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NATA Maths Syllabus and Sample questions 2022

Author : Palak Khanna

Updated On : July 29, 2022

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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

Syllabus For Maths

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

  1. Definitions of A. P. and G.P.
  2. General term
  3. Summation of first n-terms of series ∑n, ∑n²,∑n3 
  4. Arithmetic/Geometric series, A.M., G.M., and their relation
  5. Infinite G.P. series and its sum.

Logarithms

  1. Definitions
  2. General properties
  3. Change of base

Matrices

  1. Operations of addition
  2. Scalar multiplication and multiplication of matrices. 
  3. Transpose of a matrix.
  4. Determinants of a square matrix. 
  5. Properties of determinants (statement only). 
  6. The minor, cofactor, and adjoint of a matrix. 
  7. Nonsingular matrix. 
  8. The inverse of a matrix. 
  9. Finding the area of a triangle. 
  10. Solutions of a system of linear equations.

Check: NATA Exam Analysis 2022

Trigonometry

  1. Trigonometric functions
  2. Addition and Subtraction formulae
  3. Formulae involving multiple and submultiple angles
  4. The general solution of trigonometric equations. 
  5. Properties of triangles 
  6. Inverse trigonometric
  7. Functions and their properties
  8. Coordinate Geometry:
  9. Distance formula
  10. Section formula
  11. Area of a triangle 
  12. Condition of collinearity of three
  13. Points in a plane
  14. Polar coordinates 
  15. The transformation from Cartesian to polar coordinates and vice versa
  16. Parallel transformation of axes
  17. Concept of locus 
  18. Elementary locus problems
  19. The slope of a line
  20. Equation of lines in different forms
  21. Angles between two lines
  22. Condition of perpendicularity and parallelism of two lines
  23. Distance of a point from a line
  24. Distance between two parallel lines
  25. Lines through the point of intersection of two lines.
  26. Equation of a circle with a given center and radius
  27. A condition that a general equation of second degree in x, y may represent a circle
  28. Equation of a circle in terms of endpoints of a diameter
  29. Equation of tangent
  30. Normal and Chord
  31. Parametric equation of a circle
  32. The intersection of a line with a circle
  33. Equation of the common chord of two intersecting circles.
  34. 3-dimensional coordinate geometry
  35. Direction cosines and direction ratios 
  36. Distance between two points and section formula 
  37. Equation of a straight line 
  38. Equation of a plane
  39. Distance of a point from a plane.

NATA mock test

NATA Mock test

Theory of calculus

  1. Functions are the composition of two functions and inverse functions.
  2. Limit
  3. Continuity
  4. Derivative
  5. Chain rule
  6. Derivatives of implicit functions and functions defined parametrically
  7. Integration as a reverse process of differentiation
  8. The indefinite integral of standard functions
  9. Integration by parts
  10. Integration by substitution and partial fraction
  11. Definite integral as a limit of a sum with equal subdivisions
  12. Fundamental theorem of integral calculus and its applications
  13. Properties of definite integrals
  14. Formation of ordinary differential equations 
  15. Solution of homogeneous differential equations
  16. Separation of variables method
  17. linear first-order differential equations

Check: Important GK Questions for NATA

Application of calculus

  1. Tangents and normals
  2. Conditions of tangency
  3. Determination of monotonicity, maxima, and minima
  4. Differential coefficient as a measure of the rate
  5. Motion in a straight line with constant acceleration.
  6. Geometric interpretation of definite integral as area, calculation of area bounded by elementary curves and Straight lines
  7. The Area of the region included two elementary curves

Check: NATA Books

Permutation & Combination

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

Statistics & Probability

  1. Measurement of dispersion, mean, variance, standard deviation, and frequency distribution.
  2. Addition and multiplication rules of probability
  3. Conditional probability and Bayes’ Theorem
  4. Independence of events
  5. Repeated independent trials 
  6. Binomial distribution.

Previous Year Questions And Analysis

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.

Conclusion 

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.

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