The Speed Maths Project
Speed Maths
1,386+ Free Verified Practice Questions
Timed drills engineered for TMUA (Paper 1 & 2), BMO1, and SMC. Sourced from competition & admissions maths.
Zero Calc · 100% Verified with SymPy
Looking for Contributors
42 sheets live across 6 pillars · Help expand the Question Bank.
Pillar Status & Roadmap
Algebra
Polynomials, inequalities, and functional equations.
- 01 Quadratic in disguise: substitution and symmetric sums Methods:difference of squaresquadratic in disguisex + 1/x symmetry 33 questions Questions Answers
- 02 Paired products and denesting surds Methods:pairing factorsdenesting radicalsbiquadratic substitution 33 questions Questions Answers
- 03 Exponential substitution and the first inequalities Methods:exponential substitutionconstrained minimumsum-of-squares trick 33 questions Questions Answers
- 04 The t = x + 1/x device and AM–GM minima Methods:t-substitutionAM–GMreciprocal minima 33 questions Questions Answers
- 05 Symmetric systems and constrained inequalities Methods:x - 1/x formsymmetric systemsconstraint substitution 33 questions Questions Answers
- 06 Completing the square in two variables, and counterexamples Methods:surd substitutiontwo-variable completing the squaredisproof by counterexample 33 questions Questions Answers
- 07 Weighted AM–GM and harder proof structure Methods:weighted AM–GMCauchy–Schwarzequality cases 33 questions Questions Answers
Combinatorics
Counting, probability, and discrete structures.
- 01 Arrangements and the block method Methods:block methoddigit constraintsgrid counting 33 questions Questions Answers
- 02 Complementary counting and non-consecutive selection Methods:complementary countingat-least conditionsnon-consecutive selection 33 questions Questions Answers
- 03 Blocks with refusals, and circular arrangements Methods:internal block orderrefusal constraintscircular arrangements 33 questions Questions Answers
- 04 Binomial identities and double counting Methods:binomial coefficientsgreatest coefficientdouble counting 33 questions Questions Answers
- 05 Capped stars and bars, and inclusion–exclusion Methods:stars and barsinclusion–exclusionderangementscompositions 33 questions Questions Answers
- 06 Pigeonhole: guarantees, pairings and lattice points Methods:pigeonhole principlepairing argumentlattice parity 33 questions Questions Answers
- 07 Recurrences, tilings and invariants Methods:linear recurrencetiling recurrenceinvariant 33 questions Questions Answers
Number Theory
Divisibility, modular arithmetic, and primes.
- 01 Divisibility by rewriting, and reciprocal equations Methods:polynomial remainderdivisor pairsreciprocal Diophantine 33 questions Questions Answers
- 02 Factorising to force primality Methods:factorising for primalitydifference of squaresremainder trick 33 questions Questions Answers
- 03 Difference of squares and lcm–gcd pairs Methods:difference of squareslcm–gcd pairsminimal solutions 33 questions Questions Answers
- 04 Diophantine equations and the Sophie Germain identity Methods:Sophie Germain identityexponential Diophantineprime constraints 33 questions Questions Answers
- 05 Remainders, geometric sums and mod arguments Methods:polynomial remaindergeometric sum factoringmod 3 argument 33 questions Questions Answers
- 06 Simon's factoring trick, and gcd by Euclid Methods:Simon's favourite factoring trickEuclidean algorithmfactorial digits 33 questions Questions Answers
- 07 Counting divisors Methods:divisor-count formulaprime squaresparity of exponents 33 questions Questions Answers
Logic
Conditionals, proof techniques, and counterexamples.
- 01 Quantifiers: order and negation Methods:quantifier ordernegating quantifierscounterexample 33 questions Questions Answers
- 02 Necessary, sufficient, and equivalence chains Methods:necessary vs sufficientbiconditional chainsconverse 33 questions Questions Answers
- 03 Truth tables, compound conditionals, and deduction Methods:truth tablescompound conditionalsdeductionurns 33 questions Questions Answers
- 04 Disproof by counterexample and universal refutation Methods:counterexamplerefutationdisproofboundary 33 questions Questions Answers
- 05 Flawed proof step diagnosis and structural traps Methods:flawed prooferror diagnosisconverse errorextraneous roots 33 questions Questions Answers
- 06 Induction, recurrences, and base-case traps Methods:inductionbase caserecurrencestrong induction 33 questions Questions Answers
- 07 TMUA Paper 2 capstone synthesis Methods:quantifiersnecessary and sufficientimplication chainscounterexamplesflawed proofsinduction 33 questions Questions Answers
Sequences
Recurrences, series, and limiting behaviour.
- 01 Arithmetic sequences, and the sum as a quadratic in n Methods:nth-term formulaarithmetic series sumsum as a quadratic 33 questions Questions Answers
- 02 Binomial expansion, and Pascal's triangle as a sequence Methods:binomial expansionPascal's trianglegeneralised binomial series 33 questions Questions Answers
- 03 Geometric series, and when a sum to infinity exists Methods:geometric seriessum to infinityconvergence condition 33 questions Questions Answers
- 04 Recurrence relations, and solving them in closed form Methods:recurrence relationscharacteristic equationclosed-form solution 33 questions Questions Answers
- 05 Monotonicity, bounds and fixed points Methods:monotonicityboundednessfixed pointsfloor and ceiling sequences 33 questions Questions Answers
- 06 BMO1 capstone: constrained integer sequences Methods:extremal constructionconstrained integer sequencesalternating recurrences 33 questions Questions Answers
- 07 Mixed synthesis: every technique from Days 1–6 Methods:mixed synthesiscapstonetechnique selection 33 questions Questions Answers
Geometry
Coordinate geometry, polygons, circles, solids, and Euclidean proofs.
- 01 Coordinate geometry: lines, gradients, distances and polygon areas Methods:negative reciprocal gradientsperpendicular bisectorsdistance formulaperpendicular distance to a lineshoelace area 33 questions Questions Answers
- 02 Circle equations, tangents and line–circle interactions Methods:completing the square for circle equationstangent to a circleperpendicular distance line–circle testhalf-chord length 33 questions Questions Answers
- 03 Two-circle systems, radical axes and common chords Methods:relative positions of two circlesradical axis by subtractioncommon chord lengthorthogonal circlestangency to both coordinate axes 33 questions Questions Answers
- 04 Polygons and angle chasing Methods:regular polygon anglesdiagonalsstar polygonstilingsangle chasing through parallels and isosceles trianglessimilar triangles and area ratios 33 questions Questions Answers
- 05 Circles, arcs and tangency Methods:circle theoremsalternate segmentcyclic quadrilateralspower of a pointtangent lengthstouching circlescircles in anglessegments and lenses 33 questions Questions Answers
- 06 Solids and spatial reasoning Methods:3D Pythagorasvolumes and surface areas of prismspyramidscones and spheresEuler's formulanetscross-sectionsfrustumsinscribed solids 33 questions Questions Answers
- 07 TMUA-style synthesis: loci and geometric logic Methods:loci of fixed distanceApollonius ratio circlesbounding quick constraintsnecessary vs sufficient conditionsspot-the-flaw in proofsmixed multi-step synthesis 33 questions Questions Answers
No sheets match that search.