Mathematics
Chapters
1. Sets, Relations and Functions
Set operations, types of relations, types of functions, composition, invertibility.
2. Complex Numbers and Quadratic Equations
Complex algebra, modulus and argument, polar form, De Moivre, quadratic roots.
3. Matrices and Determinants
Operations, transpose, inverse, properties of determinants, Cramer's rule, system of equations.
4. Permutations and Combinations
Counting principles, nPr, nCr, applications, identical objects, circular arrangement.
5. Mathematical Induction
Principle of mathematical induction with applications.
6. Binomial Theorem
Expansion of (a+b)^n, general term, middle term, properties of binomial coefficients.
7. Sequences and Series
AP, GP, HP, AM-GM-HM inequalities, sums of special series.
8. Limit, Continuity and Differentiability
Limits, continuity tests, differentiability, standard derivatives, chain rule, implicit, parametric.
9. Integral Calculus
Indefinite integrals, definite integrals, properties, areas under curves, applications.
10. Differential Equations
Order, degree, variable separable, homogeneous, linear DE, applications.
11. Coordinate Geometry
Straight lines, circles, parabola, ellipse, hyperbola — properties and equations.
12. Three-Dimensional Geometry
Direction cosines, lines and planes in 3D, shortest distance, angle between lines.
13. Vector Algebra
Vectors, dot and cross products, scalar triple product, applications.
14. Statistics and Probability
Mean, median, mode, variance, standard deviation; conditional probability, Bayes, distributions.
15. Trigonometry
Trig identities, equations, inverse trig functions, properties of triangles.
16. Mathematical Reasoning
Statements, logical operations, validity, contradiction, contrapositive.