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Syllabus
Mathematics
Algebra: Algebra of complex numbers, addition, multiplication,
conjugation, polar representation, properties of modulus
and principal argument, triangle inequality, cube roots
of unity, geometric interpretations.
Quadratic equations with real coefficients,
relations between roots and coefficients, formation
of quadratic equations with given roots, symmetric functions
of roots.
Arithmetic, geometric and harmonic progressions,
arithmetic, geometric and harmonic means, sums of finite
arithmetic and geometric progressions, infinite geometric
series, sums of squares and cubes of the first n natural
numbers.
Logarithms and their properties.
Permutations and combinations, Binomial
theorem for a positive integral index, properties of
binomial coefficients.
Matrices as a rectangular array of real
numbers, equality of matrices, addition, multiplication
by a scalar and product of matrices, transpose of a
matrix, determinant of a square matrix of order up to
three, inverse of a square matrix of order up to three,
properties of these matrix operations, diagonal, symmetric
and skew-symmetric matrices and their properties, solutions
of simultaneous linear equations in two or three variables.
Addition and multiplication rules of probability,
conditional probability, independence of events, computation
of probability of events using permutations and combinations.
Trigonometry: Trigonometric functions, their periodicity and
graphs, addition and subtraction formulae, formulae
involving multiple and sub-multiple angles, general
solution of trigonometric equations.
Relations between sides and angles of
a triangle, sine rule, cosine rule, half-angle formula
and the area of a triangle, inverse trigonometric functions
(principal value only).
Analytical geometry:
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.
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
in standard form, their foci, directrices and eccentricity,
parametric equations, equations of tangent and normal.
Locus Problems.
Three dimensions: Direction cosines
and direction ratios, equation of a straight line in
space, equation of a plane, distance of a point from
a plane.
Differential calculus: Real valued functions of a real variable,
into, onto and one-to-one functions, sum, difference,
product and quotient of two functions, composite functions,
absolute value, polynomial, rational, trigonometric,
exponential and logarithmic functions.
Limit and continuity of a function, limit
and continuity of the sum, difference, product and quotient
of two functions, l'Hospital rule of evaluation of limits
of functions.
Even and odd functions, inverse of a function,
continuity of composite functions, intermediate value
property of continuous functions.
Derivative of a function, derivative of
the sum, difference, product and quotient of two functions,
chain rule, derivatives of polynomial, rational, trigonometric,
inverse trigonometric, exponential and logarithmic functions.
Derivatives of implicit functions, derivatives
up to order two, geometrical interpretation of the derivative,
tangents and normals, increasing and decreasing functions,
maximum and minimum values of a function, applications
of Rolle's Theorem and Lagrange's Mean Value Theorem.
Integral calculus: Integration
as the inverse process of differentiation, indefinite
integrals of standard functions, definite integrals
and their properties, application of the Fundamental
Theorem of Integral Calculus.
Integration by parts, integration by the
methods of substitution and partial fractions, application
of definite integrals to the determination of areas
involving simple curves.
Formation of ordinary differential equations,
solution of homogeneous differential equations, variables
separable method, linear first order differential equations.
Vectors: Addition of vectors, scalar multiplication, scalar
products, dot and cross products, scalar triple products
and their geometrical interpretations.
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