NATA Syllabus 2025 | NATA Sample Papers & Mock Tests 2025 - JEE PDF Download

Syllabus for Mathematics 

(i) NATA Syllabus for 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.

(ii) NATA Syllabus for Logarithms

• Definition.
• General properties.
• Change of base. 

(iii) NATA Syllabus for 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 the area of a triangle.
• Solutions of systems of linear equations (Not more than 3 variables). 

(iv) NATA Syllabus for Trigonometry

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

(v) NATA Syllabus for Coordinate Geometry

• Distance formula, section formula, area of a triangle, condition of collinearity of three points in a plane.
• Polar coordinates the transformation from Cartesian to polar coordinates and vice versa.
• Parallel transformation of axes, the concept of the locus, elementary locus problems.
• Slope of a line.
• The 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 the common chord of two intersecting circles.

(vi) NATA Syllabus for 3-Dimensional Coordinate 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.

(vii) NATA Syllabus for Theory of Calculus

• 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.
• 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, a solution of homogeneous differential equations, separation of variables method, linear first-order differential equations.

(viii) NATA Syllabus for Application of Calculus

• Tangents and normals, conditions of tangency.
• Determination of monotonicity, maxima, and minima.
• Differential coefficient as a measure of the rate.
• Motion in a straight line with constant acceleration.
• Geometric interpretation of definite integral as an area, calculation of area bounded by elementary curves and Straight lines.
• The area of the region included between two elementary curves.

(ix) NATA Syllabus for 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.

(x) NATA Syllabus for 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 trials and Binomial distribution.

Detailed syllabus of Mathematics 

NATA Syllabus for General Aptitude

• Objects, texture related to architecture and the built environment.
• Interpretation of pictorial compositions, Visualising three-dimensional objects from the 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.

NATA Syllabus for Mathematical Reasoning

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

NATA Syllabus for Sets and 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.

Syllabus for Drawing Test

• Understanding of scale and proportion of objects, geometric composition, shape, building forms and elements, aesthetics, color texture, harmony and contrast.
• Conceptualization and Visualisation through structuring objects in memory.
• Drawing of patterns - both geometrical and abstract.
• Form transformations in 2D and 3D like union, subtraction, rotation, surfaces, and volumes.
• Generating plan, elevation and 3D views of objects.
• Creating 2D and 3D compositions using given shapes and forms.
• Perspective drawing, Sketching of urbanscape and landscape, Common day-to-day life objects like furniture, equipment, etc., from memory.