Indian Political System; Governance and Public Policy.
Social Exclusion: Rights issues such as Gender, Caste, Tribe, Disability etc.and inclusive policies.
Society Culture, Civilization Heritage, Arts and Literature of India and Telangana.
General Science: India’s Achievements in Science and Technology
Environmental Issues: Disaster Management – Prevention and Mitigation Strategies and Sustainable Development.
Economic and Social Development of India and Telangana.
Socio-economic, Political and Cultural History of Telangana with special emphasis on Telangana Statehood Movement and formation of Telangana state.
Section-II: General AbilitiesAnalytical Abilities: Logical Reasoning and Data Interpretation.
Moral Values and Professional Ethics in Education.
Teaching Aptitude Section – III: Basic Proficiency in English
i) School Level English Grammar:
Articles; Tense; Noun & Pronouns; Adjectives; Adverbs; Verbs; Modals;
Subject-Verb Agreement; Non-Finites; reported speech; Degrees of
Comparison; Active and Passive Voice; Prepositions; Conjunctions;
Conditionals.
ii) Vocabulary:
Synonyms and Antonyms; Phrasal Verbs; Related Pair of Words; Idioms and Phrases; Proverbs.
iii) Words and Sentences :
Use of Words; Choosing Appropriate words and Words often Confused;
Sentence Arrangement, Completion, Fillers and Improvement;
Transformation of Sentences; Comprehension; Punctuation; Spelling Test; Spotting of Errors.Paper-2 | Pedgogy Of Mathematics
Teaching Methodology Of Mathematics
1.The Nature of Mathematics and its Historical Development including the contributions of important Mathematicians given in the school textbooks. Importance of Mathematics in School Curriculum.
2.Values, Aims and Objectives of Teaching Mathematics
3.Child Development; Psychology of Teaching and Learning Mathematics
4.Mathematics Curriculum: Construction ,Organization and Development
5.Approaches, Methods and Techniques of Teaching Mathematics with special
reference to Arithmetic, Algebra, Geometry and Trigonometry
6.Planning for Effective Instruction in Mathematics: Different Plans and Designing Learning Experiences.
7. Learning Resources and Designing Instructional Material in Mathematics; Mathematics Labs; Teaching Aids; Textbooks; ICT in Mathematics.
8. Measurement and Evaluation in Mathematics: Continuous and Comprehensive Evaluation (CCE); Tools and Techniques of Evaluation; Achievement and Diagnostic Tests.
9. Learning Disabilities/Difficulties and Education of Exceptional/ Disabled Children in Mathematics.
10. Mathematics and Everyday Life; Non-formal Mathematics Education.
Paper-3 | Discipline Knowledge in Mathematics
Subject Contents – Mathematics
1. Number System-I: Counting of Numbers; Fundamental Operations; Types of Numbers; Real Numbers; Mathematical Units and Conversions; Utility of Euclid division lemma, Problems on surds; Divisibility rules their possible remainders, Pythagorean triplets; Using alphabet in place of digit in divisibility rules, missing numbers; Prime and composite, even and odd numbers, need and applications of fundamental theorem of arithmetic, difference between factors and multiples and prime factors-LCM and HCF; Characteristics and importance in finding solutions to daily life situations (e.g.p).
2. Number System-II: Patterns of numbers; Progressions- A.P. and G.P- relating to daily life situations; Building the relation between numbers and graphical representations; Squares – Square root, Cube-Cube root; Ratio, Golden Ratio, Compound Ratio, Inverse Ratio, Addition and Subtraction of equal Ratios; Proportion – Direct and inverse; Fractions (Numerator and denominator); Applications on the above.
3. Percentages in daily life situations and SETS :Profit and loss, Discount ; Simple interest and Compound interest, VAT and their applications ; Sets-Concept in building a set and rationale; types of sets; Operations on sets Venn Diagrams and related daily life problems. Sets- Compliment, properties on operations and cardinalitySeries; Complex numbers and its fundamental operations; Conjugates;Fundamental principle of counting (Linear and Circular) Combinations and related to daily life problems.Modulus of a Real Number and absolute value.Types of statements and proofs, quantifiers; Tautology and contradictions.
4. Fundamentals of Algebra; Linear expressions and equations in one & two variables Pairs linear equations in two variables; Basic Operations on Algebraic expressions –Laws and properties of exponents; Factorization; Special products; Operations on Polynomials and Factorization; Quadratic expressions and equations. Logarithms and their use. Graphical Representations Mathematical Induction/ Quadratic Expressions/ Linear Programming / Determinants/ Matrices :Relation between two variables and there graphical representation, basic ideas related to function and respective theorems, types of functions ; Mathematical induction, problems on divisibility using principle of Mathematical Induction; Quadratic expressions – change in sign, maxima and minima values; Basis concepts of linear programming problems; Binomial theorem and approximations. Order of Matrix; Properties of Determinants of Matrices and solving of equations.
5. Geometry: Fundamental concepts; Contextual situations, basic ideas like point , line, ray, lines segment, angle, plane , curve, circle etc., and related terminology; Relations between lines and angles; Lines of a plane and their properties; Axioms , postulates, Euclid axioms, historical back ground, non-Euclidean geometry; Types and Properties of Geometrical figures; Types and Properties of triangle, quadrilateral,
Polygon etc.,; Properties of Circle and Parts of Circles; Comparison of Geometrical figures – Congruency, Similarity etc.,; BPT, Pythagoras, Theorems applications; Relations between Circles and Lines; Areas of Geometrical Figures – Related theorems; Practical Geometry; Basic constructions, Constructions of Triangles, Quadrilaterals, Circles, Similar triangles, Tangents to Circles and related problems.
6. Co-ordinate Geometry: Basic concepts, dividing a line segment in the given ratio and its usage in different situations, slope of a line, distance between two points, area of triangles, Quadrilaterals and Collinearity of points.
7. Concept of locus; Straight line – different forms of straight line and conversions; Angle between two lines; Length of perpendicular from a point to a line; Distance between two parallel lines; Circle Equation – standard form, center and radius; Position of a point in plane of circle; Relative positions of two circles –Transformation of Axes- 3-D Geometry-DR’s and DC’s and Cartesian equation of a plane. Conic Section.
8. Mensuration: Plane figures; Need and importance of Area and Perimeter of different
triangles, quadrilaterals, polygons , circles, ring etc., in daily life; Solid
figures ;
Need and importance of CSA, TSA and volume of prism, cube, cuboids, pyramid,
cylinder, cone, sphere, hemisphere; Conversions from one solid to another;
Problems with combination of solids (not more than three) in daily life; Conversions- 3- D figures and 2-D figures.
9. Statistics and Probability :Data handling : Types and representation of data; Measure of central tendency of ungrouped and grouped data specific usages; Presentation of data – different graphs and related problems ; Probability Basic concepts, outcomes
and chances; Events – mutually exclusive,
possible and impossible, complementary; Applications of probability Measures of dispersions – Range, Q.D, M.D, S.D. ; Coefficient of variation; Probability- Random experiments and events (Independent and Dependent); Addition and multiplication theorems of probability;
Random variables. Axiomatic approach.
10. Trigonometry : Basic concepts; Trigonometric ratios; Trigonometric values for specific angles; Complementary angles; Trigonometric Identities; Conversions of Trigonometric ratios – Trigonometric transformations – Heights and distances; Trigonometric ratios of compound angles; Properties of triangles – relation between sides and angles of a triangles – Inverse trigonometric functions. Multiples and submultiples –Trigonometric expansions.
