Previous research leveraged Large Language Models (LLMs) in numerous ways in the educational domain. Here, we show that they can be used to answer exam questions simulating students of different skill levels and share a prompt, engineered for GPT-3.5, that enables the simulation of varying student skill levels on questions from different educational domains. We evaluate the proposed prompt on three publicly available datasets (one from science exams and two from English reading comprehension exams) and three LLMs (two versions of GPT-3.5 and one of GPT-4), and show that it is robust to different educational domains and capable of generalising to data unseen during the prompt engineering phase. We also show that, being engineered for a specific version of GPT-3.5, the prompt does not generalise well to different LLMs, stressing the need for prompt engineering for each model in practical applications. Lastly, we find that there is not a direct correlation between the quality of the rationales obtained with chain-of-thought prompting and the accuracy in the student simulation task.