NDA I 2021 Math Preparation tips, Syllabus and Reference Books

Updated On -

Mar 11, 2021

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Sudeshna Bhar

Exams Prepmaster

The NDA or National Defence Academy exam is conducted twice every year to select cadets for the Indian Army, Indian Navy and Indian Air Force.

The tier-1 exam comprises two papers- mathematics and general ability test. With an entire paper dedicated to math and 300 marks, it calls for extra attention while you are preparing for the exam. Read NDA Exam pattern

The subject plays a vital role in attending the qualifying marks needed for the exam and have to be prepared based on your 10+2 syllabus. Check Here NDA 2021 Syllabus


NDA I Mathematics Syllabus 2021

Mathematical Topics Sub Topics
Algebra Concept of a set, operations on sets, Venn diagrams. De Morgan laws, Cartesian product relation, equivalence relation, Representation of real numbers on a line, Complex numbers – basic properties, modulus argument, Cube roots of unity, Binary system of numbers, Conversion of a number in decimal system to binary system and vice-versa, Arithmetic, Geometric and Harmonic progressions, Quadratic equations with real coefficients, Solution of linear inequations of two variables by graphs, Permutation and Combination, Binomial theorem and its application, Logarithms and their applications.
Trigonometry Angles and their measures in degrees and in radians, Trigonometric ratios, Trigonometric identities Sum and difference formulae, Multiple and Sub-multiple angles, Inverse trigonometric functions, Applications – Height and distance, properties of triangles
Matrices and Determinants Matrices and Determinants, Operations on matrices, Determinant of a matrix, basic properties of determinants, Adjoint and the inverse of a square matrix, Applications.
Analytical Geometry Rectangular Cartesian Coordinate system, Distance formula, Equation of a line in various forms, the angle between two lines, Distance of a point from a line, Equation of a circle in standard and in general form, Standard forms of parabola, Ellipse and hyperbola, Eccentricity and axis of a conic.
Vector Algebra Vectors in two and three dimensions, magnitude and direction of a vector, Unit and null vectors addition of vectors, Scalar multiplication of vectors.
Statistics and Probability Statistics: Classification of data, Frequency distribution, cumulative frequency distribution – examples. Graphical representation – Histogram, Pie Chart, Frequency Polygon – examples. Measures of Central tendency – Mean, Median and Mode. Variance and standard deviation – determination and comparison. Correlation and regression. Probability: Random experiment, outcomes and associated sample space, events, mutually exclusive and exhaustive events, impossible and certain events. Union and Intersection of events. Complementary, elementary and composite events. Definition of probability – classical and statistical – examples. Elementary theorems on probability – simple problems. Conditional probability, Bayes’ theorem – simple problems. Random variable as function on a sample space. Binomial distribution, examples of random experiments giving rise to Binomial distribution.
Differential calculus and Integral calculus Integration as inverse of differentiation, Integration by substitution and by parts, standard integrals involving algebraic expressions, Trigonometric, Exponential and hyperbolic functions, General and particular solution of a differential equation.

Question Pattern

NDA I Mathematic Paper: Question Pattern

The syllabus is entirely based on the mathematics taught at the 10+2 level at CBSE schools. The tier-1 exam is in MCQ format and conducted in conventional offline pen and paper form. The following table is a brief on the NDA I math paper-

Particulars Details
Topic Mathematics
Question Format MCQ (Multiple Choice Questions)
Number of questions 120
Marks for the correct answer 2.5 Marks
Negative marking for every wrong answer -0.83 marks
Exam duration 2 hours 30 minutes (150 minutes)
Total Marks 300

Paper Analysis

NDA I Math- Question Analysis

Mathematical Topics Marks Number of Question
Algebra + Vector Algebra 75 30
Trigonometry 50 20
Determinants and matrices 25 10
Analytical Geometry 50 20
Vector Algebra 25 10
Statistics and Probability 25 10
Differential calculus and Integral calculus 50 20
Total 300 120

The math paper is designed to test the candidate's speed and accuracy of calculations and their quantitative aptitude. The key is to practice the sections that have the maximum marks weightage such that you can get every question from these sections correct.

Check Here NDA 2021 Exam Pattern

Preparation Tips

NDA I Topic-wise Mathematics Preparation Tips

NDA I mathematics syllabus is entirely based on the 10+2 CBSE syllabus. We have prepared NDA Preparation Tips, focusing on the most important topics in Math. The following topics carry the maximum marks weightage and if you can confidently solve these sections, you can secure the qualifying marks for the paper.

NDA Mathematics Exam- Realistic Target

To make the most of the available time, it is important to set a very realistic target for your exam preparation. Scoring approximately 135-140 in the math paper is good enough to ensure you have the required marks to meet the total NDA tier-1 cut-off.

  • Out of the 120 questions, if you answer even 60 questions accurately you can secure 150 marks. By keeping a range of 3-4 wrong answers, your total score will still be 136.67 approx.
  • This approach helps you get more time to prepare only for the important topics.
  • When you are well prepared, the chances of negative marks and wrong answers are also minimized.
  • You get more time to solve each question that you are attempting instead of roughly 1.25 minutes per question when you attempt all of them.


You get approximately 40 out of the 120 questions from algebra, making it the most important topic to be prepared.

  • The maximum number of questions come from algebraic subtopics like set theory, permutation and combination, quadratic equation and inequation and functions, making them the prime topics to focus on.
  • Dedicate maximum time to solving algebra on a daily basis.
  • Complex numbers, logarithms, sequences and series are of medium priority as comparatively lesser questions come from these topics.
  • If you are taking last-minute preparation for the exam, you should focus more on the important topics rather than covering the entire syllabus minutely.

Matrices and Determinants

There are very few sub-topics under this one and hence, preparation becomes easier. Though you do not get too many questions from matrices, since the topic is not too vast, it is much easier to cover in minimum time. There are 8-12 questions asked on this topic.


There are several sub-topics of trigonometry and at the same time, it also carried major marks weightage in the exam.

  • Trigonometric ratio and trigonometric height and distance are the most important topics as you get at least 10-12 questions from them.
  • Trigonometry is related to differential calculus and if your conception of inverse trigonometry is clear, you can easily solve the problems from the differential calculus section which is another major part of the paper.
  • You can safely skip the section of properties of triangles from which you will hardly get any questions.

Probability and Statistics

Approximately 16-20 questions are from the probability and statistics section altogether. To ace, these sections, your conception of both topics should be very clear.

  • Particularly pay attention to theoretical concepts related to statistics, besides the numerical problems.

  • Practice the numerical on a regular basis and memorize the concepts and formulas associated with the topic.

Differential and Integral calculus

Combined together, these sections have a major share in the questions that you get and hence you cannot leave them out.

  • Certain sub-topics like area bound by region, and differential equations are time-consuming to prepare but you do not get many questions from these sections. Hence, they can be safely left out for later.
  • Indefinite and definite integration together has a share of 3-4 questions in the paper and should be given more time and attention while preparing.

Analytic Geometry

  • There are several sub-topics of this section and approximately 10-12 questions are asked from this section.
  • Straight lines, conic sections and lines and planes are definitely the most important sections that you must prepare.
  • Other subtopics like coordinated geometry, 3-D geometry are moderately important and if you are preparing for this section, emphasize more on these sub-topics.

Vector Algebra

There are approximately 4-5 questions asked from this section during the NDA math paper. If you are preparing for the exam at the last minute, you can skip this section, provided you are confident about your preparation for the other sections.

Math Books

NDA I 2021- Recommended Mathematics Books

For NDA Maths Paper, nothing is more helpful than the NCERT books of Class 10, 11 and 12. But once you have clarified your conceptions by following the NCERT books, you can venture for more advanced NDA math books. The following are some of the best NDA Math Reference Books you can invest in:

Books Name Author
11th and 12th Mathematics books NCERT
Mathematics for NDA and NA: National Defense Academy and Naval Academy by R S Aggarwal R S Aggarwal
Pathfinder for NDA & NA Experts Compilation
Objective General Knowledge & Current Affairs level 1 Disha Experts
Objective General Knowledge & Current Affairs level 2 Disha Experts
Mathematics for NDA/NA: National Defence Academy and Naval Academy RS Aggarwal
Study Package Mathematics NDA/NA Entrance Exam Arihant
Quantitative Aptitude for competitive examinations RS Aggarwal
NDA Entrance Exam ES Ramasamy

Setting a realistic goal for your maths exam not only make sure you ace this paper but also makes your study time table more organized. The best books, a full-proof plan of action and making the most of the available time, together can make sure you crack NDA I 2021 right in your first attempt.


NDA 2021 FAQ

Question: Is there any separate paper-wise cut-off for the NDA I exam?

Ans. No, there is no paper wise cut-off for the exam but you have to secure 33% of the total marks in order to qualify for the paper. If you get the total aggregate but fail to secure 33% marks in a paper, it will not be considered.

Question: How to manage my time and cover all the subjects?

Ans. You have to set a daily 10-11hours study routine which you must dedicatedly follow. Further, segregate this time for different subjects but make sure you allow some time for math practice every day.

Question: Is it safe to skip topics and sub-topics while practising math?

Ans. If you are confident about the topics you are preparing and know for a fact that you will make minimal mistakes with them, you can skip comparatively less important topics.

Question: I belong to a different school board than CBSE. Will that be a problem in preparation?

Ans. The syllabus of CBSE Math is more or less the same as every other board but it is best to tally the syllabus with your school-level syllabus first, to find out if there are any new topics to be covered.

*The article might have information for the previous academic years, please refer the official website of the exam.