The gap between disadvantaged youngsters and the better-off in both maths and science stands at 31 months.
The Sutton Trust study also shows in reading in they are 26 months of schooling behind.
It also suggested performance by even the ablest students is declining with a slump in maths skills since 2009.
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New research reveals poor Scottish teens are falling behind their richer classmates
First Minister Nicola Sturgeon has repeatedly staked her personal reputation on improving the education system and closing the attainment gap between the richest and poorest pupils.
The SNP government should be ashamed of these figures
Iain Gray, Scottish Labour
Last year it emerged Scotland was trailing behind other parts of the UK and former Eastern Bloc nations in maths, reading and science.
Schools recorded their worst-ever performance in the latest Programme for International Student Assessment (PISA) tests.
The latest study uses these tests to examine the performance of 10 per cent of the most able pupils in England, Scotland, Wales and Northern Ireland, taking into account their background.
Figures also reveal a slump in performance in maths skills since 2009
Scottish Labour education spokesman Iain Gray described the findings as a "scandal and a ticking timebomb for our economy".
He added: “The SNP government should be ashamed of these figures.
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"Nicola Sturgeon said education would be the defining priority of her government; she put her top minister in charge of it and has announced a stream of schemes but the gap between the richest and the poorest most able pupils is more than two and a half years."
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Sutton Trust chairman Sir Peter Lampl, said: "It is staggering that at age 16 bright but poor Scottish pupils lag behind their rich classmates by almost three years.
"This results in a huge waste of talent which is why it is important that the Scottish Government does more to stretch able students.
"The research also shows that in Scotland there is a real decline in able pupils’ performance in science, and that overall Scottish pupils are below most OECD countries in reading and maths.
"The findings worryingly also show that Scottish pupils trail behind the performance of able pupils in England in most subject areas.” The Scottish Government spokesman said its was determined to close the attainment gap over the next 10 years.
Schools have recorded their worst ever performances in PISA tests
A spokesman added: This government is already taking action to ensure that every child, no matter their background, has the chance to succeed by implementing a range of measures to strengthen our education system and to give every child an equal chance of going to university.
“We have committed £750 million of Scottish Attainment Challenge funding over the course of this parliament.
"This year alone, £120 million of Pupil Equity Funding is being allocated directly to headteachers with an additional £50 million of Attainment Scotland funding providing targeted support and resources to local authorities and schools in areas of greatest need.”
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