Mathematics is Paper I of the NDA written exam — 300 of the 900 written marks across 120 objective questions (2.5 marks each, with a one-third negative for a wrong answer). Questions are at the 10+2 level.

Based on a ten-year analysis of past papers, the highest-yield areas are Algebra, Statistics & Probability, Calculus and Trigonometry. Each topic below gives the concept, key formulas, one worked example and two practice MCQs.

Topics covered in this guide:

1. Sets, Relations and Functions · 2. Number System (incl. Binary) · 3. Complex Numbers · 4. Quadratic Equations and Inequalities · 5. Sequences and Series (AP, GP, HP) · 6. Permutations and Combinations · 7. Binomial Theorem · 8. Logarithms · 9. Matrices and Determinants · 10. Trigonometric Ratios and Identities · 11. Inverse Trigonometric Functions · 12. Properties of Triangles & Heights and Distances · 13. Coordinate Geometry: Straight Lines · 14. Circle · 15. Conic Sections (Parabola, Ellipse, Hyperbola) · 16. Three-Dimensional Geometry · 17. Limits, Continuity and Differentiability · 18. Differentiation · 19. Application of Derivatives (Tangents, Maxima & Minima) · 20. Integration (Indefinite, Definite & Area) · 21. Differential Equations · 22. Vector Algebra · 23. Statistics · 24. Probability