TMUA 2022: 33 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.

• 1Pythagorean SubstitutionThe Unit Circle BoundKey methodPureTrigonometry4 other sittings

  Same method, other sittings

  201620202021Specimen

  Worked solutionOpen the method

  AlsoThe Unit Circle Bound
• 2Completing the SquareTangency → Discriminant or DistanceTunnelPureCoordinate Geometry & Circles3 other sittings

  Same method, other sittings

  20172021Specimen

  Worked solutionOpen the method

  AlsoTangency → Discriminant or Distance
• 3Integrals as Linear UnknownsKey methodPureIntegration3 other sittings

  Same method, other sittings

  201920212023

  Worked solutionOpen the method
• 4Triangle Data → Standard FormulaeTunnelPureTrigonometry1 other sitting

  Same method, other sittings

  2017

  Worked solutionOpen the method
• 7Total Area via Split IntegralsKey methodPureIntegration4 other sittings

  Same method, other sittings

  2016201820192021

  Worked solutionOpen the method
• 9Hidden QuadraticsKey methodPureFunctions & Graphs2 other sittings

  Same method, other sittings

  20202021

  Worked solutionOpen the method
• 10Graph Moves → SubstitutionsKey methodPureFunctions & Graphs5 other sittings

  Same method, other sittings

  20162018201920202023

  Worked solutionOpen the method
• 12Two-Stage OptimisationKey methodPureDifferentiation4 other sittings

  Same method, other sittings

  2016201720182019

  Worked solutionOpen the method
• 13Quadratics in DisguiseKey methodPureAlgebra & Inequalities2 other sittings

  Same method, other sittings

  20212023

  Worked solutionOpen the method
• 14Triangle Data → Standard FormulaeTunnelPureTrigonometry1 other sitting

  Same method, other sittings

  2017

  Worked solutionOpen the method
• 15Geometric OptimisationKey methodPureDifferentiation2 other sittings

  Same method, other sittings

  20162019

  Worked solutionOpen the method
• 16Pythagorean SubstitutionKey methodPureTrigonometry4 other sittings

  Same method, other sittings

  201620202021Specimen

  Worked solutionOpen the method
• 17The SSA Ambiguous CaseKey methodPureTrigonometry2 other sittings

  Same method, other sittings

  20182023

  Worked solutionOpen the method
• 18Shape from Degree & Leading TermKey methodPureFunctions & Graphs2 other sittings

  Same method, other sittings

  2016Specimen

  Worked solutionOpen the method
• 20Testing Extreme & Boundary ValuesPavlovPureFunctions & Graphs2 other sittings

  Same method, other sittings

  2021Specimen

  Worked solutionOpen the method

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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.

• 1Factorising the DerivativeRoots, Stationary Points & RolleKey methodPureDifferentiation4 other sittings

  Same method, other sittings

  2016201720212023

  Worked solutionOpen the method

  AlsoRoots, Stationary Points & Rolle
• 2Coefficients via ConvolutionKey methodPureCombinatorics & Binomial2 other sittings

  Same method, other sittings

  2019Specimen

  Worked solutionOpen the method
• 3Counterexample by Small CasesKey methodPureProof & Number Theory3 other sittings

  Same method, other sittings

  20162023Specimen

  Worked solutionOpen the method
• 4Completing the SquareTunnelPureCoordinate Geometry & Circles3 other sittings

  Same method, other sittings

  20172021Specimen

  Worked solutionOpen the method
• 5Contrapositive vs ConverseKey methodReasoningLogic & Proof3 other sittings

  Same method, other sittings

  202020212023

  Worked solutionOpen the method
• 6Necessary & Sufficient TestsKey methodReasoningLogic & Proof3 other sittings

  Same method, other sittings

  201920212023

  Worked solutionOpen the method
• 7Spotting the Flawed StepKey methodPureProof & Number Theory2 other sittings

  Same method, other sittings

  20162023

  Worked solutionOpen the method
• 8Finite Search by BoundingKey methodPureProof & Number Theory1 other sitting

  Same method, other sittings

  2016

  Worked solutionOpen the method
• 9Quantifier Order & ScopeKey methodReasoningLogic & Proof1 other sitting

  Same method, other sittings

  2018

  Worked solutionOpen the method
• 10Quantifier Order & ScopeKey methodReasoningLogic & Proof1 other sitting

  Same method, other sittings

  2018

  Worked solutionOpen the method
• 12Comparing Integrals PointwiseKey methodPureIntegration2 other sittings

  Same method, other sittings

  20202023

  Worked solutionOpen the method
• 13Quantifier Order & ScopeKey methodReasoningLogic & Proof1 other sitting

  Same method, other sittings

  2018

  Worked solutionOpen the method
• 14Absolute Value as DistanceKey methodPureAlgebra & Inequalities2 other sittings

  Same method, other sittings

  20182019

  Worked solutionOpen the method
• 15Logs → Exponent ChainsKey methodPureExponentials & Logarithms2 other sittings

  Same method, other sittings

  20162021

  Worked solutionOpen the method
• 16Must-Be-True ChecklistsKey methodReasoningLogic & Proof4 other sittings

  Same method, other sittings

  201920202021Specimen

  Worked solutionOpen the method
• 17Contrapositive vs ConverseCubic Root Count by ShapeKey methodReasoningLogic & Proof5 other sittings

  Same method, other sittings

  20172018202020212023

  Worked solutionOpen the method

  AlsoCubic Root Count by Shape
• 18Graph Matching by FingerprintsKey methodPureFunctions & Graphs3 other sittings

  Same method, other sittings

  20172020Specimen

  Worked solutionOpen the method
• 20Testing Extreme & Boundary ValuesPavlovPureFunctions & Graphs2 other sittings

  Same method, other sittings

  2021Specimen

  Worked solutionOpen the method