Let us be completely honest with you.
When we sit with a new batch at Alpha NDA Academy, one of the first questions almost every student asks us is “Sir, which chapters are most important in NDA Maths? Should I study everything?”
And honestly, that is one of the smartest questions a student can ask.
Because here is the reality NDA Mathematics has a broad syllabus that covers topics from Class 11 and Class 12. If you try to study everything equally without knowing which chapters are heavier, you will waste precious time on topics that rarely appear while missing out on chapters that give you 30–40 marks every single year.
At Alpha NDA Academy, we have been tracking NDA question papers for years. We analyse every paper after it comes out not just which questions appeared, but which chapter they came from, how many questions per chapter, and how that compares to previous years.
This blog gives you the chapter-wise weightage for NDA Maths based on that analysis along with what it means for your preparation strategy.
If you are a student in Class 10th, 11th, or 12th preparing for NDA, read this carefully. It will save you months of misdirected effort.
NDA Maths Paper Quick Overview First
Before we get into chapter-wise weightage, you need to understand the structure of the Maths paper. Many students do not even know these basics.
| Detail | Information |
| Paper Name | Paper 1 Mathematics |
| Total Questions | 120 Questions |
| Total Marks | 300 Marks |
| Marks Per Correct Answer | +2.5 Marks |
| Negative Marking | 0.83 Marks (1/3 of 2.5) |
| Exam Duration | 2.5 Hours (150 Minutes) |
| Question Type | Objective (MCQ) with 4 options |
So you have 120 questions, 150 minutes which means roughly 75 seconds per question.
You cannot afford to spend 5 minutes on one question. Speed, accuracy, and smart topic selection all matter together.
And the best way to manage all three is to know exactly which chapters appear how many times, and prepare them accordingly.
Want to understand how marks work in detail? Read our post: NDA Marking Scheme Explained Simply
NDA Maths Chapter-Wise Weightage (2026) Based on Previous Years’ Papers
The table below shows approximate chapter-wise weightage based on our analysis of NDA question papers from the past several years (NDA I & II 2022, 2023, 2024, 2025).
These are not guesses; they are patterns observed across multiple papers. The exact number of questions shifts slightly from exam to exam, but the priority order remains remarkably consistent year after year.
| Chapter | Approximate Questions | Approximate Marks | Priority Level |
| Algebra | 22–28 | 55–70 | High |
| Trigonometry | 18–25 | 45–62 | High |
| Differential Calculus | 14–18 | 35–45 | High |
| Integral Calculus & Differential Equations | 10–14 | 25–35 | Medium-High |
| Analytical Geometry (2D) | 10–13 | 25–32 | Medium-High |
| Matrices & Determinants | 9–12 | 22–30 | Medium |
| Statistics & Probability | 8–12 | 20–30 | Medium |
| Analytical Geometry (3D) | 6–10 | 15–25 | Medium-Low |
| Vector Algebra | 5–8 | 12–20 | Low-Medium |
| Total | ~120 | ~300 |
Important note: These are approximate ranges based on pattern analysis. UPSC does not officially publish chapter-wise question count. The numbers will vary slightly by 2–3 questions per chapter from exam to exam.
Now let us go chapter by chapter and tell you exactly what comes, how to prepare it, and how much time to give it.
Chapter 1 Algebra (Highest Weightage | 22–28 Questions)
Priority: Cannot be skipped. Prepare thoroughly.
Algebra is consistently the biggest chapter in NDA Maths, year after year. With roughly 22 to 28 questions, it alone accounts for nearly 18–23% of the entire Maths paper.
If you score well in Algebra, you are already at an advantage over most other aspirants.
What Topics Come From Algebra
- Sets, Venn Diagrams, and Operations on Sets
- Complex Numbers modulus, argument, algebra of complex numbers
- Quadratic Equations with real coefficients
- Arithmetic Progression (AP), Geometric Progression (GP), and Harmonic Progression (HP)
- Permutations and Combinations
- Binomial Theorem
- Logarithms
What We See in Actual Papers
From our experience analysing NDA papers, AP/GP, Complex Numbers, Permutation & Combination, and Quadratic Equations are the most repeated sub-topics in Algebra. Almost every paper has 3–4 questions from AP/GP alone.
Sets and Venn Diagrams tend to give 2–3 straightforward questions that any student can get right with basic practice.
Preparation Tip
Start Algebra from NCERT Class 11. Build the concepts first. Then move to objective practice from NDA-specific books. Do not skip Binomial Theorem it appears every single year.
Time to invest in Algebra: 15–18% of your total Maths preparation time.
Chapter 2 Trigonometry (Very High Weightage | 18–25 Questions)
Priority: One of the most scoring chapters in NDA Maths.
Trigonometry is right behind Algebra in terms of weightage. With 18–25 questions, it accounts for roughly 15–20% of the Maths paper.
The good news Trigonometry is very formula-based. Once you know the formulas and practise applying them, questions become predictable and fast to solve.
What Topics Come From Trigonometry
- Trigonometric Ratios and Identities
- Values of standard angles (0°, 30°, 45°, 60°, 90°)
- Sum and Difference Formulas
- Multiple and Sub-Multiple Angles (2A, 3A, A/2 formulas)
- Properties of Triangles (sine rule, cosine rule, area formulas)
- Height and Distance Problems
- Inverse Trigonometric Functions
What We See in Actual Papers
Trigonometric Identities and Height & Distance are the most repeated topics. Inverse Trigonometry has been appearing more frequently in recent years. Properties of Triangles usually gives 2–3 questions per paper.
A student who masters trig identities and inverse trig can comfortably solve 12–15 questions out of 18–25 Trig questions in the exam.
Preparation Tip
Make a formula sheet literally one A4 page with every important trig formula. Revise it every night. Practice Height & Distance problems daily because they require a different mindset than formula-based questions.
Time to invest in Trigonometry: 12–16% of your total Maths preparation time.
Chapter 3 Differential Calculus (High Weightage | 14–18 Questions)
Priority: Third most important chapter. Cannot be ignored.
Calculus is the section many students fear, but it is also the section where consistent students pull far ahead of those who prepare casually.
Differential Calculus alone gives approximately 14–18 questions. That is 35–45 marks up for grabs.
What Topics Come From Differential Calculus
- Limits standard limits, evaluation of limits
- Continuity of functions
- Differentiation (first and second order)
- Derivative of composite, implicit, and inverse functions
- Applications of Derivatives Maxima and Minima, Increasing/Decreasing functions
- Tangent and Normal to curves
What We See in Actual Papers
Limits, Differentiation, and Maxima-Minima are the most frequently asked topics. Application-based questions (finding slope, tangent, maxima) appear almost every year.
Students who understand the chain rule and differentiation rules thoroughly can solve 10–12 Calculus questions in under 90 seconds each.
Preparation Tip
Do not jump to solving problems before understanding the concept. If limits are unclear, 3–4 questions will go wrong. Start with NCERT Class 12 Calculus for conceptual clarity, then shift to NDA-specific objective questions.
Time to invest in Differential Calculus: 12–14% of your total Maths prep time.
Chapter 4 Integral Calculus & Differential Equations (Medium-High | 10–14 Questions)
Priority: Important especially Integration.
Integration is the continuation of Calculus and appears in nearly every NDA paper. Differential Equations questions are usually simpler in NDA compared to JEE, which is good news for aspirants.
What Topics Come Here
- Integration by substitution and by parts
- Standard integrals
- Definite Integrals and Area under curves
- Order and Degree of Differential Equations
- Solution of first-order differential equations
What We See in Actual Papers
Definite integrals and integration by substitution are the most common. Differential equation questions are usually direct identify order and degree, or solve a simple first-order equation.
Preparation Tip
Learn the standard integral formulas by heart. Just 25–30 standard integrals cover 80% of what appears in NDA. Do not spend too much time on complex integration methods that rarely appear.
Time to invest: 10–12% of your total Maths prep time.
Chapter 5 Analytical Geometry 2D (Medium-High | 10–13 Questions)
Priority: Consistent scorer good return on effort.
2D Geometry covers straight lines, circles, and conic sections (parabola, ellipse, hyperbola). This chapter is very formula-friendly and once you know the formulas, questions are fast.
What Topics Come Here
- Distance and Section Formula
- Straight Lines slopes, equations in different forms, parallel and perpendicular lines
- Circles standard form, general form, tangent conditions
- Conic Sections Parabola, Ellipse, Hyperbola (basic properties and standard equations)
What We See in Actual Papers
Straight Line and Circle questions appear very consistently. Conic section questions are usually one or two focused on eccentricity, directrix, or focus.
Preparation Tip
Make a formula chart for Straight Lines and Circles. These sections are pure formula-recall and application. Once the formulas are solid, questions take under 60 seconds each.
Time to invest: 8–10% of your total Maths prep time.
Chapter 6 Matrices & Determinants (Medium | 9–12 Questions)
Priority: Medium but these are usually the easiest marks in the paper.
Matrices is a very systematic chapter. The questions are predictable types of matrices, operations, determinant value, finding inverse. Students who practise Matrices properly almost always get these questions right.
What Topics Come Here
- Types of Matrices (square, diagonal, identity, symmetric, etc.)
- Matrix Addition, Subtraction, Multiplication
- Determinant of a 2×2 and 3×3 matrix
- Properties of Determinants
- Adjoint and Inverse of a Matrix
- Solving simultaneous equations using matrix method
What We See in Actual Papers
Determinant value, matrix multiplication, and finding the inverse are the most repeated question types. These questions are usually straightforward if you know the process.
Preparation Tip
This is the chapter where students often leave easy marks on the table by not practising enough. 2–3 weeks of focused Matrices practice can lock in 8–10 questions that are almost certain to be correct in the exam.
Time to invest: 7–9% of your total Maths prep time.
Chapter 7 Statistics & Probability (Medium | 8–12 Questions)
Priority: Underestimated by most students very scoring.
Most NDA aspirants spend very little time on Statistics and Probability because it does not seem as “important” as Algebra or Calculus. That is a mistake we see students make repeatedly.
Statistics and Probability combined give 8–12 questions that are often among the most direct and formula-based questions in the entire paper.
What Topics Come Here
- Mean, Median, Mode, Standard Deviation, Variance
- Frequency distribution and cumulative frequency
- Probability basics events, sample space
- Conditional Probability
- Binomial distribution (basics)
What We See in Actual Papers
Mean, Standard Deviation, and basic Probability calculations appear almost every year. Conditional Probability questions have appeared consistently in recent NDA papers.
Preparation Tip
Do not treat Statistics as a last-minute topic. Give it proper time. 2 weeks of focused preparation here can easily get you 15–20 additional marks which is huge in a 300-mark paper.
Time to invest: 7–9% of your total Maths prep time.
Chapter 8 Analytical Geometry 3D (Medium-Low | 6–10 Questions)
Priority: Lower priority, but do not ignore completely.
3D Geometry covers coordinates in space, lines and planes in 3 dimensions, and spheres. The number of questions from this chapter has been around 6–10 per paper.
What Topics Come Here
- Distance between two points in space
- Direction Cosines and Direction Ratios
- Equation of a Line in space (vector and Cartesian form)
- Equation of a Plane
- Angle between two lines and two planes
- Equation of a Sphere
Preparation Tip
Focus on Direction Cosines, Line in Space, and Plane equations. These three sub-topics give most of the 3D Geometry questions. Sphere questions are rare but not absent.
Time to invest: 5–7% of your total Maths prep time.
Chapter 9 Vector Algebra (Low-Medium | 5–8 Questions)
Priority: Lower weightage prepare basics, do not over-invest time.
Vectors is the smallest chapter in terms of NDA Maths weightage. With 5–8 questions typically, it is still worth knowing because these are usually straightforward formula-based questions.
What Topics Come Here
- Types of Vectors (Unit, Null, Position)
- Addition of Vectors and Scalar Multiplication
- Dot Product (Scalar Product) angle between vectors, projection
- Cross Product (Vector Product) area of triangle, parallelogram
- Applications work done by a force, moment of a force
Preparation Tip
Learn the formulas for Dot Product and Cross Product. Questions are direct. Do not spend more than 1.5–2 weeks on this chapter.
Time to invest: 4–5% of your total Maths prep time.
The Big Picture Priority Order at a Glance
Based on everything above, here is how you should prioritise your NDA Maths preparation:
HIGH PRIORITY Master These First (Gives ~55–60% of Maths Paper)
- Algebra 22–28 questions. The backbone of the paper.
- Trigonometry 18–25 questions. Formula-based and very scoring.
- Differential Calculus 14–18 questions. Needs concept clarity.
MEDIUM PRIORITY Cannot Afford to Ignore (Gives ~30–35% of Maths Paper)
- Integral Calculus & Differential Equations 10–14 questions
- Analytical Geometry (2D) 10–13 questions. High accuracy possible.
- Matrices & Determinants 9–12 questions. Easy marks for the prepared.
- Statistics & Probability 8–12 questions. Most underrated scoring section.
LOWER PRIORITY Prepare After Completing Above (Gives ~10–15% of Maths Paper)
- Analytical Geometry (3D) 6–10 questions
- Vector Algebra 5–8 questions
How to Build Your NDA Maths Preparation Strategy Using This Weightage
Knowing the weightage is only half the job. Using it smartly is what separates students who crack NDA written from those who miss by 10–15 marks.
Here is how we approach it with our students at Alpha NDA Academy:
Phase 1 Foundation (First 6–8 Weeks)
Start with NCERT Class 11 and Class 12 Mathematics. Build the concept base for all chapters. Do not rush. A student who understands why a formula works will always outperform one who just memorised it.
Focus chapters in Phase 1: Algebra basics, Trigonometry ratios and identities, Matrices, Sets.
Phase 2 Topic-Wise Mastery (Next 8–10 Weeks)
Now go chapter by chapter in priority order. Spend more time on Algebra, Trigonometry, and Calculus. Solve 50–70 chapter-specific practice questions before moving to the next chapter.
Use NDA-specific books alongside NCERT. The question style in NDA is different from board exams it is faster, more objective, and tests application over theory.
Phase 3 Mixed Practice and Mock Tests (Next 4–6 Weeks)
Start solving full NDA Maths papers all 120 questions in 150 minutes. Time yourself. Track your chapter-wise accuracy in each mock test.
If you find you are getting only 3 out of 10 Calculus questions right, that is your signal to revise Calculus. Use mock test results like a mirror not a judgement, but a direction.
Phase 4 Revision and Speed Building (Final 3–4 Weeks Before Exam)
Stop studying new topics. Focus only on revision and speed. Revise your formula sheets daily. Solve 30–40 questions every day to keep your problem-solving speed sharp.
For a detailed month-by-month study plan, check: NDA Study Plan for 6 Months Complete Strategy
Common Maths Mistakes NDA Aspirants Make (That Cost Them Marks)
We have seen these mistakes across hundreds of students. Learn from them.
Mistake 1: Spending too much time on Vector Algebra and 3D while ignoring Algebra This is backwards. Algebra gives you 22–28 questions. Vectors give you 5–8. Time investment should match.
Mistake 2: Practising only the chapters they like Many students prepare Trigonometry and Matrices well because they enjoy them, but avoid Calculus because it feels hard. The exam does not reward comfort it rewards coverage.
Mistake 3: Attempting questions without preparation just to “try” With negative marking of 0.83 per wrong answer, 3 wrong attempts in Maths cost you 2.49 marks that is practically one full correct question lost. Never guess randomly.
Mistake 4: Skipping Statistics and Probability These are among the easiest-to-prepare chapters, yet students ignore them. 8–10 marks from Statistics could be the difference between clearing and missing the cutoff.
Mistake 5: Not practising under time pressure The biggest problem we see in mock tests is students who know the concept but take 4–5 minutes per question. At 75 seconds per question, speed is as important as accuracy.
Read more about preparation mistakes to avoid: NDA Preparation Mistakes Students Make
How Many Questions Should You Attempt in the Maths Paper?
This is one of the most practical questions, and the answer depends on your preparation level.
| Preparation Level | Ideal Questions to Attempt | Expected Score Range |
| Beginner (3–4 months) | 60–70 questions | 100–140 marks |
| Intermediate (5–6 months) | 75–90 questions | 150–200 marks |
| Well-Prepared (8+ months) | 95–110 questions | 210–260 marks |
| Expert (1+ year structured prep) | 110–120 questions | 250–290 marks |
The NDA written cutoff for Maths typically ranges between 25–40% per paper depending on the difficulty of that particular exam. So even 90–100 marks in Maths, combined with a strong GAT score, can clear the written stage.
But the students who make it to SSB comfortably are usually those scoring 180–240+ in Maths.
Understand the full NDA selection process: NDA Selection Process Written Exam to Joining
What About Chapters Not Typically in Class 10 Syllabus?
We get this question often from students who are in Class 10 or just passed Class 10.
Topics like Calculus, Matrices, Vectors, and 3D Geometry are not part of the Class 10 CBSE syllabus. So if you are just starting after Class 10, these will feel completely new.
That is completely normal. And that is exactly why joining structured NDA coaching after Class 10 makes such a big difference.
At Alpha NDA Academy, students who join our NDA Foundation After 10th Arjuna Batch get 2 full years to build these concepts from scratch step by step, with daily practice and weekly test tracking.
By the time they sit for their first NDA attempt, they are not learning the syllabus under pressure. They are revising it.
That time advantage is irreplaceable.
Learn about our early-start programme: NDA Foundation After 10th Arjuna Batch
NDA Maths Syllabus Quick Reference
Here is a quick reference of all chapters in the official NDA Maths syllabus from UPSC:
- Algebra Sets, Complex Numbers, Quadratic Equations, AP/GP/HP, Permutations, Combinations, Binomial Theorem, Logarithms
- Matrices and Determinants Types of Matrices, Operations, Determinants, Inverse, System of Equations
- Trigonometry Ratios, Identities, Inverse Trig, Height & Distance, Properties of Triangles
- Analytical Geometry (2D) Straight Line, Circle, Conic Sections
- Differential Calculus Limits, Continuity, Differentiation, Maxima-Minima, Applications
- Integral Calculus & Differential Equations Integration Methods, Definite Integrals, Area Under Curve, Differential Equations
- Vector Algebra Types of Vectors, Dot Product, Cross Product
- Analytical Geometry (3D) Coordinates in Space, Direction Cosines, Lines and Planes, Sphere
- Statistics and Probability Mean, Median, Mode, SD, Variance, Probability, Conditional Probability
For the full detailed syllabus including GAT, read: NDA Exam Syllabus 2026 Complete Subject-Wise Guide
Best Books to Prepare NDA Maths
1. NCERT Class 11 and 12 Mathematics (Both Volumes) Start here. Always. NCERT builds the foundation that NDA questions are based on. Do not skip it even if you feel confident.
2. NDA/NA Mathematics by R.S. Aggarwal (S. Chand) This is one of the most used NDA-specific Maths books in India. Chapter-wise objective questions aligned with the NDA pattern.
3. NDA/NA Previous Year Papers (Last 10–15 Years) No book replaces past papers. Solving 10 years of NDA Maths papers gives you a realistic feel of which chapters repeat, how questions are framed, and how fast you need to be.
4. Pathfinder for NDA/NA Arihant Publications A comprehensive book covering all chapters with explanations and practice exercises. Good for the later stages of preparation.
For the full booklist across all subjects: Best Books for NDA Preparation 2026
How Alpha NDA Academy Helps You Master NDA Maths
At Alpha NDA Academy in Sikar, Rajasthan, Maths is not something students figure out on their own.
Our faculty experienced in NDA preparation teaches the complete Maths syllabus in a structured, chapter-by-chapter sequence with daily practice. Here is what our students get:
Chapter-wise focused teaching: We cover every chapter with full concept explanation + objective practice questions designed specifically for the NDA exam pattern.
Weekly Full 900-Mark Mock Tests: Every Saturday, students sit for a complete NDA mock test including all 120 Maths questions under timed conditions. This builds exam temperament.
Performance Tracking: After each test, students know their chapter-wise accuracy. If a student is weak in Calculus, we address it specifically not generally.
Doubt Resolution 14 Hours a Day: Faculty is available from 7 AM to 11 PM every day. No doubt sits unresolved overnight.
Our students’ Maths scores in mock tests improve an average of 40–60 marks between their first and fifth month of preparation. That improvement comes from structured repetition, not just effort.
We offer batches for students at every stage:
- NDA Foundation After 10th Arjuna Batch Start Maths from scratch, 2 years of structured preparation
- NDA With 12th Class Bulls Eye Batch NDA Maths prep alongside Class 12 board exam preparation
- NDA After 12th Spartans Batch Intensive 1-year programme for 12th pass students
- NDA Coaching for Girls Dedicated batch for female NDA aspirants
Call: 7240040400 | WhatsApp: wa.me/917240040400 | Visit: alphandaacademy.in
FAQs NDA Maths Chapter-Wise Weightage
Q1. Which is the most important chapter in NDA Maths?
Algebra is consistently the highest-weightage chapter, with approximately 22–28 questions appearing in most NDA papers. Trigonometry is a close second.
Q2. Is Calculus compulsory for NDA Maths?
Yes. Differential Calculus and Integral Calculus together account for approximately 25–30 questions in most NDA papers. They cannot be skipped.
Q3. How many questions come from each chapter in NDA Maths?
The exact count varies by paper. However, based on previous years’ analysis Algebra (22–28), Trigonometry (18–25), Calculus (24–32 combined), Matrices (9–12), Geometry (16–23 combined), Vectors (5–8), Statistics & Probability (8–12).
Q4. Can a student from Class 10 prepare for NDA Maths?
Yes. Students from Class 10 benefit the most from starting early because they have 2 full years before their first NDA attempt. Joining NDA Foundation coaching after Class 10 gives the maximum preparation time.
Q5. How much should I score in NDA Maths to clear the exam?
The Maths paper cutoff is not separately declared by UPSC. However, based on previous years’ overall written cutoffs, scoring 120–160 in Maths (combined with a strong GAT score) is generally competitive. Students aiming for merit positions usually target 180–220+ in Maths.
Q6. Should I do all chapters or focus only on high-weightage ones?
Focus heavily on high-priority chapters (Algebra, Trigonometry, Calculus) but do not completely ignore medium-priority ones. Even Matrices and Statistics can contribute 20–30 marks if you prepare them well.
Q7. How many hours a day should I give to NDA Maths?
3–4 hours per day during the preparation phase is ideal. This should include concept study, practice questions, and revision. In the final month before the exam, shift to practice-only mode no new topics.
Final Thought Prepare Smart, Not Just Hard
Effort matters. But effort directed by the right information matters far more.
Now you know which chapters of NDA Maths are worth your maximum attention. You know that Algebra and Trigonometry together can give you 40–50 questions. You know that Statistics and Probability are underrated gold mines. And you know that Vectors and 3D Geometry, while important, are not where you start.
Use this weightage data to build a preparation plan that respects your time.
If you want a structured environment where this strategy is already built into the daily curriculum where faculty track your chapter-wise progress, weekly mock tests mirror the actual NDA pattern, and doubt resolution never waits Alpha NDA Academy is the place.
We have seen what focused, chapter-wise Maths preparation can do for a student. It can take someone who scored 60 in the first mock test to 190+ by exam time.
That is not a promise. That is a pattern we have watched repeat, batch after batch.
Join Alpha NDA Academy WhatsApp Us Now | Call: 7240040400
