The man, who is thought to be an asylum seeker from Iran, reportedly lied about his age in order to gain GCSE qualifications.
It is thought the Year 11 pupil is an asylum seeker who joined Stoke High School in September this year.
One student at the school shared a photograph of him on Snapchat, commenting: "How's there a 30 year old man in our maths class."
A spokesperson for the school said: "This is a matter for the Home Office and we have referred it to them.
"We cannot comment further on an individual case but we have followed government and local authority policies and guidance, as we do for any admissions matter."
A Home Office spokesperson said: "We do not routinely comment on individual cases."
If there is a doubt about someone's age as part of an immigration case, the Home Office can arrange for social workers to undertake an age assessment.
The claimant must be treated as an adult if their physical appearance and demeanour "very strongly suggests that they are significantly over 18 years of age".
Assessments of physical appearance can include indicators of age such as height, build, facial hair and voice pitch when there is no reliable documentary evidence to support the claimed age.
Officials can also take into account observations on the individual's mannerisms, body posture and eye contact.
Age verification processes came under scrutiny in 2016 when teenagers were transferred to the UK from Calais after the closure of the "Jungle" refugee camp.
Conservative MP David Davis sparked controversy when he claimed some of the arrivals "don't look like children to me".