NATA Syllabus 2024: Detailed Topics and Subjects Highlights

Chapter

Topics

Algebra

Definitions of A. P. and G.P.; General term; Summation of first n-terms of series; 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, 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. The inverse of a matrix. Finding the 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, the transformation from Cartesian to polar coordinates and vice versa. Parallel transformation of axes, the concept of locus, elementary locus problems. The 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 centre and radius. A 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. The 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, the distance between two points and section formula, equation of a straight line, equation of a plane, a distance of a point from a plane.

Theory of Calculus

Functions, the 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. The 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. The area of the region included between two elementary curves.

Permutation and combination

Permutation of n different things taken r at a time. Permutation of things not all different. Permutation with repetitions (circular permutation excluded). Combinations of n different things taken r at a time. A combination of n things not all different. Basic properties. Problems involving both permutations and combinations.

Statistics and Probability

The 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.

Chapters

Topics

Sets and Relations

The idea of sets, subsets, power sets, complements, 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

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. 

Particulars

Details

Mode

Computer-Based and Offline Test

Duration

3 Hours

Part A - Drawing and Composition Test - 90 Minutes

Part B - MCQs - 90 Minutes

Medium

English and Hindi

Sections

Part A - Drawing and Composition Test

Part B - MCQs 

Number of Questions

48

Division of Questions

Part A - Drawing and Composition Test

• A1 - 1 Question - Composition and Colour
• A2 - 1 Question - Sketching and Composition (Black and White)
• A3 - 1 Question - 3D Composition

Part B - MCQs 

• B1 - 30 Questions
• B2 - 15 Questions

Marking Scheme

Part A - Drawing and Composition Test

• A1 - 1 Question - Composition and Colour - 25 marks
• A2 - 1 Question - Sketching and Composition (Black and White) - 25 marks
• A3 - 1 Question - 3D Composition - 30 marks

Part B - MCQs 

• B1 - 30 Questions x 2 marks - 60 marks
• B2 - 15 Questions x 4 marks - 60 marks