## Syllabus

### NATA 2019 Syllabus ( NATA Exam 2019 portions of Study):

#### Architecture Aptitude:

Objects , Materials & components related architecture & built environment
Interpretations of pictorial compositions of historical or modern buildings, building materials, architects & their styles & works.
Visualizing 3-Dimensional objects from 2-dimensional drawing.
Visulalizing the different sides of 3 dimensional objects.
Analytical reasoning
Mental Ability ( visual , numerical & Verbal )
Awareness of national/International architects & their creations.

#### NATA Drawing Paper Syllabus:

Understanding scale & proportion of objects
Understanding geometrical compositions
Understanding the different shape & building forms & their elements
Understanding aesthetics, texture, color
Understanding the principles of harmony & contrast
Conceptualization & visualization of scenes from memory & imagination.
Drawing of patterns of geometry & abstracts.
Form transformations in 2D & 3D like additive forms, subtractive forms, rational property of surface & volumes.
Generation of plan, elevation & 3D views of Objects.
Creating 2D & 3D compositions using given shape & forms
Perspective drawing, Sketching of urbanscape & landscape.
NATA Drawing test scoring factors:

Candidate is suppose to answer 02 question in 120 minutes. The scoring in drawings is based on following  factors:

Ability to sketch a given object proportionately & rendering the same visually appealing manner
Visualising & drawing the effects of light on the object and shadows cast on surrounduings:
Sense of Perspective drawing
Combining & composing given 3-D elements to form a building or structural form.
Creating Visual harmony using colours in given cxomposition.
Understanding of scale & proportions.
Drawing from memory through pencil sketch on themes from day to day experiences.
Note: The NATA drawing paper will be evaluated by more than one  examiner & the marks are to be averaged.

#### NATA 2019 Mathematics syllabus:

Algebra,Binomial Theorem  Complex Numbers, Quadratic Equations, Matrices,VectorsLogarithms,  (positive integral index), Trigonometry,  Coordinate geometry of three dimensions, Sets, Relations & Mapping, Differential Calculus, Integral Calculus, Differential Equations,Coordinate geometry of two dimensions Application of Calculus,, Permutation & combination and Statistics & probability.

MATHEMATICS SYLLABUS IN DETAIL:
Algebra: Definitions of A. P. and G.P.; General term; Summation of first n-terms of series Σn, Σn²,Σn3 ; 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. Determinant of a square matrix. Properties of determinants (statement only). Minor, cofactor and adjoint of a matrix. Nonsingular matrix. Inverse of a matrix. Finding 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, 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. 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 common chord of two intersecting circles.

3-Dimensional Co-ordinate 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.

Theory of Calculus: Functions, 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 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, 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 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 trails and Binomial distribution.