TMUA 2016: 32 of 40 questions decoded, by method & chapter.

• 1
• 2
• 3
• 4
• 5
• 6
• 7
• 8
• 9
• 10
• 11
• 12
• 13
• 14
• 15
• 16
• 17
• 18
• 19
• 20

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

• 2Factor & Remainder TheoremKey methodPureAlgebra & Inequalities4 other sittings

  Same method, other sittings

  201720182019Specimen

  Worked solutionOpen the method
• 3Tangent & Normal LinesTunnelPureDifferentiation2 other sittings

  Same method, other sittings

  20172018

  Worked solutionOpen the method
• 4The First Few TermsIndex & Sum Modulo the PeriodSize & Sign EliminationPavlovPureSequences & Series4 other sittings

  Same method, other sittings

  201720192023Specimen

  Worked solutionOpen the method

  AlsoIndex & Sum Modulo the PeriodSize & Sign Elimination
• 5Total Area via Split IntegralsKey methodPureIntegration4 other sittings

  Same method, other sittings

  2018201920212022

  Worked solutionOpen the method
• 6Means & Percentages → TotalsKey methodProb & StatsProbability & Statistics1 other sitting

  Same method, other sittings

  2018

  Worked solutionOpen the method
• 7Means & Percentages → TotalsKey methodProb & StatsProbability & Statistics1 other sitting

  Same method, other sittings

  2018

  Worked solutionOpen the method
• 8Pythagorean SubstitutionStretching the Angle RangeKey methodPureTrigonometry6 other sittings

  Same method, other sittings

  20192020202120222023Specimen

  Worked solutionOpen the method

  AlsoStretching the Angle Range
• 9Circle Facts, Not EquationsKey methodPureCoordinate Geometry & Circles2 other sittings

  Same method, other sittings

  20172021

  Worked solutionOpen the method
• 10Sketching & Counting IntersectionsKey methodPureTrigonometry3 other sittings

  Same method, other sittings

  201820202021

  Worked solutionOpen the method
• 11Exponentials → Polynomial in $u$Common-Base ConversionCombining Logarithmic RootsKey methodPureExponentials & Logarithms7 other sittings

  Same method, other sittings

  201720182019202020212023Specimen

  Worked solutionOpen the method

  AlsoCommon-Base ConversionCombining Logarithmic Roots
• 12Geometric OptimisationKey methodPureDifferentiation2 other sittings

  Same method, other sittings

  20192022

  Worked solutionOpen the method
• 13Root Count from Stationary ValuesKey methodPureFunctions & Graphs3 other sittings

  Same method, other sittings

  20182019Specimen

  Worked solutionOpen the method
• 14Disguised Geometric SeriesKey methodPureSequences & Series2 other sittings

  Same method, other sittings

  20172023

  Worked solutionOpen the method
• 15Two-Stage OptimisationKey methodPureDifferentiation4 other sittings

  Same method, other sittings

  2017201820192022

  Worked solutionOpen the method
• 16Log Variables → Linear SystemKey methodPureExponentials & Logarithms1 other sitting

  Same method, other sittings

  2019

  Worked solutionOpen the method
• 17Sign Tables for Trig ProductsKey methodPureTrigonometry2 other sittings

  Same method, other sittings

  20172019

  Worked solutionOpen the method
• 18Factorising the DerivativeKey methodPureDifferentiation3 other sittings

  Same method, other sittings

  201720212022

  Worked solutionOpen the method
• 19Coefficient RatiosBinomial in DisguiseKey methodPureCombinatorics & Binomial5 other sittings

  Same method, other sittings

  2017201820202021Specimen

  Worked solutionOpen the method

  AlsoBinomial in Disguise
• 20Triangles & Unfolded NetsKey methodPureCoordinate Geometry & Circles2 other sittings

  Same method, other sittings

  20212023

  Worked solutionOpen the method

• 1
• 2
• 3
• 4
• 5
• 6
• 7
• 8
• 9
• 10
• 11
• 12
• 13
• 14
• 15
• 16
• 17
• 18
• 19
• 20

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

  20172018201920212023

  Worked solutionOpen the method
• 2Rewriting Before DifferentiatingTesting Options by SubstitutionTunnelPureDifferentiation5 other sittings

  Same method, other sittings

  2017201820202023Specimen

  Worked solutionOpen the method

  AlsoTesting Options by Substitution
• 3Pythagorean SubstitutionKey methodPureTrigonometry4 other sittings

  Same method, other sittings

  202020212022Specimen

  Worked solutionOpen the method
• 5Counterexample by Small CasesFinite Search by BoundingKey methodPureProof & Number Theory3 other sittings

  Same method, other sittings

  20222023Specimen

  Worked solutionOpen the method

  AlsoFinite Search by Bounding
• 6Disguised Geometric SeriesThe First Few TermsKey methodPureSequences & Series4 other sittings

  Same method, other sittings

  201720192023Specimen

  Worked solutionOpen the method

  AlsoThe First Few Terms
• 7Logs → Exponent ChainsKey methodPureExponentials & Logarithms2 other sittings

  Same method, other sittings

  20212022

  Worked solutionOpen the method
• 8Statement TriageKey methodPureAlgebra & Inequalities3 other sittings

  Same method, other sittings

  201920202021

  Worked solutionOpen the method
• 11Graph Moves → SubstitutionsKey methodPureFunctions & Graphs5 other sittings

  Same method, other sittings

  20182019202020222023

  Worked solutionOpen the method
• 12Testing Must-Be-True ClaimsAP Sums → Linear RelationsKey methodPureSequences & Series3 other sittings

  Same method, other sittings

  201820202023

  Worked solutionOpen the method

  AlsoAP Sums → Linear Relations
• 13Spotting the Flawed StepKey methodPureProof & Number Theory2 other sittings

  Same method, other sittings

  20222023

  Worked solutionOpen the method
• 14Shape from Degree & Leading TermKey methodPureFunctions & Graphs2 other sittings

  Same method, other sittings

  2022Specimen

  Worked solutionOpen the method
• 18Symmetry ShortcutsKey methodReasoningLogic & Proof3 other sittings

  Same method, other sittings

  201720192020

  Worked solutionOpen the method
• 20Finite Search by BoundingKey methodPureProof & Number Theory1 other sitting

  Same method, other sittings

  2022

  Worked solutionOpen the method