General topics:

Gaseous and liquid states:

Atomic structure and chemical bonding:

Energetics:

Chemical equilibrium:

Electrochemistry:

Chemical kinetics:

Solid state:

Solutions:

Surface chemistry:

Nuclear chemistry:

Concepts:

Preparation, properties and reactions of alkanes:

Preparation, properties and reactions of alkenes and alkynes:

Reactions of benzene:

Phenols:

Characteristic reactions of the following (including those mentioned above):

Carbohydrates:

Amino acids and peptides:

Properties and uses of some important polymers:

Practical organic chemistry:

Algebra of complex numbers,

Quadratic equations

Arithmetic, geometric and harmonic progressions, arithmetic, geometric and harmonic means,

Arithmetic, geometric and harmonic progressions, arithmetic, geometric and harmonic means,

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, the determinant of a square matrix of order up to three, the 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 the probability of events using permutations and combinations.

Trigonometric functions, their periodicity and graphs, addition and subtraction formulae, formulae involving multiple and sub-multiple angles, the 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).

Two dimensions:

Parametric equations of a circle, the intersection of a circle with a straight line or a circle, the 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.

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, the inverse of a function, continuity of composite functions, intermediate value property of continuous functions. Derivative of a function, derivative of the sum,

The 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.

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, a solution of homogeneous differential equations, separation of variables method, linear first order differential equations.

The addition of vectors, scalar multiplication, dot and cross products, scalar triple products and their geometrical interpretations.