Unit 1 Algebra 
Complex Numbers   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   Quadratic equations with real coefficients.
 Relations between roots and coefficients.
 Formation of quadratic equations with given roots.
 Symmetric functions of roots.

Sequence and Series   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   Logarithms and their properties.

Permutation and Combination   Problems on permutations and combinations.

Binomial Theorem   Binomial theorem for a positive integral index.
 Properties of binomial coefficients.

Matrices and Determinants   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, the inverse of a square matrix of order up to three.
 Properties of these matrix operations, diagonal, symmetric and skewsymmetric matrices and their properties.
 Solutions of simultaneous linear equations in two or three variables.

Probability   Addition and multiplication rules of probability, conditional probability.
 Bayes Theorem, independence of events.
 Computation of probability of events using permutations and combinations.

Unit 2 Trigonometry 
Trigonometric Functions   Trigonometric functions, their periodicity, and graphs, addition and subtraction formulae.
 Formulae involving multiple and submultiple angles.
 The general solution of trigonometric equations.

Inverse Trigonometric Functions   Relations between sides and angles of a triangle, sine rule, cosine rule.
 Halfangle formula and the area of a triangle.
 Inverse trigonometric functions (principal value only).

Unit 3 Vectors 
Properties of Vectors   The addition of vectors, scalar multiplication.
 Dot and cross products.
 Scalar triple products and their geometrical interpretations.

Unit 4 Differential Calculus 
Functions   Realvalued functions of a real variable, into, onto and onetoone functions.
 Sum, difference, product, and quotient of two functions.
 Composite functions, absolute value, polynomial, rational, trigonometric, exponential and logarithmic functions.
 Even and odd functions, the inverse of a function, continuity of composite functions, intermediate value property of continuous functions.

Limits and Continuity   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.

Derivatives   The derivative of a function, the 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.

Unit 5 Integral calculus 
Integration   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 Integration   Application of definite integrals to the determination of areas involving simple curves.

Differential Equations   Formation of ordinary differential equations.
 The solution of homogeneous differential equations, separation of variables method.
 Linear firstorder differential equations.
