Topic-wise Mathematics Preparation Tips for NDA Exam

The National Defence Academy exam is held twice a year by the UPSC to recruit candidates into the Air Force, Indian Military (Army), and Indian Navy.

The NDA selection procedure includes a written test as well as the SSB Interview, a personality and cognitive IQ test. Candidates who pass both rounds are recommended for final consideration. 

The written stage consists of two papers: Mathematics and General Ability Test. Each paper will take 2 hours and 30 minutes to complete. 

The mathematics section carries less weightage compared to General Ability Test. However, it plays a key role in shortlisting candidates. The Mathematics section of NDA is not a hard nut to crack as the standard of questions is basically of Class 11 and 12 levels. With a smart study plan and dedication, a candidate can secure good marks in the exam. 

On that note, let’s break down each topic in terms of its weightage, important sub-topics to focus on and tips that you can follow to ace the mathematics section in the upcoming NDA exam.


Algebra accounts for around 40 of the 120 questions, making it the most crucial topic to study.

Set theory, permutation and combination, quadratic equation and inequation, and functions have the highest amount of problems, making them the most important topics to study.

On a daily basis, devote as much time as possible to tackling math problems. If you’re studying for an exam at the last minute, you should concentrate on the most critical topics rather than going through the entire syllabus in detail.

Matrices and Determinants

Since there are few sub-topics under this one, preparation is made easier. Even if you don’t receive many questions from matrices, because the topic isn’t very broad, it’s much easier to cover in a short amount of time. On this subject, 8-12 questions are asked.


The most significant topics are trigonometric ratio and trigonometric height and distance, which each have at least 10-12 questions.

Trigonometry is related to differential calculus, and if you understand inverse trigonometry, you’ll have no trouble solving the problems in the differential calculus section of the paper.

You can safely skip the part on triangle properties, as there will be few questions on it.

Probability and Statistics

The probability and statistics portion has approximately 16-20 questions. To ace these parts, you must have a solid understanding of both areas.

Aside from the numerical issues, pay special attention to theoretical topics connected to statistics.

Regularly practise the numerical and memorise the concepts and formulae related to the issue.

Differential and Integral calculus

These sections, when taken collectively, account for a significant portion of the questions you’ll be asked, thus they can’t be skipped.

Certain sub-topics, such as area confined by region and differential equations, take a long time to prepare, although these parts do not receive many queries. As a result, they can be safely set aside for later.

The combined indefinite and definite integration contains 3-4 questions in the paper and should be given additional time and attention during preparation.

Analytic Geometry

This topic is divided into numerous subtopics, and approximately 10-12 questions are asked from it.

Straight lines, conic sections, and lines and planes are unquestionably the most crucial elements to prepare.

Other subtopics, such as coordinated geometry and 3-D geometry, are moderately essential, and you should focus more on them if you’re studying for this subject.

Vector Algebra

During the NDA math exam, you will be asked about 4-5 questions from this subject. If you’re cramming for the exam at the last minute, you can skip this portion if you’re confident in your other sections’ preparation. 

Go through vectors in two and three dimensions, as well as their magnitude and direction. Learn various vector operations like the addition of vectors, scalar multiplication of a vector, or dot product of two vectors.
Besides this, learn the cross product of two vectors and applications including work performed by a force and its moment, as well as geometrical issues.