2025 — JC2 H2 Maths Prelim Questions & Worked Solutions

Applications of Integration — Anglo-Chinese Junior College

Vol.: y=x ln x, x-axis

Inequalities — Anglo-Chinese Junior College

Rational and |x| substitution

System of Linear Equations — Anglo-Chinese Junior College

Two planes with parameter, line of intersection

Functions — Anglo-Chinese Junior College

Inverse and composite

Normal Distribution — Anglo-Chinese Junior College

Sum and difference

Permutations & Combinations — Anglo-Chinese Junior College

Groups of 12; restriction

Probability — Anglo-Chinese Junior College

Conditional; set algebra

Recurrence Relations — Anglo-Chinese Junior College

Periodic sequence and sigma notation

Complex Numbers — Anglo-Chinese Junior College

Quartic conjugate roots plus modulus-argument and cosine rule on an Argand diagram.

Vectors — Anglo-Chinese Junior College

Prove a vector is parallel to a plane and find the foot of perpendicular from a point.

Maclaurin Series — Anglo-Chinese Junior College

Binomial expansion of (1-4x^2)^(-1/2), then integrate term by term for arcsin 2x.

Applications of Integration — Anderson Serangoon Junior College

Area (trig sub); vol. y-axis

Arithmetic & Geometric Progressions — Anderson Serangoon Junior College

AP terms form GP; convergence; AP sigma proof

Functions — Anderson Serangoon Junior College

Inverse, area and composite

System of Linear Equations — Anderson Serangoon Junior College

Line–plane: parallel conditions and distance

Differentiation & Applications — Anderson Serangoon Junior College

Parametric; intersection

Integration Techniques — Anderson Serangoon Junior College

Substitution; IBP

Normal Distribution — Anderson Serangoon Junior College

Linear combinations

Probability — Anderson Serangoon Junior College

Complex Numbers — Anderson Serangoon Junior College

Modulus-argument form, Argand-diagram geometry, and an exact value for tan(11π/24) via a rhombus.

Binomial Expansion — Catholic Junior College

B(n,p); at-least, conditional

Correlation & Regression — Catholic Junior College

Regression; estimate

Discrete Random Variables — Catholic Junior College

Distribution in terms of n

Functions — Catholic Junior College

One-to-one and composite

Graphs & Transformations — Catholic Junior College

Infer f(x) from f(|x|) and f'(x)

Normal Distribution — Catholic Junior College

Normal; percentile, P(X

Probability — Catholic Junior College

Venn; mutually exclusive

Complex Numbers — Catholic Junior College

Conjugate roots, factorising a real quartic, and trapezium area on an Argand diagram.

Differential Equations — Dunman High School (DHS)

Substitution u=y/x

Functions — Dunman High School (DHS)

Composite fg

Graphs & Transformations — Dunman High School (DHS)

Parametric curve and symmetry

Graphs & Transformations — Dunman High School (DHS)

Infer f(x) from f'(x) and |f(x)|

Maclaurin Series — Dunman High School (DHS)

ex sin (x+ pi ); binomial match

Summation of Series — Dunman High School (DHS)

GP: sum r2 standard result

System of Linear Equations — Dunman High School (DHS)

Three planes: prism and intersection analysis

Hypothesis Testing — Dunman High School (DHS)

Multi-part hypothesis test

Normal Distribution — Dunman High School (DHS)

Independent variables

Permutations & Combinations — Dunman High School (DHS)

Airplane seating; CCA

Probability — Dunman High School (DHS)

Conditional; independence

Vectors — Dunman High School (DHS)

Pos. vectors; collinearity; angle

Complex Numbers — Dunman High School (DHS)

Parametric complex locus to ellipse, argument of a sum, and a quadratic from non-conjugate roots.

Arithmetic & Geometric Progressions — Eunoia Junior College

Mixed AP/GP: find terms and convergence

Functions — Eunoia Junior College

Restricted domain and gn pattern

Graphs & Transformations — Eunoia Junior College

Translate, reciprocal and modulus

Inequalities — Eunoia Junior College

Rational inequality and mathrm ex

Integration Techniques — Eunoia Junior College

e|x-1|; trig identity; x=u6

Recurrence Relations — Eunoia Junior College

AP and convergent GP: solve for term

Summation of Series — Eunoia Junior College

Riemann sums; ln 2 bounds

Correlation & Regression — Eunoia Junior College

Regression; interpolate

Discrete Random Variables — Eunoia Junior College

Y and function mathrm f

Graphs & Transformations — Eunoia Junior College

Rational curve, ellipse and volume

Hypothesis Testing — Eunoia Junior College

Two-stage hypothesis test

Permutations & Combinations — Eunoia Junior College

Circular glasses; at-least

Recurrence Relations — Eunoia Junior College

Logistic map: convergence for different u_1

Vectors — Eunoia Junior College

Parallel to plane; reflection

Complex Numbers — Eunoia Junior College

Complex square root, cubic roots and a substitution mapping one equation to another.

Differential Equations — Hwa Chong Institution

Substitution u=xy2

Differentiation & Applications — Hwa Chong Institution

Apps of differentiation

Graphs & Transformations — Hwa Chong Institution

Transformation to 1/f(x)

Integration Techniques — Hwa Chong Institution

IBP: (2x-1) cos x; modulus

Summation of Series — Hwa Chong Institution

Riemann sum limit

Applications of Integration — Hwa Chong Institution

Area; vol. about y-axis

Correlation & Regression — Hwa Chong Institution

PMCC; scatter diagram

Discrete Random Variables — Hwa Chong Institution

Advanced multi-part DRV

Graphs & Transformations — Hwa Chong Institution

Parametric and hyperbola

Hypothesis Testing — Hwa Chong Institution

Mean; conclusion change

Normal Distribution — Hwa Chong Institution

Comprehensive normal

Permutations & Combinations — Hwa Chong Institution

INSPIRATION word arrang.

Probability — Hwa Chong Institution

Bayes; medical screening

Complex Numbers — Hwa Chong Institution

Quartic roots via conjugate pairs and even symmetry, plus reciprocal-root substitution.

Vectors — Hwa Chong Institution

Perpendicular lines, line intersection, plane through three points, foot of perpendicular, and circle area.

Functions — Jurong Pioneer Junior College

Existence of inverse

Graphs & Transformations — Jurong Pioneer Junior College

Hyperbola, circle and periodic function

Graphs & Transformations — Jurong Pioneer Junior College

Logarithmic transformations

Inequalities — Jurong Pioneer Junior College

Sketch and solve frac 1(x-a)2 vs |x-a|

Integration Techniques — Jurong Pioneer Junior College

Algebraic sub; trig sub

Maclaurin Series — Jurong Pioneer Junior College

1/(4+9x2); arctan series

Summation of Series — Jurong Pioneer Junior College

sum r3 result; index shift

Binomial Expansion — Jurong Pioneer Junior College

Combined trials; conditional

Discrete Random Variables — Jurong Pioneer Junior College

Distribution; mean, variance

Permutations & Combinations — Jurong Pioneer Junior College

Colour orbs; at-least

Complex Numbers — Jurong Pioneer Junior College

Real-coefficient cubic roots, conjugate pairs, and showing an Argand parallelogram is a square.

Arithmetic & Geometric Progressions — Millennia Institute

Disease spread: GP model and bed capacity

Differential Equations — Millennia Institute

Salt tank; inflow/outflow DE

System of Linear Equations — Millennia Institute

Coffee blend prices and loyalty discount

Vectors — Millennia Institute

Line intersection; area; proj.

Graphs & Transformations — National Junior College

Reciprocal and transformation description

Integration Techniques — National Junior College

IBP: cos (3 ln x); substitution

Recurrence Relations — National Junior College

Factorial recurrence: general term and series convergence

System of Linear Equations — National Junior College

Currency exchange: 3-variable system

Binomial Expansion — National Junior College

Standard B(n,p) probabilities

Discrete Random Variables — National Junior College

Distribution; expected score

Graphs & Transformations — National Junior College

Ellipse, normal and volume

Hypothesis Testing — National Junior College

Sample size; conclusion

Normal Distribution — National Junior College

Normal approx; advanced

Complex Numbers — National Junior College

Solve simultaneous complex equations, then interpret w/z = i as a 90° rotation.

Maclaurin Series — National Junior College

Binomial and exponential series build a composite expansion, then integrate to approximate an integral.

Complex Numbers — National Junior College

Find modulus and argument of a complex number, then use Argand-diagram geometry to deduce arg(2-w).

Applications of Integration — Nanyang Junior College

Hyperbola; area; vol. x, y

Arithmetic & Geometric Progressions — Nanyang Junior College

AP/GP combined; common ratio

Complex Numbers — Nanyang Junior College

Argand geometry

Differential Equations — Nanyang Junior College

Biomass; growth models

Graphs & Transformations — Nanyang Junior College

Rational curve and oblique asymptote

Graphs & Transformations — Nanyang Junior College

f(a-x), |g(x)| and g(|x|)

Integration Techniques — Nanyang Junior College

Trig sub x= sin 2! theta ; modulus

Maclaurin Series — Nanyang Junior College

cos (t3); integrate; verify

Summation of Series — Nanyang Junior College

Vectors — Nanyang Junior College

Right angle; cross product

Binomial Expansion — Nanyang Junior College

Binomial; advanced

Differentiation & Applications — Nanyang Junior College

Implicit

Inequalities — Nanyang Junior College

Modulus and rational inequalities

System of Linear Equations — Nanyang Junior College

Two planes: angle, intersection and distance

Complex Numbers — Nanyang Junior College

Conjugate-pair roots of an imaginary-coefficient cubic, then x to -x substitution for the related cubic.

Applications of Integration — Raffles Institution

Substitution; area; vol. x-axis

Arithmetic & Geometric Progressions — Raffles Institution

GP: 99% of S_ infty ; modified AP

Differentiation & Applications — Raffles Institution

Rate of change

Differentiation & Applications — Raffles Institution

Rate of change

Integration Techniques — Raffles Institution

Partial fractions; IBP with ln

System of Linear Equations — Raffles Institution

Curve coefficients from geometric conditions

Correlation & Regression — Raffles Institution

Regression + PMCC + estimate

Discrete Random Variables — Raffles Institution

k(x2+x+1) formula

Hypothesis Testing — Raffles Institution

Multiple samples; range

Inequalities — Raffles Institution

Rational and ln |x| combined

Maclaurin Series — Raffles Institution

Triangle; implicit diff to x5

Normal Distribution — Raffles Institution

Multi-part normal

Permutations & Combinations — Raffles Institution

Charms: circular; keychain

Probability — Raffles Institution

Tree; conditional cases

Recurrence Relations — Raffles Institution

Rational recurrence: behavior for two initial values

Complex Numbers — Raffles Institution

Complex number argument under scaling and rotation, plus triangle geometry of f(z)=z^2-2z.

Complex Numbers — River Valley High School

Real polynomial, complex root

Complex Numbers — River Valley High School

Real polynomial, complex root

Differential Equations — River Valley High School

Coffee beans; logistics

Differentiation & Applications — River Valley High School

Differentiation

Graphs & Transformations — River Valley High School

Parametric, normals and intersection

Inequalities — River Valley High School

Rational and exponential chain

Summation of Series — River Valley High School

Telescoping; equation

Binomial Expansion — River Valley High School

B(n,p); mean and variance

Complex Numbers — River Valley High School

Triangle geometry

Discrete Random Variables — River Valley High School

Distribution; E(X), Var(X)

Permutations & Combinations — River Valley High School

Recurrence Relations — River Valley High School

Linear recurrence: behavior analysis

System of Linear Equations — River Valley High School

Line trajectories: intersection and distance

Vectors — River Valley High School

Contextual trajectories; angle; distance

Maclaurin Series — River Valley High School

Implicit differentiation of a differential equation to build the Maclaurin series for y and e^(arctan 3x).

Arithmetic & Geometric Progressions — St Andrew's Junior College

AP/GP connection: max sum and convergence

Differential Equations — St Andrew's Junior College

Particulates; separable DE

Differentiation & Applications — St Andrew's Junior College

Optimisation

Functions — St Andrew's Junior College

Periodic function and composite

Vectors — St Andrew's Junior College

Skew lines; reflection; plane

Binomial Expansion — St Andrew's Junior College

Multi-stage binomial

Complex Numbers — St Andrew's Junior College

Polynomials (complex coeff.)

Correlation & Regression — St Andrew's Junior College

Advanced; model selection

Recurrence Relations — St Andrew's Junior College

Linear recurrence: limit and GP series sum

Summation of Series — St Andrew's Junior College

GP series from recurrence

Complex Numbers — St Andrew's Junior College

Simultaneous complex equations with a modulus, plus a conjugate-point Argand argument.

Arithmetic & Geometric Progressions — Temasek Junior College

Financial: AP savings vs GP compound interest

Complex Numbers — Temasek Junior College

Simultaneous equations

Differential Equations — Temasek Junior College

Subst. w=x2y; pest model

Inequalities — Temasek Junior College

Rational then |x+1| substitution

Maclaurin Series — Temasek Junior College

Small angle; triangle approx.

Vectors — Temasek Junior College

Ratios; foot of perp; area

Binomial Expansion — Temasek Junior College

B(n,p) with extension

Correlation & Regression — Temasek Junior College

Compare models; transform

Hypothesis Testing — Temasek Junior College

Multi-stage hypothesis test

Normal Distribution — Temasek Junior College

Mean and sum; conditional

Permutations & Combinations — Temasek Junior College

Treasure; round table seating

Probability — Temasek Junior College

Two-stage; conditional

Maclaurin Series — Temasek Junior College

Implicit differentiation of a log-root function to build and deduce Maclaurin series.

Arithmetic & Geometric Progressions — Tampines Meridian Junior College

GP application; sum to infinity

Complex Numbers — Tampines Meridian Junior College

Real cubic; find roots

Maclaurin Series — Tampines Meridian Junior College

Maclaurin + sketch + approximation

Recurrence Relations — Tampines Meridian Junior College

Quadratic recurrence: fixed points and monotonicity

Vectors — Tampines Meridian Junior College

Drone rooftop; parallel planes

Binomial Expansion — Tampines Meridian Junior College

Binomial with restriction

Correlation & Regression — Tampines Meridian Junior College

PMCC; interpretation

Discrete Random Variables — Tampines Meridian Junior College

Distribution; game payoff

Hypothesis Testing — Tampines Meridian Junior College

Single sample; significance

Inequalities — Tampines Meridian Junior College

Rational and cos x restricted range

Probability — Tampines Meridian Junior College

Venn; independence

Applications of Integration — Victoria Junior College

Area; vol. x-axis; parabola

Differential Equations — Victoria Junior College

Substitution y= ln (u/x)

Functions — Victoria Junior College

Self-inverse and fn pattern

Graphs & Transformations — Victoria Junior College

Transformations and graph sketching

Graphs & Transformations — Victoria Junior College

Reflection + stretch; graph sketch

Summation of Series — Victoria Junior College

Convergence; bound; shift

Complex Numbers — Victoria Junior College

Modulus-argument form

Correlation & Regression — Victoria Junior College

PMCC; prediction

Differentiation & Applications — Victoria Junior College

Diff and application

Hypothesis Testing — Victoria Junior College

Sample mean; assumptions

Maclaurin Series — Victoria Junior College

ln (a+x); composition; integral

Complex Numbers — Victoria Junior College

Solve a modulus equation, find cube roots, and locate the circle through them.