# NDA 2023 Syllabus | NDA Paper 1 Syllabus PDF Download Free [Mathematics]

Syllabus is the primary thing for every exam, because it gives the proper orientation of how much and what to study for that examination which you are going to prepare for. Syllabus is like Overview of that Exam study Material. Before every exam preparation, every student should analyze the whole syllabus at once.

So, in this post, we elaborate on the Latest NDA 2022 Syllabus of Paper 1 which is a Mathematical paper that covers Trigonometry, Algebra, Differential Calculus, Vector Algebra, Integral Calculus, and Differential equations, Matrices and Determinants, Analytical Geometry of two and three dimensions, Statistics and Probability. This is the first Paper of the National Defence Academy (NDA) Entrance Exam which has a weightage of total of 300 marks out of 900 marks.

## NDA 2023 Syllabus | NDA Paper 1 Syllabus | NDA Maths Syllabus :-

The NDA Maths syllabus 2022 paper covers the following chapters and topics:-

Trigonometry: Trigonometrical ratios, properties of triangles, Angles and their measures in degrees and in radians, Inverse trigonometric functions, Trigonometric identities Sum and difference formulae, Applications – Height and distance, Multiple and Sub-multiple angles.

Algebra: Complex numbers – basic properties, modulus, Conversion of a number in decimal system to binary system and vice-versa, Arithmetic, argument, cube roots of unity, Geometric and Harmonic progressions, Solution of linear inequations of two variables by graphs, Representation of real numbers on a line, Binary system of numbers, Binomial theorem and its application, Quadratic equations with real coefficients, Permutation and Combination, Logarithms and their applications.

Differential Calculus: Composite functions, one-to-one, onto and inverse functions, geometrical and physical interpretation of a derivative – applications, increasing and decreasing functions, Continuity of functions – examples, algebraic operations on continuous functions, Application of derivatives in problems of maxima and minima,

Concept of a real-valued function – domain, range, and graph of a function, Notion of limit, Standard limits – examples, geometrical and physical interpretation of a derivative – applications, Derivative of a function at a point, Derivatives of sum, product and quotient of functions, a derivative of a function with respect of another function, a derivative of a composite function and Second order derivatives.

Vector Algebra: Vectors in two and three dimensions, scalar multiplication of vector, scalar product or dot product of two vectors, Applications-work done by a force and moment of a force, and in geometrical problems, magnitude and direction of a vector, Unit and null vectors, addition of vectors, Vector product and cross product of two vectors.

Integral Calculus and Differential equations: Integration by substitution and by parts, trigonometric, Definition of order and degree of a differential equation, formation of a differential equation by examples, exponential and hyperbolic functions, solution of first order and first-degree differential equations of various types – examples,

standard integrals involving algebraic expressions, Evaluation of definite integrals – determination of areas of plane regions bounded by curves – applications, General and particular solution of a differential equation, Integration as inverse of differentiation, Application in problems of growth and decay.

Matrices and Determinants: Types of Matrices, Determinant of a matrix, adjoin and inverse of a square matrix, operations on matrices, Applications – Solution of a system of linear equations in two or three unknowns by Cramer’s rule and by Matrix Method, basic properties of determinant.

Analytical Geometry of two and three dimensions: Distance formula, Equation of a circle in standard and in general form, Ellipse and hyperbola, Angle between two lines, Rectangular Cartesian Coordinate system, Equation of a line in various forms, Standard forms of parabola, Distance of a point from a line, Eccentricity and axis of a conic.

Point in a three-dimensional space, the distance between two points, Equation of a plane and a line in various forms, Equation of a sphere, Direction Cosines and direction ratios, the angle between two lines and angle between two planes.

Statistics: Frequency distribution, Classification of data, cumulative frequency distribution – examples Graphical representation – Histogram, Measures of Central tendency – mean, median and mode, Pie Chart, Frequency Polygon – examples, Variance and standard deviation – determination and comparison, Correlation and regression.

Probability: Outcomes and associated sample space, Binomial distribution, Random experiment, examples of random experiments giving rise to Binominal distribution, events, mutually exclusive and exhaustive events,

Bayes’ theorem – simple problems, impossible and certain events, Complementary, elementary and composite events, Union and Intersection of events, Definition of probability – classical and statistical – examples, Conditional probability, Random variable as function on a sample space, Elementary theorems on probability – simple problems, Binomial distribution, examples of random experiments giving rise to Binominal distribution.

It is not compulsory that the topics mentioned above will surely come in the examination. The question paper does not remain consistent, it changes every year. It may happen that the question paper will consists of the topic not discussed here.

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### What is the main NDA Maths Syllabus ?

The Paper 1 which is a Mathematical paper that covers Trigonometry, Algebra, Differential Calculus, Vector Algebra, Integral Calculus and Differential equations, Matrices and Determinants, Analytical Geometry of two and three dimensions, Statistics and Probability.

### What level of math is NDA?

The Mathematics section of NDA is not a hard nut to crack as the standard of questions are basically of Class 11 and 12 levels. With revision and practice, candidates can secure good marks in the exam.

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