RoMathExam

RoMathExam: A Longitudinal Dataset of Romanian High-School Math Exams (1895–2025) Overview RoMathExam is a longitudinal dataset of Romanian high-school mathematics examinations designed to support research on assessment analytics, curriculum evolution, and educational retrieval. The dataset contains 10,592 distinct problems organized into 600+ complete exam sets across multiple tracks (M1–M4), spanning 1895–2025 with a robust standardized core from 1957 onwards. It unifies official exam sessions and ministry-published training variants under a single schema, enriched with curriculum-aligned topic tags, vectorial embeddings, and solution complexity metrics. File Structure The dataset is distributed in two formats to accommodate different use cases: 1. RoMathExam.json (Base Dataset) Lightweight version containing the raw problem text, metadata, and curriculum tags. Ideal for NLP analysis, curriculum tracking, and basic training. 2. RoMathExam_Enriched.json (Enriched Dataset) A heavier version intended for RAG (Retrieval-Augmented Generation) and difficulty modeling. It includes 1536-dimensional embeddings for every problem and synthetic solutions generated by three frontier reasoning models. Data Schema Base Object (RoMathExam.json) interface Problem { /** The problem statement text (Markdown/LaTeX) */ cerinta: string; /** The grading key/solution text (Markdown/LaTeX). Null if unavailable. */ barem: string | null; /** Array of curriculum-aligned topic tags */ tags: string[]; /** The year the exam took place */ an: number; /** The examination session type */ sesiune: "generală" | "toamnă" | "vară" | "specială" | "simulare" | "model" | "antrenament" | null; /** The difficulty track (normalized) */ profil: "M1" | "M2" | "M3" | "M4" | null; } Enriched Object (RoMathExam_Enriched.json) interface EnrichedProblem { /** The base problem object described above */ problem: Problem; /** 1536-dimensional vector (OpenAI text-embedding-3-small) */ embedding: number[]; /** Synthetic solutions and complexity metrics from reasoning models */ solutions: { [modelName in "openai/gpt-5-mini" | "deepseek-ai/DeepSeek-R1-0528-tput" | "Qwen/Qwen3-235B-A22B-Thinking-2507"]: { /** The full Chain-of-Thought solution generated by the model */ response: string; usage: { inputTokens: number; /** Used as a proxy for solution complexity/difficulty */ outputTokens: number; }; }; }; } Metadata Definitions & Caveats 1. Tracks (Profil) To ensure longitudinal consistency, historical track designations have been mapped to the modern M1-M4 system: M1 (Matematică-Informatică): Includes modern M1, historical "Real", and intensive math variants. M2 (Științe ale Naturii): Includes modern M2, historical "Uman", and general science variants. M3 (Tehnologic) M4 (Pedagogic) 2. Session Types Generală/Vară: The standard summer session taken by the majority of students. Toamnă: The retake session. Specială: An early session specifically for students participating in International Olympiads (who cannot attend the summer session). Simulare: National diagnostic simulations held in Spring. Model: Official practice models released by the Ministry. Antrenament: A specific set of training variants released heavily during 2020-2021. 3. The "Rezervă" (Reserve) Subjects For M1 exams after 2010, the "Reserve" subjects (backup exams created but not always used) are included in the dataset. Currently, there is no explicit metadata flag to distinguish them. In any given year/session, the first 10 problems in the JSON stream are typically from the official exam variant, while the subsequent 10 problems are from the reserve variant. Taxonomy (Tags) The dataset uses a granular taxonomy of 70 tags to capture specific mathematical concepts. Algebra & Numbers Geometry & Trig Analysis progresii aritmetice distanța dintre 2 puncte limite (calcul de limite) progresii geometrice calcule trigonometrice asimptote numere complexe linii importante în forme geometrice continuitate calcule cu numere reale vectori derivabilitate ecuații exponențiale ecuația dreptei calcul de derivate ecuații logaritmice aria unei forme geometrice puncte de extrem metode de numărare cercuri puncte de inflexiune probabilități ecuații trigonometrice convexitate calcule cu permutări perimetrul unei forme geometrice ecuația tangentei binomul lui Newton măsura unui unghi funcția de gradul I matrice (operații, rang, inv.) demonstrarea unor relații geometrice funcția de gradul al II-lea determinanți geometrie în spațiu proprietățile funcțiilor sisteme de ecuații liniare curbe monotonie polinoame (calc., diviz., răd.) elipse/hiperbole reprezentarea grafică relațiile lui Viete proprietățile primitivelor legi de compoziție calcul de integrale/primitive grupuri/inele/corpuri aria suprafeței plane morfisme volumul generat prin rotire clase de resturi ecuații/inecuații cu funcții matematici financiare ecuații cu integrale/șiruri ecuații cu radicali proprietățile șirurilor Dataset Creation & Provenance Source: Official documents from the Romanian Ministry of Education and historical archives curated by the Romanian mathematics community (e.g., Sorin Borodi, Pro-Matematica). Processing: Documents were digitized using Mathpix OCR, parsed using GPT-5-mini for structural segmentation, and tagged using Gemini 3.0 Flash. Quality Control: Validated by a team of 20 senior high-school students (M1 track) and domain experts.