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Paper 1 – Mathematics: Topics and Their Actual Weight

UPSC NDA 2026

Union Public Service Commissionnational hard

The NDA written syllabus is deceptively familiar — Class 11–12 Mathematics and general school-level science and humanities. Where candidates underestimate it is depth and breadth. NDA Mathematics goes meaningfully beyond what most Class 12 boards require for passing, and the GAT demands recall across Physics, Chemistry, History, Geography, and Current Affairs simultaneously within 2.5 hours. Understanding which topics carry the most marks — and why — separates focused preparation from surface coverage. See the full marking scheme and time strategy here.

Paper 1 is 120 questions for 300 marks (2.5 marks each, -0.83 for wrong answers). The syllabus maps to NCERT Class 11–12 Maths with additional depth in Trigonometry, Algebra, and Coordinate Geometry. Based on PYQ analysis, approximate topic distribution is: Algebra and Number Theory (Sets, complex numbers, quadratics, binomial theorem, log) — 20–25 questions; Trigonometry (identities, inverse, heights and distances) — 15–20 questions; Coordinate Geometry 2D and 3D — 15–18 questions; Differential and Integral Calculus — 20–25 questions; Matrices and Determinants — 8–10 questions; Vectors — 8–10 questions; Statistics and Probability — 8–10 questions. Calculus and Trigonometry together make up roughly 40% of the paper — candidates who deprioritize either consistently score below 50% in Paper 1.

Paper 2 – GAT: English and General Knowledge Structure

Paper 2 is 150 questions for 600 marks (4 marks each, -1.33 for wrong answers). It has two distinct components: English (Part A, approximately 50 questions / 200 marks) and General Knowledge (Part B, approximately 100 questions / 400 marks). The higher per-question penalty in GAT (-1.33 versus -0.83 in Maths) means careless attempts are more costly here. The English section tests grammar, vocabulary, reading comprehension, and sentence structure at a level equivalent to a good Class 12 student — not advanced competitive English. The GK section distributes across Physics, Chemistry, General Science, History, Geography, and Current Affairs.

GK Subject Distribution Inside GAT

Physics carries the highest GK weightage — approximately 25% of the GK section. Questions span from Class 9 through Class 12: mechanics, light, electricity, magnetism, and modern physics. Chemistry is Class 9–10 focused (elements, periodic table, compounds, chemical reactions) with some Class 11–12 overlap. History covers Indian independence movement, medieval and ancient India, and world history at a broad level. Geography focuses on Indian physical geography, climate, rivers, and economic geography. Current Affairs requires active preparation — a static-only approach misses 15–20 marks in this section reliably. See the best books for each GAT subject.

What the Syllabus Does NOT Include

NDA Mathematics does not include topics from Class 12 boards that are outside the UPSC-specified syllabus — for example, Linear Programming from NCERT Class 12 is not in the NDA syllabus. Similarly, GAT does not include Economics as a standalone subject or Computer Science. Checking the official UPSC NDA syllabus document (available at upsc.gov.in) against your preparation list before the exam is a basic precaution that many candidates skip. Do not prepare topics not in the official syllabus at the cost of core topics.

How Syllabus Converts to a Preparation Priority List

If you have 4 months of preparation time, the priority sequence based on marks contribution is: (1) Calculus — highest Maths yield, most PYQ density; (2) Trigonometry — predictable question types, S.L. Loney essential; (3) Physics GAT — 25% of the 400-mark GK section, NCERT 9–12 required; (4) English — consistent 200 marks, improvable in 6–8 weeks with focused grammar and vocabulary; (5) Coordinate Geometry — mid-weight, directly learnable from NCERT; (6) History and Geography — revise from NCERT in the final month. Current Affairs cannot be stacked — it needs weekly revision throughout the preparation period. See the full 6-month preparation plan.

Frequently Asked Questions

Q.Which chapters from Class 11 Maths are directly relevant to NDA Paper 1?

Class 11 Maths contributes substantially to NDA Paper 1. Key chapters include Sets and Functions, Trigonometric Functions, Complex Numbers, Permutations and Combinations, Binomial Theorem, Sequences and Series, Straight Lines, and Conic Sections. Statistics and Probability from Class 11 also appear consistently. NCERT Class 11 Maths should be completed chapter-by-chapter before moving to supplementary references like S.L. Loney for Trigonometry.

Q.Does the NDA GAT syllabus include topics beyond NCERT school textbooks?

The GK portion of GAT is largely NCERT Class 9–12 level for Physics, Chemistry, and Biology. History and Geography follow standard school curriculum with an India-centric focus. Current Affairs — covering defence, space, government schemes, sports, and international events from the past 12 months — goes beyond NCERTs and requires consistent news reading. For Physics specifically, Class 11–12 NCERT is essential, not optional.

Q.How many questions come from Trigonometry in NDA Maths and is it the most important topic?

Trigonometry is consistently one of the highest-weightage topics in NDA Mathematics, contributing approximately 15–20 questions per paper across identities, inverse functions, heights and distances, and properties of triangles. Algebra and Calculus together contribute a comparable share. Trigonometry stands out because NDA-level questions go meaningfully beyond NCERT — S.L. Loney Parts I and II are standard references for candidates targeting 70%+ in Paper 1.

Q.Is the NDA written exam syllabus different for Army versus Air Force wing candidates?

No. The written exam syllabus is completely identical for all wings — Army, Navy, and Air Force. Both Paper 1 (Mathematics) and Paper 2 (GAT) are the same question paper regardless of which wing you applied for. Wing-specific differentiation begins only at the SSB stage, where psychological tests and interviews may probe aptitude relevant to the wing's operational requirements.

Q.How much weightage does Current Affairs carry in NDA GAT and how far back should I prepare?

Current Affairs falls under the General Knowledge section of GAT, which is broadly worth around 400 marks (shared with Physics, Chemistry, History, Geography, and other GK). Current events questions typically cover the preceding 12–18 months and focus on defence and space milestones, major government schemes, important appointments, international relations, and sports. Revise a comprehensive monthly digest alongside NCERT-based static GK preparation.

Q.Should I study Integral Calculus from NCERT or from I.A. Maron for NDA?

Start with NCERT Class 12 Maths (Chapters 7 and 8) for Integrals and Applications of Integrals — these cover the NDA baseline. I.A. Maron's Problems in Calculus of One Variable is useful for candidates targeting 75%+ in Paper 1, particularly for substitution-based integrals and areas that NCERT presents only at surface level. Do not jump to Maron before NCERT; the sequencing matters.

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