NATA Mathematics Syllabus 2027: Complete List of Topics

S. No.

NATA Mathematics Syllabus Section

Key Areas Covered

1

Algebra

A.P. and G.P., general term, series, A.M., G.M., and infinite G.P. series

2

Logarithms

Definition, general properties, and change of base

3

Matrices

Real matrices, matrix operations, determinants, inverse, and linear equations

4

Trigonometry

Trigonometric functions, formulae, trigonometric equations, properties of triangles, and inverse trigonometric functions

5

Coordinate geometry

Distance and section formulae, lines, circles, polar coordinates, locus, and related concepts

6

3-Dimensional Co-ordinate geometry

Direction cosines, direction ratios, distance, section formula, lines, planes, and distance from a plane

7

Theory of Calculus

Functions, limits, derivatives, integration, definite integrals, and differential equations

8

Application of Calculus

Tangents, normals, monotonicity, maxima and minima, motion, and area calculation

9

Permutation and combination

Permutations, combinations, repetitions, basic properties, and related problems

10

Statistics and Probability

Measures of dispersion, mean, variance, standard deviation, probability, Bayes’ Theorem, and Binomial distribution

Syllabus Section

Topics Covered

Algebra

Definitions of A. P. and G.P.

General term

Summation of first n terms of series ∑n, ∑n²,∑n3

Arithmetic/Geometric series

A.M., G.M. and their relation

Infinite G.P. series and its sum

Logarithms

Definition

General properties

Change of base

Matrices

Concepts of m x n (m ≤ 3, n ≤ 3) real matrices

Operations of addition, scalar multiplication and multiplication of matrices

Transpose of a matrix

Determinant of a square matrix

Properties of determinants (statement only)

Minor, cofactor and adjoint of a matrix

Nonsingular matrix

Inverse of a matrix

Finding area of a triangle

Solutions of system of linear equations

(Not more than 3 variables)

Trigonometry

Trigonometric functions

Addition and subtraction formulae

Formulae involving multiple and submultiple angles

General solution of trigonometric equations

Properties of triangles

Inverse trigonometric functions and their properties

Coordinate geometry

Distance formula

Section formula

Area of a triangle

Condition of collinearity of three points in a plane

Polar coordinates

Transformation from Cartesian to polar coordinates and vice versa

Parallel transformation of axes

Concept of locus

Elementary locus problems

Slope of a line

Equation of lines in different forms

Angle between two lines

Condition of perpendicularity and parallelism of two lines

Distance of a point from a line

Distance between two parallel lines

Lines through the point of intersection of two lines

Equation of a circle with a given center and radius

Condition that a general equation of second degree in x, y may represent a circle

Equation of a circle in terms of endpoints of a diameter

Equation of tangent, normal and chord

Parametric equation of a circle

Intersection of a line with a circle

Equation of common chord of two intersecting circles

3-Dimensional Co-ordinate geometry

Direction cosines and direction ratios

Distance between two points and section formula

Equation of a straight line

Equation of a plane

Distance of a point from a plane

Theory of Calculus

Functions

Composition of two functions and inverse of a function

Limit

Continuity

Derivative

Chain rule

Derivative of implicit functions and functions defined parametrically

Integration as a reverse process of differentiation

Indefinite integral of standard functions

Integration by parts

Integration by substitution and partial fraction

Definite integral as a limit of a sum with equal subdivisions

Fundamental theorem of integral calculus and its applications

Properties of definite integrals

Formation of ordinary differential equations

Solution of homogeneous differential equations

Separation of variables method

Linear first order differential equations

Application of Calculus

Tangents and normals

Conditions of tangency

Determination of monotonicity

Maxima and minima

Differential coefficient as a measure of rate

Motion in a straight line with constant acceleration

Geometric interpretation of definite integral as area

Calculation of area bounded by elementary curves and Straight lines

Area of the region included between two elementary curves

Permutation and combination

Permutation of n different things taken r at a time (r ≤ n)

Permutation of n things not all different

Permutation with repetitions (circular permutation excluded)

Combinations of n different things taken r at a time (r ≤ n)

Combination of n things not all different

Basic properties

Problems involving both permutations and combinations

Statistics and Probability

Measure of dispersion

Mean

Variance and standard deviation

Frequency distribution

Addition and multiplication rules of probability

Conditional probability and Bayes’ Theorem

Independence of events

Repeated independent trails

Binomial distribution