STEP 2018: 24 of 26 questions decoded, by method & chapter.

• 1
• 2
• 3
• 4
• 5
• 6
• 7
• 8
• 9
• 10
• 11
• 12
• 13

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

• 1Palindromic Equations → Half DegreeKey methodPureAlgebra & Inequalitiesonly this sitting

  Same method, other sittings

  This one has only struck here so far.

  Worked solutionOpen the method
• 2The Sketch Is the ProofKey methodPureFunctions & Curve Sketching2 other sittings

  Same method, other sittings

  20112013

  Worked solutionOpen the method
• 3Reflect the Interval & AddKey methodPureIntegration6 other sittings

  Same method, other sittings

  200620102015201620202022

  Worked solutionOpen the method
• 4Products to Sums, and BackKey methodPureTrigonometry2 other sittings

  Same method, other sittings

  20212023

  Worked solutionOpen the method
• 5Term-by-Term Series IntegrationKey methodPureIntegration2 other sittings

  Same method, other sittings

  20092024

  Worked solutionOpen the method
• 6Reduce Modulo a Well-Chosen ModulusKey methodPureProof & Number Theory2 other sittings

  Same method, other sittings

  20202024

  Worked solutionOpen the method
• 7Affine Ratios via VectorsKey methodPureCoordinate Geometry & Conicsonly this sitting

  Same method, other sittings

  This one has only struck here so far.

  Worked solutionOpen the method
• 8Sketching Without SolvingBernoulli & Riccati SubstitutionsKey methodPureDifferential Equations3 other sittings

  Same method, other sittings

  200820192021

  Worked solutionOpen the method

  AlsoBernoulli & Riccati Substitutions
• 91D Collisions → Two ScalarsTunnelMechanics8 other sittings

  Same method, other sittings

  20062008200920112013201920222025

  Worked solutionOpen the method
• 11Limiting EquilibriumTunnelMechanics10 other sittings

  Same method, other sittings

  2006201220132014201720192020202220232024

  Worked solutionOpen the method
• 12Optimise Expected Cost or GainKey methodProb & StatsProbability & Statistics3 other sittings

  Same method, other sittings

  200920152022

  Worked solutionOpen the method

• 1
• 2
• 3
• 4
• 5
• 6
• 7
• 8
• 9
• 10
• 11
• 12
• 13

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

• 1Stationary Points by FactoringDerivative Sign → InequalitiesRoots → Vieta's RelationsSign, Stationary Points & SymmetryOne Variable + Boundary CheckKey methodPureDifferentiation3 other sittings

  Same method, other sittings

  201720222024

  Worked solutionOpen the method

  AlsoDerivative Sign → InequalitiesRoots → Vieta's RelationsSign, Stationary Points & SymmetryOne Variable + Boundary Check
• 2Second-Order InvariantKey methodPureSequences & Series2 other sittings

  Same method, other sittings

  20082020

  Worked solutionOpen the method
• 3Spotting a Total DerivativeVariable → Constant CoefficientsKey methodPureDifferential Equations2 other sittings

  Same method, other sittings

  20152025

  Worked solutionOpen the method

  AlsoVariable → Constant Coefficients
• 4Parametrising ConicsDifference of Two SquaresKey methodPureCoordinate Geometry & Conics8 other sittings

  Same method, other sittings

  20062008200920122014201520172022

  Worked solutionOpen the method

  AlsoDifference of Two Squares
• 5Induction with an InvariantKey methodPureProof & Number Theory2 other sittings

  Same method, other sittings

  20062015

  Worked solutionOpen the method
• 6Circle Conjugates → $z^{\ast }=a^2/z$Key methodPureComplex Numbers1 other sitting

  Same method, other sittings

  2021

  Worked solutionOpen the method
• 7Half-Angle FactorisationMultiple Angle → PolynomialKey methodPureComplex Numbers4 other sittings

  Same method, other sittings

  2009201720212022

  Worked solutionOpen the method

  AlsoMultiple Angle → Polynomial
• 8Reciprocal Substitution FoldingKey methodPureIntegration6 other sittings

  Same method, other sittings

  201220142015201720232025

  Worked solutionOpen the method
• 9Repeated Impacts → RecurrenceKey methodMechanics3 other sittings

  Same method, other sittings

  201020122017

  Worked solutionOpen the method
• 10Moment of Inertia → RotationStability via Potential EnergyTunnelMechanics7 other sittings

  Same method, other sittings

  2006200820122013201520202022

  Worked solutionOpen the method

  AlsoStability via Potential Energy
• 11Motion on a Smooth CurveKey methodMechanics4 other sittings

  Same method, other sittings

  2012201620192021

  Worked solutionOpen the method
• 12Order Statistics from the CDFKey methodProb & StatsProbability & Statistics3 other sittings

  Same method, other sittings

  202020232024

  Worked solutionOpen the method
• 13Probability Generating FunctionsKey methodProb & StatsProbability & Statistics4 other sittings

  Same method, other sittings

  2008200920112025

  Worked solutionOpen the method