NDA Mathematics — Strategy Guide

How the 2,280 questions break down

All 31 chapters tested in NDA Mathematics, sized by question count across the 2017–2026 bank. Marks is what the chapter is typically worth in one 300-mark paper, so the column spans the whole paper. Click any chapter to expand its share of the 111 subtopics. Sorted by share of bank.

NDA Mathematics chapters by question count, with per-chapter subtopic breakdowns. Marks are the marks each chapter is typically worth in one 300-mark paper.
Chapter	Questions	Share	Marks	% HARD	Focus topics
Notes	181	7.9%	23.8	30%	Determinant Properties (61), Matrix Operations (34). Highest-reliability chapter — 8–11 q/paper.
Determinant Properties, Operations, and Sums	61	2.7%	8.0	48%
Matrix Operations, Polynomials, and Equations	34	1.5%	4.5	12%
Cofactors, Adjoint, and Inverse	33	1.4%	4.3	21%
Special Matrices — Skew-Symmetric, Diagonal, Idempotent, Orthogonal, Rotation	24	1.1%	3.2	8%
Special Determinants — Trig, Complex, Roots of Unity, Polynomial	20	0.9%	2.6	50%
Linear Systems — Consistency, Cramer's Rule, Solution Space	9	0.4%	1.2	22%
Notes	176	7.7%	23.2	18%	Counting dominates (90); Conditional/Bayes (31) is the harder slice. Mostly classical.
Probability via Counting	90	3.9%	11.8	20%
Conditional Probability, Total Probability, and Bayes' Theorem	31	1.4%	4.1	13%
Event Algebra — Inclusion-Exclusion, Mutually Exclusive, Exhaustive	25	1.1%	3.3	12%
Independent Events	17	0.7%	2.2	18%
Bounds on Probability	13	0.6%	1.7	31%
Notes	165	7.2%	21.7	12%	Central Tendency (75), Dispersion (47). Gentlest chapter in the bank — best marks-per-hour.
Measures of Central Tendency — Mean, Median, Mode	75	3.3%	9.9	13%
Dispersion — Standard Deviation, Variance, Mean Deviation	47	2.1%	6.2	9%
Regression and Correlation	29	1.3%	3.8	21%
Frequency Distributions and Graphical Representation	14	0.6%	1.8	0%
Notes	145	6.4%	19.1	32%	Compound Angle (42), Multi/Half-Angle (31), Product-to-Sum (27). High-HARD — cherry-pick by subtopic.
Compound Angle Formulas	42	1.8%	5.5	24%
Multiple and Half-Angle Formulas	31	1.4%	4.1	42%
Product-to-Sum and Sum-to-Product Identities	27	1.2%	3.6	44%
Specific Values and Quadrants	23	1.0%	3.0	26%
Maximum and Minimum of Trigonometric Expressions	22	1.0%	2.9	27%
Notes	115	5.0%	15.1	10%	Domain/Range (49) is 2% HARD — the cheapest marks in the bank. Skip Functional Equations.
Domain, Range, and Function Properties	49	2.1%	6.4	2%
Composition and Inverse of Functions	29	1.3%	3.8	24%
Functional Equations	20	0.9%	2.6	10%
Function Definition and Classification — Injectivity, Surjectivity, Bijectivity	9	0.4%	1.2	0%
Greatest Integer Function	8	0.4%	1.1	25%
Notes	104	4.6%	13.7	20%	Triangles/Quads (33), Equation+Slope (28), Distance+Section (27).
Triangles, Quadrilaterals, and Polygons	33	1.4%	4.3	18%
Equation, Slope, and Family of Lines	28	1.2%	3.7	14%
Distance, Section, and Locus	27	1.2%	3.6	26%
Angle Between Lines, Parallelism, and Perpendicularity	16	0.7%	2.1	25%
Notes	102	4.5%	13.4	20%	Cross/Triple Product (40), Dot Product (32). Four formulas cover ~70%.
Cross Product and Triple Product	40	1.8%	5.3	28%
Dot Product and Angle	32	1.4%	4.2	13%
Magnitude, Components, Projection, and Direction Cosines	13	0.6%	1.7	8%
Vector Geometry — Triangles, Parallelograms, Quadrilaterals	11	0.5%	1.4	9%
Position Vectors and Section	6	0.3%	0.8	50%
Notes	94	4.1%	12.4	22%	Direction Cosines (25) leads; the rest splits evenly across Sphere, Distance and the Plane.
Direction Cosines and Ratios	25	1.1%	3.3	28%
Distance, Section, and Collinearity in 3D	22	1.0%	2.9	27%
Sphere	20	0.9%	2.6	20%
The Plane	16	0.7%	2.1	19%
The Straight Line in 3D	11	0.5%	1.4	9%
Notes	93	4.1%	12.2	20%	AP (42) carries half the chapter, then GP (19). AM-GM is the cross-chapter lever.
Arithmetic Progressions	44	1.9%	5.8	14%
Geometric Progressions	20	0.9%	2.6	5%
Interrelating AP, GP and HP	16	0.7%	2.1	38%
Special Series and Special Sums	8	0.4%	1.1	38%
Harmonic Progressions and the Three Means	5	0.2%	0.7	60%
Notes	89	3.9%	11.7	24%	Chain Rule + Logarithmic (51), Parametric/Implicit (20). Differentiability questions overlap with Limits & Continuity.
Differentiation Techniques — Chain Rule, Logarithmic, Composite Functions	51	2.2%	6.7	16%
Parametric, Implicit, and Higher-Order Derivatives	20	0.9%	2.6	50%
Differentiability of Absolute Value, Piecewise, and Greatest Integer Functions	18	0.8%	2.4	17%
Notes	87	3.8%	11.4	15%	Continuity/Differentiability (36), Limit Techniques (34). Edge cases with \|x\|, ⌊x⌋ are the lever.
Continuity and Differentiability — Piecewise, Modulus, Composed, Oscillatory	36	1.6%	4.7	11%
Limit Evaluation Techniques — L'Hôpital, Rationalization, Standard Forms	34	1.5%	4.5	15%
One-Sided Limits, Greatest Integer, and Absolute Value Limits	17	0.7%	2.2	24%
Notes	80	3.5%	10.5	20%	Digit-Forming (21), Factorials (17), Arrangements with Restrictions (17).
Forming Numbers from Digits	21	0.9%	2.8	19%
Arrangements with Restrictions	17	0.7%	2.2	24%
Factorials and Binomial Coefficients	17	0.7%	2.2	29%
Geometric Counting	13	0.6%	1.7	8%
Combinations	12	0.5%	1.6	17%
Notes	76	3.3%	10.0	16%	Monotonicity/Extrema (40), Optimisation — AM-GM compound (31).
Monotonicity, Extrema, and Critical Points	40	1.8%	5.3	15%
Optimisation — Geometric, Trigonometric, AM-GM	31	1.4%	4.1	19%
Tangents and Slopes	5	0.2%	0.7	0%
Notes	76	3.3%	10.0	21%	Modulus/Argument (40), Cube Roots of Unity (18), Powers/Roots (18).
Modulus, Argument, and Conjugate	40	1.8%	5.3	15%
Cube Roots of Unity	18	0.8%	2.4	33%
Powers and Roots	18	0.8%	2.4	22%
Notes	75	3.3%	9.9	12%	Counting Sets + Inclusion-Exclusion (28), Set Operations (25). Easy 2–3 marks if given an hour.
Counting Sets, Subsets, and Inclusion-Exclusion	28	1.2%	3.7	11%
Set Operations, Identities, and Cartesian Products of Sets	25	1.1%	3.3	20%
Relations — Properties, Cartesian Product, and Counting	22	1.0%	2.9	5%
Notes	69	3.0%	9.1	19%	Properties — King's, symmetry (32), \|x\|/floor integrals (17).
Properties of Definite Integrals — Symmetry, King's, Odd/Even	33	1.4%	4.3	27%
Integration of Absolute Value, Piecewise, and Greatest Integer Functions	17	0.7%	2.2	12%
Fundamental Theorem, Periodic Integrals, and Leibniz Rule	13	0.6%	1.7	0%
Area Under Curves	3	0.1%	0.4	0%
Definite Integrals in Function Conditions	3	0.1%	0.4	67%
Notes	67	2.9%	8.8	30%	Separable/IVP (31), Order/Degree (23).
Solving and Verifying ODEs — Separable, IVP, and Applications	31	1.4%	4.1	32%
Order, Degree, and Solutions of ODE	23	1.0%	3.0	30%
Formation of ODE from Curves and General Solutions	13	0.6%	1.7	23%
Notes	67	2.9%	8.8	37%	Vieta's Relations (29), Nature of Roots (21). High-HARD; AM-GM + ω compounds live here.
Vieta's Relations and Root-Coefficient Identities	29	1.3%	3.8	38%
Nature of Roots and Boundary Conditions	21	0.9%	2.8	33%
Special Quadratics — Parametric, Logarithmic, Constructed	17	0.7%	2.2	41%
Notes	56	2.5%	7.4	18%	Coefficients & Specific Terms (31), Sum Identities (14).
Coefficients and Specific Terms in Expansion	31	1.4%	4.1	16%
Sums of Binomial Coefficients — Alternating, Weighted, and Symmetric	14	0.6%	1.8	14%
Integer and Fractional Parts of Binomial Expressions	8	0.4%	1.1	38%
Remainders and Divisibility via Binomial Expansion	3	0.1%	0.4	0%
Notes	52	2.3%	6.8	42%	Sine/Cosine Rules (32), Triangle Identities (14). High-HARD — punishing yield.
Sine and Cosine Rules — Solving Triangles	32	1.4%	4.2	41%
Triangle Identities — A+B+C=π, Half-Angle, and Double-Angle	14	0.6%	1.8	43%
In-circle and Regular Polygon Geometry	6	0.3%	0.8	50%
Notes	42	1.8%	5.5	21%	Substitution (18), Standard Forms — exp/log (13).
Integration by Substitution — Algebraic, Trigonometric, and Composite Forms	18	0.8%	2.4	22%
Standard Forms — Exponential, Logarithmic, and Paired Trigonometric Integrals	14	0.6%	1.8	21%
Integration by Partial Fractions	7	0.3%	0.9	29%
Integration by Parts	3	0.1%	0.4	0%
Notes	40	1.8%	5.3	20%	Ellipse (15), Parabola (14).
Ellipse — Foci, Eccentricity, and Focal Distances	15	0.7%	2.0	13%
Parabola — Equation, Properties, and Latus Rectum	14	0.6%	1.8	21%
Conic Sections — Identification and Eccentricity Comparison	7	0.3%	0.9	43%
Hyperbola — Foci and Eccentricity	4	0.2%	0.5	0%
Notes	36	1.6%	4.7	22%	Identities + Sum-Difference (17), Composite Evaluation (13).
Identities, Properties, and Sum-Difference Formulas	17	0.7%	2.2	12%
Evaluation of Composite Inverse Trigonometric Expressions	13	0.6%	1.7	31%
Solving Inverse Trigonometric Equations and Geometric Applications	6	0.3%	0.8	33%
Notes	34	1.5%	4.5	32%	Specific Forms — double-angle, product (13), General Solutions (14).
General Solutions and Counting Solutions of Trigonometric Equations	14	0.6%	1.8	43%
Solving Specific Forms — Double-Angle, Product, Logarithmic, and Vieta	13	0.6%	1.7	15%
Simultaneous and Combined Trigonometric Systems	7	0.3%	0.9	43%
Notes	31	1.4%	4.1	10%	Computing Probabilities (15), Mean/Variance (16). One chapter, two formulas — 60 minutes, 2 marks.
Mean, Variance, and Parameter Estimation in B(n, p)	16	0.7%	2.1	13%
Computing Binomial Probabilities — Exact, At-Least, and Complementary Events	15	0.7%	2.0	7%
Notes	28	1.2%	3.7	39%	Circle Equation — centre/radius (11) is the soft half; Concyclicity (9) runs 78% HARD.
Circle Equation — Centre, Radius, Diameter, and Properties	12	0.5%	1.6	0%
Circles Through Given Points and Concyclicity	9	0.4%	1.2	78%
Inscribed Geometry, Tangents, and Segments	7	0.3%	0.9	57%
Notes	27	1.2%	3.6	19%	Area Bounded by Curve (18).
Area Bounded by a Curve, Lines, and Axes	18	0.8%	2.4	17%
Area Between Two Curves and Intersection Points	9	0.4%	1.2	22%
Notes	27	1.2%	3.6	19%	Identities + Change of Base (16), Log Equations (11).
Logarithm Identities, Change of Base, and Sums	16	0.7%	2.1	13%
Solving Logarithmic Equations and Applications	11	0.5%	1.4	27%
Notes	26	1.1%	3.4	69%	Angles of Elevation (18). Hardest chapter in the bank — 71% HARD, and no soft subtopic to retreat to.
Heights and Distances from Angles of Elevation	18	0.8%	2.4	67%
Shadows, Leaning Structures, and Special Geometry	8	0.4%	1.1	75%
Notes	14	0.6%	1.8	29%	Tiny chapter — 0.7 q/paper average.
Binary Arithmetic — Addition, Division, and Algebraic Identities	7	0.3%	0.9	43%
Binary Representation and Number Theory	4	0.2%	0.5	25%
Binary to Decimal Conversion	3	0.1%	0.4	0%
	6	0.3%	0.8	0%	Near-irrelevant — 0.3 q/paper, zero HARD across the bank.
Linear Systems and Feasible Regions	6	0.3%	0.8	0%

What’s inside

Five sections, each answering a different question a student walks in with. Read top-to-bottom or jump to what you need.

Strategy
Score 100+ marks with 50 hours of focused, evidence-led prep.
Principles
79 atoms behind every question. Drill the 11 cross-chapter principles first.
Compound Tricks
4 principle pairs that spike HARD — 40–67% HARD vs 22.1% bank average. The chains paper-setters love.
Trends
How NDA Maths has shifted from 2017 to 2026, and what to practice first.
Traps
Distractor patterns NDA reuses. The last-step verification rules that recover marks.

Why we built this

Most NDA Maths preparation is generic — practice everything, hope something sticks. We took the opposite approach: we extracted every question from every paper since 2021, classified them by the underlying principle, and looked at the patterns.

Every claim on this site is verifiable. Click any “Drill these X questions →” link and you’ll see the exact set we’re talking about.

Data snapshot: 14 September 2026. Numbers refresh as new papers land.

How the 2,280 questions break down

What’s inside

Strategy

Principles

Compound Tricks

Trends

Traps

Why we built this