# [PDF] KVS PGT 2020 Syllabus – Mathematics

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## KVS 2018 – 2019

### Paper Pattern for KVS PGT Mathematics

 Test Component of the test Written Examination Number of questions Total marks Duration of the test Part-I 1. General English 10 10 2:30 Hours 2. General Hindi 10 10 Part-II 1. General Knowledge & Current Affairs 10 10 2. Reasoning Ability 10 10 3. Computer Literacy 10 10 4. Pedagogy 20 20 5. Subject concerned 80 80 Total (written exam.) 150 150

### Syllabus for KVS PGT Mathematics

#### KVS PGT Mathematics Syllabus 2019 TopicWise

 Topics Syllabus Sets Sets and their representations. Empty set. Finite & Infinite sets. Equal sets. Subsets. Subsets of the set of real numbers. Powerset. Universal set. Venn diagrams. Union and Intersection of sets. The difference of sets. The complement of a set. Relations & Functions Ordered pairs, Cartesian product of sets. Number of elements in the cartesian product of two finite sets. Cartesian product of the reals with itself (upto R x R x R). Definition of relation, pictorial diagrams, domain. co-domain and range of a relation. Function as a special kind of relation from one set to another. Pictorial representation a function, domain, co-domain & range of a function. Real-valued function of the real variable, domain and range of these functions. Principle of Mathematical Induction Processes of the proof by induction. The principle of mathematical induction. Permutations & Combinations Fundamental principle of counting. Factorial n. Permutations and combinations, derivation of formulae and their connections, simple applications. Complex Numbers Complex numbers, Algebraic properties of complex numbers, Argand plane and polar representation of complex numbers, Statement of Fundamental Theorem of Algebra, solution of quadratic equations in the complex number system. Linear Inequalities Linear inequalities. Algebraic solutions of linear inequalities in one variable and their representation on the number line. Graphical solution of linear inequalities in two variables. Solution of system of linear inequalities in two variables- graphically. Absolute value, Inequality of means. Binomial Theorem Statement and proof of the binomial theorem for positive integral indices. Pascal’s triangle, general and middle term in binomial expansion, simple applications. Sequence and Series Sequence and Series. Arithmetic, Geometric and Harmonic progressions (G.P.), General terms and sum to n terms of A.P., G.P. and H.P. Arithmetic Mean (A.M.), Geometric Mean (G.M.), and Harmonic Mean (H.M.), Relation between A.M., G.M. and H.M. Insertion of Arithmetic, Geometric and Harmonic means between two given numbers. Elementary Number Theory Peano’s Axioms, Principle of Induction; First Principle, Second Principle, Third Principle, Basis Representation Theorem, Greatest Integer Function Test of Divisibility, Euclid’s algorithm, The Unique Factorisation Theorem, Congruence. Quadratic Equations Quadratic equations in real and complex number system and their solutions. Relation between roots and coefficients, nature of roots, the formation of quadratic equations with given roots; Symmetric functions of roots, equations reducible to quadratic equations – application to practical problems. Matrices and Determinants Determinants and matrices of order two and three, properties of determinants, Evaluation of determinants . Area of triangles using determinants, Addition and multiplication of matrices, adjoint and inverse of matrix. Two-dimensional Geometry Cartesian system of rectangular co-ordinates in a plane, distance formula, section formula, area of a triangle, condition for the collinearity of three points, centroid and in-centre of a triangle, locus and its equation, translation of axes, slope of a line, parallel and perpendicular lines, intercepts of a line on the coordinate axes. Trigonometric Functions Positive and negative angles. Measuring angles in radians & in degrees and conversion from one measure to another. Definition of trigonometric functions with the help of unit circle. Graphs of trigonometric functions. Expressing sin (x+y) and cos (x+y) in terms of sinx, siny, cosx & cosy. Identities related to sin2x, cos2x, tan 2x, sin3x, cos3x and tan3x. Inverse Trigonometric Functions Definition, range, domain, principal value branches. Graphs of inverse trigonometric functions. Elementary properties of inverse trigonometric functions. Differential Calculus Polynomials, rational, trigonometric, logarithmic and exponential functions, Inverse functions. Graphs of simple functions. Limits, Continuity and differentiability; Derivative, Geometrical interpretation of the derivative, Derivative of sum Applications of Derivatives Applications of derivatives: rate of change, increasing/decreasing functions, tangents & normals, approximation, maxima and minima. Integral Calculus Integral as an anti-derivative. Fundamental integrals involving algebraic, trigonometric, exponential and logarithmic functions. Integration by substitution, by parts and by partial fractions. Integration using trigonometric identities. Definite integrals as a limit of a sum, Fundamental Theorem of Calculus. Basic Properties of definite integrals. Statistics Calculation of Mean, median and mode of grouped and ungrouped data. Measures of dispersion; mean deviation, variance and standard deviation of ungrouped / grouped data. Analysis of frequency distributions with equal means but different variances.