# NDA Maths Syllabus 2025 – Important Topics

NDA Mathematics Syllabus 2025- Candidates preparing for National Defence Academy examination should have the complete details on NDA Maths syllabus. UPSC releases the syllabus for NDA Mathematics 2025 at upsc.gov.in. Below is the last yearâ€™s NDA Maths exam syllabus. NDA exam syllabus include the important chapters and topics that aspirants must prepare for the exam.

## NDA Mathematics Syllabus 2025

 Chapter Topics Algebra Concept of set, operations on sets, Venn diagrams.Â  De Morgan laws, Cartesian product, relation, equivalence relation Representation of real numbers on a line.Â  Complex numbersâ€”basic properties, modulus, argument, cube roots of unity.Â  Binary system of numbers. Conversion of a number in a decimal system to a binary system and vice-versa.Â  Arithmetic, Geometric and Harmonic progressions.Â  Quadratic equations with real coefficients.Â  Solution of linear inequalities of two variables by graphs.Â  Permutation and Combination. Binomial theorem and its applications.Â  Logarithms and their applications. Matrices and Determinants Types of matrices, operations on matrices.Â  Determinant of a matrix, basic properties of determinants. Adjoint and inverse of a square matrix,Â  Applications- Solution of a system of linear equations in two or three unknowns by Cramerâ€™s rule and by Matrix Method. Trigonometry Angles and their measures in degrees and in radians.Â  Trigonometrical ratios.Â  Trigonometric identities Sum and difference formulae. Multiple and Sub-multiple angles.Â  Inverse trigonometric functions.Â  Applications-Height and distance, properties of triangles Analytical Geometry of Two and Three Dimensions Rectangular Cartesian Coordinate system. Distance formula. Equation of a line in various forms. Angle between two lines. Distance of a point from a line. Equation of a circle in standard and in general form. Standard forms of parabola, ellipse and hyperbola. Eccentricity and axis of a conic. Point in a three dimensional space, distance between two points. Direction Cosines and direction ratios. Equation two points. Direction Cosines and direction ratios. Equation of a plane and a line in various forms. Angle between two lines and angle between two planes. Equation of a sphere Differential Calculus Concept of a real valued functionâ€“domain, range and graph of a function.Â  Composite functions, one to one, onto and inverse functions.Â  Notion of limit, Standard limitsâ€”examples. Continuity of functionsâ€”examples, algebraic operations on continuous functions.Â  Derivative of function at a point, geometrical and physical interpretation of a derivativeâ€”applications.Â  Derivatives of sum, product and quotient of functions, derivative of a function with respect to another function, derivative of a composite function.Â  Second order derivatives. Increasing and decreasing functions.Â  Application of derivatives in problems of maxima and minima Integral Calculus and Differential Equations Integration as inverse of differentiation, integration by substitution and by parts, standard integrals involving algebraic expressions, trigonometric, exponential and hyperbolic functions.Â  Evaluation of definite integralsâ€”determination of areas of plane regions bounded by curvesâ€”applications.Â  Definition of order and degree of a differential equation, formation of a differential equation by examples.Â  General and particular solution of differential equations, solution of first order and first degree differential equations of various typesâ€”examples.Â  Application in problems of growth and decay. Vector Algebra Vectors in two and three dimensions, magnitude and direction of a vector.Â  Unit and null vectors, addition of vectors, scalar multiplication of a vector, scalar product or dot product of two vectors.Â  Vector product or cross product of two vectors.Â  Applicationsâ€”work done by a force and moment of a force and in geometrical problems. Statistics and ProbabilityÂ Statistics : Classification of data, Frequency distribution, cumulative frequency distributionâ€”examples.Â  Graphical representationâ€”Histogram, Pie Chart, frequency polygonâ€” examples.Â  Measures of Central tendencyâ€”Mean, median and mode.Â  Variance and standard deviationâ€”determination and comparison. Correlation and regression.Â  Probability : Random experiment, outcomes and associated sample space, events, mutually exclusive and exhaustive events, impossible and certain events.Â  Union and Intersection of events. Complementary, elementary and composite events.Â  Definition of probabilityâ€”classical and statisticalâ€”examples. Elementary theorems on probabilityâ€”simple problems.Â  Conditional probability, Bayesâ€™ theoremâ€”simple problems. Random variable as function on a sample space.Â  Binomial distribution, examples of random experiments giving rise to Binominal distribution.