There has been another increase in the A-level pass rate and the proportion of entries awarded the top A grade.
Figures from the Joint Council for Qualifications show 97.2% of entries in England, Wales and Northern Ireland passed, up from 96.9%.
A grades went to 25.9% of the entries, up from 25.3% - and in Northern Ireland more than a third achieved an A.
The results reveal striking differences in achievement across England, with south-east England getting the most As.
There, 29.1% of entries were awarded an A grade - an increase of 6.1 percentage points since 2002.
The lowest proportion of A grades were achieved in the north-east of England (19.8% of entries) - an increase of 2.1 percentage points since 2002, which was also the lowest rate of improvement across the regions.
There were a record 827,737 A-level entries and 1.13 million AS-levels this year from more than 600,000 students.
There has been a concerted effort to increase the numbers of young people pursuing the so-called "Stem" subjects (science, technology, engineering and maths) to raise UK skill levels and global competitiveness.
Only this week the Confederation of British Industry called for more to be done.
Dr Sinclair added: "This has to be a day for celebration."
As usual Northern Ireland students outperformed those elsewhere, with 98.2% of entries passing and 35.4% awarded A grades.
In England 97.2% passed with 25.6 awarded A. In Wales, 97.6% passed and 24.1% achieved an A.
Schools Minister Jim Knight said: "I heartily congratulate all students who have successfully completed their A-levels and thank teachers for their hard work.
"This year's results are a tremendous tribute to all the effort that has gone into achieving these qualifications by students, supported by parents and teachers. They also show a good return on a decade of record investment and policies which have encouraged more young people to continue and achieve in education.
The moment when A-level students find out their grades
"More pupils are now passing maths A-level than at any time in over a decade. It's crucial for society that we have talented mathematicians and maths is essential for science and innovation."
John Dunford, head of the Association of School and College Leaders, said: "We welcome the increases in maths, further maths, the sciences and languages at A-level.
"It is what we have been hoping for for several years. The concerns we were talking about last year about the declining trends in those subjects has at last been turned around."
As the results were announced, the government explained how it was making A-levels more challenging.
English regions - entries awarded grade A
South East - 29.1%
London - 28.3%
South West - 27.2%
East - 26.2%
West Midlands - 23.4%
North West - 23%
Yorks and Humber - 22.3%
North East - 19.8%
Following successful pilots, tougher A-levels will be available to all from this September.
One change involves doing an "extended project", worth the equivalent of half an A-level. More than 1,400 students have been involved in a pilot with exam boards.
And students starting A-level courses in September will become the first to be eligible for the new A* grade when they are awarded to those attaining more than 90% in 2010. The first pilot versions have been awarded this summer.
The change followed criticism that the rise in the number of A grades at A-level meant universities could no longer spot the brightest students.
The results statistics released on Thursday relate to exam entries, not students. The school-by-school breakdown - the "league tables" - is due to be published in January.
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