Mathematics syllabus

Algebra

Analytical geometry
Two dimensions: Cartesian coordinates, distance between two points, section
formulae, shift of origin.

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, Bayes
Theorem, 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. 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, 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, 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, separation of variables method, linear first order
differential equations.


Vectors

Addition of vectors, scalar multiplication, dot and cross products, scalar triple
products and their geometrical interpretations