# Official Syllabus for NATA 2018 – Mathematics, General Aptitude, Drawing Test

##### Published on : 30th April 2018    Author : Himanshu Basant Bhatt National Aptitude Test in Architecture (NATA) is conducted by the Council of Architecture (COA) for admission to the first year of 5 years B.Arch. degree course offered by the recognised institutions across the country. The actual admission is done by the concerned authorities/institutes on the basis of NATA score.

NATA 2018 is scheduled to be conducted on 29 April 2018 (Sunday) in a single session from 09:30 AM to 12:30 PM. The online exam comprises of Part A and Part B. Part A includes Multiple Choice Questions (MCQs) while Part B is a drawing test. Here is the detailed pattern of NATA 2018:

## NATA 2018 Exam Pattern

 Section Subjects Number of Questions Marks per question Total marks PART A Mathematics 20 2 marks 40 General Aptitude 40 2 marks 80 PART B Drawing 2 40 marks 80 TOTAL 62 200

Scroll left or right to view full table

Now, let’s have a look at the detailed syllabus for the National Aptitude Test in Architecture.

## NATA Exam Syllabus for 2018

As per the official notification, here is the syllabus for different sections of the test:

MATHEMATICS

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. The 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 sub-multiple angles, the 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 the locus, elementary locus problems. The slope of a line. The equation of lines in different forms, angle between two lines. The condition of perpendicularity and parallelism of two lines. The distance of a point from a line. The distance between two parallel lines. Lines through the point of intersection of two lines. The equation of a circle with a given centre and radius. The condition that a general equation of second degree in x, y may represent a circle. The equation of a circle in terms of endpoints of a diameter. The equation of tangent, normal and chord. Parametric equation of a circle. The intersection of a line with a circle. The 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, the equation of a straight line, the equation of a plane, the 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, 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 the 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, the 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 an 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 trials and Binomial distribution.

GENERAL APTITUDE

Objects, texture related to architecture and built environment. Interpretation of pictorial compositions, Visualizing 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.

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

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.

DRAWING TEST

Understanding of scale and proportion of objects, geometric composition, shape, building forms and elements, aesthetics, colour texture, harmony and contrast. Conceptualization and Visualization 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 shape and forms. Perspective drawing, Sketching of urbanscape and landscape, Common day-to-day life objects like furniture, equipment etc., from memory.