Primary 1–6
→ PSLE
→ Secondary 1–2
→ Secondary 3–4 / G1-G2-G3 / A-Math
→ JC H1 / H2 / H2 Further / H3 Mathematics
→ AnyOS transfer
→ StrategizeOS route selection

PUBLIC.ID:
EDUOS.MATH.P1.JC.CROSSWALK.v1.0
MACHINE.ID:
EDUOS.SG.MATH.P1TOJC.REQ.MAP.STRATEGIZEOS.v1.0
LATTICE.CODE:
LAT.EDUOS.MATH.S1-S7.P0-P5.Z0-Z4.T1-T12

Primary Mathematics
→ PSLE Compression Gate
→ Secondary Transition Shell
→ G1/G2/G3 Route Differentiation
→ Additional Mathematics Frontier Gate
→ JC H1/H2/H2 Further/H3 Mathematics
→ StrategizeOS Route Selection
→ AnyOS Transfer

where the student is stable
where the bridge is broken
where the shell jump is too early
where the exam gate compresses too hard
where the student should rebuild, hold, accelerate, or open frontier

Primary 1 Math
Primary 2 Math
Primary 3 Math
Primary 4 Math
Primary 5 Math
Primary 6 PSLE Math
Secondary 1 Math
Secondary 2 Math
Secondary 3 Math
Secondary 4 Math
JC H1 / H2 Math

Primary number sense did not stabilise.
PSLE modelling was passed but not transferred.
Sec 1 algebra entry was weak.
Sec 2 graph-function bridge was broken.
Sec 3 A-Math was entered before algebra was strong.
Sec 4 exam compression exposed accumulated debt.
JC calculus and statistics overloaded the weak base.

PRIMARY.MATH =
number sense
+ operation control
+ representation
+ proportional reasoning
+ spatial reasoning
+ measurement
+ word-problem modelling
+ checking discipline

PRIMARY.FAILURE.LAW:
If Primary nodes are unstable, Secondary algebra becomes expensive.

accuracy
speed
reasoning
modelling
method communication
checking discipline
secondary readiness

PSLE.MATH =
Primary capability compressed into a route signal.

SEC1-2.MATH =
Primary transfer
+ algebra entry
+ negative-number stability
+ ratio/rate expansion
+ graph representation
+ geometry reasoning
+ statistics/probability entry
+ G1/G2/G3 route clarification

SEC1-2.LAW:
Lower Secondary does not merely teach new topics.
It reveals whether PSLE competence was transferable.

SEC3-4.FAIL.SENSORS =
foundation debt
+ algebra drift
+ graph-function mismatch
+ trigonometry instability
+ coordinate geometry weakness
+ calculus overload
+ exam timing collapse
+ post-secondary route mismatch

Can the student calculate?

Can the student model?
Can the student reason abstractly?
Can the student use functions under load?
Can the student handle change, uncertainty, vectors, statistics, proof, and symbolic systems?
Can the student transfer mathematics into science, economics, computing, engineering, medicine, AI, finance, and research?

business
social sciences
economics
psychology
statistics-based university courses
applied decision-making

H1.MATH =
applied mathematical literacy for university-readiness in non-heavy-STEM routes.

engineering
physics
computing
data science
economics
mathematics-heavy university courses
advanced quantitative reasoning

H2.MATH =
advanced mathematical operating system for change, space, uncertainty, modelling, and abstraction.

deeper abstraction
proof discipline
structure recognition
generalisation
mathematical argument
research-style thinking

FRONTIER.MATH.SENSOR =
Can the student produce mathematics,
not merely consume mathematics?

P1:
quantity
P2:
operation
P3:
part-whole
P4:
representation
P5:
proportion
P6:
PSLE compression
Sec 1:
algebra entry
Sec 2:
relationship strengthening
Sec 3:
route divergence
Sec 4:
exam closure
JC H1:
applied modelling and statistics
JC H2:
advanced abstraction and STEM transfer
H2 Further / H3:
frontier mathematics and proof

Number → Operation → Representation → Proportion → Algebra → Function → Calculus → Statistics → Proof → Frontier

What topic is weak?

What route is now correct?

MATHOS.P1TOJC.CROSSWALK.ALGORITHM.v1.0
INPUT:
    student_level
    topic_performance
    paper_performance
    error_pattern
    speed_pressure
    transfer_result
    next_route_requirement
STEP 1:
    identify current shell
        P1-P6
        PSLE
        Sec1-Sec4
        A-Math
        JC H1/H2/Further/H3
STEP 2:
    detect base stability
        number
        operation
        proportion
        algebra
        functions
        calculus
        statistics
        proof
STEP 3:
    locate failure type
        missing_node
        broken_bridge
        shell_jump
        ledger_breach
        compression_failure
        tool_dependency
        false_pass
        environment_drag
        frontier_cannibalisation
        genesis_pin_error
STEP 4:
    assign StrategizeOS route
        rebuild
        bridge
        hold
        rebuffer
        verify
        pressure_train
        de_automate
        transfer_test
        protect_base
        repin
STEP 5:
    retest under realistic load
STEP 6:
    confirm transfer into next shell
OUTPUT:
    current mathematical state
    failure pattern
    correct repair route
    next viable mathematics corridor

Do not wait until the exam year to discover the missing node.

How many marks did my child lose?

Which future corridor did this error expose?

PRIMARY_TO_JC_MATH_CROSSWALK =
P1:
    build quantity
P2:
    stabilise operations
P3:
    introduce part-whole and word-problem representation
P4:
    expand representation, measurement, and spatial logic
P5:
    build proportion, rate, percentage, and model transfer
P6:
    compress six years into PSLE route signal
SEC1:
    test Primary-to-Secondary transfer
SEC2:
    strengthen algebra, graph, geometry, and route readiness
SEC3:
    split into G1/G2/G3/A-Math corridors
SEC4:
    validate secondary mathematics under exam compression
JC_H1:
    apply functions, calculus, probability, and statistics for non-heavy-STEM routes
JC_H2:
    build advanced abstraction for STEM and quantitative university pathways
JC_FURTHER_H3:
    open frontier mathematics through proof, structure, and advanced reasoning
IF failure_detected:
    classify pattern
    select StrategizeOS route
    repair correct layer
    retest under load
    confirm transfer
OUTPUT:
    mathematics capability route from Primary 1 to JC

If the base is weak, the future becomes expensive.
If the bridge is broken, the next shell becomes unstable.
If the route is correctly read, repair can begin early.
If the student stabilises each shell, Mathematics becomes transferable power.

This is the **full Primary Mathematics build system**.
Everything in Primary 1–6 is not random topics — it is a **layered construction of capability nodes** that must hold together before PSLE compression.
---
# 1. Primary Mathematics Core Reading

---
# 2. Primary 1–6 Shell Structure
| Level     | PUBLIC.ID     | MACHINE.ID         | LATTICE.CODE                     |
| --------- | ------------- | ------------------ | -------------------------------- |
| Primary 1 | EDUOS.MATH.P1 | EDUOS.MATH.P1.v1.0 | LAT.EDUOS.MATH.S2.P0-P1.Z0.T3    |
| Primary 2 | EDUOS.MATH.P2 | EDUOS.MATH.P2.v1.0 | LAT.EDUOS.MATH.S2.P1.Z0.T4       |
| Primary 3 | EDUOS.MATH.P3 | EDUOS.MATH.P3.v1.0 | LAT.EDUOS.MATH.S2.P1-P2.Z1.T5    |
| Primary 4 | EDUOS.MATH.P4 | EDUOS.MATH.P4.v1.0 | LAT.EDUOS.MATH.S2.P2.Z1.T6       |
| Primary 5 | EDUOS.MATH.P5 | EDUOS.MATH.P5.v1.0 | LAT.EDUOS.MATH.S2.P2-P3.Z1-Z2.T7 |
| Primary 6 | EDUOS.MATH.P6 | EDUOS.MATH.P6.v1.0 | LAT.EDUOS.MATH.S2.P3-P4.Z2.T8-T9 |
---
# 3. Topic Node Build (Across P1–P6)
| Core Node     | EducationOS Function    | Built Across |
| ------------- | ----------------------- | ------------ |
| Whole Numbers | number-stability engine | P1–P6        |
| Fractions     | part-whole system       | P3–P6        |
| Decimals      | place-value extension   | P4–P6        |
| Ratio         | comparison system       | P5–P6        |
| Percentage    | proportional system     | P5–P6        |
| Rate / Speed  | transfer system         | P5–P6        |
| Algebra       | unknown-value entry     | P5–P6        |
| Geometry      | spatial reasoning       | P1–P6        |
| Measurement   | unit-formula system     | P2–P6        |
| Statistics    | data-reading system     | P3–P6        |
| Word Problems | modelling engine        | P1–P6        |
---
# 4. Primary Phase Build (Critical)

---
# 5. Primary Failure Sensor Map

---
# 6. Primary Repair Codes
| Repair Code                    | Use                                         |
| ------------------------------ | ------------------------------------------- |
| EDUOS.REPAIR.P1P2.NUMBER.SENSE | when basic counting and operations are weak |
| EDUOS.REPAIR.P3.FRACTIONS      | when fractions concept fails                |
| EDUOS.REPAIR.P4.DECIMALS       | when place-value extension breaks           |
| EDUOS.REPAIR.P5.RATIO.PERCENT  | when proportional reasoning is weak         |
| EDUOS.REPAIR.P5P6.RATE.SPEED   | when rate/speed transfer fails              |
| EDUOS.REPAIR.P1P6.GEOMETRY     | when spatial reasoning is weak              |
| EDUOS.REPAIR.P2P6.MEASUREMENT  | when units/formulas are confused            |
| EDUOS.REPAIR.P3P6.STATISTICS   | when data reading fails                     |
| EDUOS.REPAIR.P1P6.WORD.PROBLEM | when modelling fails                        |
| EDUOS.REPAIR.PSLE.PRECOMPRESS  | when P6 cannot handle PSLE-level load       |
---
# 7. Hidden Structure (Most Important Insight)

---
# 8. Full Primary → PSLE Transition

---
# 9. Final EducationOS Code

PUBLIC.ID:
EDUOS.MATH.PRIMARY.100NODE.REGISTRY.v1.0
MACHINE.ID:
EDUOS.SG.PRIMARY.MATH.NODE.REGISTRY.100PLUS.v1.0
LATTICE.CODE:
LAT.EDUOS.MATH.S2-S3.P0-P4.Z0-Z2.T3-T9

PRIMARY.MATH.FAIL.SENSORS =
NUMBER.DRIFT
+ PLACEVALUE.WEAKNESS
+ OPERATION.ERROR
+ FRACTION.CONFUSION
+ RATIO.PERCENT.COLLAPSE
+ UNIT.CONVERSION.ERROR
+ GEOMETRY.MISREAD
+ DATA.INTERPRETATION.WEAKNESS
+ MODEL.DRAWING.FAILURE
+ WORD.PROBLEM.PARALYSIS
+ CARELESS.ERROR.REPEAT
+ PAPER.COMPRESSION.FAILURE

EDUOS.REPAIR.PRIMARY.NUMBER
EDUOS.REPAIR.PRIMARY.OPERATION
EDUOS.REPAIR.PRIMARY.FRACTION
EDUOS.REPAIR.PRIMARY.RATIO.PERCENT
EDUOS.REPAIR.PRIMARY.MEASUREMENT
EDUOS.REPAIR.PRIMARY.GEOMETRY
EDUOS.REPAIR.PRIMARY.STATISTICS
EDUOS.REPAIR.PRIMARY.MODEL.DRAWING
EDUOS.REPAIR.PRIMARY.WORD.PROBLEM
EDUOS.REPAIR.PRIMARY.EXAM.COMPRESSION

PRIMARY.MATH.100NODE.EDUOS =
A full Primary Mathematics node registry where every topic,
skill, model, representation, mistake pattern, and exam behaviour
is encoded as a visible capability node.
The purpose is not only to teach Primary Mathematics.
The purpose is to detect where the child’s mathematical route is
building, drifting, overloading, or preparing for PSLE compression.

PSLE Mathematics is the **Primary 1–6 compression gate**. It tests whether number, algebra, geometry, measurement, statistics, problem solving, reasoning, and communication can hold under exam pressure.
## 1. PSLE Mathematics Core Reading

MOE’s PSLE AL bands for Standard subjects are: AL1 ≥90, AL2 85–89, AL3 80–84, AL4 75–79, AL5 65–74, AL6 45–64, AL7 20–44, AL8 <20. ([Ministry of Education][1])
## 2. PSLE Math EducationOS Registry
| Layer                        | PUBLIC.ID                  | MACHINE.ID                      | LATTICE.CODE                        |
| ---------------------------- | -------------------------- | ------------------------------- | ----------------------------------- |
| PSLE Mathematics Root        | EDUOS.MATH.PSLE.ROOT       | EDUOS.MATH.PSLE.REG.v1.0        | LAT.EDUOS.MATH.S3.P2-P4.Z2-Z3.T8-T9 |
| PSLE Standard Math           | EDUOS.MATH.PSLE.STANDARD   | EDUOS.MATH.PSLE.STD.v1.0        | LAT.EDUOS.MATH.S3.P2-P4.Z2-Z3.T8-T9 |
| PSLE Foundation Math         | EDUOS.MATH.PSLE.FOUNDATION | EDUOS.MATH.PSLE.FOUND.v1.0      | LAT.EDUOS.MATH.S3.P1-P3.Z2.T8-T9    |
| PSLE AL1–AL4 Corridor        | EDUOS.MATH.PSLE.AL1.AL4    | EDUOS.MATH.PSLE.HIGHBAND.v1.0   | LAT.EDUOS.MATH.S3.P3-P4.Z3.T9       |
| PSLE AL5–AL8 Repair Corridor | EDUOS.MATH.PSLE.AL5.AL8    | EDUOS.MATH.PSLE.REPAIRBAND.v1.0 | LAT.EDUOS.MATH.S3.P1-P3.Z2.T9       |
## 3. PSLE Paper Gate
For 2026 PSLE Mathematics, SEAB lists two written papers: Paper 1 is non-calculator and Paper 2 allows calculators; both papers are scheduled on the same day with a break between them. ([SEAB][2])
| Paper               | EducationOS Function                        | Main Risk                                    |
| ------------------- | ------------------------------------------- | -------------------------------------------- |
| Paper 1             | speed, fluency, arithmetic discipline       | careless errors, weak mental structure       |
| Paper 2             | reasoning, modelling, long-answer structure | cannot start, wrong method, poor explanation |
| Calculator Boundary | tool discipline                             | over-reliance or wrong input                 |
| Mark Scheme         | method ledger                               | answer without valid working                 |
## 4. PSLE Topic Nodes
| Topic Node    | EducationOS Function  | Failure Sensor                  | Repair Route                    |
| ------------- | --------------------- | ------------------------------- | ------------------------------- |
| Whole Numbers | number-stability node | place value / operation errors  | rebuild number sense            |
| Fractions     | part-whole node       | denominator / comparison errors | visual model repair             |
| Decimals      | place-value extension | rounding / alignment errors     | place-value grid                |
| Percentages   | proportion node       | wrong base                      | fraction-decimal-percent bridge |
| Ratio         | comparison node       | wrong quantity pairing          | bar model repair                |
| Rate / Speed  | transfer node         | unit confusion                  | units + formula discipline      |
| Algebra       | unknown-value node    | cannot form equation            | word-to-symbol bridge           |
| Geometry      | shape-reasoning node  | wrong property                  | diagram annotation              |
| Measurement   | unit-formula node     | area/volume confusion           | formula ledger                  |
| Statistics    | data-reading node     | graph/table misread             | representation drill            |
| Word Problems | modelling gate        | cannot choose method            | heuristic route map             |
## 5. PSLE Failure Sensor Map

## 6. PSLE Repair Codes
| Repair Code                              | Use                                          |
| ---------------------------------------- | -------------------------------------------- |
| EDUOS.REPAIR.PSLE.NUMBER.SENSE           | unstable whole number / operation foundation |
| EDUOS.REPAIR.PSLE.FRACTION.RATIO.PERCENT | weak proportional reasoning                  |
| EDUOS.REPAIR.PSLE.MODEL.DRAWING          | poor bar model / comparison modelling        |
| EDUOS.REPAIR.PSLE.SPEED.RATE.UNIT        | weak unit and rate handling                  |
| EDUOS.REPAIR.PSLE.GEOMETRY.MEASURE       | geometry / mensuration confusion             |
| EDUOS.REPAIR.PSLE.DATA.STATISTICS        | weak table, chart, or data reading           |
| EDUOS.REPAIR.PSLE.PAPER1.ACCURACY        | Paper 1 careless-error control               |
| EDUOS.REPAIR.PSLE.PAPER2.REASONING       | Paper 2 structured reasoning repair          |
| EDUOS.REPAIR.PSLE.AL.ROUTE               | AL band and secondary route recalibration    |
## 7. Final PSLE EducationOS Code

PUBLIC.ID:
EDUOS.MATH.PSLE.QUESTIONTYPE.CROSSWALK.v1.0
MACHINE.ID:
EDUOS.SG.PSLE.MATH.QTYPE.PATTERNENGINE.v1.0
LATTICE.CODE:
LAT.EDUOS.MATH.PSLE.S3.P2-P4.Z2-Z3.T8-T9

QUESTION TYPE
→ TOPIC NODE
→ THINKING DEMAND
→ FAILURE SIGNAL
→ PATTERN ID
→ REPAIR CODE
→ LEDGER STATUS

What the child knows
+ how the child chooses methods
+ whether the child can transfer
+ whether the child collapses under pressure
+ whether the child is ready for Secondary 1 Mathematics

PSLE.PATTERN.F01 = careless arithmetic drift
PSLE.PATTERN.F02 = place-value misalignment
PSLE.PATTERN.F03 = fraction-ratio-percent confusion
PSLE.PATTERN.F04 = wrong comparison base
PSLE.PATTERN.F05 = unit conversion drift
PSLE.PATTERN.F06 = geometry rule misread
PSLE.PATTERN.F07 = formula selection error
PSLE.PATTERN.F08 = graph/table interpretation weakness
PSLE.PATTERN.F09 = word-problem paralysis
PSLE.PATTERN.F10 = heuristic mismatch
PSLE.PATTERN.F11 = multi-step route collapse
PSLE.PATTERN.F12 = weak method communication
PSLE.PATTERN.F13 = calculator/input discipline failure
PSLE.PATTERN.F14 = time-pressure collapse
PSLE.PATTERN.F15 = no checking loop

INPUT:
PSLE question attempted by student
SENSOR:
question type + topic + method used + error pattern
ENGINE:
match error to Pattern ID
OUTPUT:
repair code + next drill + ledger status

PSLE.QTYPE.PATTERNENGINE =
A diagnostic system that reads PSLE Mathematics questions as sensors,
not worksheets.
Each question reveals:
1. topic mastery,
2. method choice,
3. transfer ability,
4. pressure stability,
5. repair need,
6. Secondary 1 readiness.

PSLE QUESTION TYPES =
Paper-level sensors.
MCQ tests recognition and trap resistance.
Short-answer tests fluency and accuracy.
Structured questions test route control.
Non-routine questions test heuristic selection.
Paper 2 tests whether the child can think under load.
When enough questions are logged,
EducationOS can detect the child’s repeating mathematical failure pattern
before the final PSLE result exposes it.

Secondary 1 Mathematics now sits inside Singapore’s **Full Subject-Based Banding** structure, where Mathematics may be offered at **G1, G2, or G3** levels instead of the older Express / Normal stream labels. MOE states that from the 2024 Secondary 1 cohort, students are posted through Posting Groups 1, 2, and 3, with flexibility to take subjects at different subject levels. ([Ministry of Education][1])
## 1. Secondary 1 Mathematics Core Reading

## 2. Sec 1 Math EducationOS Registry
| Layer                  | PUBLIC.ID            | MACHINE.ID               | LATTICE.CODE                     |
| ---------------------- | -------------------- | ------------------------ | -------------------------------- |
| Sec 1 Mathematics Root | EDUOS.MATH.SEC1.ROOT | EDUOS.MATH.SEC1.REG.v1.0 | LAT.EDUOS.MATH.S4.P1-P4.Z2.T9    |
| Sec 1 G1 Mathematics   | EDUOS.MATH.SEC1.G1   | EDUOS.MATH.SEC1.G1.v1.0  | LAT.EDUOS.MATH.S4.P1-P2.Z2.T9    |
| Sec 1 G2 Mathematics   | EDUOS.MATH.SEC1.G2   | EDUOS.MATH.SEC1.G2.v1.0  | LAT.EDUOS.MATH.S4.P2-P3.Z2.T9    |
| Sec 1 G3 Mathematics   | EDUOS.MATH.SEC1.G3   | EDUOS.MATH.SEC1.G3.v1.0  | LAT.EDUOS.MATH.S4.P3-P4.Z2-Z3.T9 |
## 3. Sec 1 Topic Nodes
The official secondary mathematics curriculum is organised around the major strands **Number and Algebra**, **Geometry and Measurement**, and **Statistics and Probability**. ([Ministry of Education][2])
| Topic Node                  | EducationOS Function        | Failure Sensor                    | Repair Route                             |
| --------------------------- | --------------------------- | --------------------------------- | ---------------------------------------- |
| Numbers / Prime Factors     | number-structure node       | weak factorisation                | rebuild factors, multiples, divisibility |
| Integers / Rational Numbers | sign-control node           | negative-number errors            | number-line repair                       |
| Ratio / Percentage / Rate   | proportional reasoning node | wrong comparison base             | bar model → algebra bridge               |
| Speed                       | rate-transfer node          | unit confusion                    | unit conversion + formula discipline     |
| Algebraic Expressions       | symbolic entry node         | cannot translate words to symbols | concrete-to-symbol bridge                |
| Linear Equations            | solving-control node        | inverse operation errors          | equation balance repair                  |
| Graphs                      | representation node         | table-to-graph mismatch           | coordinate-grid training                 |
| Angles                      | geometry logic node         | wrong angle rule                  | diagram annotation repair                |
| Mensuration                 | measurement node            | formula misuse                    | unit-shape-formula ledger                |
| Statistics / Probability    | data reasoning node         | graph/table misread               | representation comparison drill          |
## 4. G1 / G2 / G3 EducationOS Meaning
| Level | EducationOS Corridor   | Main Aim                                                        |
| ----- | ---------------------- | --------------------------------------------------------------- |
| G1    | Stabilisation corridor | secure usable numeracy and practical mathematics                |
| G2    | Competence corridor    | build reliable secondary mathematics foundations                |
| G3    | Acceleration corridor  | prepare for higher secondary load and possible A-Math readiness |
## 5. Sec 1 Failure Sensor Map

## 6. Sec 1 Repair Codes
| Repair Code                        | Use                                            |
| ---------------------------------- | ---------------------------------------------- |
| EDUOS.REPAIR.SEC1.PSLE.TRANSITION  | when Primary-to-Secondary jump causes collapse |
| EDUOS.REPAIR.SEC1.NUMBER.STABILITY | when number operations are unstable            |
| EDUOS.REPAIR.SEC1.ALGEBRA.ENTRY    | when algebra entry fails                       |
| EDUOS.REPAIR.SEC1.RATIO.RATE       | when ratio, percentage, rate, or speed is weak |
| EDUOS.REPAIR.SEC1.GEOMETRY.RULES   | when angle / shape rules are confused          |
| EDUOS.REPAIR.SEC1.GRAPH.DATA       | when tables, graphs, or data readings are weak |
| EDUOS.REPAIR.SEC1.GLEVEL.ROUTE     | when G1/G2/G3 level fit needs review           |
## 7. Final Sec 1 EducationOS Code

Secondary 2 Mathematics is still under Singapore’s **Full Subject-Based Banding** structure, where Mathematics is offered at **G1, G2, and G3** levels. MOE states that from the 2024 Secondary 1 cohort, students are posted through Posting Groups 1, 2, and 3 and may offer subjects at different subject levels as they progress through secondary school. ([Ministry of Education][1])
## 1. Secondary 2 Mathematics Core Reading

## 2. Sec 2 Math EducationOS Registry
| Layer                  | PUBLIC.ID            | MACHINE.ID               | LATTICE.CODE                      |
| ---------------------- | -------------------- | ------------------------ | --------------------------------- |
| Sec 2 Mathematics Root | EDUOS.MATH.SEC2.ROOT | EDUOS.MATH.SEC2.REG.v1.0 | LAT.EDUOS.MATH.S4.P1-P4.Z2-Z3.T10 |
| Sec 2 G1 Mathematics   | EDUOS.MATH.SEC2.G1   | EDUOS.MATH.SEC2.G1.v1.0  | LAT.EDUOS.MATH.S4.P1-P2.Z2.T10    |
| Sec 2 G2 Mathematics   | EDUOS.MATH.SEC2.G2   | EDUOS.MATH.SEC2.G2.v1.0  | LAT.EDUOS.MATH.S4.P2-P3.Z2.T10    |
| Sec 2 G3 Mathematics   | EDUOS.MATH.SEC2.G3   | EDUOS.MATH.SEC2.G3.v1.0  | LAT.EDUOS.MATH.S4.P3-P4.Z2-Z3.T10 |
## 3. Sec 2 Topic Nodes
MOE’s secondary mathematics framework covers **G1, G2, G3 Mathematics**, plus **G2 and G3 Additional Mathematics**, and the broad curriculum strands include Number & Algebra, Geometry & Measurement, and Statistics & Probability. ([Ministry of Education][2])
| Topic Node                        | EducationOS Function        | Failure Sensor                    | Repair Route                        |
| --------------------------------- | --------------------------- | --------------------------------- | ----------------------------------- |
| Algebraic Manipulation            | symbolic-control node       | expansion / factorisation errors  | expression drill + inverse checking |
| Linear Equations / Inequalities   | balance-control node        | wrong operation sequence          | equation-balance repair             |
| Graphs of Linear Functions        | representation node         | gradient/intercept confusion      | table → graph → equation bridge     |
| Ratio / Rate / Percentage         | proportional reasoning node | wrong base / wrong unit           | bar model → algebra bridge          |
| Direct / Inverse Proportion       | relationship-transfer node  | cannot identify relation type     | pattern-table repair                |
| Geometry / Angles                 | spatial logic node          | wrong theorem / missing reason    | diagram annotation repair           |
| Congruence / Similarity Readiness | shape-transformation node   | scale factor confusion            | corresponding-side mapping          |
| Pythagoras Readiness              | right-triangle node         | hypotenuse misread                | triangle-labelling repair           |
| Mensuration                       | formula-control node        | area/volume formula misuse        | unit-shape-formula ledger           |
| Statistics / Probability          | uncertainty/data node       | poor graph or probability reading | representation comparison drill     |
## 4. G1 / G2 / G3 EducationOS Meaning
| Level | EducationOS Corridor   | Sec 2 Main Aim                                          |
| ----- | ---------------------- | ------------------------------------------------------- |
| G1    | Stabilisation corridor | make mathematics usable and practical                   |
| G2    | Upgrade corridor       | strengthen core Sec 3 readiness                         |
| G3    | Acceleration corridor  | prepare for Sec 3 G3 load and possible A-Math readiness |
## 5. Sec 2 Failure Sensor Map

## 6. Sec 2 Repair Codes
| Repair Code                            | Use                                                     |
| -------------------------------------- | ------------------------------------------------------- |
| EDUOS.REPAIR.SEC2.SEC1.CARRYOVER       | when Sec 1 foundations remain unstable                  |
| EDUOS.REPAIR.SEC2.ALGEBRA.MANIPULATION | when expansion, factorisation, or simplification fails  |
| EDUOS.REPAIR.SEC2.LINEAR.GRAPHS        | when graphs, gradient, intercept, or equations are weak |
| EDUOS.REPAIR.SEC2.RATIO.PROPORTION     | when ratio, percentage, rate, or proportion is unstable |
| EDUOS.REPAIR.SEC2.GEOMETRY.REASONING   | when angle rules and geometry explanations fail         |
| EDUOS.REPAIR.SEC2.MENSURATION.UNITS    | when formulas and units are misused                     |
| EDUOS.REPAIR.SEC2.SEC3.ROUTE           | when G1/G2/G3 or A-Math readiness needs review          |
## 7. Final Sec 2 EducationOS Code

Secondary 3 is the **route-divergence year**. Singapore’s secondary mathematics curriculum includes **G1, G2, G3 Mathematics**, plus **G2 and G3 Additional Mathematics**; the core Mathematics syllabus is organised around **Number & Algebra, Geometry & Measurement, and Statistics & Probability**, while Additional Mathematics is organised around **Algebra, Geometry & Trigonometry, and Calculus**. ([Ministry of Education][1])
## 1. Secondary 3 Mathematics Core Reading

## 2. Sec 3 Math EducationOS Registry
| Layer                        | PUBLIC.ID             | MACHINE.ID                 | LATTICE.CODE                         |
| ---------------------------- | --------------------- | -------------------------- | ------------------------------------ |
| Sec 3 Mathematics Root       | EDUOS.MATH.SEC3.ROOT  | EDUOS.MATH.SEC3.REG.v1.0   | LAT.EDUOS.MATH.S4-S5.P2-P4.Z2-Z3.T11 |
| Sec 3 G1 Mathematics         | EDUOS.MATH.SEC3.G1    | EDUOS.MATH.SEC3.G1.v1.0    | LAT.EDUOS.MATH.S4.P1-P2.Z2.T11       |
| Sec 3 G2 Mathematics         | EDUOS.MATH.SEC3.G2    | EDUOS.MATH.SEC3.G2.v1.0    | LAT.EDUOS.MATH.S4.P2-P3.Z2.T11       |
| Sec 3 G3 Mathematics         | EDUOS.MATH.SEC3.G3    | EDUOS.MATH.SEC3.G3.v1.0    | LAT.EDUOS.MATH.S4.P3-P4.Z3.T11       |
| Sec 3 Additional Mathematics | EDUOS.MATH.SEC3.AMATH | EDUOS.MATH.SEC3.AMATH.v1.0 | LAT.EDUOS.MATH.S5.P2-P4.Z3.T11       |
## 3. Sec 3 Topic Nodes
| Topic Node                | EducationOS Function      | Failure Sensor                        | Repair Route                       |
| ------------------------- | ------------------------- | ------------------------------------- | ---------------------------------- |
| Algebraic Manipulation    | symbolic-control engine   | expansion / factorisation collapse    | factorisation ladder repair        |
| Quadratic Equations       | nonlinear-solving node    | wrong method selection                | factorise → formula → graph bridge |
| Simultaneous Equations    | system-solving node       | substitution / elimination confusion  | equation-pair route training       |
| Indices / Surds           | symbolic compression node | law misuse                            | index-law ledger                   |
| Linear / Quadratic Graphs | graph-function node       | equation-to-graph mismatch            | table → graph → equation drill     |
| Coordinate Geometry       | spatial-algebra node      | gradient / midpoint / distance errors | coordinate formula repair          |
| Trigonometry              | ratio-angle node          | SOHCAHTOA / angle confusion           | triangle labelling repair          |
| Mensuration               | shape-measure node        | formula / unit mismatch               | formula selection ledger           |
| Statistics / Probability  | uncertainty-data node     | weak representation / event logic     | probability-tree and table repair  |
| Real-World Problems       | modelling-transfer gate   | cannot convert words to equations     | language-to-symbol bridge          |
## 4. A-Math Entry Layer
Additional Mathematics prepares students for higher mathematical study and emphasises reasoning, communication, application, and modelling. SEAB’s 2027 G3 Additional Mathematics syllabus states that it prepares students for A-Level H2 Mathematics and is organised into **Algebra, Geometry & Trigonometry, and Calculus**. ([SEAB][2])
| A-Math Node                        | EducationOS Function    | Failure Sensor                      | Repair Route                    |
| ---------------------------------- | ----------------------- | ----------------------------------- | ------------------------------- |
| Advanced Algebra                   | P4 symbolic engine      | manipulation overload               | slow symbolic reconstruction    |
| Quadratics / Polynomials           | function-structure node | no factor theorem / remainder logic | polynomial route map            |
| Exponential / Logarithmic Thinking | growth-scale node       | cannot read inverse relationships   | function-family bridge          |
| Trigonometric Identities           | transformation node     | identity memorised but not usable   | identity-movement drills        |
| Coordinate Geometry                | algebra-spatial bridge  | line/circle confusion               | graph-geometry ledger           |
| Calculus Entry                     | change-rate engine      | weak functions foundation           | function-before-calculus repair |
## 5. G1 / G2 / G3 EducationOS Meaning
| Level  | EducationOS Corridor    | Sec 3 Main Aim                                                 |
| ------ | ----------------------- | -------------------------------------------------------------- |
| G1     | Practical stabilisation | preserve usable mathematics and prevent collapse               |
| G2     | Exam competence         | build stable SEC/O-Level equivalent readiness                  |
| G3     | Distinction / transfer  | prepare for stronger STEM, A-Math, JC, IP, IB, or IGCSE routes |
| A-Math | Frontier compression    | test whether symbolic load and abstraction can be sustained    |
## 6. Sec 3 Failure Sensor Map

## 7. Sec 3 Repair Codes
| Repair Code                       | Use                                                    |
| --------------------------------- | ------------------------------------------------------ |
| EDUOS.REPAIR.SEC3.SEC2.CARRYOVER  | when lower-secondary gaps remain active                |
| EDUOS.REPAIR.SEC3.ALGEBRA.CORE    | when algebra manipulation is unstable                  |
| EDUOS.REPAIR.SEC3.QUADRATIC.ROUTE | when quadratic methods are confused                    |
| EDUOS.REPAIR.SEC3.GRAPH.FUNCTION  | when equations, tables, and graphs do not connect      |
| EDUOS.REPAIR.SEC3.TRIG.ENTRY      | when trigonometry entry fails                          |
| EDUOS.REPAIR.SEC3.COORD.GEOM      | when coordinate geometry is unstable                   |
| EDUOS.REPAIR.SEC3.STAT.PROB       | when statistics/probability questions fail             |
| EDUOS.REPAIR.SEC3.AMATH.BUFFER    | when A-Math load is too high                           |
| EDUOS.REPAIR.SEC3.EXAM.TRACK      | when the student’s G-level / A-Math route needs review |
## 8. Final Sec 3 EducationOS Code

Secondary 4 is the **exam-compression shell**. Under Full SBB, Mathematics is offered at **G1, G2, and G3** subject levels, while SEAB’s 2026 O-Level Mathematics syllabus organises Mathematics into **Number & Algebra, Geometry & Measurement, and Statistics & Probability**. Additional Mathematics is organised into **Algebra, Geometry & Trigonometry, and Calculus**. ([Ministry of Education][1])
## 1. Secondary 4 Mathematics Core Reading

## 2. Sec 4 Math EducationOS Registry
| Layer                        | PUBLIC.ID             | MACHINE.ID                 | LATTICE.CODE                      |
| ---------------------------- | --------------------- | -------------------------- | --------------------------------- |
| Sec 4 Mathematics Root       | EDUOS.MATH.SEC4.ROOT  | EDUOS.MATH.SEC4.REG.v1.0   | LAT.EDUOS.MATH.S4-S5.P2-P4.Z3.T12 |
| Sec 4 G1 Mathematics         | EDUOS.MATH.SEC4.G1    | EDUOS.MATH.SEC4.G1.v1.0    | LAT.EDUOS.MATH.S4.P1-P2.Z2-Z3.T12 |
| Sec 4 G2 Mathematics         | EDUOS.MATH.SEC4.G2    | EDUOS.MATH.SEC4.G2.v1.0    | LAT.EDUOS.MATH.S4.P2-P3.Z3.T12    |
| Sec 4 G3 Mathematics         | EDUOS.MATH.SEC4.G3    | EDUOS.MATH.SEC4.G3.v1.0    | LAT.EDUOS.MATH.S4.P3-P4.Z3.T12    |
| Sec 4 Additional Mathematics | EDUOS.MATH.SEC4.AMATH | EDUOS.MATH.SEC4.AMATH.v1.0 | LAT.EDUOS.MATH.S5.P3-P4.Z3.T12    |
## 3. Sec 4 Topic Nodes
| Topic Node             | EducationOS Function      | Failure Sensor                        | Repair Route                      |
| ---------------------- | ------------------------- | ------------------------------------- | --------------------------------- |
| Algebra Revision       | symbolic stability engine | sign, expansion, factorisation errors | algebra error ledger              |
| Quadratics / Functions | nonlinear function node   | wrong method selection                | graph-factor-formula bridge       |
| Coordinate Geometry    | spatial-algebra node      | gradient, distance, midpoint drift    | coordinate formula repair         |
| Trigonometry           | angle-ratio engine        | identity / angle / calculator errors  | triangle + unit-circle discipline |
| Mensuration            | formula-selection node    | area/volume/surface-area misuse       | shape-formula-unit ledger         |
| Vectors / Geometry     | direction-structure node  | weak representation                   | diagram-to-symbol bridge          |
| Statistics             | data interpretation node  | graph/table inference weakness        | data representation drills        |
| Probability            | uncertainty node          | event logic confusion                 | tree/table/set repair             |
| Real-World Problems    | modelling gate            | cannot translate context              | language-to-equation bridge       |
| Exam Paper Strategy    | compression-control node  | panic, time loss, careless errors     | paper route protocol              |
## 4. A-Math Sec 4 Layer
| A-Math Node               | EducationOS Function      | Failure Sensor                       | Repair Route              |
| ------------------------- | ------------------------- | ------------------------------------ | ------------------------- |
| Advanced Algebra          | high-load symbolic engine | manipulation collapse                | symbolic reconstruction   |
| Logarithms / Exponentials | growth-scale engine       | inverse relation confusion           | function-family repair    |
| Trigonometry              | transformation engine     | identity / equation failure          | identity movement drill   |
| Coordinate Geometry       | algebra-geometry bridge   | line/circle instability              | coordinate graph ledger   |
| Differentiation           | rate-of-change engine     | weak function foundation             | derivative meaning repair |
| Integration               | accumulation engine       | formula memorised but not understood | area-under-curve bridge   |
| Kinematics / Applications | modelling-transfer gate   | cannot map motion to calculus        | context-to-symbol repair  |
## 5. G1 / G2 / G3 EducationOS Meaning
| Level  | Sec 4 Corridor                 | Main Aim                                                   |
| ------ | ------------------------------ | ---------------------------------------------------------- |
| G1     | practical mathematics closure  | usable numeracy and technical/service pathway readiness    |
| G2     | exam competence closure        | stable post-secondary access and applied pathway readiness |
| G3     | distinction / transfer closure | JC, poly, IP, IB, STEM, and higher mathematics readiness   |
| A-Math | advanced transfer closure      | H2 Math / STEM / engineering / computing readiness         |
## 6. Sec 4 Failure Sensor Map

## 7. Sec 4 Repair Codes
| Repair Code                           | Use                                                    |
| ------------------------------------- | ------------------------------------------------------ |
| EDUOS.REPAIR.SEC4.FOUNDATION.DEBT     | when Sec 1-3 gaps still affect exam performance        |
| EDUOS.REPAIR.SEC4.ALGEBRA.ERRORLEDGER | when symbolic manipulation remains unstable            |
| EDUOS.REPAIR.SEC4.GRAPH.FUNCTION      | when graphs, functions, and equations are disconnected |
| EDUOS.REPAIR.SEC4.TRIG.STABILITY      | when trigonometry repeatedly fails                     |
| EDUOS.REPAIR.SEC4.STAT.PROB           | when statistics/probability marks are leaking          |
| EDUOS.REPAIR.SEC4.AMATH.CALCULUS      | when differentiation/integration overload appears      |
| EDUOS.REPAIR.SEC4.PAPER.STRATEGY      | when timing, question order, or paper management fails |
| EDUOS.REPAIR.SEC4.CARELESS.ERROR      | when repeated preventable errors occur                 |
| EDUOS.REPAIR.SEC4.POSTSEC.ROUTE       | when JC/poly/IP/IB/STEM route fit needs recalibration  |
## 8. Final Sec 4 EducationOS Code

PUBLIC.ID:
EDUOS.MATH.SECONDARY.AMATH.100NODE.REGISTRY.v1.0
MACHINE.ID:
EDUOS.SG.SECONDARY.MATH.AMATH.NODE.REGISTRY.100PLUS.v1.0
LATTICE.CODE:
LAT.EDUOS.MATH.S4-S5.P1-P4.Z2-Z3.T9-T12

SECONDARY.MATH.FAIL.SENSORS =
INTEGER.SIGN.ERROR
+ ALGEBRA.TRANSLATION.FAIL
+ EXPANSION.FACTORISATION.DRIFT
+ EQUATION.BALANCE.COLLAPSE
+ GRAPH.FUNCTION.DISCONNECT
+ GEOMETRY.REASON.WEAKNESS
+ TRIG.RATIO.CONFUSION
+ MENSURATION.FORMULA.ERROR
+ STATISTICS.INTERPRETATION.WEAKNESS
+ PROBABILITY.EVENT.ERROR
+ CALCULUS.MEANING.FAIL
+ EXAM.COMPRESSION.FAILURE

EDUOS.REPAIR.SEC.NUMBER
EDUOS.REPAIR.SEC.ALGEBRA
EDUOS.REPAIR.SEC.GRAPH.FUNCTION
EDUOS.REPAIR.SEC.GEOMETRY
EDUOS.REPAIR.SEC.TRIGONOMETRY
EDUOS.REPAIR.SEC.MENSURATION
EDUOS.REPAIR.SEC.STATISTICS
EDUOS.REPAIR.SEC.PROBABILITY
EDUOS.REPAIR.AMATH.ALGEBRA
EDUOS.REPAIR.AMATH.TRIG
EDUOS.REPAIR.AMATH.CALCULUS
EDUOS.REPAIR.SEC.EXAM.COMPRESSION

SECONDARY.AMATH.100NODE.EDUOS =
A full Secondary Mathematics and Additional Mathematics node registry
where every topic, representation, error pattern, paper behaviour,
and post-secondary route signal becomes visible.
Secondary Mathematics builds the exam-stable core.
Additional Mathematics tests whether the student can sustain
high-load symbolic reasoning, abstraction, modelling, and calculus
before JC, Poly, IB, engineering, computing, economics, finance,
or university STEM pathways.

PUBLIC.ID:
EDUOS.MATH.SEC.AMATH.QUESTIONTYPE.CROSSWALK.v1.0
MACHINE.ID:
EDUOS.SG.SEC.AMATH.QTYPE.PATTERNENGINE.v1.0
LATTICE.CODE:
LAT.EDUOS.MATH.S4-S5.P1-P4.Z2-Z3.T9-T12

SECONDARY / A-MATH QUESTION
→ TOPIC NODE
→ METHOD DEMAND
→ ABSTRACTION LOAD
→ FAILURE SIGNAL
→ PATTERN ID
→ REPAIR CODE
→ ROUTE STATUS

G1 stable
G2 competent
G3 distinction-ready
A-Math suitable
JC / Poly / IB / IGCSE ready
or still carrying foundation debt.

SEC.PATTERN.F01 = arithmetic / sign drift
SEC.PATTERN.F02 = algebra manipulation weakness
SEC.PATTERN.F03 = equation balance failure
SEC.PATTERN.F04 = formula substitution error
SEC.PATTERN.F05 = change-subject collapse
SEC.PATTERN.F06 = graph-equation mismatch
SEC.PATTERN.F07 = gradient/intercept confusion
SEC.PATTERN.F08 = geometry rule misread
SEC.PATTERN.F09 = trigonometry setup error
SEC.PATTERN.F10 = mensuration formula misuse
SEC.PATTERN.F11 = statistics/probability interpretation weakness
SEC.PATTERN.F12 = real-world modelling failure
SEC.PATTERN.F13 = multi-step route collapse
SEC.PATTERN.F14 = reasoning/communication weakness
SEC.PATTERN.F15 = exam timing compression failure

AMATH.PATTERN.F01 = symbolic overload
AMATH.PATTERN.F02 = factorisation / quadratic route failure
AMATH.PATTERN.F03 = function notation confusion
AMATH.PATTERN.F04 = log-exponential inverse confusion
AMATH.PATTERN.F05 = polynomial structure failure
AMATH.PATTERN.F06 = trigonometric identity misuse
AMATH.PATTERN.F07 = trigonometric equation route collapse
AMATH.PATTERN.F08 = coordinate geometry algebra drift
AMATH.PATTERN.F09 = differentiation meaning failure
AMATH.PATTERN.F10 = tangent/normal gradient mismatch
AMATH.PATTERN.F11 = maxima/minima interpretation failure
AMATH.PATTERN.F12 = integration as memorised formula only
AMATH.PATTERN.F13 = area-under-curve setup failure
AMATH.PATTERN.F14 = kinematics model-transfer failure
AMATH.PATTERN.F15 = mixed-topic overload under exam pressure

INPUT:
Secondary Math / A-Math question attempted by student
SENSOR:
question type + topic + method used + error pattern + exam behaviour
ENGINE:
match error to SEC.PATTERN or AMATH.PATTERN
OUTPUT:
repair code + next drill + route status

SEC.AMATH.QTYPE.PATTERNENGINE =
A diagnostic engine that reads Secondary Mathematics and Additional Mathematics
questions as sensors for algebra control, graph transfer, geometry reasoning,
modelling ability, symbolic load, calculus readiness, exam pressure, and
post-secondary route viability.

Secondary Mathematics detects:
Can the student operate the core mathematics system?
Additional Mathematics detects:
Can the student sustain high-symbolic-load mathematics without collapse?

JC Mathematics sits at the **pre-university compression layer**. MOE’s pre-university mathematics family includes **H1 Mathematics, H2 Mathematics, H2 Further Mathematics, and H3 Mathematics**, while SEAB lists the 2026 A-Level Mathematics syllabuses for H1, H2, and H3 examination levels. ([Ministry of Education][1])
## 1. JC Mathematics Core Reading

## 2. JC Math EducationOS Registry
| Layer                  | PUBLIC.ID              | MACHINE.ID                  | LATTICE.CODE                           |
| ---------------------- | ---------------------- | --------------------------- | -------------------------------------- |
| JC Mathematics Root    | EDUOS.MATH.JC.ROOT     | EDUOS.MATH.JC.REG.v1.0      | LAT.EDUOS.MATH.S10.P3-P5.Z3-Z4.T13-T14 |
| H1 Mathematics         | EDUOS.MATH.JC.H1       | EDUOS.MATH.JC.H1.v1.0       | LAT.EDUOS.MATH.S10.P2-P3.Z3.T13-T14    |
| H2 Mathematics         | EDUOS.MATH.JC.H2       | EDUOS.MATH.JC.H2.v1.0       | LAT.EDUOS.MATH.S10.P3-P4.Z3-Z4.T13-T14 |
| H2 Further Mathematics | EDUOS.MATH.JC.H2.FMATH | EDUOS.MATH.JC.H2.FMATH.v1.0 | LAT.EDUOS.MATH.S10.P4-P5.Z4.T13-T14    |
| H3 Mathematics         | EDUOS.MATH.JC.H3       | EDUOS.MATH.JC.H3.v1.0       | LAT.EDUOS.MATH.S10.P4-P5.Z4.T14        |
## 3. H1 / H2 / H3 EducationOS Meaning
| JC Level               | EducationOS Corridor                | Main Function                                                                                    |
| ---------------------- | ----------------------------------- | ------------------------------------------------------------------------------------------------ |
| H1 Mathematics         | quantitative literacy corridor      | supports business, social sciences, economics, statistics, and general university numeracy       |
| H2 Mathematics         | university STEM gateway             | supports science, engineering, computing, mathematics, economics, and quantitative degrees       |
| H2 Further Mathematics | advanced mathematical load corridor | supports students needing deeper mathematical exposure before university                         |
| H3 Mathematics         | frontier / proof corridor           | supports students with strong passion and ability who can handle challenging problems and proofs |
The H1 syllabus is designed to support students in business or social science studies and is especially suitable for students without an Additional Mathematics background; H2 prepares students for university courses needing a strong mathematics foundation; H3 targets students with passion and ability in mathematics and includes more challenging problem solving and proof. ([Ministry of Education][1])
## 4. JC Topic Nodes
| Topic Node             | EducationOS Function                 | Failure Sensor                                 | Repair Route                  |
| ---------------------- | ------------------------------------ | ---------------------------------------------- | ----------------------------- |
| Functions and Graphs   | relationship / transformation engine | cannot connect equation, graph, domain, range  | function-family repair        |
| Calculus               | change-rate and accumulation engine  | derivative/integral as memorised formulas only | meaning-first calculus repair |
| Sequences and Series   | pattern-limit engine                 | weak sigma / convergence handling              | term-to-sum bridge            |
| Vectors                | spatial-direction engine             | poor 2D/3D representation                      | diagram-to-symbol repair      |
| Complex Numbers        | extended-number system               | Argand / polar form confusion                  | representation bridge         |
| Differential Equations | dynamic-system modelling             | cannot connect rate statement to equation      | context-to-DE route           |
| Probability            | uncertainty engine                   | event logic failure                            | tree/table/set repair         |
| Statistics             | inference engine                     | sampling / distribution / hypothesis confusion | data-to-decision repair       |
| Hypothesis Testing     | evidence gate                        | wrong test / wrong conclusion                  | claim-evidence protocol       |
| Graphing Calculator    | tool discipline                      | blind calculator use / wrong mode              | GC ledger protocol            |
| Modelling              | world-to-symbol transfer             | cannot translate real situation                | language-to-math bridge       |
| Proof / Reasoning      | validity layer                       | answer without justification                   | reasoning ledger repair       |
## 5. JC Failure Sensor Map

## 6. JC Repair Codes
| Repair Code                      | Use                                                                    |
| -------------------------------- | ---------------------------------------------------------------------- |
| EDUOS.REPAIR.JC.AMATH.DEBT       | when Sec 3–4 A-Math foundation is weak                                 |
| EDUOS.REPAIR.JC.FUNCTIONS.GRAPHS | when functions, transformations, domain/range, and graphs are unstable |
| EDUOS.REPAIR.JC.CALCULUS.MEANING | when differentiation/integration are procedural but not understood     |
| EDUOS.REPAIR.JC.VECTORS.SPATIAL  | when vector geometry and 3D reasoning fail                             |
| EDUOS.REPAIR.JC.STAT.PROB        | when statistics/probability questions are unstable                     |
| EDUOS.REPAIR.JC.HYPOTHESIS.TEST  | when test selection or conclusion wording fails                        |
| EDUOS.REPAIR.JC.GC.DISCIPLINE    | when graphing calculator use creates false confidence                  |
| EDUOS.REPAIR.JC.PROOF.REASONING  | when mathematical justification is weak                                |
| EDUOS.REPAIR.JC.UNI.ROUTE        | when university-course mathematics fit needs recalibration             |
## 7. Final JC EducationOS Code

PUBLIC.ID:
EDUOS.MATH.JC.100NODE.REGISTRY.v1.0
MACHINE.ID:
EDUOS.SG.JC.MATH.NODE.REGISTRY.100PLUS.v1.0
LATTICE.CODE:
LAT.EDUOS.MATH.S10.P3-P5.Z3-Z4.T13-T14

H1 = quantitative literacy / applied statistics corridor
H2 = university STEM gateway corridor
H3 = proof, abstraction, and frontier-readiness corridor

JC.MATH.FAIL.SENSORS =
FUNCTION.DOMAIN.DRIFT
+ GRAPH.TRANSFORMATION.ERROR
+ ALGEBRA.STAMINA.COLLAPSE
+ CALCULUS.MEANING.FAIL
+ INTEGRATION.ROUTE.FAIL
+ VECTOR.SPATIAL.DISCONNECT
+ COMPLEX.NUMBER.MISREAD
+ PROBABILITY.CONDITIONING.ERROR
+ DISTRIBUTION.SELECTION.ERROR
+ HYPOTHESIS.TESTING.CONFUSION
+ GC.OVERRELIANCE
+ LONG.QUESTION.COMPRESSION.FAILURE
+ PROOF.CONSTRUCTION.WEAKNESS

EDUOS.REPAIR.JC.FUNCTIONS
EDUOS.REPAIR.JC.ALGEBRA
EDUOS.REPAIR.JC.CALCULUS
EDUOS.REPAIR.JC.VECTORS
EDUOS.REPAIR.JC.COMPLEX
EDUOS.REPAIR.JC.STATISTICS
EDUOS.REPAIR.JC.PROBABILITY
EDUOS.REPAIR.JC.HYPOTHESIS.TESTING
EDUOS.REPAIR.JC.GC.DISCIPLINE
EDUOS.REPAIR.JC.H3.PROOF
EDUOS.REPAIR.JC.EXAM.COMPRESSION

JC.MATH.100NODE.EDUOS =
A full Junior College Mathematics node registry where H1, H2, and H3
Mathematics are encoded as capability corridors.
H1 Mathematics = quantitative literacy and statistics corridor.
H2 Mathematics = university STEM and advanced modelling gateway.
H3 Mathematics = proof, abstraction, and frontier-readiness corridor.
JC Mathematics is where Secondary and Additional Mathematics stop being
only exam subjects and become a route test for university, engineering,
computing, data science, economics, finance, and research capability.

PUBLIC.ID:
EDUOS.MATH.JC.QUESTIONTYPE.CROSSWALK.v1.0
MACHINE.ID:
EDUOS.SG.JC.MATH.QTYPE.PATTERNENGINE.v1.0
LATTICE.CODE:
LAT.EDUOS.MATH.S10.P3-P5.Z3-Z4.T13-T14

JC MATH QUESTION
→ H1 / H2 / H3 LEVEL
→ TOPIC NODE
→ ABSTRACTION LOAD
→ GRAPHING CALCULATOR / FORMULA USE
→ FAILURE SIGNAL
→ PATTERN ID
→ REPAIR CODE
→ UNIVERSITY ROUTE STATUS

H1 = quantitative literacy and applied reasoning
H2 = STEM-gateway abstraction and compression
H3 = proof, structure, extension, and frontier readiness

JC.PATTERN.F01 = function-domain/range confusion
JC.PATTERN.F02 = graph-transformation misread
JC.PATTERN.F03 = calculus meaning failure
JC.PATTERN.F04 = differentiation/integration technique drift
JC.PATTERN.F05 = vector representation failure
JC.PATTERN.F06 = complex-number structure confusion
JC.PATTERN.F07 = sequence/series convergence weakness
JC.PATTERN.F08 = differential-equation modelling failure
JC.PATTERN.F09 = probability condition/event confusion
JC.PATTERN.F10 = random-variable/distribution mismatch
JC.PATTERN.F11 = hypothesis-test setup failure
JC.PATTERN.F12 = regression/correlation interpretation error
JC.PATTERN.F13 = graphing-calculator overdependence
JC.PATTERN.F14 = multi-topic synthesis collapse
JC.PATTERN.F15 = proof/communication weakness

INPUT:
JC H1 / H2 / H3 Mathematics question attempted by student
SENSOR:
level + topic + method + abstraction load + GC/formula use + error pattern
ENGINE:
match to JC.PATTERN ID
OUTPUT:
repair code + next drill + university-route status

JC.MATH.QTYPE.PATTERNENGINE =
A diagnostic engine that reads H1, H2, H3 and Further Mathematics questions
as sensors for abstraction load, calculus control, statistical decision-making,
symbolic transfer, proof readiness, graphing-calculator discipline, and
university-route viability.

H1 Mathematics detects:
Can the student use mathematics for quantitative reasoning and applied decisions?
H2 Mathematics detects:
Can the student sustain university-gateway mathematics for STEM, computing,
economics, engineering, science, and quantitative fields?
H3 Mathematics detects:
Can the student reason near the frontier with proof, structure, extension,
and high-abstraction mathematical discipline?