TMUA 2021: 32 of 40 questions decoded, by method & chapter.

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The paper at a glance, coloured by move. Click a square to open its question; empty squares are not decoded yet.

• 2Equal Areas → Signed Integral ZeroKey methodPureIntegration1 other sitting

  Same method, other sittings

  2020

  Worked solutionOpen the method
• 3Discarding the Extraneous RootAP & GP → EquationsKey methodPureSequences & Series5 other sittings

  Same method, other sittings

  2017201920202023Specimen

  Worked solutionOpen the method

  AlsoAP & GP → Equations
• 4Exponentials → Polynomial in $u$Constrained Vertex in $u=a^x$Key methodPureExponentials & Logarithms6 other sittings

  Same method, other sittings

  20162018201920202023Specimen

  Worked solutionOpen the method

  AlsoConstrained Vertex in $u=a^x$
• 5Exponents of Prime FactorsKey methodPureProof & Number Theory2 other sittings

  Same method, other sittings

  2018Specimen

  Worked solutionOpen the method
• 6Pythagorean SubstitutionKey methodPureTrigonometry4 other sittings

  Same method, other sittings

  201620202022Specimen

  Worked solutionOpen the method
• 7Total Area via Split IntegralsReusing Integrals via TransformationIntegrals as Linear UnknownsKey methodPureIntegration6 other sittings

  Same method, other sittings

  201620172018201920222023

  Worked solutionOpen the method

  AlsoReusing Integrals via TransformationIntegrals as Linear Unknowns
• 8Tangency → Discriminant or DistanceKey methodPureCoordinate Geometry & Circles2 other sittings

  Same method, other sittings

  20172022

  Worked solutionOpen the method
• 9Triangles & Unfolded NetsKey methodPureCoordinate Geometry & Circles2 other sittings

  Same method, other sittings

  20162023

  Worked solutionOpen the method
• 11Factorising the DerivativeKey methodPureDifferentiation3 other sittings

  Same method, other sittings

  201620172022

  Worked solutionOpen the method
• 12Quadratics in DisguiseKey methodPureAlgebra & Inequalities2 other sittings

  Same method, other sittings

  20222023

  Worked solutionOpen the method
• 13Integral-Defined Sequences & SumsKey methodPureIntegration2 other sittings

  Same method, other sittings

  20172023

  Worked solutionOpen the method
• 14Sketching & Counting IntersectionsKey methodPureTrigonometry3 other sittings

  Same method, other sittings

  201620182020

  Worked solutionOpen the method
• 15Integral-Defined Sequences & SumsReusing Integrals via TransformationKey methodPureIntegration3 other sittings

  Same method, other sittings

  201720192023

  Worked solutionOpen the method

  AlsoReusing Integrals via Transformation
• 16Coefficient RatiosKey methodPureCombinatorics & Binomial3 other sittings

  Same method, other sittings

  201620172018

  Worked solutionOpen the method
• 18Completing the SquareTunnelPureCoordinate Geometry & Circles3 other sittings

  Same method, other sittings

  20172022Specimen

  Worked solutionOpen the method
• 19Stretching the Angle RangeThe Unit Circle BoundKey methodPureTrigonometry5 other sittings

  Same method, other sittings

  2016201920222023Specimen

  Worked solutionOpen the method

  AlsoThe Unit Circle Bound

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The paper at a glance, coloured by move. Click a square to open its question; empty squares are not decoded yet.

• 1Integrand → Sum of PowersTunnelPureIntegration5 other sittings

  Same method, other sittings

  20162017201820192023

  Worked solutionOpen the method
• 2Perpendicular GradientsPavlovPureCoordinate Geometry & Circles3 other sittings

  Same method, other sittings

  20172023Specimen

  Worked solutionOpen the method
• 4Counterexamples to 'For All'PavlovReasoningLogic & Proof4 other sittings

  Same method, other sittings

  201720182020Specimen

  Worked solutionOpen the method
• 5Spotting the First Wrong LineKey methodReasoningLogic & Proof5 other sittings

  Same method, other sittings

  2017201820192020Specimen

  Worked solutionOpen the method
• 6Necessary & Sufficient TestsCubic Root Count by ShapeKey methodReasoningLogic & Proof6 other sittings

  Same method, other sittings

  201720182019202020222023

  Worked solutionOpen the method

  AlsoCubic Root Count by Shape
• 7Circle Facts, Not EquationsKey methodPureCoordinate Geometry & Circles2 other sittings

  Same method, other sittings

  20162017

  Worked solutionOpen the method
• 8Necessary & Sufficient TestsKey methodReasoningLogic & Proof3 other sittings

  Same method, other sittings

  201920222023

  Worked solutionOpen the method
• 9Necessary & Sufficient TestsCubic Root Count by ShapeKey methodReasoningLogic & Proof6 other sittings

  Same method, other sittings

  201720182019202020222023

  Worked solutionOpen the method

  AlsoCubic Root Count by Shape
• 10Counterexamples to 'For All'PavlovReasoningLogic & Proof4 other sittings

  Same method, other sittings

  201720182020Specimen

  Worked solutionOpen the method
• 11Contrapositive vs ConverseKey methodReasoningLogic & Proof3 other sittings

  Same method, other sittings

  202020222023

  Worked solutionOpen the method
• 12Must-Be-True ChecklistsKey methodReasoningLogic & Proof4 other sittings

  Same method, other sittings

  201920202022Specimen

  Worked solutionOpen the method
• 13Statement TriageKey methodPureAlgebra & Inequalities3 other sittings

  Same method, other sittings

  201620192020

  Worked solutionOpen the method
• 15Completing the SquareTangency → Discriminant or DistanceTunnelPureCoordinate Geometry & Circles3 other sittings

  Same method, other sittings

  20172022Specimen

  Worked solutionOpen the method

  AlsoTangency → Discriminant or Distance
• 16Hidden QuadraticsTesting Extreme & Boundary ValuesKey methodPureFunctions & Graphs3 other sittings

  Same method, other sittings

  20202022Specimen

  Worked solutionOpen the method

  AlsoTesting Extreme & Boundary Values
• 17Logs → Exponent ChainsKey methodPureExponentials & Logarithms2 other sittings

  Same method, other sittings

  20162022

  Worked solutionOpen the method
• 20Integral-Defined Sequences & SumsKey methodPureIntegration2 other sittings

  Same method, other sittings

  20172023

  Worked solutionOpen the method