Police have been called in to investigate another exam leak after an unknown number of students had advance sight of part of a GCSE religious studies (RS) paper last month.

It is the latest of a series of damaging security breaches to hit summer exams in recent years, with social media enabling cheats to disseminate leaked questions quickly and easily.

Such is the level of concern that a review of exam malpractice is under way, which is due to report later this summer. Hoaxes about leaked exam papers, again shared widely online, have compounded students’ stress and anxiety.

The latest security breach involved an AQA GCSE RS paper sat by thousands of pupils on 20 May. One parent told the Guardian a number of students went home and said an element of the paper had been circulating on Snapchat ahead of the exam.

AQA confirmed that police had been contacted and an investigation was under way. The exam board said only one page was affected. The “lack of online conversations about this issue suggests that it may not have been widely shared”, it said.

In a separate incident, an Edexcel A-level further maths exam had to be withdrawn and replaced last week because of concerns about a possible security breach. The move was linked to a leak this month when another A-level maths paper was offered for sale via social media. Two questions from the paper first appeared on Twitter, offering students the whole paper for £70.

The rules governing exam security are detailed and rigorous. Papers are kept in sealed packets and delivered by courier to exam centres where they have to be signed for, with the date and time of receipt recorded. They then have to be immediately locked in a secure room solely assigned to exams, ideally without windows and on an upper floor.

The use of smartphones and social media has changed the landscape for both cheats and regulators. One deputy headteacher, who asked to remain anonymous, said: “We are running a 20th century-style paper-based examination system in a 21st-century world. We generally have confidence in the system, but these reported security breaches clearly knock that confidence.”

Exam boards have taken measures to try to keep up with the cheats. Pearson, which owns Edexcel, said in April that it was piloting a scheme in which exam papers are microchipped to track the date, time and location of each bundle. AQA says it has a dedicated team using “state-of-the-art” online monitoring systems.

“We’ve substantially increased our online monitoring this year and introduced new ways of dealing with social media posts claiming to offer exam questions,” the board said. “We have tried-and-tested plans in place to make sure no one gets away with cheating – including advanced statistical monitoring during the marking process.”

After the latest incident, a headteacher in Gloucestershire wrote to parents saying the potential leak had been reported at a number of schools and was under investigation. “We have been assured by the board that as our students are not involved in sourcing or releasing the material there will be no consequences for them.”

One parent whose child sat the affected exam said: “There was this photo of a paper doing the rounds on Snapchat. Nobody at my child’s school was responsible for the leak, but it was going between schools. That’s the thing with social media. The spread is almost immediate. As soon as somebody knows something secret, it spreads like wildfire.”

Louisa Fyans, AQA’s head of exams integrity and inspection, said: “We were extremely disappointed to discover that some students were able to see a page from a GCSE religious studies paper before the exam. We contacted the police straight away and we’ve been doing our own investigation too.”

Fyans reassured students that action was being taken to ensure no one would benefit from the leak. “We realise students might be concerned, but we’d like to reassure them that there are lots of things we can do to make sure no one gets away with cheating, such as monitoring for students with inconsistent marks for this page.”

Pupils and their parents, however, remain anxious. “My daughter felt cheated,” said the parent previously quoted. “She’s predicted the top grade. She’s a conscientious student. If everyone else sitting the paper has seen some of the questions, they are at an unfair advantage. It undermines confidence in the system and it undermines results.”

The exams regulator Ofqual said it was monitoring AQA’s response to the RS exam leak and the measures it takes to ensure no student is advantaged. The watchdog reported 68 exam security breaches last summer, 59% of which involved papers being incorrectly opened or handed out by centres.

“We take the integrity of exams very seriously,” a spokesperson said. “Any leak is completely unacceptable and causes unnecessary distress to students. Exam delivery relies on the integrity of everyone involved and malpractice is rare in a system of this size, involving around 2,000 exam papers each year.

“When this exam series has finished, we will review and report on how the series has gone and consider what more the system needs to do to counter threats to its integrity.

The Joint Council for Qualifications (JCQ), which represents the seven largest qualification providers in the UK, commissioned an independent report into exam malpractice last year following a number of concerning incidents. The chair of the commission, Sir John Dunford, is due to report later this summer.

Pearson was forced to make changes to statistics and further pure maths A-level papers in 2017 after reports that some students had seen questions in advance, police investigations were launched into suspected leaks involving Edexcel’s A-level maths papers in 2017 and 2018. Twenty-nine candidates had their results annulled. The criminal investigation into the 2017 case continues, with details forwarded to prosecutors by the police last April.

Commenting on this year’s leaks, a JCQ spokesperson said: “All evidence suggests that relatively few students have seen these questions and that these breaches of security are limited. The exam boards have rigorous procedures, including the digital marking and tracking of papers, to ensure the security of their materials and continually keep these under review.”