NDA Maths Formula Sheet 2026: All Chapters, Quick Revision
NDA Maths Formula Sheet 2026: All Chapters, Quick Revision Table of Contents Every NDA aspirant eventually types the same search: “NDA Maths Formula Sheet 2026.” It’s the first thing you bookmark and the last thing you open before the exam. But here’s the honest truth our Maths faculty at Cadets Defence Academy tells every batch on day one — formulas alone won’t get you past 240/300. The NDA Maths paper rewards speed and formula-to-answer conversion, not formula memorization in isolation. Two students can know the same identity; the one who’s drilled it into 50 practice questions finishes the paper 20 minutes earlier and with fewer silly errors. That said, you cannot build speed without a rock-solid, error-free formula base. This is exactly why we built this NDA Maths Formula Sheet 2026 — a single reference document that mirrors the actual UPSC NDA syllabus weightage, so your last 15 days of revision are spent recalling, not searching. How to use this cheat sheet for last-15-day revision: Days 1–5: Read each section once, out loud, and rewrite the formulas you keep forgetting on a separate sheet. Days 6–10: Solve 10 previous-year questions per chapter using only this sheet as reference — no textbook. Days 11–13: Attempt full-length mock tests and circle every formula you hesitated on. Days 14–15: Only revise the circled formulas plus the Quick-Revision Summary Table in Section 11. This NDA Maths Formula Sheet 2026 is designed to work alongside — not replace — regular problem-solving practice, which is exactly the approach followed in our NDA Foundation and NDA-after-12th batches in Dehradun. Think of this NDA Maths Formula Sheet 2026 as your single source of truth during revision week. Instead of flipping between three different textbooks and a dozen browser tabs, you scroll through one page, chapter by chapter, in the exact order the NDA syllabus is usually taught. That alone can save 30–40 minutes of daily revision time, which adds up fast over the final two weeks before the exam. Algebra Algebra typically carries the single largest weightage in the NDA Maths paper, so this part of the NDA Maths Formula Sheet 2026 deserves the most attention. Sets, Relations & Functions n(A∪B) = n(A) + n(B) − n(A∩B) n(A∪B∪C) = n(A)+n(B)+n(C)−n(A∩B)−n(B∩C)−n(A∩C)+n(A∩B∩C) A relation R is an equivalence relation if it is reflexive, symmetric, and transitive. Quadratic Equations For ax² + bx + c = 0: roots = [−b ± √(b²−4ac)] / 2a Sum of roots = −b/a; Product of roots = c/a Discriminant D = b² − 4ac; D > 0 (real, distinct), D = 0 (real, equal), D < 0 (imaginary) Complex Numbers Modulus |z| = √(a² + b²) for z = a + ib Argument θ = tan⁻¹(b/a) De Moivre’s Theorem: (cosθ + i sinθ)ⁿ = cos(nθ) + i sin(nθ) Binary Numbers — Conversion between binary, decimal, octal, and hexadecimal follows base-2, base-8, and base-16 positional value rules; practice at least 5 conversions daily in the last two weeks. Sequences & Series AP: nth term = a + (n−1)d; Sum = n/2 [2a + (n−1)d] GP: nth term = arⁿ⁻¹; Sum = a(rⁿ−1)/(r−1) HP: reciprocal of terms forms an AP Binomial Theorem General term: T(r+1) = ⁿCr aⁿ⁻ʳ bʳ Middle term depends on whether n is even or odd Logarithms log(mn) = log m + log n log(m/n) = log m − log n log(mⁿ) = n log m Permutation & Combination ⁿPr = n! / (n−r)! ⁿCr = n! / [r!(n−r)!] Trigonometry Trigonometry questions in NDA are formula-heavy but pattern-repetitive, which makes this section of the NDA Maths Formula Sheet 2026 extremely high-yield. sin²θ + cos²θ = 1; 1 + tan²θ = sec²θ; 1 + cot²θ = cosec²θ sin(A±B) = sinA cosB ± cosA sinB cos(A±B) = cosA cosB ∓ sinA sinB tan(A±B) = (tanA ± tanB) / (1 ∓ tanA tanB) sin2θ = 2sinθcosθ; cos2θ = 1−2sin²θ = 2cos²θ−1 Inverse functions: sin⁻¹x + cos⁻¹x = π/2; tan⁻¹x + cot⁻¹x = π/2 Heights & Distances: use angle of elevation/depression with tanθ = height/base Matrices & Determinants Matrix addition/subtraction requires identical order; multiplication requires columns of first = rows of second Transpose: (Aᵀ)ᵀ = A; (AB)ᵀ = BᵀAᵀ For a 2×2 matrix, determinant = ad − bc Inverse of matrix A: A⁻¹ = adj(A) / |A|, valid only when |A| ≠ 0 Cramer’s Rule solves linear equations using determinant ratios: x = Dx/D, y = Dy/D, z = Dz/D Coordinate Geometry (2D) Distance formula: √[(x₂−x₁)² + (y₂−y₁)²] Section formula: [(mx₂+nx₁)/(m+n), (my₂+ny₁)/(m+n)] Slope: m = (y₂−y₁)/(x₂−x₁) Distance of a point from a line: |Ax₁+By₁+C| / √(A²+B²) Circle: (x−h)² + (y−k)² = r²; tangent condition — distance from centre equals radius Conics: Parabola y² = 4ax; Ellipse x²/a² + y²/b² = 1; Hyperbola x²/a² − y²/b² = 1 Coordinate Geometry (3D) Distance: √[(x₂−x₁)² + (y₂−y₁)² + (z₂−z₁)²] Direction cosines: l² + m² + n² = 1 Direction ratios are proportional to direction cosines Equation of a line in symmetric form: (x−x₁)/l = (y−y₁)/m = (z−z₁)/n Equation of a plane: ax + by + cz = d Differential Calculus Standard limits: lim(x→0) sinx/x = 1; lim(x→0) (1−cosx)/x = 0 Product rule: d/dx(uv) = u’v + uv’ Quotient rule: d/dx(u/v) = (u’v − uv’) / v² Chain rule: dy/dx = dy/du × du/dx d/dx(xⁿ) = nxⁿ⁻¹; d/dx(sinx) = cosx; d/dx(eˣ) = eˣ Integral Calculus & Differential Equations ∫xⁿ dx = xⁿ⁺¹/(n+1) + C ∫1/x dx = ln|x| + C ∫eˣ dx = eˣ + C Definite integral property: ∫ₐᵇ f(x)dx = −∫ᵇₐ f(x)dx Area under a curve: A = ∫ₐᵇ y dxFirst-order differential equations are solved using variable separation or an integrating factor Vector Algebra Dot product: a·b = |a||b|cosθ Cross product: a×b = |a||b|sinθ n̂ Scalar triple product: [a b c] = a·(b×c) Area of a parallelogram = |a×b|; Volume of a parallelepiped = |a·(b×c)| Statistics & Probability Mean = Σx/n; Median = middle value of ordered data; Mode = most frequent value Variance = Σ(x−x̄)²/n; Standard Deviation = √Variance Addition theorem: P(A∪B) = P(A) + P(B) − P(A∩B)
