Syllabus NATA 2019

Mathematics

General Aptitude 
Drawing Test

Algebra:
 A. P. and G.P.
 General term
 Summation of first nterms of series ∑n, ∑n²,..
 Arithmetic/Geometric series, and their relation
 Infinite G.P. series: its sum

Mathematical Reasoning

Logical operations like “and”, “or”, “if” and “only if”, implies, implied by, statements.

Understanding of tautology, converse, contrapositive, and contradiction.


Understanding of scale and proportion of objects.

Geometric composition, and shape.

Conceptualization and visualization through structuring objects in memory.

Drawing of patterns geometrical and abstract

Form transformations in 2D and 3D like union, surfaces, subtraction, rotation, and volumes.

Generating plan, elevation, 3D views of objects.

Creating 2D and 3D compositions using given forms & shapes.

Perspective drawing, sketching of urbanscape, landscape, common daytoday life objects like furniture, equipment etc., from memory.

Logarithms
 Definition
 Change of base
 General properties

Sets & Relations

Idea of sets, power set, subsets, complement, union, intersection and difference of sets,

Venn diagram, De Morgan’s Law, Relation and properties.

Equivalence relation —definition and elementary examples


Matrices
 Concepts of m x n (m ≤ 3, n ≤ 3) real matrices, operations of addition, multiplication of matrices, and scalar multiplication.
 Transpose of a matrix.
 A 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 an area of a triangle.
 Solutions of system of linear equations with one and two variables.


Texture, Objects related to architecture and built environment.

Interpretation of pictorial composition.

Visualizing threedimensional objects from the twodimensional drawing. Visualizing different sides of 3D objects.

Mental ability (visual, numerical and verbal), analytical reasoning.

General awareness of international/national architects.

General awareness of famous architectural creations.


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



Coordinate Geometry
 Section formula, Distance formula, area of a triangle, condition of collinearity of 3 points in a plane.
 Polar coordinates, the transformation from polar to cartesian coordinates and vice versa.
 Locus: Parallel transformation of axes, concept of locus, elementary locus problems.
 Line: Slope of a line. Equation of lines in different forms, angle between two lines, condition of perpendicularity and parallelism of two lines, lines through the point of intersection of two lines.
 The distance of a point from a line. The distance between two parallel lines.
 Circle : Equation of a circle with a given radius and center, condition of 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.
 Tangents & Chords: equation of tangent, normal and chord, parametric equation of a circle, the intersection of a line with a circle, and equation of common chord of two intersecting circles.



3D Coordinate Geometry
 Direction ratios and direction cosines
 The distance between the two points and section formula.
 The equation of a straight line.
 Distance of a point from a plane and the equation of a plane.



Theory & Application of Calculus
 The composition of two functions and inverse of a function, function limit, continuity, derivative, chain rule, derivative of implicit functions, and functions defined parametrically.
 Indefinite integral of standard functions and Integration as a reverse process of differentiation.
 Integration, integration by parts, integration by substitution, and partial fraction.
 Definite integral: Properties of definite integrals, definite integrals as a limit of a sum with equal subdivisions. The fundamental theorem of integral calculus and its applications.
 Differentiation: Formation of ordinary differential equations, the solution of homogeneous differential equations, separation of variables method, linear first order differential equations.
 Tangents, normals, conditions of tangency.
 Determination of monotonicity, minima, and maxima.
 Motion in a straight line with constant acceleration and differential coefficient as a measure of rate
 Geometric interpretation of definite integral as an area, calculation of area bounded by straight lines and elementary curves.
 Area of the region included between the two elementary curves.



Permutation & Combination
 Permutation of n different things taking r at a time (r ≤ n), permutation of n things not all different.
 The permutation with repetition (circular permutation excluded).
 Combinations of n different things taking r at a time (r ≤ n).
 Combination of n things not all different and basic properties.
 Problems involving the two together permutations and combinations.



Statistics & Probability
 Measure of dispersion, mean, standard deviation, variance, and frequency distribution.
 Multiplication and Addition rules of probability, conditional probability, and Bayes’ Theorem.
 Independence of events, repeated independent trials, and Binomial distribution


