hey,

the syllabus of UPSC NDA and NA(1) Written test is as follows

paper 1 ; mathematics (300 marks)

syllabus- concept of set, operation on sets, venn diagram , de morgan laws, cartesian product , relations , equivalence relation

1. algebra - representation of real number on a line complex numbers - basic properties, modulus,argument, cube roots of unity binary number system conversion of a number in decimal system to binary system and vice versa , arithmetic geometric and harmonic progression. quadratic equation with real coefficients. solution of linear inequation of 2 variable by graph permutation and combination. binomial theorem and its  applications. logarithms and their applications.

2. matrices and determinants  - type of matrices, operation on matrices . determinantof a matrix, basic properties of determinant, adjoint and inverse of a square matrix, application solution of a system of linear equations in two or three  unknowns by cramer's rule and by matrix method

3. trigonometry - angles and their measures in degree and in Radian.trigonometrical ratios. trigonomertric indentities sum and difference  formulae. multiple and sub multiple angles. inverse trigonometric function application height and distance, properties of triangle.

4. analytical geometry of two and three dimensions - rectangular cartesian coordinate system. distance formula. equation of a line 10 various forms. angle between 2 lines. distance of a point from a line. equation of a circle in standard and in genral form. standard form of parabola ellipse and hyperbola eccentricity and axis of a conic. point in a 3 dimensional space, distance between 2 points direction cosines in direction ratios. equation 2 points. Directions cosine and direction ratios. equation of a plane and a line in various forms. angle between 2 line and angle between 2 planes. equation of a sphere.

5. differential calculus - concept of a real valued function domain, range and  graph of a function. composite functions, one to one , onto and inverse function. notion  of limits, standard limits  example. continuity of functions examples, algebraic operation on continuous function.derivative of function at a point , geometrical and physical interpretation of a derivative application. derivatives of sum, products and quotient of functions, derivative of a function with respect to another function, derivative of a composite function. second order derivatives. Increasing and decreasing functions. application of derivatives in  problem of maxima and minima

6. integral calculus and differential equations - integration as inverse of differentiation, integration by substitution and by parts , standard integrals involving algebraic expression, trigonometric exponential and hyperbolic functions. Evaluation of definite integral determination of areas of planes regions bounded by curves  application. Definition of orders find degree of a differential equations formation of a differential equations by example. general and particular solution of  differential equations, solution of a first order and first degree differential equations of various types examples. application in problem of growth and decay.

7.  vector algebra - vectors in two and three dimensions , magnitude and direction of a vector. unit and null vector addition of vectors, scalar of multiplication of a vector, scalar product or dot product of two vectors. vector product or cross product of two vectors .application work done by a force and moment of a force and in grammatical problems

8. statistics and probability - statistics and classification of data , frequency distribution , cumulative frequency distribution examples. Graphical representation, histogram ,pie chart, frequency Polygon examples. measures of central tendency mean median and mode. variance and standard deviation determination and comparison. correlation and regression probability random experiment, outcomes and associated sample space, events mutually exclusive and exhaustive events, impossible uncertain events .union and intersection of events. Complementary . elementary and composite events. Definition of probability classical and statistical examples. elementary theorems on probability simple problems .conditional probability .bayes's theorems simple problems .random variable as function on a sample  space  binomial distribution, example of random experiments giving rise to binomial distribution.

hope it helps!

Hey aspirant

UPSC NDA examination consists of written exam which has two sections -

• Mathematics
• General ability test

For paper-1 Mathematics, the syllabus includes

• Algebra
• Matrices and determinants
• Trigonometry
• Analytical geometry of 2 and 3 dimensions
• Differential calculus
• Integral calculus and differential equations
• Vector Algebra
• Statistics and probability

For paper-2, General ability test, the syllabus is

• Part A: English - Grammar and usage, vocabulary, comprehension and cohesion in extended text
• Part B: General Science - Physics, Chemistry, General Science, Social Studies, Geography and Current Events