Mathematics

1. Sets

Sets and their representation, types of sets, subsets, Venn diagrams and operations on sets.

2. Relations and Functions

Cartesian products, relations, functions, domain, co-domain and range, and real-valued functions.

3. Trigonometric Functions

Radian measure, trigonometric functions and their graphs, compound and multiple angle identities, and general solutions of trigonometric equations.

4. Complex Numbers

Algebra of complex numbers, modulus and argument, the Argand plane and square roots of a complex number.

5. Quadratic Equations

Roots of a quadratic equation with real and complex coefficients, the discriminant, and relations between roots and coefficients.

6. Permutations and Combinations

The fundamental principle of counting, permutations, combinations and their applications.

7. Binomial Theorem

Binomial theorem for a positive integral index, general term, middle term and simple applications.

8. Sequence and Series

Arithmetic and geometric progressions, arithmetic and geometric means, and the sums of special series.

9. Straight Lines

Slope of a line, the forms of the equation of a straight line, the angle between two lines and the distance of a point from a line.

10. Circles

Standard and general equations of a circle, and problems on tangents, chords and points of intersection.

11. Conic Sections

Parabola, ellipse and hyperbola: standard equations, focus, directrix, eccentricity and latus rectum.

12. Introduction to Three-Dimensional Geometry

Coordinate axes and coordinate planes in space, the distance between two points and the section formula.

13. Limits and Derivatives

Limits of algebraic and trigonometric functions, the derivative from first principles, and the rules of differentiation.

14. Statistics

Measures of dispersion: range, mean deviation, variance and standard deviation, and the coefficient of variation.

15. Probability

Random experiments, sample space, events, and the axiomatic approach to probability.

16. Correlation Analysis

Scatter diagrams, Karl Pearson's coefficient of correlation and Spearman's rank correlation.

17. Index Numbers and Moving Averages

Price index numbers, methods of construction, and smoothing a time series by moving averages.