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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Exam board defends convoluted and labyrinthine Maths exam questions

A Qualifications Scotland spokesperson has defended a controversial Higher Maths paper after pupils said that it was "unrecognisable" from the paper they had prepared for in class. The pupils said that the wording of the questions was so confusing that they did not know what was being asked.

Sir Humphrey responded: " A constriction of the channels of communication, that culminated in a condition of organisational atrophy and administrative paralysis may have lead to the mix-up.  Whilst we accept that there is a real dilemma here, in that, while it has been exam board policy to regard the responsibility of teachers and adjudicators as a responsibility of the Exam board, the question of questions policy can cause confusion between the policy of questions and the question of policy, especially when responsibility for the administration of the policy of questions conflicts, or overlaps with, responsibility for the question of the administration of questions. I hope that clears things up".

He added. "Please put you pens down and turn over your papers. Application forms for jobs at McDonalds are available as you leave".

Image credit: Wix AI (edited)

American Pi

'If those goddamn interfering Euroland bureaucrat busybodies can change the inch to 25.4mm exactly, just to make their sums a bit easier, then we in the free world - i.e., not in the republic of Eurolandshire - can do the same.

'As from tomorrow, Pi in America will be 3.142 - precisely.  No ifs, no buts.  No more of this never-ending number of decimal places or 'irrational number' bollosck.  Irrational numbers are just that - irrational. Which means 'lacking usual or normal mental clarity or coherence' and 'not endowed with reason or understanding'.  We're going to fix that.

'The next thing we'll sort out is Plank's constant.  At 6.62607015 × 10-34 m2 kg / s, it's so small, it's not worth bothering with, and anyway it's metric, so it's got to be rubbish.  So we'll just abolish it, and save a ton of money.  No, not a tonne, just a good, straight ton.  Of US dollars, obviously.

'But e is a bit bigger - a more sensible size.  It just needs tidying up a bit.  2.718 should work just fine.  (Who the Hell is Euler?  Another goddamn foreigner from Europland?  You might want e to have a different value, but that's just Europinion.  We in America believe in democracy, i.e., doing whatever democratically-elected I - decide.)

'But the biggest and greatest, of course, will be the Golden Ratio, which I have decided will bea nice, round 1.6180 exactly.  Well, until I change my mind again.

Picture credit: Wix AI