Our Core Algorithms

Standard Prep is built on a solid foundation of proven educational theories combined with modern GenAI. Here is an inside look at the algorithms powering your learning journey.

1. IRT (Item Response Theory)

Instead of just counting how many questions you got right, we use IRT to evaluate your latent ability (Theta $\theta$).

• When you answer a difficult question correctly, your score increases more than if you answered an easy one.
• We use this dynamic rating to rank your percentile globally and to serve as the engine for our adaptive Smart Practice.

2. CDM (Cognitive Diagnosis Models) & BKT

Standard Prep builds a Directed Acyclic Graph (DAG) of all exam skills (e.g., Vocabulary $\rightarrow$ Complex Sentences $\rightarrow$ Main Idea Inference). Using Bayesian Knowledge Tracing (BKT), we distribute the “credit” or “blame” for your answers.

1. You get an “Inference” question wrong. 2. The engine looks at your skill profile. If your Vocabulary skill is historically 90%, but your Logic skill is 30%, the algorithm assigns the failure to Logic. 3. The system dynamically updates the DAG, slightly dropping your Logic score and propagating this data up and down the skill tree.

3. FSRS (Free Spaced Repetition Scheduler)

Traditional spaced repetition (like SM-2 used in early Anki) is outdated. We utilize FSRS, a modern, data-driven spaced repetition algorithm. Whether it’s a new vocabulary word, a grammatical mistake, or a poorly structured sentence in your writing, the system automatically creates a flashcard and schedules it for review precisely when you are about to forget it.