NDA Mathematics — Strategy Guide

How the 2,160 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	170	7.9%	23.6	31%	Determinant Properties (59), Matrix Operations (33). Highest-reliability chapter — 8–11 q/paper.
Determinant Properties, Operations, and Sums	59	2.7%	8.2	46%
Matrix Operations, Polynomials, and Equations	33	1.5%	4.6	12%
Cofactors, Adjoint, and Inverse	28	1.3%	3.9	25%
Special Matrices — Skew-Symmetric, Diagonal, Idempotent, Orthogonal, Rotation	22	1.0%	3.1	9%
Special Determinants — Trig, Complex, Roots of Unity, Polynomial	20	0.9%	2.8	50%
Linear Systems — Consistency, Cramer's Rule, Solution Space	8	0.4%	1.1	25%
Notes	162	7.5%	22.5	17%	Counting dominates (85); Conditional/Bayes (29) is the harder slice. Mostly classical.
Probability via Counting	85	3.9%	11.8	19%
Conditional Probability, Total Probability, and Bayes' Theorem	29	1.3%	4.0	14%
Event Algebra — Inclusion-Exclusion, Mutually Exclusive, Exhaustive	21	1.0%	2.9	14%
Independent Events	15	0.7%	2.1	13%
Bounds on Probability	12	0.6%	1.7	25%
Notes	160	7.4%	22.2	13%	Central Tendency (75), Dispersion (44). Gentlest chapter in the bank — best marks-per-hour.
Measures of Central Tendency — Mean, Median, Mode	75	3.5%	10.4	13%
Dispersion — Standard Deviation, Variance, Mean Deviation	44	2.0%	6.1	9%
Regression and Correlation	27	1.3%	3.8	22%
Frequency Distributions and Graphical Representation	14	0.6%	1.9	0%
Notes	138	6.4%	19.2	34%	Compound Angle (38), Multi/Half-Angle (30), Product-to-Sum (27). High-HARD — cherry-pick by subtopic.
Compound Angle Formulas	38	1.8%	5.3	26%
Multiple and Half-Angle Formulas	30	1.4%	4.2	43%
Product-to-Sum and Sum-to-Product Identities	27	1.3%	3.8	44%
Maximum and Minimum of Trigonometric Expressions	22	1.0%	3.1	27%
Specific Values and Quadrants	21	1.0%	2.9	29%
Notes	109	5.0%	15.1	10%	Domain/Range (48) is 2% HARD — the cheapest marks in the bank. Skip Functional Equations.
Domain, Range, and Function Properties	48	2.2%	6.7	2%
Composition and Inverse of Functions	28	1.3%	3.9	25%
Functional Equations	18	0.8%	2.5	6%
Function Definition and Classification — Injectivity, Surjectivity, Bijectivity	8	0.4%	1.1	0%
Greatest Integer Function	7	0.3%	1.0	29%
Notes	97	4.5%	13.5	20%	Cross/Triple Product (37), Dot Product (32). Four formulas cover ~70%.
Cross Product and Triple Product	37	1.7%	5.1	27%
Dot Product and Angle	32	1.5%	4.4	13%
Magnitude, Components, Projection, and Direction Cosines	11	0.5%	1.5	9%
Vector Geometry — Triangles, Parallelograms, Quadrilaterals	11	0.5%	1.5	9%
Position Vectors and Section	6	0.3%	0.8	50%
Notes	97	4.5%	13.5	21%	Triangles/Quads (32), Equation+Slope (27), Distance+Section (22).
Triangles, Quadrilaterals, and Polygons	32	1.5%	4.4	19%
Equation, Slope, and Family of Lines	27	1.3%	3.8	15%
Distance, Section, and Locus	22	1.0%	3.1	27%
Angle Between Lines, Parallelism, and Perpendicularity	16	0.7%	2.2	25%
Notes	89	4.1%	12.4	21%	AP (42) carries half the chapter, then GP (19). AM-GM is the cross-chapter lever.
Arithmetic Progressions	42	1.9%	5.8	14%
Geometric Progressions	19	0.9%	2.6	5%
Interrelating AP, GP and HP	15	0.7%	2.1	40%
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	4.1%	12.4	22%	Direction Cosines (24) leads; the rest splits evenly across Sphere, Distance and the Plane.
Direction Cosines and Ratios	24	1.1%	3.3	25%
Sphere	20	0.9%	2.8	20%
Distance, Section, and Collinearity in 3D	20	0.9%	2.8	30%
The Plane	14	0.6%	1.9	21%
The Straight Line in 3D	11	0.5%	1.5	9%
Notes	85	3.9%	11.8	24%	Chain Rule + Logarithmic (49), Parametric/Implicit (20). Differentiability questions overlap with Limits & Continuity.
Differentiation Techniques — Chain Rule, Logarithmic, Composite Functions	49	2.3%	6.8	14%
Parametric, Implicit, and Higher-Order Derivatives	20	0.9%	2.8	50%
Differentiability of Absolute Value, Piecewise, and Greatest Integer Functions	16	0.7%	2.2	19%
Notes	81	3.8%	11.3	14%	Continuity/Differentiability (34), Limit Techniques (31). Edge cases with \|x\|, ⌊x⌋ are the lever.
Continuity and Differentiability — Piecewise, Modulus, Composed, Oscillatory	34	1.6%	4.7	12%
Limit Evaluation Techniques — L'Hôpital, Rationalization, Standard Forms	31	1.4%	4.3	10%
One-Sided Limits, Greatest Integer, and Absolute Value Limits	16	0.7%	2.2	25%
Notes	78	3.6%	10.8	19%	Digit-Forming (20), Factorials (17), Arrangements with Restrictions (17).
Forming Numbers from Digits	20	0.9%	2.8	20%
Arrangements with Restrictions	17	0.8%	2.4	24%
Factorials and Binomial Coefficients	17	0.8%	2.4	29%
Geometric Counting	13	0.6%	1.8	8%
Combinations	11	0.5%	1.5	9%
Notes	73	3.4%	10.1	16%	Monotonicity/Extrema (38), Optimisation — AM-GM compound (30).
Monotonicity, Extrema, and Critical Points	38	1.8%	5.3	16%
Optimisation — Geometric, Trigonometric, AM-GM	30	1.4%	4.2	20%
Tangents and Slopes	5	0.2%	0.7	0%
Notes	72	3.3%	10.0	22%	Modulus/Argument (39), Cube Roots of Unity (18), Powers/Roots (15).
Modulus, Argument, and Conjugate	39	1.8%	5.4	15%
Cube Roots of Unity	18	0.8%	2.5	33%
Powers and Roots	15	0.7%	2.1	27%
Notes	69	3.2%	9.6	13%	Counting Sets + Inclusion-Exclusion (27), Set Operations (23). Easy 2–3 marks if given an hour.
Counting Sets, Subsets, and Inclusion-Exclusion	27	1.3%	3.8	11%
Set Operations, Identities, and Cartesian Products of Sets	23	1.1%	3.2	22%
Relations — Properties, Cartesian Product, and Counting	19	0.9%	2.6	5%
Notes	66	3.1%	9.2	20%	Properties — King's, symmetry (32), \|x\|/floor integrals (17).
Properties of Definite Integrals — Symmetry, King's, Odd/Even	32	1.5%	4.4	28%
Integration of Absolute Value, Piecewise, and Greatest Integer Functions	17	0.8%	2.4	12%
Fundamental Theorem, Periodic Integrals, and Leibniz Rule	11	0.5%	1.5	0%
Definite Integrals in Function Conditions	3	0.1%	0.4	67%
Area Under Curves	3	0.1%	0.4	0%
Notes	63	2.9%	8.8	40%	Vieta's Relations (26), Nature of Roots (21). High-HARD; AM-GM + ω compounds live here.
Vieta's Relations and Root-Coefficient Identities	26	1.2%	3.6	42%
Nature of Roots and Boundary Conditions	21	1.0%	2.9	33%
Special Quadratics — Parametric, Logarithmic, Constructed	16	0.7%	2.2	44%
Notes	63	2.9%	8.8	29%	Separable/IVP (29), Order/Degree (22).
Solving and Verifying ODEs — Separable, IVP, and Applications	29	1.3%	4.0	28%
Order, Degree, and Solutions of ODE	22	1.0%	3.1	32%
Formation of ODE from Curves and General Solutions	12	0.6%	1.7	25%
Notes	54	2.5%	7.5	17%	Coefficients & Specific Terms (29), Sum Identities (14).
Coefficients and Specific Terms in Expansion	29	1.3%	4.0	14%
Sums of Binomial Coefficients — Alternating, Weighted, and Symmetric	14	0.6%	1.9	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	49	2.3%	6.8	45%	Sine/Cosine Rules (29), Triangle Identities (14). High-HARD — punishing yield.
Sine and Cosine Rules — Solving Triangles	29	1.3%	4.0	45%
Triangle Identities — A+B+C=π, Half-Angle, and Double-Angle	14	0.6%	1.9	43%
In-circle and Regular Polygon Geometry	6	0.3%	0.8	50%
Notes	40	1.9%	5.6	23%	Substitution (17), Standard Forms — exp/log (13).
Integration by Substitution — Algebraic, Trigonometric, and Composite Forms	17	0.8%	2.4	24%
Standard Forms — Exponential, Logarithmic, and Paired Trigonometric Integrals	13	0.6%	1.8	23%
Integration by Partial Fractions	7	0.3%	1.0	29%
Integration by Parts	3	0.1%	0.4	0%
Notes	38	1.8%	5.3	21%	Ellipse (14), Parabola (13).
Ellipse — Foci, Eccentricity, and Focal Distances	14	0.6%	1.9	14%
Parabola — Equation, Properties, and Latus Rectum	13	0.6%	1.8	23%
Conic Sections — Identification and Eccentricity Comparison	7	0.3%	1.0	43%
Hyperbola — Foci and Eccentricity	4	0.2%	0.6	0%
Notes	34	1.6%	4.7	24%	Identities + Sum-Difference (17), Composite Evaluation (11).
Identities, Properties, and Sum-Difference Formulas	17	0.8%	2.4	12%
Evaluation of Composite Inverse Trigonometric Expressions	11	0.5%	1.5	36%
Solving Inverse Trigonometric Equations and Geometric Applications	6	0.3%	0.8	33%
Notes	33	1.5%	4.6	33%	Specific Forms — double-angle, product (13), General Solutions (13).
General Solutions and Counting Solutions of Trigonometric Equations	13	0.6%	1.8	46%
Solving Specific Forms — Double-Angle, Product, Logarithmic, and Vieta	13	0.6%	1.8	15%
Simultaneous and Combined Trigonometric Systems	7	0.3%	1.0	43%
Notes	30	1.4%	4.2	10%	Computing Probabilities (15), Mean/Variance (15). One chapter, two formulas — 60 minutes, 2 marks.
Mean, Variance, and Parameter Estimation in B(n, p)	15	0.7%	2.1	13%
Computing Binomial Probabilities — Exact, At-Least, and Complementary Events	15	0.7%	2.1	7%
Notes	27	1.3%	3.8	19%	Identities + Change of Base (16), Log Equations (11).
Logarithm Identities, Change of Base, and Sums	16	0.7%	2.2	13%
Solving Logarithmic Equations and Applications	11	0.5%	1.5	27%
Notes	27	1.3%	3.8	41%	Circle Equation — centre/radius (11) is the soft half; Concyclicity (9) runs 78% HARD.
Circle Equation — Centre, Radius, Diameter, and Properties	11	0.5%	1.5	0%
Circles Through Given Points and Concyclicity	9	0.4%	1.3	78%
Inscribed Geometry, Tangents, and Segments	7	0.3%	1.0	57%
Notes	25	1.2%	3.5	20%	Area Bounded by Curve (16).
Area Bounded by a Curve, Lines, and Axes	16	0.7%	2.2	19%
Area Between Two Curves and Intersection Points	9	0.4%	1.3	22%
Notes	24	1.1%	3.3	71%	Angles of Elevation (16). Hardest chapter in the bank — 71% HARD, and no soft subtopic to retreat to.
Heights and Distances from Angles of Elevation	16	0.7%	2.2	69%
Shadows, Leaning Structures, and Special Geometry	8	0.4%	1.1	75%
Notes	13	0.6%	1.8	31%	Tiny chapter — 0.7 q/paper average.
Binary Arithmetic — Addition, Division, and Algebraic Identities	7	0.3%	1.0	43%
Binary Representation and Number Theory	3	0.1%	0.4	33%
Binary to Decimal Conversion	3	0.1%	0.4	0%
	5	0.2%	0.7	0%	Near-irrelevant — 0.3 q/paper, zero HARD across the bank.
Linear Systems and Feasible Regions	5	0.2%	0.7	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 22.5% 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: 17 May 2026. Numbers refresh as new papers land.

How the 2,160 questions break down

What’s inside

Strategy

Principles

Compound Tricks

Trends

Traps

Why we built this