{"id":1284,"date":"2026-02-18T03:27:31","date_gmt":"2026-02-18T03:27:31","guid":{"rendered":"https:\/\/vracademy.in\/?p=1284"},"modified":"2026-02-18T03:30:42","modified_gmt":"2026-02-18T03:30:42","slug":"syllabus-for-the-exam-of-teacher-mathematics-tobe-conducted-by-hprca","status":"publish","type":"post","link":"https:\/\/vracademy.in\/?p=1284","title":{"rendered":"Syllabus for the Exam of Teacher-Mathematics tobe Conducted by HPRCA"},"content":{"rendered":"\n
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Syllabus for the Exam of Teacher-Mathematics tobe Conducted by HPRCA<\/h2>\n\n\n\n

1 | P a g e
Syllabus for the Exam of Teacher-Mathematics to
be Conducted by HPRCA<\/p>\n\n\n\n

    \n
  1. MATHEMATICS OF POST GRADUATION LEVEL AS PER
    ESSENTIAL QUALIFICATION:
    a) NUMBER SYSTEMS: Review of representation of natural numbers, integers,
    and rational numbers on the number line, Rational and irrational numbers as
    recurring \/ terminating decimals. Operations on real numbers, definition of nth
    root of a real number, Fundamental Theorem of Arithmetic.
    b) POLYNOMIALS AND EQUATIONS: Definition of a polynomial in one
    variable, Coefficients of a polynomial, terms of a polynomial and zero
    polynomial, Degree of a polynomial, Constant, linear, quadratic and cubic
    polynomials, Monomials, binomials, trinomials, Factors and multiples, Zeros of a
    polynomial, Relationship between zeros and coefficients of quadratic
    polynomials, Quadratic equation, Cubic equation, biquadratic equations, roots
    and relations between roots and coefficients of these equations, Relationship
    between discriminant and nature of roots.
    c) SETS, RELATION AND FUNCTIONS: Sets and their representations, Empty
    set, Finite and Infinite sets, Equal sets, Subsets, Subsets of the set of real
    numbers especially intervals (with notations), Power set, Universal set, Venn
    diagrams, Union and intersection of sets, Difference of sets, Complement of a
    set, Properties of Complement sets, Definition of relation, Function as a special
    kind of relation from one set to another, Real valued function of the real
    variable, domain and range of these functions, constant, identity, polynomial,
    rational, modulus, signum and greatest integer functions with their graphs,
    Sum, difference, product and quotients of functions.
    d) SEQUENCE AND SERIES: Arithmetic Progression (A.P.), Arithmetic Mean
    (A.M.), Geometric Progression (G.P.), general term of a G.P., sum of n terms of a
    G.P. Arithmetic and geometric series, infinite G.P. and its sum, geometric mean
    (G.M.). Relation between A.M. and G.M. Sum to n terms of the special
    series: \ud835\udc5b, \ud835\udc5b
    2
    and \ud835\udc5b
    3
    .
    e) REAL ANALYSIS: Definition of Limit, different formulae of limits, Continuity,
    discontinuity and Types of discontinuities, Real Sequence, Bounded sequence,
    Cauchy convergence criterion for sequences, Cauchy\u2019s theorem on limits, order
    preservation and squeeze theorem, monotone sequences and their convergence
    (monotone convergence theorem without proof). Cauchy convergence criterion
    for series, positive term series, geometric series, comparison test, convergence
    2 | P a g e
    of p-series, Root test, Ratio test, alternating series, Leibnitz\u2019s test, Definition and
    examples of absolute and conditional convergence.
    f) DERIVATIVES AND THEIR APPLICATIONS: Derivative of a function,
    derivative of composite functions, chain rule, derivatives of trigonometric and
    inverse trigonometric functions, derivative of implicit function., Concepts of
    exponential, logarithmic functions. Logarithmic differentiation. Derivative of
    functions expressed in parametric forms. Second order derivatives. Successive
    differentiation, Leibnitz\u2019s theorem. Indeterminate forms, Rolle\u2019s theorem,
    Lagrange\u2019s & Cauchy Mean Value theorems, Taylor\u2019s theorem with Lagrange\u2019s
    and Cauchy\u2019s forms of remainder, Taylor\u2019s series. Maclaurin\u2019s series. Concavity,
    Convexity & Points of Inflexion, Curvature, Radius of curvature, center of
    curvature, Asymptotes, Singular points, Double point, Functions of several
    variables (upto three variables): Limit and Continuity of these functions Partial
    differentiation, Euler\u2019s theorem on homogeneous functions, Maxima and
    Minima with Lagrange Multipliers Method (two variables), Jacobian (upto three
    variables).Applications of derivatives: Rate of change, increasing\/decreasing
    functions, tangents and normals, approximation, maxima and minima (first
    derivative test motivated geometrically and second derivative test. Problems
    (that illustrate basic principles and understanding of the subject as well as reallife situations).
    g) INTEGRALS AND THEIR APPLICATIONS: Integration of a variety of
    functions by substitution, by partial fractions and by parts, Definite integrals as a
    limit of a sum, Fundamental Theorem of Integral Calculus, Properties of definite
    integrals and evaluation of definite integrals, Applications in finding the area
    under simple curves, especially lines, arcs of circles\/parabolas\/ellipses (in
    standard form only), area between the two curves and length of curves.
    h) DIFFERENTIAL EQUATIONS: Definition, order and degree, general and
    particular solutions of a differential equation, Formation of differential equation
    whose general solution is given, Solution of differential equations by method of
    separation of variables, homogeneous differential equations of first order and
    first degree. Solutions of linear differential equation of the type \u2013
    \ud835\udc51\ud835\udc66
    \ud835\udc51\ud835\udc65<\/li>\n<\/ol>\n\n\n\n