TMUA Specimen: 25 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.

• 1Vieta's FormulasSystem → Single QuadraticKey methodPureAlgebra & Inequalities4 other sittings

  Same method, other sittings

  2017201820202023

  Worked solutionOpen the method

  AlsoSystem → Single Quadratic
• 2Pythagorean SubstitutionStretching the Angle RangeThe Unit Circle BoundKey methodPureTrigonometry6 other sittings

  Same method, other sittings

  201620192020202120222023

  Worked solutionOpen the method

  AlsoStretching the Angle RangeThe Unit Circle Bound
• 3Perpendicular GradientsPavlovPureCoordinate Geometry & Circles3 other sittings

  Same method, other sittings

  201720212023

  Worked solutionOpen the method
• 4Polynomial InequalitiesTunnelPureAlgebra & Inequalities2 other sittings

  Same method, other sittings

  20172020

  Worked solutionOpen the method
• 6Factor & Remainder TheoremVieta's FormulasKey methodPureAlgebra & Inequalities5 other sittings

  Same method, other sittings

  20162017201820192020

  Worked solutionOpen the method

  AlsoVieta's Formulas
• 11Exponentials → Polynomial in $u$Combining Logarithmic RootsKey methodPureExponentials & Logarithms7 other sittings

  Same method, other sittings

  2016201720182019202020212023

  Worked solutionOpen the method

  AlsoCombining Logarithmic Roots
• 13Root Count from Stationary ValuesShape from Degree & Leading TermKey methodPureFunctions & Graphs4 other sittings

  Same method, other sittings

  2016201820192022

  Worked solutionOpen the method

  AlsoShape from Degree & Leading Term
• 16Exponents of Prime FactorsKey methodPureProof & Number Theory2 other sittings

  Same method, other sittings

  20182021

  Worked solutionOpen the method
• 17Roots via the DiscriminantKey methodPureAlgebra & Inequalities4 other sittings

  Same method, other sittings

  2018201920202023

  Worked solutionOpen the method
• 19Discarding the Extraneous RootAP & GP → EquationsKey methodPureSequences & Series5 other sittings

  Same method, other sittings

  20172019202020212023

  Worked solutionOpen the method

  AlsoAP & GP → Equations
• 20Binomial in DisguiseCoefficients via ConvolutionKey methodPureCombinatorics & Binomial4 other sittings

  Same method, other sittings

  2016201920202022

  Worked solutionOpen the method

  AlsoCoefficients via Convolution

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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.

• 1Completing the SquareTunnelPureCoordinate Geometry & Circles3 other sittings

  Same method, other sittings

  201720212022

  Worked solutionOpen the method
• 2Rewriting Before DifferentiatingTunnelPureDifferentiation4 other sittings

  Same method, other sittings

  2016201720182020

  Worked solutionOpen the method
• 3Spotting the First Wrong LineKey methodReasoningLogic & Proof5 other sittings

  Same method, other sittings

  20172018201920202021

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

  Same method, other sittings

  2017201820202021

  Worked solutionOpen the method
• 5Sandwiching Logs & PowersKey methodPureExponentials & Logarithms1 other sitting

  Same method, other sittings

  2017

  Worked solutionOpen the method
• 7Graph Matching by FingerprintsKey methodPureFunctions & Graphs3 other sittings

  Same method, other sittings

  201720202022

  Worked solutionOpen the method
• 8Counterexample by Small CasesKey methodPureProof & Number Theory3 other sittings

  Same method, other sittings

  201620222023

  Worked solutionOpen the method
• 9Negating QuantifiersKey methodReasoningLogic & Proof2 other sittings

  Same method, other sittings

  20172018

  Worked solutionOpen the method
• 11Sandwiching Logs & PowersKey methodPureExponentials & Logarithms1 other sitting

  Same method, other sittings

  2017

  Worked solutionOpen the method
• 12Factor & Remainder TheoremKey methodPureAlgebra & Inequalities4 other sittings

  Same method, other sittings

  2016201720182019

  Worked solutionOpen the method
• 14Shape from Degree & Leading TermTesting Extreme & Boundary ValuesKey methodPureFunctions & Graphs3 other sittings

  Same method, other sittings

  201620212022

  Worked solutionOpen the method

  AlsoTesting Extreme & Boundary Values
• 15Must-Be-True ChecklistsKey methodReasoningLogic & Proof4 other sittings

  Same method, other sittings

  2019202020212022

  Worked solutionOpen the method
• 16The First Few TermsIndex & Sum Modulo the PeriodSize & Sign EliminationPavlovPureSequences & Series4 other sittings

  Same method, other sittings

  2016201720192023

  Worked solutionOpen the method

  AlsoIndex & Sum Modulo the PeriodSize & Sign Elimination
• 17Negating QuantifiersKey methodReasoningLogic & Proof2 other sittings

  Same method, other sittings

  20172018

  Worked solutionOpen the method