How to Prepare for NDA Mathematics? Know Complete Strategy
National Defence Academy & Naval Academy Exam 2026 ( NDA )
Exam On - 12 Apr '26
NDA Preparation Tips 2025 for Maths: The Maths section of NDA exam carries questions from Algebra, Calculus, Matrices and Determinants, Integral Calculus and Differential Equations, Trigonometry, Vector Algebra etc. To ace this section, candidates can prepare by solving the previous years' question papers and mock tests. It is also important to remember the theorem and formulas. Besides, candidates must also revise the important topics for the exam. Candidates must learn the shortcut tricks of solving questions. Read below NDA preparation tips for Maths.
NDA Maths Preparation Tips 2025: Are you preparing for NDA 2025 exam? If yes, this article on 'How to prepare the Maths section for NDA exam' will be helpful. The Maths section of the NDA 2025 exam comprises questions from Algebra, Calculus, Matrices and Determinants, Integral Calculus and Differential Equations, Trigonometry, Vector Algebra etc. NDA Maths section carries 120 objective-type multiple-choice questions for 300 marks. The standard of questions asked in the NDA Maths section is of Class 11 and 12 levels. To do well in this section, candidates must practice the previous years' question papers, practice mock tests, and refer to good study materials. It is better to clarify the concept of the topics from the school-level books. Here are a few tips and tricks on how to prepare for NDA Mathematics.
- NDA Exam Pattern 2025 for Mathematics
- NDA Mathematics Syllabus
- Topic-Wise Distribution of Questions in NDA Maths Paper
- How to Prepare for NDA Mathematics?
- Best Books for Mathematics
NDA Exam Pattern 2025 for Mathematics
The Mathematics section of NDA carries a total of 120 objective-type multiple-choice questions. The total marks allotted to this section are 300. Candidates get two hours and 30 minutes to solve the question paper. For the correct answer, candidates score 2.5 marks while 0.83 marks are deducted for wrong answers. Candidates need to follow the NCERT books thoroughly to understand all the concepts.
NDA Exam comprises two papers-English and Hindi. Total marks allotted to the written exam are 900. Candidates qualifying the written exam are called for SSB Interview. The SSB Interview carries 900 marks.
To clear the NDA exam, you generally need to score between 340 to 360 out of 900 marks. NDA cut off for written exam is calculated out of 900. NDA cut off for final selection is calculated out of 1800. NDA cut off is calculated based on difficulty level of the exam, number of test takers, number of vacancies.
Also Read:
NDA Mathematics Syllabus
NDA syllabus comprises topics from Algebra, Matrices and Determinants, Trigonometry, Analytical Geometry of two and three dimensions, Differential Calculus, Integral Calculus and Differential Equations, Vector Algebra and Statistics and Probability. The detailed syllabus for Maths paper is given below:
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| Topics | Sub-Topics |
|---|---|
| Algebra |
Sets, Venn diagrams, De Morgan laws, Cartesian product, relation, equivalence relation. Real numbers, Complex numbers, Modulus, Cube roots, Conversion of a number in Binary system to Decimals and vice-versa. Arithmetic, Geometric and Harmonic progressions. Quadratic equations, Linear inequations, Permutation and Combination, Binomial theorem and Logarithms. |
| Calculus |
Concept of a real-valued function, domain, range and graph of a function. Composite functions, one-to-one, onto and inverse functions. Notion of limit, Standard limits, Continuity of functions, algebraic operations on continuous functions. Derivative of function at a point, geometrical and physical interpretation of a derivative application. Derivatives of sum, product and quotient of functions, derivative of a function with respect to another function, derivative of a composite function. Second-order derivatives. Increasing and decreasing functions. Application of derivatives in problems of maxima and minima |
| Matrices and Determinants |
Types of matrices, operations on matrices. Determinant of a matrix, basic properties of determinants. Adjoint and inverse of a square matrix, Applications-Solution of a system of linear equations in two or three unknowns by Cramer’s rule and by Matrix Method. |
| Integration as inverse of differentiation, integration by substitution and by parts, standard integrals involving algebraic expressions, trigonometric, exponential and hyperbolic functions. Evaluation of definite integrals—determination of areas of plane regions bounded by curves-applications. Definition of order and degree of a differential equation, formation of a differential equation by examples. General and particular solutions of differential equations, solutions of the first order and first-degree differential equations of various types-examples. Application in problems of growth and decay. |
|
| 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. |
| Vectors in two and three dimensions, magnitude, and direction of vector. Unit and null vectors, the addition of vectors, scalar multiplication of a vector, scalar product, or dot product of two vectors. Vector product or cross product of two vectors. Applications—work done by a force and moment of a force and in geometrical problems. |
|
| Analytical Geometry Of Two and Three Dimension |
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 a general form. Standard forms of parabola, ellipse, and hyperbola. Eccentricity and axis of a conic. Point in a three-dimensional space, the distance between two points. Direction Cosines and direction ratios. Equation two points. Direction Cosines and direction ratios. Equation of a plane and a line in various forms. Angle between two lines and angle between two planes. Equation of a sphere. |
| Statistics and Probability |
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. |
Topic-Wise Distribution of Questions in NDA Maths Paper
The topic-wise distribution of questions in Mathematics is given below:
| Subjects | Number of Question |
|---|---|
| Algebra |
30 |
| Trigonometry |
20 |
| Determinants and matrices |
10 |
| Analytical Geometry |
20 |
| Vector Algebra |
10 |
| Statistics and Probability |
10 |
| Differential calculus and Integral calculus |
20 |
| Total |
120 |
How to Prepare for NDA Mathematics?
Follow the tips and tricks below for the Mathematics section:
- Candidates must have a clear understanding of the NDA syllabus and mark the important topics after analyzing the previous years’ question papers.
- Start preparing the important topics first, and at the same time, delegate time for the difficult topics.
- Solve mock tests to decide how much time to dedicate to each type of question. Also, candidates must solve the previous year's question papers to get an idea about the type of questions asked in the exam.
- Candidates must learn tips, tricks and shortcuts for efficient time management.
- Memorise simple calculations such as squares and cubes.
- Make notes of shortcuts and formulas to refer to during last-minute revision.
- As there is a negative marking in the exam, they should mark the answer only if they are sure about it. Do not guess the answers during the exam.
- Candidates must refer to good Mathematics books for NDA preparation
- During the final phase of preparation, devote at least three hours for going through the formula.
- Do not get confused while converting the numbers from decimal to a binary system.
- Trigonometry can be tricky. So be clear with the concepts such as Properties of Triangles and Inverse Trigonometric functions. Hence, solve such questions at the end.
- Vector Algebra is the most important unit in the syllabus. Practice questions from Vector Product or Cross Product of two vectors.
- The statistics part can be easy to crack but be careful while taking the figures.
- In Probability, the Elementary Theorems, Bayes' Theorem and Binomial Distribution are important.
Best Books for Mathematics
It is important that candidates choose a good book for the Mathematics section of NDA:
- NCERT Class 11 and 12 books
- Mathematics for NDA and NA: National Defense Academy and Naval Academy by R S Aggarwal
- Quantitative Aptitude for Competitive exam by RS Aggarwal
- NDA and NA examination: Previous solved papers by R Gupta
Also Read: NDA Books
UPSC releases the list of test cities along with the notification. Candidates are required to choose one test city as per their preferences while filling the application form. One test city can have multiple exam centres. The details regarding the NDA exam centres are mentioned on the admit card. Candidates need to appear for the exam at the allotted test centre or else their answer scripts are not evaluated. While appearing for the exam, candidates need to carry the printed copy of their admit cards along with one photo-identity proof to the allotted NDA exam centre.
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