KIITEE 2015 Mathematics Syllabus:
Unit 1: Sets, Relations and Functions:
Sets and their Representations, Union, intersection and complements of sets, and their algebraic properties, Relations, equivalence relations, mappings, one-one, into and onto mappings, compositions of mappings.
Unit 2: Complex Numbers:
Complex numbers in the form a+ib and their representations in a plane. Argand diagram. Algebra of complex numbers, Modulus and Argument (or amplitude) of a complex number, square root of a complex number. Cube root of unity, triangle inequality.
Unit 3: Matrices and Determinants:
Determinants and matrices of order two and three, properties of determinants, Evaluation of determinants. Area of Triangle using determinants; Addition and multiplication of matrices, adjoint and inverse of matrix. Test of consistency and solution of simultaneous linear equations using determinants and matrices.
Unit 4: Quadratic Equations:
Quadratic equations in real and complex number system and their solutions. Relation between roots and co-efficients, nature of roots, formation of quadratic equation with given roots; Symmetric functions of roots, equations reducible to quadratic equations-applications to practical problems.
Unit 5: 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 6: Mathematical Inductions and its Applications
Unit 7: Bionomial Theorem and its Applications:
Binomial Theorem for a positive integral index, general term and middle term; Binomial Theorem for any index. Properties of Binomial Co-efficients. Simple applications for approximations.
Unit 8: Sequences and Series:
Arithmetic, Geometric and Harmonic progressions. Insertions of Arithmetic Geometric and Harmonic means between two given numbers. Relation between A.M, G.M and H.M Special series: Sn, Sn2, Sn3. Arithmetico-Geometric Series, Exponential and Logarithmic Series.
Unit 9: Differential Calculus:
Polynomials, rational, trigonometric, logarithmic and exponential functions, Inverse functions. Graphs of simple functions. Limits, Continuity; differentiation of the sum, difference, product and quotient of two functions: differential of trigonometric, inverse trigonometric, logarithmic, exponential, composite and implicit functions, derivatives of order upto two. Applications of derivatives: Rate of change of quantities, monotonic-increasing and decreasing functions, Maxima and minima of functions on one variable, tangents and normals. Rolle’s and Lagrange’s Mean Value therorems.
Unit 10: Integral Calculus:
Integral as an anti-derivative. Fundamentals integrals involving algebraic, trigonometric, exponential nad logarithmic functions. Integration by substitution, by parts and partial fractions. Integration using trigonometric identities. Integral as limit of a sum. Properties of definite integrals. Evaluation of definite integrals; determining areas of the regions bounded by simple curves.
Unit 11: Differential Equations:
Ordinary differential equations, their order and degree. Formation of differential equations. Solution of differential equations by the method of separation of variables. Solutions of homogeneous and linear differential equations, and those of the type.
Unit 12: Two Dimensional Geometry:
Recall of Cartesian system of rectangular coordinates in a plane, distance formula, area of a triangle, condition of the collinearity of three points and section formula, centroid and incentre 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.
(a)The straight line and pair of straight lines:
Various forms of equations of a line, intersection of line, angles between two lines, conditions for concurrence of three lines, distance of a point from a line Equations of internal and external bisectors of angles between two lines, coordinates of centroid, orthocenter and circumcentre of a triangle, equation of family of lines passing through the point of intersection of two lines, homogeneous equation of second degree in x and y, angle between pair of lines through the origin, combined equation of the bisectors of the angles between a pair of lines, condition for the general second degree equation to a represent a pair of lines, point of intersection and angle between two lines.
(b)Circles and Family of Circles:
Standard form of equation of a circle, general form of the equation of a circle, its radius and centre, equation of a circle in the parametric form, 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 conditions for the line to be tangent to the circle, length of the tangent, equation of the tangent, equation of a family of circles through the intersection of two circles, condition for two intersecting circles to be orthogonal.
Sections of cones, equations of conic sections (parabola, ellipse and hyperbola) in standard form, condition for y=mx+c to be tangent and points (s) of tangency.
Unit 13: Three Dimensional Geometry:
Coordinates 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. Equation of a line and a plane in different forms; intersection of a line and a plane, coplanar lines, equation of a sphere, its centre and radius. Diameter form of the equation of a sphere.
Unit 14: Vector Algebra:
Vectors and Scalars, addition of vectors, components of a vector in two dimensions and three dimensions space, scalar and vector products, scalar and triple product. Application of vectors to plane geometry.
Unit 15: Measures of Central Tendency and Dispersion:
Calculation of Mean, median and mode of grouped and ungrouped data. Calculation of standard deviation, variance and mean deviation for grouped and ungrouped data.
Unit 16: Probability:
Probability of an event, addition and multiplication theorems of probability and their application; conditional probability; Bayes’ Theorem, probability distribution of a random variate; Binomial and Poisson distributions and their properties
Unit 17: Trigonometry:
Trigonometrical identities and equations. Inverse trigonometric functions and their properties. Properties of triangles, including centroid, incentre, circum-centre and orthocenter, solution of triangles. Heights and Distances.
Unit 18: Statics:
Introduction, basis concepts and basic law of mechanics, force, resultant of forces acting at a point, parallelogram law of forces, resolved parts of a force, Equilibrium of a particle under three concurrent forces, triangle law of forces and its converse, Lami’s theorem and its converse, Two parallel forces, like and unlike parallel forces, couple and its moment.
Unit 19: Dynamics:
Speed and velocity, average speed, instantaneous speed, acceleration and retardation, resultant to two velocities. Motion of a particle along a line, moving with constant acceleration. Motion under gravity. Laws of motion, Projectile motion.
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