Updated On : July 29, 2022

The Nationwide Aptitude Test in Architecture (**NATA**) is a national test administered by the Council of Architecture for admission to the 5-year B. Arch Degree Course at all approved universities in India. The following are some of the significant subjects that bear weightage in the exam:

- Mathematics.
- Physics and Geometry.
- Language and interpretation.
- Elements and principles of design.
- Aesthetic sensitivity.
- Colour theory.
- Lateral thinking and logical reasoning.

In order to appear for the NATA exam, a candidate should have mathematics as a compulsory subject for 10+2.

Numerical reasoning is an important part of the exam. It tests the candidate's mathematical ability through simple problems. The article walks you through the **NATA exam pattern** and topics for NATA preparations.

Download Free Study Material for NATA Exam 2022 by Creative Edge

This year, the disciplines of **Mathematics**, Physics, and Chemistry were not featured as the primary topics in the NATA official brochure 2022. Instead, Aptitude will be the critical portion from which questions in the test will be asked.

The official brochure, on the other hand, offers numerous related topics in the NATA test curriculum that may be questioned in the exam from the three courses. As a result, for reference, the following topics were mostly asked in the prior year's NATA exam.

Check out the **NATA syllabus** as listed below:

**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**

- Definitions
- General properties
- Change of base

**Matrices**

- Operations of addition
- Scalar multiplication and multiplication of matrices.
- Transpose of a matrix.
- Determinants of a square matrix.
- Properties of determinants (statement only).
- The minor, cofactor, and adjoint of a matrix.
- Nonsingular matrix.
- The inverse of a matrix.
- Finding the area of a triangle.
- Solutions of a system of linear equations.

Check: **NATA Exam Analysis 2022**

**Trigonometry**

- Trigonometric functions
- Addition and Subtraction formulae
- Formulae involving multiple and submultiple 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
- Concept of locus
- Elementary locus problems
- The slope of a line
- Equation of lines in different forms
- Angles 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
- 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 the common chord of two intersecting circles.
- 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.

**Theory of calculus**

- Functions are the composition of two functions and inverse functions.
- Limit
- Continuity
- Derivative
- Chain rule
- Derivatives of implicit functions and functions defined parametrically
- Integration as a reverse process of differentiation
- The 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

Check: **Important GK Questions for NATA**

**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 area, calculation of area bounded by elementary curves and Straight lines
- The Area of the region included two elementary curves

Check: **NATA Books**

**Permutation & Combination**

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

**Statistics & Probability**

- Measurement of dispersion, mean, variance, standard deviation, and frequency distribution.
- Addition and multiplication rules of probability
- Conditional probability and Bayes’ Theorem
- Independence of events
- Repeated independent trials
- Binomial distribution.

According to the analysis of the previous year’s maths questions, almost all the questions ranged from **easy to moderate level**.

Mathematics is very easy and basic. Mostly the questions were asked from matrices and determinants, relations, and functions. The simple area-based questions also form an important part of the exam.

The Maximum number of questions was based on ratio & proportion, and percentage; the questions in algebra were a little tricky. Students also said that Maths wasn't very calculative, and about 70% of questions were based on geometry.

Mathematical Reasoning based questions were asked, and the level of the questions was from class 6th to 10th based on the syllabus.

Overall, from the past some years the maths section has been very easy and scoring; perform your **NATA preparations**** **well and don't leave any topic since everything is pretty basic. You can easily score good marks in this section without wasting much time. Do keep in mind to go through and solve as many samples and previous year’s papers in order to understand the type of questions that may come in the exam.