Name of Topic
NDA Maths Syllabus
Set concept, Sets operations, Venn diagrams, Laws of De Morgan, Cartesian product, Relations, Equivalence relation, Real number representation on a line, Complex numbers - basic properties, module, argument, cube roots, Binary number system, Conversion to the binary system of a number in the decimal system and vice versa, Progressions in arithmetic, geometry, and harmony, Solution of linear inequations of two variables by graphs, Permutation and Combination, Binomial theorem and its applications, Logarithms and their applications.
Matrices and Determinants
Matrix types, Operations, The determinant of a matrix, Determinants' properties, Application-Solution of a system of linear equations in two or three unknowns by the Cranmer's Rule and by the Matrix method, etc.
Angles and their degree and measurements, Trigonometric ratios, Sum of trigonometric identities and formulas, Multiple angles and sub-multiples, Trigonometric functions & their inverse, Applications-Height and Distance, Triangle Properties.
Analytical geometry of two and three dimensions
The Cartesian Rectangular Coordinate System, Formula of distance, Equation of a line in different shapes, Two lines of angle, A point's distance from a line, Standard and general equation of a circle, parabola, ellipse, and hyperbola, A conic's eccentricity and axis, Point the distance between two points in a three-dimensional space, Cosines of direction and ratios of direction, Two points of the equation, Cosines of direction and ratios of direction, A plane equation and a line in different forms, Two lines of the angle between two planes, Sphere's equation, etc.
Concept of a valued function - a function's domain, range, and graph, Composite functions, one by one, on, and vice versa, Limit notion, default limits — examples, Continuity of functions— examples, Continuous functional algebraic operations, Function derivative at a point, geometric and physical interpretation of an application derivative, Summary derivatives, product, and function quotient derivatives, function derivatives for another function, 20 composite function derivatives, Derivatives of the second order. Increasing and diminishing functions, Application of derivatives in maxima and minima problems, etc.
Integral Calculus and Differential Equations
Differentiation and integration, standard integrals with algebraic expressions, trigonometric, exponential, and hyperbolic functions.Definite integrals — determination of areas of curved plane regions — applications, General and particular solutions of differential equations, Solutions of the first order, and 1st-degree differential equations of various types—examples, Applications in problems of growth and decay.
2D and 3D vectors, vector magnitude, and direction, Unit and null vectors, vector adding, scalar-vector multiplication, scalar product or dot product, vector product, or cross product, Applications — work done through force and moment of force and in geometric problems.
Statistics & Probability
Statistics: data classification, distribution of frequencies, the cumulative distribution of frequencies — examples, Examples of graphic representation— histogram, pie chart, polygon frequency. Central tendency measurements — mean, median, and mode. Variance and deviation of standard — determination, and comparison, Correlation and regression, Sample space, events, exhaustive events & mutually exclusive, impossible and certain events associated with random experiments, results and associated, Union and events intersection, Complementary, composite, and elementary events, Probability, Bayes Theorem, Random variable on a sample space as a function, Binomial distribution, examples of random experiments, the binomial distribution.