2025 A-Level H2 Math — prelim questions & solutions
Anglo-Chinese Junior College · Paper 1Quartic conjugate roots plus modulus-argument and cosine rule on an Argand diagram.Anglo-Chinese Junior College · Paper 1Prove a vector is parallel to a plane and find the foot of perpendicular from a point.Anglo-Chinese Junior College · Paper 2Binomial expansion of (1-4x^2)^(-1/2), then integrate term by term for arcsin 2x.Anderson Serangoon Junior College · Paper 2Modulus-argument form, Argand-diagram geometry, and an exact value for tan(11π/24) via a rhombus.Catholic Junior College · Paper 2Conjugate roots, factorising a real quartic, and trapezium area on an Argand diagram.Dunman High School (DHS) · Paper 1Parametric complex locus to ellipse, argument of a sum, and a quadratic from non-conjugate roots.Dunman High School (DHS) · Paper 1Expand e^x sin(x+pi) by series multiplication, then match a binomial expansion to find constants.Dunman High School (DHS) · Paper 2Position vectors, line equation, collinearity, and angle between vectors via scalar product.Eunoia Junior College · Paper 1Complex square root, cubic roots and a substitution mapping one equation to another.Eunoia Junior College · Paper 2Line parallel to a plane, angle between lines, perpendicular distance, and reflecting a line in a plane.Hwa Chong Institution · Paper 1Quartic roots via conjugate pairs and even symmetry, plus reciprocal-root substitution.Hwa Chong Institution · Paper 1Perpendicular lines, line intersection, plane through three points, foot of perpendicular, and circle area.Jurong Pioneer Junior College · Paper 1Binomial expansion of 1/(4+9x^2) integrated to build the arctan Maclaurin series.Jurong Pioneer Junior College · Paper 2Real-coefficient cubic roots, conjugate pairs, and showing an Argand parallelogram is a square.Meridian Junior College · Paper 1Ratio theorem, intersection of two lines, triangle area via cross product, and projection distance.National Junior College · Paper 1Solve simultaneous complex equations, then interpret w/z = i as a 90° rotation.National Junior College · Paper 1Binomial and exponential series build a composite expansion, then integrate to approximate an integral.National Junior College · Paper 2Find modulus and argument of a complex number, then use Argand-diagram geometry to deduce arg(2-w).Nanyang Junior College · Paper 1Argand geometry: rhombus from equal moduli, arg of sum, and reflecting a point in OP.Nanyang Junior College · Paper 1Expand cos(t^3), integrate term by term, then verify the integral exactly via sin(x^3).Nanyang Junior College · Paper 1Prove a right angle using dot products and find a triangle's area via cross product.Nanyang Junior College · Paper 2Conjugate-pair roots of an imaginary-coefficient cubic, then x to -x substitution for the related cubic.Raffles Institution · Paper 1Complex number argument under scaling and rotation, plus triangle geometry of f(z)=z^2-2z.Raffles Institution · Paper 2Sine Rule small-angle expansion of a triangle side, then implicit differentiation for a Maclaurin series.River Valley High School · Paper 1Use the conjugate root theorem to find cubic coefficients b, c, d in terms of a.River Valley High School · Paper 1Solve a quadratic with complex coefficients via a complex square root.River Valley High School · Paper 1Implicit differentiation of a differential equation to build the Maclaurin series for y and e^(arctan 3x).River Valley High School · Paper 2Rotate a complex vector 90° and use parallelogram diagonals to find vertices.River Valley High School · Paper 2NEO trajectories: line-plane crossing, non-intersection condition, angle between lines, and shortest distance.St Andrew's Junior College · Paper 1Simultaneous complex equations with a modulus, plus a conjugate-point Argand argument.St Andrew's Junior College · Paper 1Show two lines are skew, reflect a point in a plane, find a plane's equation.St Andrew's Junior College · Paper 2Root symmetry, conjugate roots, and factorising a complex-coefficient cubic.Temasek Junior College · Paper 1Solve simultaneous complex equations with modulus, then find square vertices on an Argand diagram.Temasek Junior College · Paper 1Sine Rule and small-angle binomial approximation for a triangle side in powers of theta.Temasek Junior College · Paper 1Ratio theorem, dot product, foot of perpendicular by projection, and triangle area via cross product.Temasek Junior College · Paper 2Implicit differentiation of a log-root function to build and deduce Maclaurin series.Tampines Meridian Junior College · Paper 1Conjugate roots of a real cubic, Argand geometry, and proving tan(3π/8)=1+√2.Tampines Meridian Junior College · Paper 1Drone and rooftop: reflecting a line in a plane, foot of perpendicular, and parallel planes.Victoria Junior College · Paper 1Solve a modulus equation, find cube roots, and locate the circle through them.Victoria Junior College · Paper 2Argand diagram geometry from multiplication-as-rotation, Cartesian form, and an exact tan value.Victoria Junior College · Paper 2Expand ln(a+x), compose inside sin and cos, and judge an integral approximation.