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NDA Maths Formula Sheet 2026: All Chapters, Quick Revision

Table of Contents

NDA Maths Formula Sheet 2026: All Chapters, Quick Revision

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)
  • Multiplication theorem: P(A∩B) = P(A) × P(B|A)
  • Bayes’ Theorem (basic form): P(A|B) = [P(B|A)P(A)] / P(B)

Quick-Revision Formula Summary Table

Topic High-Weightage Formula Where Students Lose Marks
Quadratic Equations Sum = −b/a, Product = c/a Sign errors with negative b, c
Trigonometric Identities sin²θ + cos²θ = 1 Confusing sin(A−B) vs cos(A−B)
Matrices A⁻¹ = adj(A)/|A| Forgetting |A| ≠ 0 condition
Straight Lines Distance = |Ax₁+By₁+C|/√(A²+B²) Wrong sign under the modulus
3D Geometry l² + m² + n² = 1 Mixing direction cosines with ratios
Differentiation Chain rule Missing the inner-function derivative
Integration ∫xⁿ dx = xⁿ⁺¹/(n+1) Forgetting “+C” (loses marks in SSB-linked papers too)
Vectors |a×b| = area Confusing dot and cross product outputs
Probability P(A∩B) = P(A)P(B|A) Applying independent-event formula to dependent events

This is the print-friendly, one-page version of the entire NDA Maths Formula Sheet 2026 — stick it above your study desk.

How to Memorize These Formulas Fast (Bonus Tips)

Formula recall is a muscle. The Maths and Tech-Maths faculty at Cadets Defence Academy — Robin Sir, Kapil Sir, and Mukesh Sir — train NDA Foundation students on a simple spaced-repetition schedule that works even in the last 30 days:

  • Week 1: Learn all formulas chapter-wise, writing each one by hand at least 3 times.
  • Week 2: Revise Week 1 formulas on Day 1, Day 3, and Day 6 (spaced recall, not daily cramming).
  • Week 3: Mix formula recall with timed problem-solving — 20 minutes formulas, 40 minutes practice.
  • Week 4: Full mock tests every alternate day; revise only the formulas you got wrong in the mock.
  • Keep a small “error formula” notebook — every time a formula trips you up in a mock test, it goes into this notebook for daily 5-minute review.

Consistent spaced repetition of the NDA Maths Formula Sheet 2026 beats last-minute cramming by a wide margin, especially under exam-hall time pressure.

Free NDA Maths Formula Sheet 2026 vs Coaching-Provided Formula Sheets

Not all formula sheets are built equally, and this is where most self-study aspirants lose time without realizing it. A generic NDA Maths Formula Sheet 2026 downloaded from a random website may list the same equations you see above, but it usually stops there — no weightage guidance, no revision structure, no way to ask a doubt when a formula doesn’t make sense. Here’s how a typical free PDF compares with the structured formula material used in the Cadets Defence Academy NDA Foundation course.

Feature Free Online NDA Maths Formula Sheet 2026 Cadets Defence Academy Formula Material
Syllabus alignment with latest UPSC pattern Often outdated or generic Updated yearly to match 2026 exam pattern
Chapter-wise weightage guidance Rarely included Included, based on previous year trends
Linked practice questions Usually absent Backed by regular doubt-clearing sessions
Expert doubt resolution Not available Direct access to Maths faculty (Robin Sir & team)
Mock test integration Standalone document Integrated with regular practice tests
Revision tracking support None Guided last-30-day revision schedule

A formula sheet is a strong starting point, but pairing it with structured practice and faculty feedback — the kind offered in our NDA Foundation and NDA-after-12th batches in Dehradun — is what actually converts formula knowledge into exam marks. In other words, treat any NDA Maths Formula Sheet 2026, including this one, as the map — your daily practice is still the journey.

Conclusion

The NDA Maths Formula Sheet 2026 is a powerful revision tool for the final 15 days before the exam. Instead of trying to learn new concepts at the last moment, focus on revising important formulas, shortcuts, and frequently tested topics from Algebra, Trigonometry, Geometry, Calculus, Matrices, Statistics, and Probability. Use the formula sheet alongside previous-year questions and mock tests to improve speed and accuracy. A consistent daily revision routine can help you recall formulas faster and approach the NDA Mathematics paper with greater confidence. Make these final 15 days count by revising smartly, practising regularly, and avoiding unnecessary distractions.

FAQ:

Algebra, Trigonometry, and Calculus (Differential + Integral) together account for the largest share of the 120 questions in NDA Maths. Coordinate Geometry (2D & 3D) and Vectors follow closely, while Statistics & Probability, though scoring fewer questions, are high-accuracy, low-time chapters worth mastering fully. If you only have time to revise three sections from this NDA Maths Formula Sheet 2026 before the exam, prioritize Algebra, Trigonometry, and Calculus first.

Algebra generally has a slightly higher number of questions across NDA 1 and NDA 2 papers historically, but Calculus questions tend to be quicker to solve once formulas are memorized, making it a high-efficiency scoring section. Neither should be skipped — both are core to any serious NDA Maths Formula Sheet 2026 preparation plan.

No. Formulas get you to the starting line, not the finish line. NDA Maths tests application under time pressure, so formulas must be combined with regular previous-year-paper practice, timed mock tests, and error analysis. Students who pair a formula sheet with structured guidance — like the classroom and doubt-session model at Cadets Defence Academy — consistently perform better than those relying on formulas in isolation.

Print this NDA Maths Formula Sheet 2026, keep it inside your practice-test folder, and treat the Quick-Revision Summary Table as your final checklist on exam eve. Formulas will get you into the exam hall with confidence — consistent practice, timed mocks, and expert doubt-clearing are what carry you to a 240+/300 score and beyond.

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