A level Mathematics paper leaked on line

June 2026, Queston 1

The probability that the government retrospectively changes the student loan scheme in a way unfavourable to students is determined, from historic data, to be p=0.2 in any given year.

The probability of an unfavourable change in any year is independent from all previous years.

A newly qualified student has 40 years to repay their student loan before it is written off.

Calculate:

(a) The expected number of unfavourable changes to student loan repayment terms in the next 40 years. Show your workings . Expletives should be written in pencil and crossed through. [ 4 marks ]

(b) The probability that students will vote for any of the political parties involved in stitching them up. [ 1 mark ]

(c) The probability that graduates will avoid promotions or reduce their working hours or go sick and claim benefits in order to reduce or avoid their student loan repayments [ 1 mark ]

(d) Companies employing new graduates have not been offering to repay student debt. What is the probability that this situation will improve in the next 3 years? Explain your answer. [ 2 marks ]

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Royal Family to be turned into Data Centres

In a bold move to modernise the Royal Family, plans have been drawn up to turn the entire institution into a data centre.

'It was either this or turn them into Turkey Twizzlers', a spokesman said. 'And the hygiene people put their foot down.

Princesses Eugenie and Beatrice will make a unique contribution - the heatsink design for the microprocessors will be based on their trademark 'fascinators'. They will not be forgotten, sadly.

Regular Royal duties - waving, opening things, making small talk - will all be done by AI, enabling the whole venture to break even in its first week of operation. Graphs have been drawn. To be fair, they were done by AI so might be total fantasy, but it isn't as if the whole Royalty thing was overly committed to grim reality.

Andrew Mountbatten will play a unique part - in the foundations of Buck House Data Centre, a new central London facility which will be owned by some of the people he used to party with.

Balmoral, Sandringham and vast swathes of British countryside will be covered in computer warehouses so that students will no longer need to write their own essays. It's all fairly asinine, but still slightly less daft than having an actual Royal Family.

Image: WixAI

Academy schools sponsored by Organised Crime groups

The Department for Education has discovered that at least six Academy schools are sponsored by companies that are believed to be fronts for organised crime gangs.

Supply teachers and ‘careers advisors’ single out vulnerable students for work experience in illegal gambling, gun running, drug distribution and prostitution.  Students who do well are rewarded with doubles who take their exams for them, and may finish school with better qualifications than their peers – on paper at least.  Exceptional students may also have their driving tests taken for them, and in some cases get to go on all-expenses-paid school trips to Colombia or Mexico.

‘Our suspicions were aroused by some excellent academic achievements at Academy schools in deprived areas,’ said a spokesman, who wanted to remain anonymous. 'And these schools also had excellent results in getting students into jobs.

‘We had asked our experts were looking for examples of high performing schools, so that they could identify best practice and share it with other schools.  Unfortunately, one after another, these experts disappeared and have not been heard of since.  We are particularly concerned about one professional who was reviewing some excellent performance in Building and Construction exams.  When we tried to track him down, the school told us that there was no concrete evidence that he’d been abducted. and that our fears were ‘without foundation’.

The Department is currently considering whether to close down the schools that are involved, or – given the excellent exam results– to roll out the model more widely.

image from Google Gemini