Mathematics

1. Relations and Functions

Types of relations, one-one and onto functions, composition of functions, invertible functions and binary operations.

2. Inverse Trigonometric Functions

Definitions, principal value branches, graphs and the elementary properties of inverse trigonometric functions.

3. Matrices

Types of matrices, addition, scalar multiplication, matrix multiplication, transpose and the inverse of a matrix by elementary operations.

4. Determinants

Properties of determinants, minors and cofactors, the adjoint and inverse of a matrix, and solving a system of linear equations.

5. Continuity and Differentiability

Continuity, differentiability, derivatives of composite, implicit, inverse trigonometric, exponential and logarithmic functions, and Rolle's and Lagrange's theorems.

6. Applications of Derivatives

Rate of change, increasing and decreasing functions, tangents and normals, maxima and minima, and approximations.

7. Integrals

Integration as the inverse of differentiation, integration by substitution, by parts and by partial fractions, and the definite integral and its properties.

8. Applications of Integrals

Area under simple curves and the area between two curves.

9. Differential Equations

Order and degree, variables separable, homogeneous and linear differential equations of the first order.

10. Vectors

Vectors and scalars, direction cosines, addition of vectors, and the scalar and vector products.

11. Three-Dimensional Geometry

Direction cosines and ratios, the equation of a line and of a plane, the angle between them and the shortest distance between two lines.

12. Probability

Conditional probability, the multiplication theorem, independent events, Bayes' theorem and probability distributions.

13. Linear Regression

Lines of regression of y on x and x on y, the regression coefficients and their properties.

15. Application of Calculus in Commerce and Economics

Cost, revenue and profit functions, marginal cost and revenue, break-even point and elasticity of demand.

14. Linear Programming

Formulating a linear programming problem and solving it graphically in two variables.