NATA 2025 Syllabus PDF - Download Latest NATA Syllabus for All Subjects

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

Theory of calculus

Definite integral as a limit of a sum with equal subdivisions. Fundamental theorem of integral calculus and its applications. Integration by parts. Integration by substitution and partial fraction. Properties of definite integrals.Functions, composition of two functions and inverse of a function, limit, continuity, derivative, chain rule, derivatives of implicit functions and functions defined parametrically. Integration as a reverse process of differentiation, indefinite integral of standard functions. 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 is between two elementary curves.

Coordinate Geometry

Distance formula, section formula, area of a triangle, condition of collinearity of three points in a plane. Distance of a point from a line. Distance between two parallel lines. Lines through the point of intersection of two lines. 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. 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.

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. Nonsingular matrix. Inverse of a matrix. Finding the area of a triangle. Solutions of systems of linear equations. (Not more than 3 variables). Determinant of a square matrix. Properties of determinants (statement only). Minor, cofactor and adjoint of a matrix.

Permutation & 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 & 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 and Binomial distribution.

Trigonometry

Properties of triangles, inverse trigonometric functions and their properties. Trigonometric functions, addition and subtraction formulae, formulae involving multiple and submultiple angles, general solution of trigonometric equations. 

General

• Objects, texture related to architecture and the built environment. Interpretation of pictorial compositions,
• Visualizing three-dimensional objects from two-dimensional drawing. Visualizing different sides of 3D objects. Analytical reasoning, mental ability (visual, numerical and verbal), General awareness of national/ international architects and famous architectural creations

Sets & Relations

Idea of sets, subsets, power set, complement, union, intersection and difference of sets, Venn diagram, De Morgan's Laws, Relation and its properties. Equivalence relation — definition and elementary examples.

Mathematical Reasoning

Statements, logical operations like and, or, if and only if, implies, implied by. Understanding of tautology, converse, contradiction and contrapositive.

Drawing

Scale and Proportions of Objects, Building Forms and Elements, Pattern Drawing, Shape, Day to Day Object Drawing, Color Harmony, Creating Shapes and Forms, Perspective Drawing, Surfaces and Volumes, Urban Landscape, Conceptualization, and Visualization, Aesthetics, 3D and 2D Transformation, Generating Plan, Geometric Composition