Teacher shares GCSE maths question many 16-year-olds get wrong
Most of the things you learned in school will be forgotten once you enter the world of work. Very few jobs nowadays require detailed knowledge of Tudor history or the structure of a frog’s eye.
Maths is a special case, though. Many things we do at home – such as cookery or DIY – require at least a basic grasp of mathematics. Even though nearly all of us carry a potent little computer in our pockets, we still need to know what questions to ask it.
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It's when we have to do maths in exam-room conditions, without any technological help, that errors can so easily slip through. Secondary school maths teacher Natasha Hall has shared this classic example of a puzzle that is straightforward enough to solve – yet incredibly easy to get wrong if you misread it.
The past AQA exam paper question reads: "A bag contains 72 blue beads and some red beads. Blue beads : red beads = 4:5. Work out the number of red beads."
The student is being asked to use the ratio of blue to red beads to determine precisely how many red beads are in the bag. When you're under pressure and working against the clock, however, it's all too easy to get it wrong.
Natasha explains: "Most people read this as meaning that there are 72 beads and so they add up the two ratios and divide 72 by 9 (4 + 5). 72 divides by 9 to give 8 and then 8 × 5 (number of red beads) = 40.
However, if you re-read the question it says there are 72 BLUE beads. So the correct method is to divide 72 by 4 (number of blue beads) to get 18 and then multiply 18 × 5 to get the correct answer, 90."
There is nothing inherently wrong with the question itself, though it is straightforward to misread. On occasion, however, the error lies within the paper.
In June this year, an exam board issued an apology after discovering mistakes in "all versions" of a GCSE science paper. Tes magazine, the publication for teachers and school leaders formerly known as the Times Educational Supplement, reported that England's largest exam board, AQA, apologised for the blunder and was compelled to flag the error to exams regulator Ofqual.
Michael Turner, the exam board's chief commercial officer, stressed that AQA "has processes in place to make sure that no learners are disadvantaged by it".
He stated in an email sent to exams officers: "We're sorry to let you know that there was a mistake on all versions of the GCSE Combined Science Trilogy higher paper 2, which students sat on Monday 15 June 2026."
Within one of the paper's questions, students were instructed to "calculate the mass of a system", but the answer prompt stated "mass of glider" – which would only make up a portion of the system.
It marked the second such mistake in just over a week. Pupils taking a foundation-tier GCSE maths paper earlier that month opened their sealed examination papers only to find an insert containing information meant for a different paper.
One teacher told Tes that schools had received no communication from AQA regarding the incorrect inserts, stating: "In this series of exams we've had two erratum notices for minor typos (geography and physics) but nothing at all for this. Schools only found out via text and email from colleagues working elsewhere.
"Exams officers downloaded new inserts and rushed to print them. Some disruption to smooth starts, but exams started within the rules - still nothing from AQA now."