NDA Maths Important Formulas: Chapter-Wise Formula Sheet

NDA Mathematics has 300 marks across topics like Algebra, Trigonometry, Calculus, Vector Algebra, and Matrices. This NDA Maths formula sheet lists the must-know formula from every chapter in the syllabus, so you can revise the whole paper in one sitting instead of flipping through several notebooks.

Most students collect formulas from five different sources — a coaching notebook, a YouTube video, an old PDF, a friend's notes — and end up with half of them wrong or outdated by exam day. This page brings every important NDA Maths formula together, chapter by chapter, in the same order as the official syllabus. Bookmark it and use it as your one-stop revision sheet in the final weeks before the exam.

NDA Maths Chapter-Wise Weightage

Before jumping into formulas, it helps to know where the marks actually come from. Based on past NDA papers, here is roughly how the 120 questions are spread out:

Algebra, Trigonometry, and Calculus alone make up more than half the paper. Keep this in mind while revising if you're short on time, start with these NDA Maths formulas first.

1. Algebra

Algebra is the single biggest chapter in the NDA Maths formula list, so this section alone is worth memorising properly.

Sets

• 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)

Complex Numbers

• i² = −1

• z = a + ib, Modulus: |z| = √(a² + b²)

• Argument: θ = tan⁻¹(b/a)

• Cube roots of unity: 1, ω, ω², where 1 + ω + ω² = 0 and ω³ = 1

Progressions (AP, GP, HP)

• AP nth term: aₙ = a + (n − 1)d

• AP sum: Sₙ = n/2 [2a + (n − 1)d]

• GP nth term: aₙ = a·r^(n−1)

• GP sum (r ≠ 1): Sₙ = a(rⁿ − 1)/(r − 1)

• GP sum to infinity (|r| < 1): S∞ = a/(1 − r)

• HP: terms are reciprocals of an AP

Quadratic Equations

• Standard form: ax² + bx + c = 0

• Roots: x = (−b ± √(b² − 4ac)) / 2a

• Discriminant: D = b² − 4ac

• Sum of roots: α + β = −b/a

• Product of roots: αβ = c/a

Logarithms

• log_a(mn) = log_a m + log_a n

• log_a(m/n) = log_a m − log_a n

• log_a(mⁿ) = n·log_a m

• Change of base: log_a b = log_c b / log_c a

Binomial Theorem

• (a + b)ⁿ = Σ ⁿCᵣ aⁿ⁻ʳ bʳ

• General term: T(r+1) = ⁿCᵣ aⁿ⁻ʳ bʳ

Permutations and Combinations

• ⁿPᵣ = n! / (n − r)!

• ⁿCᵣ = n! / [r!(n − r)!]

2. Matrices and Determinants

• Matrix multiplication: (AB)ᵢₖ = Σⱼ aᵢⱼ bⱼₖ

• Determinant of a 2×2 matrix: |A| = ad − bc

• Inverse of a matrix: A⁻¹ = adj(A) / |A|

• Property: |AB| = |A| × |B|

• A matrix has an inverse only if |A| ≠ 0 (a non-singular matrix)

3. Trigonometry

Trigonometry is the second-highest scoring chapter, so treat these NDA Maths formulas as non-negotiable.

Basic Identities

• sin²θ + cos²θ = 1

• 1 + tan²θ = sec²θ

• 1 + cot²θ = cosec²θ

Sum and Difference Formulas

• sin(A ± B) = sinA cosB ± cosA sinB

• cos(A ± B) = cosA cosB ∓ sinA sinB

• tan(A ± B) = (tanA ± tanB) / (1 ∓ tanA tanB)

Double Angle Formulas

• sin2A = 2 sinA cosA

• cos2A = cos²A − sin²A = 1 − 2sin²A = 2cos²A − 1

• tan2A = 2tanA / (1 − tan²A)

Sum-to-Product

• sinA + sinB = 2 sin[(A+B)/2] cos[(A−B)/2]

• cosA + cosB = 2 cos[(A+B)/2] cos[(A−B)/2]

4. Analytical Geometry (Two Dimensions)

• Distance formula: d = √[(x₂−x₁)² + (y₂−y₁)²]

• Slope of a line: m = (y₂ − y₁) / (x₂ − x₁)

• Equation of a line (point-slope form): y − y₁ = m(x − x₁)

• General line equation: ax + by + c = 0

• Circle: (x − h)² + (y − k)² = r²

• Parabola: y² = 4ax

• Ellipse: x²/a² + y²/b² = 1

• Hyperbola: x²/a² − y²/b² = 1

5. Analytical Geometry (Three Dimensions)

• Distance between two points: d = √[(x₂−x₁)² + (y₂−y₁)² + (z₂−z₁)²]

• Direction cosines relation: l² + m² + n² = 1

• Equation of a plane: ax + by + cz + d = 0

• Angle between two lines with direction ratios (a₁,b₁,c₁) and (a₂,b₂,c₂):
  cosθ = (a₁a₂ + b₁b₂ + c₁c₂) / [√(a₁²+b₁²+c₁²) × √(a₂²+b₂²+c₂²)]

6. Differential Calculus

• Power rule: d/dx(xⁿ) = n·xⁿ⁻¹

• 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(sinx) = cosx

• d/dx(cosx) = −sinx

• d/dx(eˣ) = eˣ

• d/dx(lnx) = 1/x

• Maxima/minima condition: f'(x) = 0, then check sign of f''(x)

7. Integral Calculus and Differential Equations

• ∫xⁿ dx = xⁿ⁺¹/(n+1) + C (n ≠ −1)

• ∫1/x dx = ln|x| + C

• ∫eˣ dx = eˣ + C

• ∫sinx dx = −cosx + C

• ∫cosx dx = sinx + C

• Definite integral: ∫ₐᵇ f(x) dx = F(b) − F(a)

• A differential equation's order = highest derivative present; degree = power of that highest derivative (after removing radicals/fractions)

8. Vector Algebra

• Dot product: a · b = |a||b| cosθ

• Cross product: a × b = |a||b| sinθ n̂

• Magnitude of a vector: |a| = √(a₁² + a₂² + a₃²)

• Unit vector: â = a / |a|

• Scalar triple product: [a b c] = a · (b × c)

9. Statistics and Probability

Statistics

• Mean: x̄ = Σx / n

• Variance: σ² = Σ(x − x̄)² / n

• Standard deviation: σ = √variance

Probability

• P(A) = Number of favourable outcomes / Total outcomes

• P(A ∪ B) = P(A) + P(B) − P(A ∩ B)

• For independent events: P(A ∩ B) = P(A) × P(B)

• Conditional probability: P(A|B) = P(A ∩ B) / P(B)

• Binomial distribution: P(X = r) = ⁿCᵣ pʳ qⁿ⁻ʳ

How to Use This NDA Maths Formula Sheet

A formula list only helps if you use it the right way:

• Don't just read and write. Copy each formula by hand once. It sticks far better than reading it ten times on a screen.

• Attach one solved example to every formula. A formula without context is easy to forget under exam pressure.

• Revise chapter-wise, not randomly. Go in the same order as this page  Algebra and Trigonometry first, since they carry the most marks.

• Test yourself blind. Cover the formula sheet and try writing it from memory. Only check after you've tried.

• Keep this page open during mock tests. After every mock, note which formulas you forgot or mixed up, and revise only those the next day.

Final Word

You don't need to memorise the whole NDA Maths syllabus by rote — you need instant recall of the right formula at the right moment. Keep this chapter-wise formula sheet as your final revision tool in the last month before the exam, and pair it with regular mock tests to see how quickly you can apply each one under time pressureFrequently Asked Questions

Which chapter has the most formulas in NDA Maths?
Algebra and Trigonometry together account for the largest share of formulas and marks in the NDA Maths paper.

Is Vector Algebra important for NDA Maths?
Yes, though it carries fewer questions (around 7) compared to Algebra or Trigonometry, its formulas are simple to remember and are considered easy scoring marks.

How many marks does Calculus carry in NDA?
Differential and Integral Calculus together make up around 26 questions, worth roughly 64 marks out of 300.

Can I download this NDA Maths formula sheet as a PDF?
Yes, a printable PDF version is available at the end of this page for offline revision.

How should I revise formulas in the last week before the NDA exam?
Focus only on high-weightage chapters -Algebra, Trigonometry, and Calculus — and do a quick self-test on each formula rather than re-reading the whole list.