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Maths

UNIT 1: SETS RELATIONS AND FUNCTIONS:

Set and their representation: Union intersection and complement of sets and their algebraic properties and complement of sets and their algebraic properties: Power set: Relation. Types of relations, equivalence relations, Functions: one-one into and onto functions, Composition of functions.

UNIT 1: COMPLEX NUMBERS AND QUDRATIC EQUATIONS:

Complex number as ordered pair of reals, Representation of complex number in the form a + b and their representation in a plan, Argrand diagram, algebra of complex number modulus and argument for aptitude of a complex number, square root of a complex number, triangle inequality. Quadratic equations in real and complex number system and their solutions, Relation between roots and co- efficient s, nature of roots, formation of quadratic with given roots.

UNIT 3: MATRICS AND DETERMINANTS:

Matrices, algebra of matrices, types of matrices, determinants and matrices of order two and three, Properties of determinants, evaluation of determinants, area of triangles using 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 matrix

UNIT 4: PERMUTATIONS AND COMBINATIONS:

Fundamental principle of counting, permutation as an arrangement and combination as selection, Meaning of P (n. r) and C (n.r.), simple applications

UNIT 5: MATHEMATICAL INDUCTION:

Principle of Mathematical Induction and its simple application

UNIT 6: BINOMIAL THEOREM AND ITS SIMPLE APPLICATIONS:

Binomial theorem for a positive integral index general term and middle term, properties of Binomial coefficient and simple applications

UNIT 7: SEQUENCES AND SERIES:

Arithmetic and Geometric progressions insertion of arithmetic, geometric means between two given number, Relation between A.M. and G.M. Sum up to n terms of special series. Sn, Sn2, Sn3, Arithmetic, Geometric progression.

UNIT 8: LIMIT. CONTINUTTY AND DEFERENTIABILITY:

Real – valued functions, algebra of functions, polynomials, rational, trigonometric, logarithmic and exponential functions, inverse functions, Graphs of simple functions, Limits. Continuity and differentiability, Differentiation of the sum, difference, product and quotient of two functions, Differentiation of trigonometric, logarithmic, exponential, composite and implicit functions: derivatives of order up to two Rolle’s and Lagrange’s Mean value Theorems, Application of derivatives, Rate of change of quantities, monotonic increasing and decreasing functions. Maxima and minima of functions of one variable, tangent and normal

UNIT 9: 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.

Evaluation of simple integrals of the type

∫dx/(x2 ± a2) ∫dx/(√x2 ± a2) ∫dx/(a2 - x2) ∫dx/(√a2 - x2) ∫dx/(ax2 + b x2+c) ∫dx/(√ax2 + b x2+c) ∫((px+q)dx)/(√ax2 + b x2+c) ∫√a2± b2 dx ∫√x2- a2 dx

Integral as limit of a sum, Fundamental theorem of Calculus, properties of definite integrals, Evaluation of definite integrals, determining areas of the regions bounded by simple curves in standard form

UNIT 10: DIFFERENTIAL EQUATIONS:

Ordinary differential equations, their order and degree, Formation of differential equations, Solutions of differential equations by the method of separation of variables, solution of homogeneous and linear differential equations of the type:

dy/dx + P (x) y = q (x)

UNIT 11: CO- ORDINATE GEOMETRY:

Cartesian system rectangular co- ordinate 10 in a plan, distance formula, section formula, locus and its equation translation of axes, slope of a line, parallel and perpendicular lines, intercepts of a line on the coordinate axes

Straight lines

Various forms of equations of a line, intersection of lines, angles between two lines, conditions for concurrence of three lines, distance of a point from a line, equations internal and external bisectors of angles between two lines, co- ordinates of centroid, orthocenter and circumcentre of a triangle, equation of family of lines passing through the point of intersection of two lines

Circles, conic sections

Standard form of equation of a circle, general form of the equation of a circle. Its radius and centre, equation of a circle when the end points of a diameter are given points of intersection of a line and a circle with the centre at the origin and condition for a line to be tangent to a circle, equation of the tangent, Sections of cones, equations of conic section (parabola, ellipse and hyperbola) in standard forms, condition for y = mx + c to be a tangent and point (s) of tangency

UNIT 12: THREE DIMENSIONAL GEOMETRY:

Co- ordinates of a point in space, distance between two points, section formula direction ratios and direction cosines, angle between two intersecting lines, skew lines, the shortest distance between them and its equation, equations of a line and a plane in different forms, intersection of a line and a plan, co- planar lines

UNIT 13: VECTOR ALGEBRA

Vectors and scalar, addition of vectors, components of a vector in two dimensions and three dimensional spaces, scalar and vector products, scalar and vector triple product.

UNIT 14: STATICS AND PROBABILITY:

Measures of Dispersion: Calculation of mean, median, mode of grouped and ungrouped data calculation of standard deviation, variation and mean deviation for grouped and ungrouped data.

Probability: Probability of an event, addition and multiplication theorems of probability, Baye’s theorem, probability distribution of a random variate, Bernoulli trials and Binomial distribution

UNIT 15: TRIGONMETRY:

Trigonometrical identities and equations, Trigonometrical functions, inverse Trigonometrical functions and their properties Height and Distances