NDA Maths Syllabus – UPSC NDA Maths Paper Strategy & Key Topics

The Union Public Service Commission (UPSC) conducts the NDA (National Defence Academy) Exam twice a year to select candidates for the Indian Army, Navy, and Air Force. Among the two written papers Mathematics and General Ability, Mathematics often becomes the deciding factor in whether a candidate makes it to the next stage or not. With 300 marks riding on it, the NDA Maths paper demands not just hard work, but also smart strategy and deep understanding of concepts.

NDA SYLLABUS

Overview of NDA Maths Exam

Total Marks and Time Duration

The NDA Mathematics paper carries 300 marks and has a duration of 2.5 hours. There are 120 questions, each carrying 2.5 marks, but beware — 0.83 marks are deducted for each wrong answer.

Importance of Maths Paper in NDA

Scoring well in the Maths paper is crucial. Even if you ace the GAT (General Ability Test), failing in Maths can ruin your selection chances. You need at least 25% marks in each paper to qualify.

Official Guidelines from UPSC

The Union Public Service Commission (UPSC) releases the official NDA syllabus annually. The maths syllabus is based on the 10+2 level and includes topics from algebra, calculus, trigonometry, geometry, and statistics.

NDA MATHS SYLLABUS

S. NO	TOPICS	SUB TOPICS
1.	ALGEBRA	- Concept of 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 number system, conversions of a number in decimal system to binary system and vice-versa. - Arithmetic, Geometric, Harmonic progressions - Quadratic equations with real coefficients - Solution of Linear inequations of two variables by graph - Permutation and Combination - Binomial theorem & applications - Logarithms & applications
2.	MATRICES AND DETERMINANTS	-Types and 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.
3.	TRIGONOMETRY	- Angles and their measures in degrees and in radians - Trigonometric ratios and identities - Sum and difference formulas - Multiple and sub-multiple angles - Inverse trigonometric functions - Heights & distances - Properties of triangles
4.	ANALYTICAL GEOMENTRY ( 2D & 3D)	- Rectangular Cartesian coordinate system - Distance formula, equation of a line in various forms. - Angle between lines, distance from a point to a line - Circles (standard/general form) - Parabola, ellipse, hyperbola (standard forms) - Eccentricity and axis of conics - Point in a three dimensional space, distance between two points. Direction Cosines & Direction ratios. - Equation of plane and line in various forms - Angle between two lines and angle between two planes - Equation of sphere
5.	DIFFERENTIAL CALCULUS	- Real valued functions: domain, range, graphs - Composite, one-one, onto, inverse functions - Notion of Limit and standard limit examples - Continuity of functions—examples, algebraic operations on continuous functions. - Derivative of function at a point, geometrical and physical interpretation of a derivative—applications. - 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.
6.	INTEGRAL CALCULUS & DIFFERENTIAL EQUATONS	- Integration as inverse of differentiation - Integration by substitution and by parts - Standard integrals involving algebraic, trigonometric, exponential, and hyperbolic functions - Definite integrals and area determination - Applications of definite integrals (area under curves) - Order and degree of differential equations - Formation of differential equations with examples - General and particular solutions - First-order, first-degree differential equations (various types) - Applications in growth and decay problems
7.	VECTOR ALGEBRA	- Vectors in 2D and 3D - Magnitude and direction of a vector - Unit and null vectors - Vector addition and scalar multiplication - Dot product (scalar product) - Cross product (vector product) - Applications: work done by a force, moment of a force, and geometrical problems
8.	STATISTICS AND PROBABILITY	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 Binominal distribution.

Marking Scheme in NDA Maths – 2025

Understanding the marking scheme is non-negotiable. It helps you plan your attempts wisely and reduce silly mistakes.

1. Total Marks

Paper 1 – Mathematics
Total Questions: 120
Total Marks: 300
Each Correct Answer: +2.5 Marks

So, if you get 60 questions right:
60 × 2.5 = 150 marks

2. Negative Marking

Each Wrong Answer: –0.83 marks
This means if you randomly guess 10 questions and get all wrong, you lose 8.3 marks.

3. Time Duration

You get 2.5 hours to solve 120 questions
That’s approximately 1.25 minutes per question. Time is tight—practice is your only savior.

4. Cut-Off Insight

Expected NDA Maths Cut-off for 2025: Between 120 and 150 marks
The overall NDA written exam cut-off is around 350–370, and Maths plays a big part.

5. Importance of Accuracy

You don’t have to solve all 120 questions.
If you attempt just 70–75 questions accurately, you can easily hit 150+ marks.
It’s about quality over quantity.

Tips to Crack NDA Maths 2025

Cracking NDA Maths isn't about solving every question—it's about solving the right questions with speed and accuracy. Here's how you can ace it:

1. Master the Basics First

Before diving into advanced problems, make sure you’re solid with Class 11 and 12 fundamentals.

2. Focus on High-Weightage Topics

Don't waste time on rarely asked topics. Prioritize:

Algebra (Progressions, Quadratic Equations, Complex Numbers)
Trigonometry (Identities, Heights & Distances)
Calculus (Differentiation, Integration)
Matrices & Determinants
Coordinate Geometry

These topics often make up 60–70% of the paper.

3. Time Yourself

Practice under time pressure. Practice solving previous years question papers. Take mock tests where you solve 120 questions in 2.5 hours—just like the real exam.

4. Don’t Fear Tricky Chapters

Many aspirants avoid calculus or complex numbers. But if you tackle them early with the right resources, they become your scoring assets.

5. Avoid Guesswork

With negative marking (-0.83 per wrong answer), blind guessing can sink your score. Attempt only when you're at least 70% confident.

6. Make Formula Charts

Create a small notebook with all key formulas from:

Algebra identities
Trigonometric ratios
Derivatives and Integrals
Coordinate Geometry slopes and equations

Revise them daily for 15 minutes.

7. Use Short Tricks—but Only After You Understand the Concept

Vedic maths and shortcut methods save time, but only use them once your understanding is solid. Don’t blindly apply tricks.

CONCLUSION

Cracking NDA Maths in 2025 is absolutely possible—if you follow the syllabus smartly, focus on high-weightage topics like Algebra, Trigonometry, and Calculus, and avoid common pitfalls like cramming or skipping concepts. Understand the marking scheme, practice religiously, and stick to a routine.

FAQ

Q1: Which topics are most important in NDA Maths?
A: Key topics include Trigonometry, Algebra, Coordinate Geometry, Calculus, and Statistics. These areas carry significant weight in the exam, so focus more on them during your preparation.

Q2: How important is trigonometry for NDA?
A: Very! It’s one of the most asked topics in NDA Maths, and mastering it gives you quick and accurate marks.

Q3: How many marks are required to clear NDA Maths?
A: The safe score range is 120–150 marks, but aiming higher increases your SSB interview chances.

Q4: Is algebra tough in the NDA exam?
A: Not if you’ve practiced enough. Algebra has consistent patterns and identities. Practice is key.

Q5: Can I clear NDA Maths if I’m weak in maths basics?
A: Yes, start early and focus on understanding concepts rather than just memorizing. Basics matter more than shortcuts.

NDA Maths Syllabus 2025 UPSC Exam Guide