As Large Language Models (LLMs) are increasingly integrated into educational settings, understanding their potential biases is critical. This study examines sociodemographic biases in LLM-based educational counselling. We evaluate responses from six LLMs answering questions about 900 vignettes describing students in diverse circumstances. Each vignette is systematically tested across 14 sociodemographic identifiers - spanning race and gender, socioeconomic status, and immigrant background - along with a control condition, yielding 243,000 model responses. Our findings indicate that (1) all models exhibit measurable biases, (2) bias patterns partially align with documented human biases but diverge in notable ways, (3) the magnitude of these biases is strongly influenced by the precision of the student descriptions, where vague or minimal information amplifies disparities nearly threefold, while concrete, individualised metrics substantially reduce them, and (4) bias profiles vary substantially across models. These results demonstrate the importance of context-rich and personalised educational representations, suggesting that AI-driven educational decisions benefit from detailed student-specific information to promote fairness and equity.