In this guide
Paper I is the largest single paper in the NDA written exam, and the one that most often decides whether a candidate reaches the SSB. It is also the paper where preparation pays most predictably: the syllabus is fixed, the question styles repeat, and speed is a skill you can build week by week. What it does not reward is the way most students prepare for board exams.
This guide sets out the paper, the syllabus units, an order of study with a 16-week plan, the speed techniques that separate NDA maths from board maths, and a routine for exam day.
The paper at a glance
| Feature | Detail |
|---|---|
| Marks | 300 |
| Questions (recent papers) | 120, each worth 2.5 marks |
| Time | 2 hours 30 minutes, about 75 seconds a question |
| Wrong answer | Loses one-third of 2.5, about 0.83 |
| Two options marked | Treated as a wrong answer |
| Aids | No calculators or log tables |
The eight units and what they ask
| Unit | Main topics | What the questions usually test |
|---|---|---|
| Algebra | Sets, relations, complex numbers, quadratics, sequences, permutations and combinations, binomial theorem, logarithms, binary numbers | Standard results applied quickly |
| Matrices and determinants | Operations, determinants, adjoint, inverse, linear equations | Properties that avoid long expansion |
| Trigonometry | Identities, multiple angles, inverse functions, heights and distances, properties of triangles | Identities and standard values |
| Analytical geometry | Lines, circles, conics; direction cosines, planes, lines and spheres in 3D | Formula recall and careful substitution |
| Differential calculus | Functions, limits, continuity, derivatives, maxima and minima | Standard limits and rules; shortcuts |
| Integral calculus and differential equations | Indefinite and definite integrals, areas, order and degree, solving simple equations | Properties of definite integrals |
| Vector algebra | Dot and cross products, projections, work and moment | Direct formula use |
| Statistics and probability | Mean, median, variance, correlation, regression, probability, Bayes' theorem, binomial distribution | Clean definitions; conditional probability |
The share of each unit varies from paper to paper. Algebra, trigonometry and calculus are broad units and together cover much of the syllabus, but no unit can be skipped safely. Old UPSC papers are the best guide to the balance.
Board maths versus NDA maths
Board exams reward full, step-by-step working. NDA rewards picking the right option fast. You need the same understanding, used differently. Three techniques do most of the work.
1. Substitute the options
Example: Solve √(x + 5) + √x = 5.
(a) 1 (b) 4 (c) 9 (d) 16
Try (b): √9 + √4 = 3 + 2 = 5. Done in ten seconds. Solving directly (isolate a root, square, simplify) gives 10√x = 20, so x = 4, but takes three times as long. Answer: (b).
2. Put in a special value
Example: sin⁴θ − cos⁴θ equals:
(a) 1 (b) sin²θ − cos²θ (c) 2sin²θ (d) 1 − 2sin²θ
Put θ = 0: the left side is 0 − 1 = −1. The options give 1, −1, 0 and 1. Only (b) matches. Answer: (b). (Algebraically, it factorises as (sin²θ − cos²θ)(sin²θ + cos²θ) and the second bracket is 1.)
Always check that only one option survives. If two options match, try a second value, such as θ = π/6.
3. Recognise a standard result
Example: The value of the integral of sin x ÷ (sin x + cos x) from 0 to π/2 is:
(a) 0 (b) π/4 (c) π/2 (d) 1
Replacing x by (π/2 − x) turns the integrand into cos x ÷ (cos x + sin x). Adding the two forms of the same integral gives 2I = the integral of 1 from 0 to π/2 = π/2, so I = π/4. Answer: (b). A prepared candidate sees this in seconds because it is a standard form.
An order of study
Study in an order where each topic supports the next:
- Algebra foundations: sets, functions, quadratics, sequences. They appear inside questions from every other unit.
- Trigonometry. Calculus and coordinate geometry both lean on it.
- Matrices and determinants. Short, self-contained and scoring.
- Coordinate geometry, 2D first, then 3D.
- Calculus: limits, derivatives, applications, integrals, differential equations.
- Vectors, which connect naturally to 3D geometry.
- Statistics and probability.
A 16-week plan
| Weeks | Topics | Weekly target |
|---|---|---|
| 1–3 | Sets and functions, complex numbers, quadratics, sequences, permutations and combinations, binomial theorem, logarithms and binary numbers | 150 questions |
| 4–5 | Matrices and determinants | 100 questions |
| 6–8 | Trigonometry, inverse functions, heights and distances, properties of triangles | 150 questions |
| 9–10 | Straight lines, circles, conics, 3D geometry | 120 questions |
| 11–13 | Limits, derivatives, maxima and minima, integration, areas, differential equations | 150 questions |
| 14 | Vectors | 80 questions |
| 15 | Statistics and probability | 100 questions |
| 16 | Mixed revision and two full papers | 240 questions |
From week 9 onwards, sit one full 120-question paper every weekend, even if you have not finished the syllabus. It trains stamina and shows early which units are slow.
Our chapter guides, starting with sets, relations and functions, follow this order.
A daily routine
| Time | Activity |
|---|---|
| 60 minutes | Learn or revise one topic; write its results on your formula sheet |
| 45 minutes | 30 questions on that topic, timed at 90 seconds each |
| 15 minutes | Review every error; note whether it was a gap, a slip or slowness |
Tighten the timing to 75 seconds a question once a unit is familiar. The review is not optional: an error you do not understand today will come back in the exam.
Build a formula sheet as you go
Keep one notebook, a few pages per unit, with only results, not derivations: identities, standard limits, integral properties, conditions such as "D < 0 means non-real roots". Read it for ten minutes daily in the last month. Our maths revision guide lists what belongs on it.
Scoring: what a realistic target looks like
Suppose a candidate attempts 90 questions and gets 76 right and 14 wrong.
- Score = 76 × 2.5 − 14 × 0.83 = 190 − 11.7 ≈ 178 out of 300.
- If the same candidate had attempted 110 with 80 right and 30 wrong, the score would be 200 − 25 = 175: more attempts, fewer marks.
Accuracy above about 85% on attempted questions is a sound aim. The arithmetic of guessing is in our guide to negative marking.
Exam-day tactics
- First pass (70–80 minutes): every question you can do quickly and surely. Skip anything that needs more than a minute.
- Second pass: longer questions you know how to solve.
- Third pass: questions where you can eliminate two options with a reason.
- Never guess blindly, and bubble the OMR at fixed checkpoints, not at the very end.
Common mistakes
- Solving every question the board-exam way, with full working, even when substitution would take seconds.
- Leaving 3D geometry, statistics or probability for the end and then running out of time.
- Practising untimed. Understanding without speed does not convert into marks here.
- No error log. The same slip repeated across ten mocks costs more than any single topic.
Your checklist
- I have the syllabus units and my 16-week plan on one page.
- I solve at least 30 timed questions a day.
- My formula sheet grows with every chapter.
- I review every error and label it as a gap, a slip or slowness.
- From week 9, I sit one full paper every weekend.
A note on dates and numbers. Exam patterns, vacancies and schedules change from year to year. Always confirm the current details in the latest notification on the Union Public Service Commission website .
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