C. QUADRATIC EQUATIONS: Quadratic equations and their solutions, relation between roots and coefficients, nature of roots, formation of quadratic equations with given roots.
D. PERMUTATIONS AND COMBINATIONS: Fundamental principle of counting; permutation as an arrangement and combination as a selection, meaning of P(n, r) and C(n, r), simple applications.
E. SEQUENCES AND SERIES: Arithmetic, Geometric and Harmonic progressions. Relation between A.M., G.M. and H.M.. Special series’ n, n2, n3, Arithmetico-Geometric series, exponential and logarithmic series.
F. VECTOR ALGEBRA: Vectors and scalars, addition of two vectors, components of a vector in two and three dimensional space, scalar and vector products, scalar and vector triple products. Application of vectors to plane geometry.
G. TRIGONOMETRY: Trigonometrical identities and equations. Inverse trigonometric functions and their properties. Properties of triangles including centroid, incentre, circumcentre and orthocentre. Solution of triangles. Heights and distances.
H. MEASURES OF CENTRAL TENDENCY AND DISPERSION: Calculation of mean, median and mode, standard deviation, variance and mean deviation for grouped and ungrouped data.
I. PROBABILITY: Probability of an event, addition and multiplication theorems of probability and their applications. Conditional probability; Bayes’ theorem. Probability distribution of a random variate- Binomial and Poisson distributions and their properties.
J. DIFFERENTIAL CALCULUS: Polynomial, rational, trigonometric, logarithmic and exponential functions. Graphs of simple functions. Limits, continuity and differentiation of the sum, difference, product and quotient of two functions. Differentiation of trigonometric, inverse trigonometric, logarithmic, exponential, composite and implicit functions; derivatives of order up to two. Applications of derivatives-maxima and minima of functions of one variable, tangents and normals, Rolle’s and Lagrange’s mean value theorems.
K. 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. Integral as a limit of sum. Properties of definite integrals. Evaluation of definite integral, determining areas of the regions bounded by simple curves.
L. DIFFERENTIAL EQUATIONS: Formation of differential equations. Solutions of first order differential equations- the method of separation of variables, homogeneous and linear differential equations.
M. TWO DIMENSIONAL GEOMETRY: Review of cartesian system of rectangular co-ordinates in a plane, distance formula, area of a triangle, condition for the collinearity of three points, slope of a line, parallel and perpendicular lines, intercepts of a line on the coordinate axes.
N. THE STRAIGHT LINE AND PAIR OF 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 of internal and external bisectors of angles between two lines, equation of a family of lines passing through the point of intersection of two lines, point of intersections and angles between two lines. Pair of straight lines- condition for the general second degree equation to represent a pair of lines, point of intersection and angle between pair of lines through the origin, combined equation of the bisectors of the angles between a pair of lines
O. CIRCLES AND FAMILY OF CIRCLES: Equation of a circle- standard form, general form, parametric form, equation of a circle when the end points of a diameter are given. Radius and centre of a circle, points of intersection of a line and a circle. Condition for a line to be tangent, equation of a family of circles through the intersection of two circles, condition for two intersecting circles to be orthogonal.
P. CONIC SECTIONS: Sections of cones, equations of conic sections (parabola, ellipse and hyperbola) in standard forms, conditions for a line to be a tangent and point(s) of tangency.
Amrita Engineering Exam 2010 Syllabus for Mathematics
