2025 A-Level H2 Maths — Prelim Questions & Worked Solutions
Anglo-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 2 · Complex NumbersModulus-argument form, Argand-diagram geometry, and an exact value for tan(11π/24) via a rhombus.●●●Catholic Junior College · Paper 2 · Complex NumbersConjugate roots, factorising a real quartic, and trapezium area on an Argand diagram.●●●Dunman High School (DHS) · Paper 1 · Complex NumbersParametric complex locus to ellipse, argument of a sum, and a quadratic from non-conjugate roots.●●●Dunman High School (DHS) · Paper 1 · Maclaurin SeriesExpand e^x sin(x+pi) by series multiplication, then match a binomial expansion to find constants.●●○Dunman High School (DHS) · Paper 2 · VectorsPosition vectors, line equation, collinearity, and angle between vectors via scalar product.●●○Eunoia Junior College · Paper 1 · Complex NumbersComplex square root, cubic roots and a substitution mapping one equation to another.●●●Eunoia Junior College · Paper 2 · VectorsLine parallel to a plane, angle between lines, perpendicular distance, and reflecting a line in a plane.●●●Hwa 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 · Maclaurin SeriesBinomial expansion of 1/(4+9x^2) integrated to build the arctan Maclaurin series.●●●Jurong 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 · VectorsRatio theorem, intersection of two lines, triangle area via cross product, and projection distance.●●○National 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 · Complex NumbersArgand geometry: rhombus from equal moduli, arg of sum, and reflecting a point in OP.●●●Nanyang Junior College · Paper 1 · Maclaurin SeriesExpand cos(t^3), integrate term by term, then verify the integral exactly via sin(x^3).●●○Nanyang Junior College · Paper 1 · VectorsProve a right angle using dot products and find a triangle's area via cross product.●●○Nanyang 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 · Complex NumbersComplex number argument under scaling and rotation, plus triangle geometry of f(z)=z^2-2z.●●●Raffles Institution · Paper 2 · Maclaurin SeriesSine Rule small-angle expansion of a triangle side, then implicit differentiation for a Maclaurin series.●●●River Valley High School · Paper 1 · Complex NumbersUse the conjugate root theorem to find cubic coefficients b, c, d in terms of a.●●○River Valley High School · Paper 1 · Complex NumbersSolve a quadratic with complex coefficients via a complex square root.●●●River Valley High School · Paper 1 · Maclaurin SeriesImplicit differentiation of a differential equation to build the Maclaurin series for y and e^(arctan 3x).●●○River Valley High School · Paper 2 · Complex NumbersRotate a complex vector 90° and use parallelogram diagonals to find vertices.●●○River Valley High School · Paper 2 · VectorsNEO trajectories: line-plane crossing, non-intersection condition, angle between lines, and shortest distance.●●●St Andrew's Junior College · Paper 1 · Complex NumbersSimultaneous complex equations with a modulus, plus a conjugate-point Argand argument.●●○St Andrew's Junior College · Paper 1 · VectorsShow two lines are skew, reflect a point in a plane, find a plane's equation.●●○St Andrew's Junior College · Paper 2 · Complex NumbersRoot symmetry, conjugate roots, and factorising a complex-coefficient cubic.●●○Temasek Junior College · Paper 1 · Complex NumbersSolve simultaneous complex equations with modulus, then find square vertices on an Argand diagram.●●○Temasek Junior College · Paper 1 · Maclaurin SeriesSine Rule and small-angle binomial approximation for a triangle side in powers of theta.●●○Temasek Junior College · Paper 1 · VectorsRatio theorem, dot product, foot of perpendicular by projection, and triangle area via cross product.●●○Temasek Junior College · Paper 2 · Maclaurin SeriesImplicit differentiation of a log-root function to build and deduce Maclaurin series.●●○Tampines Meridian Junior College · Paper 1 · Complex NumbersConjugate roots of a real cubic, Argand geometry, and proving tan(3π/8)=1+√2.●●●Tampines Meridian Junior College · Paper 1 · VectorsDrone and rooftop: reflecting a line in a plane, foot of perpendicular, and parallel planes.●●●Victoria Junior College · Paper 1 · Complex NumbersSolve a modulus equation, find cube roots, and locate the circle through them.●●●Victoria Junior College · Paper 2 · Complex NumbersArgand diagram geometry from multiplication-as-rotation, Cartesian form, and an exact tan value.●●○Victoria Junior College · Paper 2 · Maclaurin SeriesExpand ln(a+x), compose inside sin and cos, and judge an integral approximation.●●○