Unit | Subtopics |
Matrices and their Applications | Algebra of matrices |
Determinants and its properties |
Adjoint and inverse of a square matrix (using determinants & elementary transformations) |
Rank of a matrix |
Test of consistency & solution of simultaneous linear equations (up to 3 variables) |
Solution of Linear Programming problem (in 2 Variables) |
Trigonometry and Complex Numbers | Fundamentals of Trigonometry |
Trigonometric functions & inverse trigonometric functions with properties |
Heights and distances |
Complex number system – conjugate, properties, ordered pair representation |
Argand diagram |
Algebra of complex numbers |
Modulus and argument (polar form) |
Solution of polynomial equations |
De Moivre’s theorem and its applications |
Roots of a complex number – cube roots & fourth roots |
Analytical Geometry of Two Dimensions | Equation of a straight line & family of straight lines |
Properties of straight lines |
General equation of a conic & its classification |
Eccentricity of conics |
Parabola – standard & general forms |
Ellipse – standard & general forms |
Hyperbola – standard & general forms |
Directrix, Focus & Latus rectum |
Parametric form of conics & chords |
Tangents and normals (Cartesian form & parametric form) |
Equation of the chord of contact of tangents |
Vector Algebra | Scalar product of vectors – properties & applications |
Vector product of vectors – properties & applications |
Scalar triple product |
Vector triple product – properties |
Analytical Geometry of Three Dimensions | Coordinates of a point in space |
Distance between two points |
Section formula |
Direction ratios & direction cosines |
Angle between two intersecting lines |
Skew lines |
Shortest distance between skew lines & its equation |
Equation of a line (different forms) |
Equation of a plane (different forms) |
Intersection of a line & a plane |
Coplanar lines |
Differential Calculus | Limits of functions |
Continuity of functions |
Differentiability of functions |
Tangent, normal & angle between curves |
Rolle’s Theorem |
Lagrange Mean Value Theorem |
Taylor’s series |
Maclaurin’s series |
Stationary points |
Increasing & decreasing functions |
Maxima & minima of functions (one variable) |
Concavity & points of inflexion |
Errors & approximations |
Integral Calculus and Its Applications | Simple definite integrals |
Fundamental theorems of calculus |
Properties of definite integrals |
Reduction formulae |
Area of bounded regions |
Length of curves |
Differential Equations | Formation of differential equations |
Order & degree of DE |
Solution of first-order DE by the variable separable method |
Solution of first-order DE by the homogeneous method |
Solution of first-order DE by the Linear equations method |
Applications of differential equations |
Probability and Distributions | Basics of probability & axioms |
Addition law of probability |
Conditional probability |
Multiplicative law of probability |
Bayes’ theorem |
Random variables |
Probability density function |
Distribution function |
Mathematical expectation |
Variance |
Binomial distribution |
Poisson distribution |
Discrete Mathematics | Sets |
Relations |
Functions |
Binary Operations |
Sequences & Series – AP |
Sequences & Series – GP |
Sequences & Series – HP |
Binomial Theorem |
Counting Techniques |
Mathematical Logic – logical statements |
Logical connectives |
Truth tables |
Logical equivalence |
Tautology |
Contradiction |