In this article we are sharing 2nd grade paper -II mathematics syllabus. candidates can download syllabus via given link below.
SYLLABUS FOR EXAMINATION FOR THE POST OF SR. TEACHER
SECONDARY EDUCATION DEPARTMENT
Secondary and Senior Secondary Standard:
Rational numbers as recurring/terminating decimals. Existence of non-rational numbers (irrational numbers), Real Numbers and their Decimal Expansions, Operations on Real Numbers, Laws of Exponents for Real Numbers. Euclid’s division lemma, Fundamental Theorem of Arithmetic.
Lines and Angles, Properties of angles at a point, Parallel Lines and a Transversal, Sides and angles of a triangle, Properties of a triangle, Congruency of triangle, Similar triangles, Inequalities in a triangle, Concurrence of medians and altitudes, Quadrilaterals, Properties of angles, sides and diagonals of a Parallelogram, Rectangle, Rhombus, Trapezium and square. The Mid-point Theorem. Circle and terms related to it. Perpendicular from the Centre to a Chord, Equal Chords and their Distances from the Centre Angle Subtended by an Arc of a Circle, Cyclic Quadrilaterals. Tangents from a Point on a Circle.
(i) Areas: Area of plane figures involving triangles, quadrilaterals and circle. Area of sectors and segments of a circle. Problems based on areas and perimeter/circumference of the above said plane figures.
(ii)Surface Areas and Volumes: Surface areas and volumes of cubes, cuboids, spheres (including hemispheres) and right circular cylinders/cones. Problems involving converting one type of metallic solid into another and other mixed problems.
Degree of a polynomial. Constant, linear, quadratic, cubic polynomials; Zeros/roots of a polynomial/equation. Relationship between zeros/roots and coefficients of a polynomial/equation. Problems based on Remainder Theorem and Factor Theorem Quadratic equations with real coefficients, relations between roots and coefficients, formation of quadratic equations with given roots. Linear and Quadratic in equations. Algebra of complex numbers, addition, multiplication, conjugation, polar representation, properties of modulus and principal argument, triangle inequality, cube roots of unity, geometric interpretations. Arithmetic and geometric progressions, arithmetic and geometric means, sums of finite arithmetic and geometric progressions, infinite geometric series, Arithmetico-Geometric Progression. Sum of the first n natural numbers, sums of squares and cubes of the first n natural numbers, Fundamental principle of counting. Factorial n. Permutations and combinations and simple applications. Binomial theorem for a positive integral index, general term and middle term, properties of Binomial
Matrices and Determinants:
Matrices, algebra of matrices, type of matrices, determinants of order two and three, properties of determinants, Adjoint and evaluation of inverse of a square matrix using determinants and elementary transformations, Test of consistency and solution of simultaneous linear equations in two or three variables using determinants and matrices.
Sets, Relations and Functions:
Sets and their representations. Different kinds of sets.Venn diagrams. Operation on Sets. De-Morgan’s laws and practical problems based on them. Ordered pair, relations, domain and co-domain of relations, equivalence relation. Function as a special case of relation, domain, co-domain, range of functions, invertible functions, even and odd functions, into, onto and one-to-one functions, special functions (polynomial, trigonometric, exponential, logarithmic, power, absolute value, greatest integer etc.), sum, difference, product and composition of functions.
Positive and negative angles. Measuring angles in radians and in degrees and conversion from one measure to another. Trigonometric ratios of allied angles. Trigonometric functions and their periodicity, addition and subtraction formulae, formulae involving multiple and sub-multiple angles, general solution of trigonometric equations. Inverse trigonometric functions (principal value only) and their elementary properties. Problems on heights and distances.
(i)Two dimensions: Cartesian coordinates, distance between two points, section formulae, shift of origin. Equation of a straight line in various forms, angle between two lines, distance of a point from a line; Lines through the point of intersection of two given lines, equation of the bisector of the angle between two lines, concurrency of lines; Centroid, orthocentre, incentre and circumcentre of a triangle. General equation of second degree. Nature of conic. Equation of a circle in various forms, equations of tangent, normal and chord. Parametric equations of a circle, intersection of a circle with a straight line or a circle, equation of a circle through the points of intersection of two circles and those of a circle and a straight line. Equations of a parabola, ellipse and hyperbola, their foci, directrices and eccentricity, parametric equations, equations of tangent and normal. Problems based on locus. Polar equation of a conic, polar equations of tangent, normal, asymptotes, chord of contact, auxiliary circle, director circle of a conic and related problems.
(ii)Three dimensions: Distance between two points, direction cosines and direction ratios, equation of a straight line in space, skew lines, shortest distance between two lines, equation of a plane, distance of a point from a plane and a line, Cartesian and vector equation of a plane and a line. Angle between (i) two lines, (ii) two planes (iii) a line and a plane. Coplanar lines.
Limits, continuity and differentiability. Differentiation of the sum, difference, product and quotient of two functions. Differentiation of trigonometric, inverse trigonometric, logarithmic, exponential, composite and implicit functions; Second and third order derivatives. Rolle’s and Lagrange’s Mean value Theorems, Applications of derivatives: Rate of change of quantities, monotonic Increasing and decreasing functions, Maxima and minima of functions of one variable, tangents and normal.
Integral as an anti-derivative, Integration of a variety of functions by substitution, by partial fractions and by Integration using trigonometric identities. Definite integral and their properties, application of definite integrals in finding the area under simple curves, especially lines, arcs of circles/parabolas/ellipses etc., area between the said curves (the region should be clearly identifiable).
Vectors and scalars, magnitude and direction of a vector. Direction cosines/ratios of vectors. Types of vectors (equal, unit, zero, parallel and collinear vectors etc.), position vector of a point, negative of a vector, components of a vector, addition of vectors, multiplication of a vector by a scalar, position vector of a point dividing a line segment in a given ratio. Scalar (dot) product of vectors, projection of a vector on a line. Vector (cross) product of vectors. Scalar and Vector triple product and problems related to them.
Statistics and Probability:
Mean, median, mode of grouped and ungrouped data, calculation of standard deviation, variance and mean deviation for grouped and ungrouped data. Probability: Probability of an event, addition and multiplication theorems of probability, conditional probability, Bayes’ theorem, probability distribution of a random variate, Bernoulli trials and binomial distribution.
Definition and example of groups. General properties of groups, Order of an element of a group. Permutations: Even and Odd permutations. Groups of permutations. Cyclic group, Cayley’s theorem. Subgroups, Cosets, Lagrange’s theorem, Product Theorem of subgroups, Conjugate elements, conjugate complexes, Centre of a group, Simple group, centre of group, Normaliser of an element and of a complex. Normal subgroups, quotient Groups, Group homomorphism and isomorphism with elementary basic properties, fundamental theorem of homomorphism in groups. Isomorphism theorems of groups.
Real numbers as a complete ordered field, linear sets, lower and upper bounds, limit points, closed and open sets, Real sequence, limit and convergence of a sequence, convergence of series, tests for convergence of a series, absolute convergence, uniform convergence of sequence and series of functions.
Functions, Limits, continuity and differentiability of complex functions. Concept of an analytic function, Cartesian and Polar form of Cauchy-Riemann equations. Harmonic function, Conjugate function, Conformal mapping.
Polar Co-ordinates. Angle between radius vector and the tangent. Angle between curves in polar form. Length of polar sub-tangent and polar subnormal, Pedal equation of a curve, Derivatives of an arc, curvature, various formulae, Centre of curvature and chord of curvature and related problems. Partial differentiation, Euler’s theorem on homogeneous functions, chain rule of partial differentiation, Maxima and Minima of functions of two independent variables and of three variables connected by a relation, Lagrange’s Method of undetermined multipliers. Asymptotes, double points, curve tracing, Envelopes and evolutes. Theory of Beta and Gamma functions. Quadrature and Rectification. Volume and Surfaces of solids of revolution. Differentiation and integration under the sign of integration. Evaluation of double and triple integrals and their applications in finding areas and volumes. Dirichlet’s integral. Change of order of integration and changing into polar co-ordinates.
Ordinary differential equations of first order and first degree, differential equations of first order but not of first degree, Clairaut’s equations, general and singular solutions, linear differential equations with constant coefficients, homogeneous differential equation, second order linear differential equations, simultaneous linear differential equations of first order.
Curl, Gradient and Divergence & Identities involving these operators and related problems. Problems based on Stoke, Green and Gauss theorems.
Analytical Geometry of Three dimensions:
(i) Sphere: General Equation, Tangent Plane, Pole and Polar, Intersection of two spheres.
(ii) Cone: Enveloping cone, Tangent plane, Reciprocal cone, Three mutually Perpendicular generators, Right circular cone.
(iii) Cylinder: Right circular cylinder, Enveloping cylinder.
Statics and Dynamics:
Composition and resolution of co-planer forces, component of a force in two given directions, equilibrium of concurrent forces, parallel forces and moment, velocity and acceleration, simple linear motion under constant acceleration, Laws of motion, projectile.
Introduction, related terminology such as constraints, objective function, optimization, different types of linear programming (L.P.) problems, mathematical formulation of L.P. problems, graphical method of solution for problems in two variables, feasible and infeasible regions, feasible and infeasible solutions, optimal feasible solutions (up to three non-trivial constrains). Convex sets and their properties. Simplex Method. Concepts of duality in linear programming. Framing of dual programming. Assignment problems, Transportation problems.
Numerical Analysis and Difference Equation:
Difference operators and factorial notation, Differences of polynomial, Newton’s formulae for forward and backward interpolations. Divided differences, relation between divided differences and Simple difference. Newton’s general interpolation formulae, Lagrange interpolation formula. Central differences, Gauss, Stirling and Bessel interpolation formulae. Numerical Differentiation. Numerical integration, Newton-Cotes quadrature formula, Gauss’s quadrature formulae, convergence, Estimation of errors, Transcendental and polynomial equations, bisection method, method of iteration, Trapezoidal, Simpson’s and Weddle’s rules. Solution of linear difference equations with constant and variable coefficients. Solution of Algebraic and Transcendental equations, Iterative, Regula Falsi and Newton Raphson methods. Convergence, First and higher order homogeneous linear difference equations, non-homogenous linear difference equations, Complementary functions, Particular integral.
- Meaning and Nature of Mathematics.
- General and Specific objectives of Mathematics Teaching and Bloom Taxonomy.
- Methods of Mathematics Teaching (analytic, synthetic, inductive, deductive, heuristic, Project & Laboratory).
- Supervised – study, Programmed Learning, Constructive Learning in Mathematics.
- Importance & meaning of Lesson Plan (Herbertian Approach), Unit Plan (Morrison Approach).
- Audio-Visual aids in Mathematics.
- Concept of Correlation and its types in context of relationship with other school subjects.
- Academic & Professional characteristics of Mathematics Teacher.
- Principle of curriculum development in mathematics.
- Contribution of Indian Mathematician.
- Evaluation in Mathematics in terms of Cognitive, Affective and Psycho-motor Domain.
- Importance and characteristics of Unit test, Achievement test, Diagnostic test and steps of their preparation.
- Diagnostic & Remedial programmes for retarded children and enrichment programmes for gifted children.