Strategy
Score 65+ by learning the right chapters first
25 questions × 4 marks = 100, with 1 mark lost for each wrong answer, on a clock shared with Physics and Chemistry. Two decisions matter: which chapters to learn first, and on the day, which answers to guess and which to leave blank.
- marks out of 100
- 65+
- questions solved
- 20/25
- accuracy on those
- 85%
- of the shared clock
- ~60 min
The arithmetic of 65+
20 solved questions at 85% accuracy is 17 right and 3 wrong: 17 × 4 − 3 = 65 marks. The other 5 are not simply left blank. Every multiple-choice question among them still gets an answer at the end, because a guess there is worth more than a blank:
| Question | Expected marks from a guess | Verdict |
|---|---|---|
| MCQ, 4 options left | +0.25 | A blind guess still pays on average. Never leave an MCQ blank at the end. |
| MCQ, 3 options left | +0.67 | Rule out one option and the guess is worth two-thirds of a mark. |
| MCQ, 2 options left | +1.5 | Down to two, a guess is worth more than a mark. |
| Numeric answer | close to −1 | A numeric answer has no options, so a guess is almost never right and still costs a mark. Enter one only when you have worked it out. |
So the formats split. A numeric question is worth something only when you can finish it, which is why the chapters heavy in numeric answers need to be owned, not half-learned. A multiple-choice question is worth something even when you cannot, and more once one option is ruled out on sight.
The shared clock
180 minutes cover all three subjects, and every question pays the same 4 marks. The plan below is a starting budget, not a measurement; adjust it from your own mock tests.
- 1
Give Maths about an hour
The three subjects share one clock. Maths questions run longer than most Chemistry ones, so an equal split usually runs Maths short. Adjust from your own mock tests.
- 2
First pass: what opens up quickly
Go through all the questions once. Answer what you can see how to do, and mark the rest. A question that has not opened up in a few minutes is marked, not fought.
- 3
Second pass: the marked questions
Come back once every subject has had its first pass. Work the marked questions in the order you think you can finish them.
- 4
Last minutes: fill every MCQ
Any multiple-choice question still blank gets an answer, after ruling out what you can. Numeric answers you have not worked out stay blank.
Cornerstone — 4 chapters, 8.1 questions a paper
Chapters setting 1.5 or more a paper on the 2025–26 papers.
Each of these sets more than one and a half questions a paper, and together they are about a third of the paper. Conic Sections alone is the largest chapter by a distance.
The approach
- Learn these first. Every one has full notes at /notes/jee-mains-maths; read a chapter's notes once, then drill page by page.
- Conic Sections and Relations and Functions have both grown since the early papers. If time is short, they come before everything else.
- Much of this tier is numeric-answer. A numeric question you cannot finish is left blank, so these chapters must be owned, not half-learned.
Conic Sections
2.97 a paper in 2025–26 · 2.24 in 2021–24 · 30% numeric
The largest chapter on the paper, and it has grown. The circle, parabola, ellipse and hyperbola each come with their tangents; one tangency condition per curve answers most of them.
Drill — in teaching order
- Equation of a CircleDrill Equation of a Circle in Conic Sections
- Chords and Tangents of a CircleDrill Chords and Tangents of a Circle in Conic Sections
- Two Circles and Families of CirclesDrill Two Circles and Families of Circles in Conic Sections
- Parabola and Its Focal ChordsDrill Parabola and Its Focal Chords in Conic Sections
- Tangents and Normals to a ParabolaDrill Tangents and Normals to a Parabola in Conic Sections
- Ellipse: Axes, Eccentricity and Focal DistancesDrill Ellipse: Axes, Eccentricity and Focal Distances in Conic Sections
- Tangents, Normals and Chords of an EllipseDrill Tangents, Normals and Chords of an Ellipse in Conic Sections
- Hyperbola: Axes, Eccentricity and Focal DistancesDrill Hyperbola: Axes, Eccentricity and Focal Distances in Conic Sections
- Tangents and Normals to a HyperbolaDrill Tangents and Normals to a Hyperbola in Conic Sections
- Common Tangents and Loci Across ConicsDrill Common Tangents and Loci Across Conics in Conic Sections
Three Dimensional Geometry
1.76 a paper in 2025–26 · 1.93 in 2021–24 · 28% numeric
Lines and planes in space: the foot, image and distance, and the shortest distance between skew lines. Each task is one formula once the direction ratios are read correctly.
Drill — in teaching order
- Direction Cosines and Equations of LinesDrill Direction Cosines and Equations of Lines in Three Dimensional Geometry
- Foot, Image and Distance from a LineDrill Foot, Image and Distance from a Line in Three Dimensional Geometry
- Shortest Distance, Intersection and Coplanar LinesDrill Shortest Distance, Intersection and Coplanar Lines in Three Dimensional Geometry
- Equation of a PlaneDrill Equation of a Plane in Three Dimensional Geometry
- Distance, Foot and Image in a PlaneDrill Distance, Foot and Image in a Plane in Three Dimensional Geometry
- Lines Meeting PlanesDrill Lines Meeting Planes in Three Dimensional Geometry
Relations and Functions
1.73 a paper in 2025–26 · 1.28 in 2021–24 · 24% numeric
Grown into a cornerstone. Relations are careful counting, often with a numeric answer; functions are domain, range, counting maps and functional equations.
Drill — in teaching order
- Sets and Counting ElementsDrill Sets and Counting Elements in Relations and Functions
- Reflexive, Symmetric, Transitive and EquivalenceDrill Reflexive, Symmetric, Transitive and Equivalence in Relations and Functions
- Counting Relations and Their ElementsDrill Counting Relations and Their Elements in Relations and Functions
- Domain of a FunctionDrill Domain of a Function in Relations and Functions
- Range, One-One and OntoDrill Range, One-One and Onto in Relations and Functions
- Counting FunctionsDrill Counting Functions in Relations and Functions
- Composition, Inverse and IteratesDrill Composition, Inverse and Iterates in Relations and Functions
- Functional EquationsDrill Functional Equations in Relations and Functions
Sequences and Series
1.65 a paper in 2025–26 · 1.52 in 2021–24 · 37% numeric
Two conditions on an AP or a GP, then a term or a sum; the series pages ask you to find the kth term first. A large share has numeric answers.
Drill — in teaching order
- AP: Terms and SumsDrill AP: Terms and Sums in Sequences and Series
- Common Terms and Sub-ProgressionsDrill Common Terms and Sub-Progressions in Sequences and Series
- GP: Terms and SumsDrill GP: Terms and Sums in Sequences and Series
- AP and GP Conditions, Means and AM-GMDrill AP and GP Conditions, Means and AM-GM in Sequences and Series
- Infinite Geometric SeriesDrill Infinite Geometric Series in Sequences and Series
- Sums by Standard FormulasDrill Sums by Standard Formulas in Sequences and Series
- Telescoping SumsDrill Telescoping Sums in Sequences and Series
- Arithmetico-Geometric and Exponential SeriesDrill Arithmetico-Geometric and Exponential Series in Sequences and Series
Core — 9 chapters, 10.0 questions a paper
Chapters setting 1 or more a paper on the 2025–26 papers.
About one question a paper each, and together about two in every five questions. None can be skipped; the order among them matters less than finishing all of them.
The approach
- Permutations and Combinations and the Binomial Theorem carry the most numeric answers here. Drill them for accuracy, because no option will catch a slip.
- Probability, Application of Integrals and Definite Integration share tools with the cornerstone chapters; learn them straight after, while those tools are fresh.
- Complex Numbers and Quadratic Equations sit on the line between core and long tail. Treat them as core.
Definite Integration
1.30 a paper in 2025–26 · 1.41 in 2021–24 · 33% numeric
Direct evaluation and piecewise integrands carry much of it; the a + b − x property is the time-saver when a direct attack looks hopeless.
Drill — in teaching order
- Evaluating by Substitution, Parts and Partial FractionsDrill Evaluating by Substitution, Parts and Partial Fractions in Definite Integration
- The a + b - x Property and Other SymmetriesDrill The a + b - x Property and Other Symmetries in Definite Integration
- Odd, Even and Periodic IntegrandsDrill Odd, Even and Periodic Integrands in Definite Integration
- Greatest Integer, Modulus and Max-Min IntegrandsDrill Greatest Integer, Modulus and Max-Min Integrands in Definite Integration
- Integral Equations and Leibniz's RuleDrill Integral Equations and Leibniz's Rule in Definite Integration
- Reduction Formulas and Beta IntegralsDrill Reduction Formulas and Beta Integrals in Definite Integration
- Limits of Sums as IntegralsDrill Limits of Sums as Integrals in Definite Integration
Permutations and Combinations
1.22 a paper in 2025–26 · 1.09 in 2021–24 · 58% numeric
More of it is numeric-answer than any other chapter still on the paper, so there are no options to catch a slip. Own it outright.
Drill — in teaching order
- Arrangements with RestrictionsDrill Arrangements with Restrictions in Permutations and Combinations
- Dictionary Order and RanksDrill Dictionary Order and Ranks in Permutations and Combinations
- Forming Numbers from DigitsDrill Forming Numbers from Digits in Permutations and Combinations
- Selections and CommitteesDrill Selections and Committees in Permutations and Combinations
- Distributions and Integer SolutionsDrill Distributions and Integer Solutions in Permutations and Combinations
- Counting Functions, Matrices and SubsetsDrill Counting Functions, Matrices and Subsets in Permutations and Combinations
- Points, Lines and PolygonsDrill Points, Lines and Polygons in Permutations and Combinations
- Divisibility, Divisors and FactorialsDrill Divisibility, Divisors and Factorials in Permutations and Combinations
Vector Algebra
1.19 a paper in 2025–26 · 1.31 in 2021–24 · 24% numeric
Vector equations, magnitudes from lengths and angles, areas and triple products. Short questions; marks are lost to sign and order slips.
Drill — in teaching order
- Dot Product: Angles and ProjectionsDrill Dot Product: Angles and Projections in Vector Algebra
- Magnitudes and Unit-Vector IdentitiesDrill Magnitudes and Unit-Vector Identities in Vector Algebra
- Cross Product: Areas and Perpendicular VectorsDrill Cross Product: Areas and Perpendicular Vectors in Vector Algebra
- Solving Vector EquationsDrill Solving Vector Equations in Vector Algebra
- Triple Products and CoplanarityDrill Triple Products and Coplanarity in Vector Algebra
- Vectors in Geometry and RotationDrill Vectors in Geometry and Rotation in Vector Algebra
Differential Equations
1.14 a paper in 2025–26 · 1.31 in 2021–24 · 26% numeric
Three solving methods and the pages that disguise them. The answer is often a second step: a value, a maximum or an integral of the solution.
Drill — in teaching order
- Forming a Differential EquationDrill Forming a Differential Equation in Differential Equations
- Separating the VariablesDrill Separating the Variables in Differential Equations
- Homogeneous EquationsDrill Homogeneous Equations in Differential Equations
- Linear Equations: The Integrating FactorDrill Linear Equations: The Integrating Factor in Differential Equations
- Integrating Factors in DisguiseDrill Integrating Factors in Disguise in Differential Equations
- Equations Reducible to LinearDrill Equations Reducible to Linear in Differential Equations
- Using a Linear SolutionDrill Using a Linear Solution in Differential Equations
- Equations Hidden in Integrals and LimitsDrill Equations Hidden in Integrals and Limits in Differential Equations
- Curves and Growth from RatesDrill Curves and Growth from Rates in Differential Equations
Probability
1.11 a paper in 2025–26 · 1.03 in 2021–24 · 19% numeric
Counting in disguise, then Bayes' theorem and the binomial distribution. Set up the sample space once and count both parts the same way.
Drill — in teaching order
- Counting Favourable OutcomesDrill Counting Favourable Outcomes in Probability
- Dice, Digits and DivisibilityDrill Dice, Digits and Divisibility in Probability
- Random Coefficients and InequalitiesDrill Random Coefficients and Inequalities in Probability
- Addition, Conditional Probability and IndependenceDrill Addition, Conditional Probability and Independence in Probability
- Total Probability and Bayes' TheoremDrill Total Probability and Bayes' Theorem in Probability
- Binomial DistributionDrill Binomial Distribution in Probability
- Random Variables: Mean and VarianceDrill Random Variables: Mean and Variance in Probability
Binomial Theorem
1.05 a paper in 2025–26 · 1.20 in 2021–24 · 45% numeric
The general term does half the work, coefficient sums the other half. Nearly half its questions have numeric answers, so accuracy matters more than speed here.
Drill — in teaching order
- The General TermDrill The General Term in Binomial Theorem
- Consecutive Coefficients and Special TermsDrill Consecutive Coefficients and Special Terms in Binomial Theorem
- Products and Multinomial ExpansionsDrill Products and Multinomial Expansions in Binomial Theorem
- Rational and Integral TermsDrill Rational and Integral Terms in Binomial Theorem
- Coefficient Sums by Substitution and DifferentiationDrill Coefficient Sums by Substitution and Differentiation in Binomial Theorem
- Sums with Fractions and Products of CoefficientsDrill Sums with Fractions and Products of Coefficients in Binomial Theorem
- Sums of Expansions: Hockey Stick and Geometric SeriesDrill Sums of Expansions: Hockey Stick and Geometric Series in Binomial Theorem
- Remainders and DivisibilityDrill Remainders and Divisibility in Binomial Theorem
Application of Integrals
1.03 a paper in 2025–26 · 0.75 in 2021–24 · 35% numeric
Area between curves, every time: sketch first, then integrate top minus bottom. It has grown since the early papers.
Drill — in teaching order
- Curves and Lines: Vertical StripsDrill Curves and Lines: Vertical Strips in Application of Integrals
- Horizontal Strips and Sideways ParabolasDrill Horizontal Strips and Sideways Parabolas in Application of Integrals
- Circles, Ellipses and Other ConicsDrill Circles, Ellipses and Other Conics in Application of Integrals
- Modulus CurvesDrill Modulus Curves in Application of Integrals
- Max, Min and Piecewise BoundariesDrill Max, Min and Piecewise Boundaries in Application of Integrals
- Trigonometric, Exponential and Reciprocal CurvesDrill Trigonometric, Exponential and Reciprocal Curves in Application of Integrals
- Unknown Parameters and Area RatiosDrill Unknown Parameters and Area Ratios in Application of Integrals
Complex Numbers
1.00 a paper in 2025–26 · 1.00 in 2021–24 · 29% numeric
Half algebra, half geometry. Choose the right form, and draw a locus before expanding it into x and y.
Drill — in teaching order
- Algebra of Complex NumbersDrill Algebra of Complex Numbers in Complex Numbers
- Polar Form, Argument and De MoivreDrill Polar Form, Argument and De Moivre in Complex Numbers
- Roots of UnityDrill Roots of Unity in Complex Numbers
- Quadratic Equations with Complex RootsDrill Quadratic Equations with Complex Roots in Complex Numbers
- Lines and Circles in the Complex PlaneDrill Lines and Circles in the Complex Plane in Complex Numbers
- Arcs and Conic LociDrill Arcs and Conic Loci in Complex Numbers
- Regions and Extreme DistancesDrill Regions and Extreme Distances in Complex Numbers
Quadratic Equations
1.00 a paper in 2025–26 · 0.78 in 2021–24 · 32% numeric
Vieta and the discriminant, plus equations that are quadratics after a substitution. Most wrong answers keep a root the substitution should have dropped.
Drill — in teaching order
- Roots and CoefficientsDrill Roots and Coefficients in Quadratic Equations
- Symmetric Functions and Power SumsDrill Symmetric Functions and Power Sums in Quadratic Equations
- Common Roots and New EquationsDrill Common Roots and New Equations in Quadratic Equations
- Discriminant and Location of RootsDrill Discriminant and Location of Roots in Quadratic Equations
- Equations with Modulus and Greatest IntegerDrill Equations with Modulus and Greatest Integer in Quadratic Equations
- Equations Reducible to QuadraticsDrill Equations Reducible to Quadratics in Quadratic Equations
Long tail — 11 chapters, 6.9 questions a paper
Chapters setting under one a paper on the 2025–26 papers.
Each sets under one question a paper, but together they are still a large block of marks. Their questions are often short, which makes them cheap marks in a first pass.
The approach
- Do not skip this tier. Most of these chapters are quick to learn, and a paper sets several of them.
- Application of Derivatives and Differentiation have shrunk since the early papers. Learn them, but after the rising chapters.
- Matrices, Determinants and Statistics are mostly routine once the identities are known: good first-pass questions.
Limits and Continuity
0.92 a paper in 2025–26 · 0.97 in 2021–24 · 25% numeric
Standard limits, series expansions and the one-to-the-power-infinity rule; continuity is one equation. Counting points of discontinuity takes the longest.
Drill — in teaching order
- Standard Limits and Algebraic FormsDrill Standard Limits and Algebraic Forms in Limits and Continuity
- Series Expansions and Unknown ConstantsDrill Series Expansions and Unknown Constants in Limits and Continuity
- Exponential Limits (1 to the Power Infinity)Drill Exponential Limits (1 to the Power Infinity) in Limits and Continuity
- Limits at Infinity and Limits of SumsDrill Limits at Infinity and Limits of Sums in Limits and Continuity
- Limits via Derivatives and IntegralsDrill Limits via Derivatives and Integrals in Limits and Continuity
- Greatest Integer and One-Sided LimitsDrill Greatest Integer and One-Sided Limits in Limits and Continuity
- Continuity at a PointDrill Continuity at a Point in Limits and Continuity
- Counting Discontinuities and Non-DifferentiabilityDrill Counting Discontinuities and Non-Differentiability in Limits and Continuity
Straight Lines
0.92 a paper in 2025–26 · 0.74 in 2021–24 · 18% numeric
A small toolkit — slope, distance, image — used two or three times in a row. The centres of a triangle are the most common setting.
Drill — in teaching order
- Slope, Angle and Forms of a LineDrill Slope, Angle and Forms of a Line in Straight Lines
- Distance from a Line and Parallel LinesDrill Distance from a Line and Parallel Lines in Straight Lines
- Image of a Point and Reflected RaysDrill Image of a Point and Reflected Rays in Straight Lines
- Angle Bisectors and Pairs of LinesDrill Angle Bisectors and Pairs of Lines in Straight Lines
- Centres of a TriangleDrill Centres of a Triangle in Straight Lines
- Area of Triangles and QuadrilateralsDrill Area of Triangles and Quadrilaterals in Straight Lines
- Family of Lines and LocusDrill Family of Lines and Locus in Straight Lines
Matrices
0.89 a paper in 2025–26 · 0.78 in 2021–24 · 38% numeric
High powers of a matrix by spotting a pattern, and the adjoint and determinant identities. Few long calculations.
Drill — in teaching order
- Matrix Algebra, Types and OperationsDrill Matrix Algebra, Types and Operations in Matrices
- Powers of a Matrix and Cayley-Hamilton TheoremDrill Powers of a Matrix and Cayley-Hamilton Theorem in Matrices
- Symmetric, Skew-Symmetric and Orthogonal MatricesDrill Symmetric, Skew-Symmetric and Orthogonal Matrices in Matrices
- Adjoint, Inverse and Determinant IdentitiesDrill Adjoint, Inverse and Determinant Identities in Matrices
Determinants
0.84 a paper in 2025–26 · 1.00 in 2021–24 · 16% numeric
Mostly systems of three equations with a constant left open: which values give one, none or infinitely many solutions.
Drill — in teaching order
- Infinitely Many Solutions: One Equation Holds the ParametersDrill Infinitely Many Solutions: One Equation Holds the Parameters in Determinants
- Infinitely Many Solutions: Parameters in Two EquationsDrill Infinitely Many Solutions: Parameters in Two Equations in Determinants
- No Solution and Inconsistent SystemsDrill No Solution and Inconsistent Systems in Determinants
- Classifying a System: Unique, Infinite or NoneDrill Classifying a System: Unique, Infinite or None in Determinants
- Homogeneous Systems and Non-trivial SolutionsDrill Homogeneous Systems and Non-trivial Solutions in Determinants
- Determinants of kA, adj A and ProductsDrill Determinants of kA, adj A and Products in Determinants
- Simplifying Determinants by Row and Column OperationsDrill Simplifying Determinants by Row and Column Operations in Determinants
- Determinants as Functions of xDrill Determinants as Functions of x in Determinants
Statistics
0.62 a paper in 2025–26 · 0.62 in 2021–24 · 34% numeric
Nearly all variance: write down Σx and Σx² first, and missing, wrong or combined data become a few lines of arithmetic.
Drill — in teaching order
- Variance from Sums and ShiftsDrill Variance from Sums and Shifts in Statistics
- Finding Unknown ObservationsDrill Finding Unknown Observations in Statistics
- Correcting Data and Combining GroupsDrill Correcting Data and Combining Groups in Statistics
- Mean Deviation and MedianDrill Mean Deviation and Median in Statistics
- Frequency DistributionsDrill Frequency Distributions in Statistics
Application of Derivatives
0.59 a paper in 2025–26 · 1.12 in 2021–24 · 27% numeric
Maxima and minima, monotonicity and tangents. It has shrunk by about half since the early papers, but still appears on many papers.
Drill — in teaching order
- Tangents, Normals and Rates of ChangeDrill Tangents, Normals and Rates of Change in Application of Derivatives
- Increasing and Decreasing FunctionsDrill Increasing and Decreasing Functions in Application of Derivatives
- Counting Real RootsDrill Counting Real Roots in Application of Derivatives
- Local Maxima and MinimaDrill Local Maxima and Minima in Application of Derivatives
- Functions Built from Their ExtremaDrill Functions Built from Their Extrema in Application of Derivatives
- Greatest and Least ValuesDrill Greatest and Least Values in Application of Derivatives
- Optimisation ProblemsDrill Optimisation Problems in Application of Derivatives
- Rolle's and Mean Value TheoremsDrill Rolle's and Mean Value Theorems in Application of Derivatives
Trigonometric Identities
0.51 a paper in 2025–26 · 0.28 in 2021–24 · 13% numeric
The formula kit for all of trigonometry: evaluate a product or a power sum with the one identity that collapses it.
Drill — in teaching order
- Compound Angle FormulaeDrill Compound Angle Formulae in Trigonometric Identities
- Standard Values and Multiple AnglesDrill Standard Values and Multiple Angles in Trigonometric Identities
- Powers of Sine and CosineDrill Powers of Sine and Cosine in Trigonometric Identities
- Sum-Product Formulas and TelescopingDrill Sum-Product Formulas and Telescoping in Trigonometric Identities
- Maximum, Minimum and RangeDrill Maximum, Minimum and Range in Trigonometric Identities
Inverse Trigonometric Functions
0.49 a paper in 2025–26 · 0.49 in 2021–24 · 23% numeric
Every question turns on the principal ranges; sums of inverse tangents often telescope.
Drill — in teaching order
- Domain, Range and Principal ValuesDrill Domain, Range and Principal Values in Inverse Trigonometric Functions
- Trigonometric Values of Inverse ExpressionsDrill Trigonometric Values of Inverse Expressions in Inverse Trigonometric Functions
- Simplifying Inverse Functions of a VariableDrill Simplifying Inverse Functions of a Variable in Inverse Trigonometric Functions
- Sums of Inverse Tangents and Telescoping SeriesDrill Sums of Inverse Tangents and Telescoping Series in Inverse Trigonometric Functions
- Equations in Inverse Trigonometric FunctionsDrill Equations in Inverse Trigonometric Functions in Inverse Trigonometric Functions
Indefinite Integration
0.41 a paper in 2025–26 · 0.29 in 2021–24 · 30% numeric
An antiderivative matched to a printed form or evaluated at a point, so the constant matters. Choosing the substitution is the whole question.
Drill — in teaching order
- Algebraic SubstitutionDrill Algebraic Substitution in Indefinite Integration
- Rational Functions and Standard FormsDrill Rational Functions and Standard Forms in Indefinite Integration
- Trigonometric IntegralsDrill Trigonometric Integrals in Indefinite Integration
- Integration by Parts and Reverse DifferentiationDrill Integration by Parts and Reverse Differentiation in Indefinite Integration
Differentiation
0.35 a paper in 2025–26 · 0.61 in 2021–24 · 31% numeric
Simplify before differentiating, and count the points where a derivative fails to exist. Lighter than in the early papers.
Drill — in teaching order
- Chain Rule and Inverse-Trig SimplificationDrill Chain Rule and Inverse-Trig Simplification in Differentiation
- Implicit, Parametric and Logarithmic DifferentiationDrill Implicit, Parametric and Logarithmic Differentiation in Differentiation
- Functional Equations and Derivative ConstantsDrill Functional Equations and Derivative Constants in Differentiation
- Differentiability of Piecewise FunctionsDrill Differentiability of Piecewise Functions in Differentiation
- Counting Points of Non-DifferentiabilityDrill Counting Points of Non-Differentiability in Differentiation
Trigonometric Equations
0.32 a paper in 2025–26 · 0.37 in 2021–24 · 33% numeric
How many solutions lie in an interval. Reduce to one ratio of one angle, then count the roots on the interval itself.
Drill — in teaching order
- Quadratic in One RatioDrill Quadratic in One Ratio in Trigonometric Equations
- Product-to-Sum and Multiple AnglesDrill Product-to-Sum and Multiple Angles in Trigonometric Equations
- Range and Existence of SolutionsDrill Range and Existence of Solutions in Trigonometric Equations
- Exponential, Bounded and Graphical EquationsDrill Exponential, Bounded and Graphical Equations in Trigonometric Equations
The 3 chapters that have left the paper
None of these set a question on the 2025–26 papers, so none has a playbook. They are listed so the 27-chapter bank is accounted for, and their notes stay up for anyone working through older papers.
| Chapter | Questions | Last set |
|---|---|---|
| Mathematical ReasoningA question on most papers in the early years; none since. Its notes stay up for older papers. | 67 | 2023 |
| Heights and DistancesSet only in the early papers, and no longer on the paper. | 15 | 2023 |
| Properties of TriangleRare in the early papers and absent from the recent ones. | 11 | 2024 |
Start with the 4 cornerstone chapters
They set 8.1 of the 25 questions on a recent paper. No good score is possible without them.