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 Abilities**

**Analytical 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

**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**

**Paper-3**

**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.