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- 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 & harmonic progressions.
- Arithmetic, geometric & 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.

- Problems on permutations & 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, 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 probability of events using permutations & combinations.

- Trigonometric functions, their periodicity and graphs, addition and subtraction formulae.
- Formulae involving multiple and sub-multiple angles.
- The general solution of trigonometric equations.

- 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.
- Even and odd functions, the inverse of a function, continuity of composite functions, intermediate value property of continuous functions.

- The addition of vectors, scalar multiplication.
- Dot and cross products
- Scalar triple products & their geometrical interpretations.

- Vectors and scalars, the addition of vectors.
- Components of a vector in two dimensions and three-dimensional space.
- Scalar and vector products, scalar and vector triple product.

- 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.

- 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..

- 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.
- The solution of homogeneous differential equations, separation of variables method.
- Linear first order differential equations.