Navodaya Vidhyalaya Samiti ( NVS ) TGT Exam Pattern /
Syllabus / Scheme / Old Question Paper

NVS organizes TGT (Trained Graduate Teachers ) test each year
for the Appointment in its various schools in India. A written test is held for
the appointment of Applicants as a Teacher in Schools in India. The Exam
Pattern / syllabus / Scheme / Old Question Paper of written Examination of
five subjects like Hindi, English, Math, Science, Social science. MVS Trained
Graduate Teacher Patternn / syllabus of every subject is available to
download for you all applicants. The syllabus of every subjects like Hindi,
English, Math, Science, Social science has been published on the
authorized web portal of NVS.

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__SYLLABUS FOR WRITTEN EXAMINATION FOR TGT(ENGLISH)__

**Reading Comprehension (Section – A) :**Ability to comprehend, analyze and interpret an unseen text Three/four unseen texts of varying lengths (150-250 words) with a variety of objective type, multiple choice questions ( including questions to test vocabulary) testing factual and global comprehension.

**Writing ability (Section –B) :**Testing ability to express facts views/opinions in a coherent and logical manner in a style suitable to the task set. B.1 One short writing task such as: notice, message or a postcard. B.2 Writing a report of an event, process, or place. B.3 Writing an article / debate / speech based on visual / verbal input on a given concurrent topic for e.g. environment, education, child labour, gender bias, drug-abuse etc presenting own views fluently. B.4 Writing a letter (formal/informal) on the basis of verbal / visual input. Letter types include: (a) letter to the editor; (b) letter of complaint; (c) letter of request; (d) descriptive, personal letters.

**Grammar and Usage (Section – C) :**Ability to apply the knowledge of syntax, language/grammatical items and to use them accurately in context. The following grammatical structures will be tested: (1) Tenses (2) Modals (3) Voice (4) Subject – verb concord (5) Connectors (6) Clauses (7) Parts of speech (8) Punctuation (9) Sequencing to form a coherent sentence or a paragraph

**Literature (Section – D) :**To test the candidate’s familiarity with the works of writers of different genres and periods of English Literature. The candidate should have a thorough knowledge of :- ü Shakespeare’s works. ü Romantic Period ( e.g. Shelley, Wordswoth, Keats, Coleridge, Byron etc.) ü 19th & 20th Century American and English Literature (e.g. Robert Frost Hemingway, Ted Hudges, Whitman, Hawthorne, Emily Dickinson, Bernard Shaw etc.) ü Modern Indian Writing in English (e.g. Anita Desai, Vikram Seth, Nissim Ezekiel, K.N. Daruwala, Ruskin Bond, R.K. Narayan, Mulk Raj Anand, Khushwant Singh etc.) ü Modern Writings in English from different parts of the world.

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__Syllabus for written examination of TGT(Mathematics) __

**Real Number:**Representation of natural numbers, integers, rational numbers on the number line. Representation of terminating / non-terminating recurring decimals, on the number line through successive magnification. Rational numbers as recurring / terminating decimals. Examples of nonrecurring /non-terminating decimals. Existence of non-rational numbers (irrational numbers) and their representation on the number line. Explaining that every real number is represented by a unique point on the number line and conversely, every point on the number line represents a unique real number. Laws of exponents with integral powers. Rational exponents with positive real bases. Rationalization of real numbers. Euclid’s division lemma, Fundamental Theorem of Arithmetic. Expansions of rational numbers in terms of terminating / non-terminating recurring decimals.

Elementary Number Theory: Peano’s Axioms, Principle of
Induction; First Principal, Second Principle, Third Principle, Basis
Representation Theorem, Greatest Integer Function, Test of Divisibility,
Euclid’s algorithm, The Unique Factorisation Theorem, Congruence, Chinese
Remainder Theorem, Sum of divisors of a number. Euler’s totient function,
Theorems of Fermat and Wilson.

Matrices R, R2, R3 as vector spaces over R and concept of
Rn. Standard basis for each of them. Linear Independence and examples of
different bases. Subspaces of R2, R3. Translation, Dilation, Rotation,
Reflection in a point, line and plane. Matrix form of basic geometric
transformations. Interpretation of eigenvalues and eigenvectors for such
transformations and eigenspaces as invariant subspaces. Matrices in diagonal
form. Reduction to diagonal form upto matrices of order 3. Computation of
matrix inverses using elementary row operations. Rank of matrix, Solutions of a
system of linear equations using matrices.

**Polynomials:**Definition of a polynomial in one variable, its coefficients, with examples and counter examples, its terms, zero polynomial. Degree of a polynomial, Constant, linear, quadratic, cubic polynomials; monomials, binomials, trinomials. Factors and multiples. Zeros / roots of a polynomial / equation. Remainder Theorem with examples and analogy to integers. Statement and proof of the Factor Theorem. Factorization of quadratic and of cubic polynomials using the Factor Theorem. Algebraic expressions and identities and their use in factorization of polynomials. Simple expressions reducible to these polynomials.

Linear Equations in two variables: Introduction to the
equation in two variables. Proof that a linear equation in two variables has
infinitely many solutions and justify their being written as ordered pairs of
real numbers, Algebraic and graphical solutions.

Pair of Linear Equations in two variables: Pair of linear
equations in two variables. Geometric representation of different possibilities
of solutions / inconsistency. Algebraic conditions for number of solutions.
Solution of pair of linear equations in two variables algebraically – by
substitution, by elimination and by cross multiplication.

**Quadratic Equations:**Standard form of a quadratic equation. Solution of the quadratic equations (only real roots) by factorization and by completing the square, i.e. by using quadratic formula. Relationship between discriminant and nature of roots. Relation between roots and coefficients, Symmetric functions of the roots of an equation. Common roots.

Arithmetic Progressions: Derivation of standard results of
finding the nth term and sum of first n terms.

**Inequalities:**Elementary Inequalities, Absolute value, Inequality of means, Cauchy – Schwarz Inequality, Tchebychef’s Inequality.

Combinatorics: Principle of Inclusion and Exclusion, Pigeon
Hole Principle, Recurrence Relations, Binomial Coefficients.

**Calculus:**Sets. Functions and their graphs : polynomial, sine, cosine, exponential and logarithmic functions. Step function, Limits and continuity. Differentiation, Methods of differentiation like Chain rule, Product rule and Quotient rule. Second order derivatives of above functions. Integration as reverse process of differentiation. Integrals of the functions introduced above.

Euclidean Geometry: Axioms / postulates and theorems. The
five postulates and Euclid. Equivalent versions of the fifth postulate.
Relationship between axiom and theorem. Theorems and lines and angles,
triangles and quadrilaterals, Theorems on areas of parallelograms and
triangles, Circles, theorems on circles, Similar triangles, Theorem on similar
triangles. Constructions. Ceva’s Theorem, Menalus Theorem, Nine Point Circle,
Simson’s Line, Centres of Similitude of Two Circles, Lehmus Steiner Theorem,
Ptolemy’s Theorem.

**Coordinate Geometry:**The Cartesian plane, coordinates of a point, Distance between two points and section formula, Area of a triangle.

Areas and Volumes: Area of a triangle using Hero’s formula
and its application in finding the area of a quadrilateral. Surface areas and
volumes of cubes, cuboids, spheres (including hemispheres) and right circular
cylinders/cones. Frustum of a cone. Area of a circle: area of sectors and
segments of a circle.

**Trigonometry:**Trigonometric ratios of an acute angle of a right – angled triangle. Relationships between the rations. Trigonometric identities. Trigonometric ratios of complementary angles. Heights and distances.

**Statistics:**Introduction to Statistics : Collection of data, presentation of data, tabular form, ungrouped / grouped, bar graphs, histograms, frequency polygons, qualitative analysis of data to choose the correct form of presentation for the collected data. Mean, median, mode of ungrouped data. Mean, median and mode of grouped data. Cumulative frequency graph.

**Probability:**Elementary Probability and basic laws. Discrete and Continuous Random variable, Mathematical Expectation, Mean and Variance of Binomial, Poisson and Normal distribution. Sample mean and Sampling Variance. Hypothesis testing using standard normal variate. Curve Fitting. Correlation and Regression.

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