2025 A-Level H2 Maths — Prelim Questions & Worked Solutions
Anglo-Chinese Junior College · Paper 1 · Applications of IntegrationVol.: y=x ln x, x-axisAnglo-Chinese Junior College · Paper 1 · InequalitiesRational and |x| substitutionAnglo-Chinese Junior College · Paper 1 · System of Linear EquationsTwo planes with parameter, line of intersectionAnglo-Chinese Junior College · Paper 2 · FunctionsInverse and compositeAnglo-Chinese Junior College · Paper 2 · Normal DistributionSum and differenceAnglo-Chinese Junior College · Paper 2 · Permutations & CombinationsGroups of 12; restrictionAnglo-Chinese Junior College · Paper 2 · ProbabilityConditional; set algebraAnglo-Chinese Junior College · Paper 2 · Recurrence RelationsPeriodic sequence and sigma notationAnglo-Chinese Junior College · Paper 1 · Complex NumbersQuartic conjugate roots plus modulus-argument and cosine rule on an Argand diagram.●●●Anglo-Chinese Junior College · Paper 1 · VectorsProve a vector is parallel to a plane and find the foot of perpendicular from a point.●●○Anglo-Chinese Junior College · Paper 2 · Maclaurin SeriesBinomial expansion of (1-4x^2)^(-1/2), then integrate term by term for arcsin 2x.●●○Anderson Serangoon Junior College · Paper 1 · Applications of IntegrationArea (trig sub); vol. y-axisAnderson Serangoon Junior College · Paper 1 · Arithmetic & Geometric ProgressionsAP terms form GP; convergence; AP sigma proofAnderson Serangoon Junior College · Paper 1 · FunctionsInverse, area and compositeAnderson Serangoon Junior College · Paper 1 · System of Linear EquationsLine–plane: parallel conditions and distanceAnderson Serangoon Junior College · Paper 2 · Differentiation & ApplicationsParametric; intersectionAnderson Serangoon Junior College · Paper 2 · Integration TechniquesSubstitution; IBPAnderson Serangoon Junior College · Paper 2 · Normal DistributionLinear combinationsAnderson Serangoon Junior College · Paper 2 · ProbabilityProbabilityAnderson Serangoon Junior College · Paper 2 · Complex NumbersModulus-argument form, Argand-diagram geometry, and an exact value for tan(11π/24) via a rhombus.●●●Catholic Junior College · Paper 2 · Binomial ExpansionB(n,p); at-least, conditionalCatholic Junior College · Paper 2 · Correlation & RegressionRegression; estimateCatholic Junior College · Paper 2 · Discrete Random VariablesDistribution in terms of nCatholic Junior College · Paper 2 · FunctionsOne-to-one and compositeCatholic Junior College · Paper 2 · Graphs & TransformationsInfer f(x) from f(|x|) and f'(x)Catholic Junior College · Paper 2 · Normal DistributionNormal; percentile, P(X<a)Catholic Junior College · Paper 2 · ProbabilityVenn; mutually exclusiveCatholic Junior College · Paper 2 · Complex NumbersConjugate roots, factorising a real quartic, and trapezium area on an Argand diagram.●●●Dunman High School (DHS) · Paper 1 · Differential EquationsSubstitution u=y/xDunman High School (DHS) · Paper 1 · FunctionsComposite fgDunman High School (DHS) · Paper 1 · Graphs & TransformationsParametric curve and symmetryDunman High School (DHS) · Paper 1 · Graphs & TransformationsInfer f(x) from f'(x) and |f(x)|Dunman High School (DHS) · Paper 1 · Maclaurin Seriesex sin (x+ pi ); binomial match●●○Dunman High School (DHS) · Paper 1 · Summation of SeriesGP: sum r2 standard resultDunman High School (DHS) · Paper 1 · System of Linear EquationsThree planes: prism and intersection analysisDunman High School (DHS) · Paper 2 · Hypothesis TestingMulti-part hypothesis testDunman High School (DHS) · Paper 2 · Normal DistributionIndependent variablesDunman High School (DHS) · Paper 2 · Permutations & CombinationsAirplane seating; CCADunman High School (DHS) · Paper 2 · ProbabilityConditional; independenceDunman High School (DHS) · Paper 2 · VectorsPos. vectors; collinearity; angle●●○Dunman High School (DHS) · Paper 1 · Complex NumbersParametric complex locus to ellipse, argument of a sum, and a quadratic from non-conjugate roots.●●●Eunoia Junior College · Paper 1 · Arithmetic & Geometric ProgressionsMixed AP/GP: find terms and convergenceEunoia Junior College · Paper 1 · FunctionsRestricted domain and gn patternEunoia Junior College · Paper 1 · Graphs & TransformationsTranslate, reciprocal and modulusEunoia Junior College · Paper 1 · InequalitiesRational inequality and mathrm exEunoia Junior College · Paper 1 · Integration Techniquese|x-1|; trig identity; x=u6Eunoia Junior College · Paper 1 · Recurrence RelationsAP and convergent GP: solve for termEunoia Junior College · Paper 1 · Summation of SeriesRiemann sums; ln 2 boundsEunoia Junior College · Paper 2 · Correlation & RegressionRegression; interpolateEunoia Junior College · Paper 2 · Discrete Random VariablesY and function mathrm fEunoia Junior College · Paper 2 · Graphs & TransformationsRational curve, ellipse and volumeEunoia Junior College · Paper 2 · Hypothesis TestingTwo-stage hypothesis testEunoia Junior College · Paper 2 · Permutations & CombinationsCircular glasses; at-leastEunoia Junior College · Paper 2 · Recurrence RelationsLogistic map: convergence for different u_1Eunoia Junior College · Paper 2 · VectorsParallel to plane; reflection●●●Eunoia Junior College · Paper 1 · Complex NumbersComplex square root, cubic roots and a substitution mapping one equation to another.●●●Hwa Chong Institution · Paper 1 · Differential EquationsSubstitution u=xy2Hwa Chong Institution · Paper 1 · Differentiation & ApplicationsApps of differentiationHwa Chong Institution · Paper 1 · Graphs & TransformationsTransformation to 1/f(x)Hwa Chong Institution · Paper 1 · Integration TechniquesIBP: (2x-1) cos x; modulusHwa Chong Institution · Paper 1 · Summation of SeriesRiemann sum limitHwa Chong Institution · Paper 2 · Applications of IntegrationArea; vol. about y-axisHwa Chong Institution · Paper 2 · Correlation & RegressionPMCC; scatter diagramHwa Chong Institution · Paper 2 · Discrete Random VariablesAdvanced multi-part DRVHwa Chong Institution · Paper 2 · Graphs & TransformationsParametric and hyperbolaHwa Chong Institution · Paper 2 · Hypothesis TestingMean; conclusion changeHwa Chong Institution · Paper 2 · Normal DistributionComprehensive normalHwa Chong Institution · Paper 2 · Permutations & CombinationsINSPIRATION word arrang.Hwa Chong Institution · Paper 2 · ProbabilityBayes; medical screeningHwa Chong Institution · Paper 1 · Complex NumbersQuartic roots via conjugate pairs and even symmetry, plus reciprocal-root substitution.●●●Hwa Chong Institution · Paper 1 · VectorsPerpendicular lines, line intersection, plane through three points, foot of perpendicular, and circle area.●●●Jurong Pioneer Junior College · Paper 1 · FunctionsExistence of inverseJurong Pioneer Junior College · Paper 1 · Graphs & TransformationsHyperbola, circle and periodic functionJurong Pioneer Junior College · Paper 1 · Graphs & TransformationsLogarithmic transformationsJurong Pioneer Junior College · Paper 1 · InequalitiesSketch and solve frac 1(x-a)2 vs |x-a|Jurong Pioneer Junior College · Paper 1 · Integration TechniquesAlgebraic sub; trig subJurong Pioneer Junior College · Paper 1 · Maclaurin Series1/(4+9x2); arctan series●●●Jurong Pioneer Junior College · Paper 1 · Summation of Seriessum r3 result; index shiftJurong Pioneer Junior College · Paper 2 · Binomial ExpansionCombined trials; conditionalJurong Pioneer Junior College · Paper 2 · Discrete Random VariablesDistribution; mean, varianceJurong Pioneer Junior College · Paper 2 · Permutations & CombinationsColour orbs; at-leastJurong Pioneer Junior College · Paper 2 · Complex NumbersReal-coefficient cubic roots, conjugate pairs, and showing an Argand parallelogram is a square.●●○Meridian Junior College · Paper 1 · Arithmetic & Geometric ProgressionsDisease spread: GP model and bed capacityMeridian Junior College · Paper 1 · Differential EquationsSalt tank; inflow/outflow DEMeridian Junior College · Paper 1 · System of Linear EquationsCoffee blend prices and loyalty discountMeridian Junior College · Paper 1 · VectorsLine intersection; area; proj.●●○National Junior College · Paper 1 · Graphs & TransformationsReciprocal and transformation descriptionNational Junior College · Paper 1 · Integration TechniquesIBP: cos (3 ln x); substitutionNational Junior College · Paper 1 · Recurrence RelationsFactorial recurrence: general term and series convergenceNational Junior College · Paper 1 · System of Linear EquationsCurrency exchange: 3-variable systemNational Junior College · Paper 2 · Binomial ExpansionStandard B(n,p) probabilitiesNational Junior College · Paper 2 · Discrete Random VariablesDistribution; expected scoreNational Junior College · Paper 2 · Graphs & TransformationsEllipse, normal and volumeNational Junior College · Paper 2 · Hypothesis TestingSample size; conclusionNational Junior College · Paper 2 · Normal DistributionNormal approx; advancedNational Junior College · Paper 1 · Complex NumbersSolve simultaneous complex equations, then interpret w/z = i as a 90° rotation.●●○National Junior College · Paper 1 · Maclaurin SeriesBinomial and exponential series build a composite expansion, then integrate to approximate an integral.●●●National Junior College · Paper 2 · Complex NumbersFind modulus and argument of a complex number, then use Argand-diagram geometry to deduce arg(2-w).●●○Nanyang Junior College · Paper 1 · Applications of IntegrationHyperbola; area; vol. x, yNanyang Junior College · Paper 1 · Arithmetic & Geometric ProgressionsAP/GP combined; common ratioNanyang Junior College · Paper 1 · Complex NumbersArgand geometry●●●Nanyang Junior College · Paper 1 · Differential EquationsBiomass; growth modelsNanyang Junior College · Paper 1 · Graphs & TransformationsRational curve and oblique asymptoteNanyang Junior College · Paper 1 · Graphs & Transformationsf(a-x), |g(x)| and g(|x|)Nanyang Junior College · Paper 1 · Integration TechniquesTrig sub x= sin 2! theta ; modulusNanyang Junior College · Paper 1 · Maclaurin Seriescos (t3); integrate; verify●●○Nanyang Junior College · Paper 1 · Summation of SeriesSummation of SeriesNanyang Junior College · Paper 1 · VectorsRight angle; cross product●●○Nanyang Junior College · Paper 2 · Binomial ExpansionBinomial; advancedNanyang Junior College · Paper 2 · Differentiation & ApplicationsImplicitNanyang Junior College · Paper 2 · InequalitiesModulus and rational inequalitiesNanyang Junior College · Paper 2 · System of Linear EquationsTwo planes: angle, intersection and distanceNanyang Junior College · Paper 2 · Complex NumbersConjugate-pair roots of an imaginary-coefficient cubic, then x to -x substitution for the related cubic.●●○Raffles Institution · Paper 1 · Applications of IntegrationSubstitution; area; vol. x-axisRaffles Institution · Paper 1 · Arithmetic & Geometric ProgressionsGP: 99% of S_ infty ; modified APRaffles Institution · Paper 1 · Differentiation & ApplicationsRate of changeRaffles Institution · Paper 1 · Differentiation & ApplicationsRate of changeRaffles Institution · Paper 1 · Integration TechniquesPartial fractions; IBP with lnRaffles Institution · Paper 1 · System of Linear EquationsCurve coefficients from geometric conditionsRaffles Institution · Paper 2 · Correlation & RegressionRegression + PMCC + estimateRaffles Institution · Paper 2 · Discrete Random Variablesk(x2+x+1) formulaRaffles Institution · Paper 2 · Hypothesis TestingMultiple samples; rangeRaffles Institution · Paper 2 · InequalitiesRational and ln |x| combinedRaffles Institution · Paper 2 · Maclaurin SeriesTriangle; implicit diff to x5●●●Raffles Institution · Paper 2 · Normal DistributionMulti-part normalRaffles Institution · Paper 2 · Permutations & CombinationsCharms: circular; keychainRaffles Institution · Paper 2 · ProbabilityTree; conditional casesRaffles Institution · Paper 2 · Recurrence RelationsRational recurrence: behavior for two initial valuesRaffles Institution · Paper 1 · Complex NumbersComplex number argument under scaling and rotation, plus triangle geometry of f(z)=z^2-2z.●●●River Valley High School · Paper 1 · Complex NumbersReal polynomial, complex root●●○River Valley High School · Paper 1 · Complex NumbersReal polynomial, complex root●●●River Valley High School · Paper 1 · Differential EquationsCoffee beans; logisticsRiver Valley High School · Paper 1 · Differentiation & ApplicationsDifferentiationRiver Valley High School · Paper 1 · Graphs & TransformationsParametric, normals and intersectionRiver Valley High School · Paper 1 · InequalitiesRational and exponential chainRiver Valley High School · Paper 1 · Summation of SeriesTelescoping; equationRiver Valley High School · Paper 2 · Binomial ExpansionB(n,p); mean and varianceRiver Valley High School · Paper 2 · Complex NumbersTriangle geometry●●○River Valley High School · Paper 2 · Discrete Random VariablesDistribution; E(X), Var(X)River Valley High School · Paper 2 · Permutations & CombinationsPermutations & CombinationsRiver Valley High School · Paper 2 · Recurrence RelationsLinear recurrence: behavior analysisRiver Valley High School · Paper 2 · System of Linear EquationsLine trajectories: intersection and distanceRiver Valley High School · Paper 2 · VectorsContextual trajectories; angle; distance●●●River Valley High School · Paper 1 · Maclaurin SeriesImplicit differentiation of a differential equation to build the Maclaurin series for y and e^(arctan 3x).●●○St Andrew's Junior College · Paper 1 · Arithmetic & Geometric ProgressionsAP/GP connection: max sum and convergenceSt Andrew's Junior College · Paper 1 · Differential EquationsParticulates; separable DESt Andrew's Junior College · Paper 1 · Differentiation & ApplicationsOptimisationSt Andrew's Junior College · Paper 1 · FunctionsPeriodic function and compositeSt Andrew's Junior College · Paper 1 · VectorsSkew lines; reflection; plane●●○St Andrew's Junior College · Paper 2 · Binomial ExpansionMulti-stage binomialSt Andrew's Junior College · Paper 2 · Complex NumbersPolynomials (complex coeff.)●●○St Andrew's Junior College · Paper 2 · Correlation & RegressionAdvanced; model selectionSt Andrew's Junior College · Paper 2 · Recurrence RelationsLinear recurrence: limit and GP series sumSt Andrew's Junior College · Paper 2 · Summation of SeriesGP series from recurrenceSt Andrew's Junior College · Paper 1 · Complex NumbersSimultaneous complex equations with a modulus, plus a conjugate-point Argand argument.●●○Temasek Junior College · Paper 1 · Arithmetic & Geometric ProgressionsFinancial: AP savings vs GP compound interestTemasek Junior College · Paper 1 · Complex NumbersSimultaneous equations●●○Temasek Junior College · Paper 1 · Differential EquationsSubst. w=x2y; pest modelTemasek Junior College · Paper 1 · InequalitiesRational then |x+1| substitutionTemasek Junior College · Paper 1 · Maclaurin SeriesSmall angle; triangle approx.●●○Temasek Junior College · Paper 1 · VectorsRatios; foot of perp; area●●○Temasek Junior College · Paper 2 · Binomial ExpansionB(n,p) with extensionTemasek Junior College · Paper 2 · Correlation & RegressionCompare models; transformTemasek Junior College · Paper 2 · Hypothesis TestingMulti-stage hypothesis testTemasek Junior College · Paper 2 · Normal DistributionMean and sum; conditionalTemasek Junior College · Paper 2 · Permutations & CombinationsTreasure; round table seatingTemasek Junior College · Paper 2 · ProbabilityTwo-stage; conditionalTemasek Junior College · Paper 2 · Maclaurin SeriesImplicit differentiation of a log-root function to build and deduce Maclaurin series.●●○Tampines Meridian Junior College · Paper 1 · Arithmetic & Geometric ProgressionsGP application; sum to infinityTampines Meridian Junior College · Paper 1 · Complex NumbersReal cubic; find roots●●●Tampines Meridian Junior College · Paper 1 · Maclaurin SeriesMaclaurin + sketch + approximationTampines Meridian Junior College · Paper 1 · Recurrence RelationsQuadratic recurrence: fixed points and monotonicityTampines Meridian Junior College · Paper 1 · VectorsDrone rooftop; parallel planes●●●Tampines Meridian Junior College · Paper 2 · Binomial ExpansionBinomial with restrictionTampines Meridian Junior College · Paper 2 · Correlation & RegressionPMCC; interpretationTampines Meridian Junior College · Paper 2 · Discrete Random VariablesDistribution; game payoffTampines Meridian Junior College · Paper 2 · Hypothesis TestingSingle sample; significanceTampines Meridian Junior College · Paper 2 · InequalitiesRational and cos x restricted rangeTampines Meridian Junior College · Paper 2 · ProbabilityVenn; independenceVictoria Junior College · Paper 1 · Applications of IntegrationArea; vol. x-axis; parabolaVictoria Junior College · Paper 1 · Differential EquationsSubstitution y= ln (u/x)Victoria Junior College · Paper 1 · FunctionsSelf-inverse and fn patternVictoria Junior College · Paper 1 · Graphs & TransformationsTransformations and graph sketchingVictoria Junior College · Paper 1 · Graphs & TransformationsReflection + stretch; graph sketchVictoria Junior College · Paper 1 · Summation of SeriesConvergence; bound; shiftVictoria Junior College · Paper 2 · Complex NumbersModulus-argument form●●○Victoria Junior College · Paper 2 · Correlation & RegressionPMCC; predictionVictoria Junior College · Paper 2 · Differentiation & ApplicationsDiff and applicationVictoria Junior College · Paper 2 · Hypothesis TestingSample mean; assumptionsVictoria Junior College · Paper 2 · Maclaurin Seriesln (a+x); composition; integral●●○Victoria Junior College · Paper 1 · Complex NumbersSolve a modulus equation, find cube roots, and locate the circle through them.●●●
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