Which Mathematics topics matter most for NDA?

Algebra, Trigonometry carry the highest question counts based on previous-year analyses.

Is this Mathematics material free?

Yes — every chapter, practice set and flashcard deck here is free. Premium mock tests and live courses from tutors are labelled separately.

NDAMathematics

Mathematics for NDA

120 questions, no calculator — Algebra and Trigonometry alone are over a third of the paper.

📊 120 Q · 300 marks (33% of the written exam)

How toppers play this section

NDA Mathematics is 120 questions in 150 minutes with no calculator, so speed and formula recall matter more than derivation. Algebra is the single heaviest topic — not one dense chapter but seven compressed CBSE topics (complex numbers, quadratic theory, sets, AP/GP/HP, the binomial theorem, logarithms, permutations & combinations), so breadth beats depth: know all seven formula banks rather than mastering one at the expense of the rest. Trigonometry is second-heaviest and rewards the opposite approach — a small core built on the addition formula and the general-solution results generates almost every question across five recognisable families (ratios/identities, compound & multiple angles, trigonometric equations, inverse trig, heights & distances). Analytical Geometry fuses 2D coordinate geometry with a shallow 3D layer built directly on algebra already known. The two calculus chapters — Differential, then Integral Calculus & Differential Equations — are the newest material for most aspirants and the least forgiving of careless multi-step execution, where a single sign slip costs the mark. Matrices & Determinants is the most mechanical, rule-based topic in the whole paper and should be a near-certain scoring block, while Vector Algebra and Statistics & Probability are the lightest topics by count but run on fewer than a dozen formulas each — the best marks-per-minute in the syllabus if revised last.

Chapters

Built to the NDA blueprint — notes, shortcuts, solved PYQ-style examples and practice in every chapter.

1Algebra — Complex Numbers, Quadratics, Sequences & Binomial TheoremNDA Algebra is not one trick repeated — it's seven Class 11-12 chapters compressed into a fifth of the Maths paper — complex numbers and De Moivre's theorem, the theory of quadratic equations, sets, AP/GP/HP, the binomial theorem, logarithms, and permutations & combinations. At 2.5 marks a question with a 1/3rd penalty, the highest-yield habit is naming which formula bank a question belongs to before you touch a pencil.⏱ 34 min read

2Trigonometry — Identities, Equations & TrianglesTrigonometry is NDA Maths' second-highest-weight topic after Algebra — roughly 21–22 of 120 questions, worth about 54 marks. It is five games in one paper: identity manipulation, compound/multiple-angle formulas, general solutions of equations, inverse trig functions, and triangle/heights-and-distances applications. One addition formula and its corollaries generate almost the whole kit.⏱ 40 min read

3Analytical Geometry — Lines, Circles, Conics & Three DimensionsAnalytical Geometry is NDA Maths' third-highest-weight topic — about 18 of 120 questions, worth roughly 45 marks — and it is really two exams stitched into one. Two-dimensional coordinate geometry (distance, lines, circles, conics) is built on algebra you already know; three-dimensional geometry (direction cosines, lines, planes) extends the same handful of ideas by one extra coordinate. No calculator, no proofs, just correct substitution into the right formula under a 1/3rd-mark penalty.⏱ 48 min read

4Differential Calculus — Limits, Derivatives & ApplicationsDifferential Calculus carries 13% of the NDA Mathematics paper — roughly 15 of 120 questions — split almost evenly between limits/continuity, standard derivatives, and applications (tangents, rate of change, maxima-minima). It rewards a fixed toolkit executed without arithmetic slips, not deep theory. Learn the standard-limit table, the derivative list, and the three differentiation rules cold, and this becomes the fastest 15 marks on the paper.⏱ 26 min read

5Integral Calculus & Differential Equations — NDA MathematicsNDA integral calculus is a closed toolkit — a dozen standard forms, three techniques (substitution, parts, partial fractions), six properties of definite integrals, and first-order-first-degree differential equations solved by separating variables. No JEE-style trig substitutions, no second-order DEs. Learn the forms cold, know which technique a given integral is begging for, and never read off a DE's degree before clearing the radicals.⏱ 24 min read

6Matrices & DeterminantsNDA does not test insight here — it tests flawless, fast execution of a short rule list under negative marking. Worth 10% of the Mathematics paper (10–12 of 120 questions), matrices & determinants is pure property-recall — the sign checkerboard, the "divide by |A|" step, Cramer's rule. Get the dozen rules automatic and this becomes the fastest marks in the paper.⏱ 14 min read

7Vector AlgebraVector algebra at NDA level is Class 11–12 CBSE mechanics dressed in symbols — vectors added by the parallelogram law, then multiplied two different ways: the dot product for angles and projections, the cross product for areas and perpendiculars. Six percent of the paper, and one of the highest formula-to-marks ratios in the syllabus.⏱ 18 min read

8Statistics & ProbabilityThe lightest topic in NDA Mathematics, tied with Vector Algebra at 6% of the paper — but it packs two full CBSE Class 11–12 chapters into that weight. Statistics is mean/median/mode and dispersion computed correctly by hand under a no-calculator clock; probability is the addition and multiplication theorems, conditional probability, Bayes' theorem, and an introduction to the binomial distribution. Neither sub-area is conceptually hard — the marks are lost or won entirely on careful arithmetic and knowing which formula the wording is pointing at.⏱ 20 min read

Topic-wise weightage in NDA

Expected question counts from previous-year paper analyses. Topics with an arrow already have a full chapter.

Topic	Written Exam Q	Priority
Algebra	22–26	Very high
Trigonometry	20–23	Very high
Analytical Geometry (2D & 3D)	16–20	High
Differential Calculus	14–17	High
Integral Calculus & Differential Equations	13–16	High
Matrices & Determinants	10–13	Medium
Vector Algebra	6–8	Low
Statistics & Probability	6–8	Low