essai × talentcoop · math QB · 23 Apr 2026

Math P1–S3 Question Bank — Build Checklist

Exhaustive task breakdown · MC + fill-in + short-answer · Variety and difficulty handles · All 110 curriculum units

110

P1–S3 curriculum units

~550

Templates to build (avg 5 per unit)

~1,100

Target questions (2 per template)

Diagram units (SVG only)

300

Already live (P6+DSE)

15–20

Est. dev days to full P1–S3

Milestone plan Variety handle Difficulty handle M1: S1–S3 M2: P6 gap-close Short-answer mode M3: P4–P5 M4: P1–P3 Long-Q / DSE Section B

Milestone Plan

M	Scope	Units	Qs target	Effort	Why this order
M1	S1–S3 generators — Number/Algebra, Geometry, Mensuration, Data, Coord+Trig	31	~310	4–5 days	Highest Leslie priority. Best data (UPEP 14,597 records + TSA S3 exam-points). Closes loop on acquired corpus.
M2	P6 diagram gap-close — angles (protractor), circles (geometry), symmetry, composite volume	5 gaps	+30 Qs	1–2 days	P6 is live. Diagrams are the last gap to Grade A. Quick demo win.
SA	Short-answer mode — build-mode switch (skip MC options), fill-in display format	all	—	1 day	Leslie already asked about non-MC. Cross-cutting; run in parallel with M1.
M3	P4–P5 generators — fractions, decimals, percentages, area/vol, algebra intro, data	26	~260	3–4 days	After M1 validates the pattern. Bridges P6 (live) and P1–P3.
M4	P1–P3 generators — number sense, 4 ops, basic shapes, money, time, fractions intro	38	~380	2–3 days	Simplest math = fastest to build. Diagram bank (3D recognition) uses static SVG assets.
M5	Long-Q / DSE Section B — multi-part structured questions with mark scheme	~15 topics	~150	5–7 days	Separate milestone. Flag for Leslie to prioritise — conditional feasibility on complex geometry proof.

Task Definition (per unit)

Every unit gets 8 build tasks. A unit is "production-grade" when all 8 are green. Same standard as the live DSE14/DSE17/P6 bank.

Map — Competency map JSON: skills DAG, exam-point examples, past paper count, generator constraints
Gen-MC — Generator templates for MC (4 options, error-modeled distractors) — 5–7 templates per unit
Traps — 100% trap builders: every template has error-modeled distractors in traps.js
Fill-in — Same generator, short-answer output mode (no options, just answer) — 1-day cross-cutting build switch
Solutions — Step-by-step solution builder in solutions.js
ZH — Chinese stems + solutions + trap analysis in chinese.js
Verify — Independent numeric verifier in verify_answers.js
Diagram — SVG generator (only for units with needsDiagram: true)

Variety Handle

Three levers for question variety

Lever	Mechanism	Status	Notes
Parameter ranges	Each unit in `curriculum.json` has `constraints` (e.g. P1: `maxDigits:2, resultMax:100, noBorrowing:true`). Generator draws from these ranges — same template, different numbers each run.	Done for P1–P6	S1–S3 constraints not yet in curriculum.json — fill during M1 competency map step
Template count	Target 5–7 templates per unit. Each template = one exam question pattern. More templates = more surface variety. DSE14 benchmark: 16 templates, 7 sub-topics.	Needed for M1–M4	Use UPEP + TSA corpus to identify which question patterns actually appear in practice
Context wrappers	10–15 hand-written scenario contexts per topic (e.g. "A shop sells X…", "A school bus…", "Mum buys…"). Generator picks one per question. Prevents robotic "A train travels X km at Y km/h…" repetition. ~2h per grade band.	P6 has ~8 wrappers	Critical for word-problem topics. Not needed for pure computation (MC format)

UPEP corpus as variety ground truth: the 14,597 UPEP records cover S1–S3 topics with high density. Before writing templates, scan the corpus for each unit to see what question patterns actually appear most. This prevents building templates for patterns students never see.

Difficulty Handle

3-tier difficulty system

Tier	Label	UPEP calibration	TSA calibration	Target %
1	Basic	`qtc: 2_LV1` — direct application, 1 step	`difficulty: "basic"`	~40%
2	Intermediate	`qtc: 2_LV2` — multi-step, 2–3 steps	`difficulty: "intermediate"`	~40%
3	Advanced	`qtc: 2_LV3` — multi-step, requires synthesis	—	~20%

Rules live in generators/difficulty.js. Overrides per template. Constraint: no tier > 85% of a topic's total questions. The UPEP distribution confirms this target: avg ~43% LV1 / 43% LV2 / 6% LV3 / 8% MC per book.

Empirical UPEP distribution (6 books): 2_LV1 ≈ 43%, 2_LV2 ≈ 43%, 2_LV3 ≈ 6%, 2_MC ≈ 8%. Our generator targets should mirror this — don't over-index on MC (which UPEP uses sparingly) or over-produce advanced questions.

M1 S1–S3 Generators — 31 units

Data available: TSA 2025 S3 exam-points JSON (80+ questions mapped) · UPEP 14,597 records with curriculum codes · EdCity STAR 11,826 records with topic labels · curriculum.json 31 units with objectives
Generator file plan: generators/s1s3_number_algebra.js · generators/s1s3_geometry.js · generators/s1s3_mensuration.js · generators/s1s3_data.js · generators/s1s3_coord_trig.js

Number and Algebra (units 1–14)

Unit	Topic	Strand	Types	Map	Gen-MC	Traps	Fill-in	Solve	ZH	Verify	Diag
1	Basic computation (integers, HCF/LCM)	N&A	MC+fill-in	todo	todo	todo	todo	todo	todo	todo	n/a
2	Directed numbers	N&A	MC+fill-in+word	todo	todo	todo	todo	todo	todo	todo	n/a
3	Approx values + numerical estimation	N&A	MC+fill-in	todo	todo	todo	todo	todo	todo	todo	n/a
4	Rational and irrational numbers	N&A	MC+fill-in	todo	todo	todo	todo	todo	todo	todo	n/a
5	Using percentages	N&A	MC+fill-in+word	todo	todo	todo	todo	todo	todo	todo	n/a
6	Rates, ratios and proportions	N&A	MC+fill-in+word	todo	todo	todo	todo	todo	todo	todo	n/a
7	Algebraic expressions	N&A	MC+fill-in	todo	todo	todo	todo	todo	todo	todo	n/a
8	Linear equations in one unknown	N&A	MC+fill-in+word	todo	todo	todo	todo	todo	todo	todo	n/a
9	Linear equations in two unknowns (simultaneous)	N&A	MC+fill-in+word	todo	todo	todo	todo	todo	todo	todo	n/a
10	Laws of integral indices	N&A	MC+fill-in	todo	todo	todo	todo	todo	todo	todo	n/a
11	Polynomials	N&A	MC+fill-in	todo	todo	todo	todo	todo	todo	todo	n/a
12	Identities	N&A	MC+fill-in	todo	todo	todo	todo	todo	todo	todo	n/a
13	Formulae (substitution + manipulation)	N&A	MC+fill-in+word	todo	todo	todo	todo	todo	todo	todo	n/a
14	Linear inequalities in one unknown	N&A	MC+fill-in+word	todo	todo	todo	todo	todo	todo	todo	n/a

Measures, Shape and Space (units 15–27)

Unit	Topic	Strand	Types	Map	Gen-MC	Traps	Fill-in	Solve	ZH	Verify	Diag
15	Errors in measurement	MSS	MC+fill-in+word	todo	todo	todo	todo	todo	todo	todo	n/a
16	Arc lengths + areas of sectors	MSS	MC+fill-in+word	todo	todo	todo	todo	todo	todo	todo	n/a
17	3-D figures (identification + nets)	MSS	MC 🖼	todo	todo	todo	n/a	todo	todo	todo	static SVG bank
18	Mensuration (surface area, volume)	MSS	MC+fill-in+word	todo	todo	todo	todo	todo	todo	todo	n/a
19	Angles and parallel lines	MSS	MC+fill-in 🖼	todo	todo	todo	todo	todo	todo	todo	SVG angles
20	Polygons (interior angles, sum)	MSS	MC+fill-in	todo	todo	todo	todo	todo	todo	todo	n/a
21	Congruent triangles	MSS	MC+fill-in 🖼	todo	todo	todo	todo	todo	todo	todo	SVG triangle pairs
22	Similar triangles	MSS	MC+fill-in 🖼	todo	todo	todo	todo	todo	todo	todo	SVG triangle pairs
23	Quadrilaterals (properties)	MSS	MC+fill-in 🖼	todo	todo	todo	todo	todo	todo	todo	SVG quad
24	Centres of triangles (centroid, incircle etc)	MSS	MC+fill-in 🖼	todo	todo	todo	todo	todo	todo	todo	SVG triangle+centre
25	Pythagoras' theorem	MSS	MC+fill-in+word	todo	todo	todo	todo	todo	todo	todo	extends 2d.js
26	Rectangular coordinate system (distance, mid-pt, slope)	MSS	MC+fill-in+word	todo	todo	todo	todo	todo	todo	todo	extends DSE10
27	Trigonometry (sin/cos/tan, right triangle)	MSS	MC+fill-in+word	todo	todo	todo	todo	todo	todo	todo	extends 2d.js

Data Handling (units 28–31)

Unit	Topic	Strand	Types	Map	Gen-MC	Traps	Fill-in	Solve	ZH	Verify	Diag
28	Organisation of data (tally, freq tables)	Data	MC+fill-in	todo	todo	todo	todo	todo	todo	todo	n/a
29	Presentation of data (bar, pie, broken-line)	Data	MC+fill-in 🖼	todo	todo	todo	todo	todo	todo	todo	extends p6_data.js
30	Measures of central tendency (mean/median/mode)	Data	MC+fill-in+word	todo	todo	todo	todo	todo	todo	todo	n/a
31	Probability (basic, equally likely)	Data	MC+fill-in+word	todo	todo	todo	todo	todo	todo	todo	n/a

M2 P6 Gap-Close — 5 diagram items

P6 generators are live (54 templates, 100 Qs). Gap to Grade A: add diagrams for 5 topic types. These are quick-win SVG additions.

Topic	Gap	Diagram type	Effort
p6-angles	No protractor/angle diagram	SVG angle arc on labelled lines	S
p6-circles	Circle geometry (arc, chord)	Extend p6_circles.js	S
p6-volume-composite	No 3D composite solid	SVG 2D cross-section of composite solid	M
p6-symmetry	No symmetry line on shape	SVG shape with dashed axis	S
p6-stats-misuse	No misleading chart	SVG bar chart with broken axis	S

SA Short-Answer / Fill-in Mode (cross-cutting, 1 day)

What this is: Every existing MC generator can emit a fill-in version — same stem, same answer, no options. One --mode fill-in flag in generate_questions.js + a display-mode flag in the DB schema (question_mode: 'mc' | 'fill-in'). No new templates needed.

Change generate_questions.js COVERAGE_TARGETS to accept mode: 'mc' | 'fill-in' | 'both'
Skip mc_options.js call when mode === 'fill-in'
Add question_mode column to dbo.math_questions (migration + seed update)
Frontend filter: show options when question_mode === 'mc', show blank answer input when fill-in
Applies to all existing 300 Qs + all future Qs immediately

M3 P4–P5 Generators — 26 units

Depends on M1 for pattern validation. P6 generators already cover the upper end (percentages, equations, averages, circles). P4–P5 fills the bridge.

Unit	Grade	Topic	Types	Diag
4N1–4N2	P4	Multiplication II + Division II (long mult/div)	MC+fill-in+word	n/a
4N3–4N4	P4	Multiples + factors / HCF + LCM	MC+fill-in	n/a
4N5	P4	Four arithmetic operations II (brackets, order)	MC+fill-in+word	n/a
4N6	P4	Fractions II (add/sub, mixed)	MC+fill-in+word	n/a
4N7–4N8	P4	Decimals I + II (place value, ops)	MC+fill-in+word	n/a
4M1–4M2	P4	Perimeter I + Area I	MC+fill-in+word	n/a
4S1–4S2	P4	Quadrilaterals III + Dissecting shapes	MC 🖼	SVG shapes
4S3	P4	Directions + positions III (4+8 compass, coordinates)	MC	n/a
4D1	P4	Bar charts II (grouped)	MC+fill-in 🖼	extends p6_data.js
5N1	P5	Multi-digit numbers (millions)	MC+fill-in	n/a
5N2–5N5	P5	Fractions III–V (mult, div, mixed ops)	MC+fill-in+word	n/a
5N4	P5	Decimals III (mult/div by powers of 10)	MC+fill-in+word	n/a
5A1–5A2	P5	Elementary algebra + Simple equations I	MC+fill-in+word	n/a
5M1–5M2	P5	Area II (circles) + Volume I (cubes/cuboids)	MC+fill-in+word	n/a (circle = p6_circles)
5S1–5S2	P5	Circles + 3-D shapes III	MC 🖼	extends p6_circles.js + static bank
5D1	P5	Bar charts III (percentage bar)	MC+fill-in 🖼	extends p6_data.js

M4 P1–P3 Generators — 38 units

Simplest math = fastest to build. All P1–P3 arithmetic is fully deterministic. Static SVG bank (15–20 labelled 3D-shape images) handles shape-recognition units. No TikZ needed anywhere.

Unit	Grade	Topic	Types	Diag
1N1–1N3	P1	Numbers to 20/100, place value	MC+fill-in	n/a
1N4	P1	Addition + subtraction I (≤100, no carry)	MC+fill-in+word	n/a
1M1–1M4	P1	Length (cm), Money (HK coins), Time (hr/half-hr)	MC+fill-in	n/a
1S1–1S2	P1	3-D shapes I + 2-D shapes (recognition)	MC 🖼	static SVG bank
1S3	P1	Directions + positions I (over/under/left/right)	MC	n/a
2N1–2N6	P2	3/4-digit numbers, add/sub II+III, mult, div	MC+fill-in+word	n/a
2M1–2M3	P2	Length (m), Time (min/am/pm), Money (notes)	MC+fill-in	n/a
2S1–2S4	P2	3-D shapes II, Angles, Directions, Quadrilaterals I	MC 🖼	static SVG bank + SVG angle
2D1	P2	Pictograms	MC+fill-in 🖼	SVG pictogram
3N1–3N5	P3	5-digit numbers, mult I, div I, 4-ops I, fractions I	MC+fill-in+word	n/a (fractions: SVG bar)
3M1–3M5	P3	Length (km/mm), Time (s/24h), Capacity (L/mL), Weight (kg/g)	MC+fill-in	n/a
3S1–3S2	P3	Quadrilaterals II + Triangles	MC 🖼	SVG shapes
3D1	P3	Bar charts I	MC+fill-in 🖼	extends p6_data.js

M5 Long-Q / DSE Section B — Flag for Leslie

Feasibility: ~65% of DSE Section B patterns are algorithmically generatable. The remaining ~35% (multi-theorem geometric proof, open algebraic reasoning) hit the limits of pure templates.

Pattern	Generatable?	Notes
Percentage / profit-loss word problems (multi-step)	✓ Yes	Template + context wrapper
Statistics (grouped freq table, box-whisker, mean)	✓ Yes	Extends DSE17 dispersion generators
Quadratics (find roots, sketch parabola)	✓ Yes	Constrain discriminant for clean answers
Mensuration + composite figures	✓ Yes	Multi-part: (a) area (b) volume — link parts by template design
Coordinate geometry (prove + find)	⚠ Partial	"Prove P, Q, R collinear" is generatable; open-ended proofs are harder
Multi-theorem geometry (circle + angle chasing)	✗ Hard	DSE11 circles: some 2-step is OK; 4-step theorem chains need LLM rewrite layer
TSA Section B written (P6 + S3, multi-step)	✓ Yes	Use TSA corpus as gold standard — 760+452 real examples with answers

Schema change needed: add parts: [{stem, answer, marks}] array to question record + marks_total field.

essai × talentcoop · math QB build checklist · 23 Apr 2026 · 110 units · generated from knowledge/curriculum.json + codebase scout