Their answers were fed into the Jiig-Cal computer, which filled an entire building at Edinburgh University and promised to reveal their ideal job.
The arrival of the Jiig-Cal results was met with hysterical excitement in classrooms across the country.
Many children had their dreams of Hollywood or football stardom shattered as the computer predicted they would become wig makers or lighthouse keepers.
But the questionnaire - and the often bizarre career suggestions it produced - remains one of the defining childhood memories for most of the estimated four million pupils across Scotland, England and Wales who completed it.
Now a BBC Radio Scotland documentary is to transport listeners back to the early 1980s, when today's generation of tech-savvy 30-somethings were still in short trousers, and computers were something most had only seen in science fiction movies.
The Jiig-Cal system - an acronym of Job Ideas and Information Generator Computer Assisted Learning - was the brainchild of Jim Closs, an occupational psychologist teaching in the business studies department of Edinburgh University.
[The computer] had a whole building to itself and a team of specially trained computer operators to work it
Jim Closs Jiig-Cal developer
Mr Closs, an enthusiastic pioneer of early computer technology, believed he could harness its fledgling power to improve the careers advice pupils were given at school.
In those days, the sum total of pupil's career guidance was a 30-minute chat with a careers officer shortly before they left school, much of which was spent by the officer gently attempting to persuade the youngster that their dreams of becoming an astronaut or model were perhaps a little fanciful.
Mr Closs recalled: "This of course was a big disappointment to the pupil and it didn't leave much time for the careers officers to get down to what would really suit the student.
"What needed to be done was for the schools to do some work on helping the kids to begin thinking on what was going to happen after they left school, so when the careers advisor came in there was a basis there already."
Mr Closs spent several years in the mid-1970s perfecting his system before unleashing it on the nation's youth, who were immediately awe struck at the thought of a supercomputer that could predict their futures.
The first pupils to undergo the test found themselves confronted by a pencil and an A4 sheet of multiple choice questions, which asked them about their aptitudes, interests, likes and dislikes.
They were quizzed on how much they enjoyed working outdoors, if they minded being very hot or very cold, and whether they liked children, animals and getting dirty.
Their response sheets were carefully sealed and delivered by van to the university, where they were fed into the computer through an optical reader which could determine where they had placed their pencil marks.
The computer would then churn away and do all the matching operations between the pupil's answers and its database of potential jobs before producing its results on green and white lined dot-matrix computer paper.
The early 1980s was a pioneering time for the computer industry
"The computer was very large, a huge great beast in fact - this was the days of mainframe technology, not the kind of desktop microcomputer that everybody is familiar with now," Mr Closs said.
"It had a whole building to itself which was air-conditioned and it had a team of specially trained computer operators to work it."
The results were not returned to the school for several weeks, leading to teachers the length and breadth of the country being pestered by pupils anxious to learn what awaited them in their adult lives.
But while many ripped open the sealed envelope to discover they were to become doctors, lawyers or scientists, others were not quite so lucky.
For those unfortunate children, the mythical computer foretold a future of pig farming, funeral directing or wig making - jobs which no self-respecting 13-year-old would ever consider.
Mr Closs admitted: "Sometimes pupils would react quite negatively to jobs of that kind being suggested to them, but one of the principles of careers guidance is to broaden the pupil's horizons by putting before them ideas that they would never otherwise have considered.
"I am sure we had some pupils who were offended when they got funeral director on their printouts, but are now actually practising funeral directors."
He revealed that his own daughter went on to become a teacher, which was one of the options Jiig-Cal had presented to her, while a study later found 70% of pupils went into jobs suggested for them by the computer.
The Computer That Predicted the Future will be broadcast on Radio Scotland at 1130 BST on Friday.
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