“I thought I was going to fail maths – I’ve been dreaming about it every night,” said Niamh Jamieson, holding a tear-stained GCSE results sheet up for her friends to see.

After four weeks of not being able to sleep properly, the 16-year-old received nine GCSEs on Thursday – including an 8 (equivalent to an A*) in maths. “I’m really, really pleased. I’m going to chill out now,” she said.

Niamh, a pupil at King David high school in Liverpool, now plans to take A-levels in maths, biology and chemistry and hopes to go on to study dentistry at university.

Throughout England, Wales and Northern Ireland, more than one in four exam entries by girls received top grades of 7, or A, in this summer’s exams – an improvement of a percentage point to 25.3% compared with last year.

Fellow pupil Esme Smith’s results also followed the trend – she received 7 to 9 (equivalent to A to A*) in all of her GCSEs. “It’s a bit of a surprise. I didn’t expect to do this well,” she said.

Esme Smith (left), Isabella Simpson and Nathan Rischer receiving their GCSE exam results on Thursday. Photograph: Colin McPherson/The Guardian

But, with the introduction of tough GCSE courses, she admitted that the run-up to the exam period hadn’t been easy. “I was revising every single night,” said Smith. “At the time, it was really difficult – I was just excited to get it over with.”

Now though, she feels bolstered ahead of beginning A-levels in English literature, history, and government and politics. “I’m really interested in politics – always have been. I’d love to work for the Foreign Office,” she said.

Out of about 90 pupils collecting their results from King David, a local authority-maintained Jewish school which takes children from 11 to 18 of all faiths, the pass rate was above the national average, at 68.4% compared with 67.3%.

‘There’s so much pressure on them now’ – headteacher Michael Sutton sympathises with his pupils. Photograph: Colin McPherson/The Guardian

But although headteacher Michael Sutton is rightly delighted by the result, like Niamh and Esme he had been expecting a more disappointing outcome.

“There’s so much pressure on them now, and on staff,” said Sutton, adding that he thought reforms to the qualifications by the former education secretary Michael Gove had been “a dreadful idea”.

“There’s so much more content to fit in. If you don’t extend the length of the school year, you have to just cram everything in,” he added.

Now, he hopes to keep as many as possible of those who defied his expectations on at the school’s sixth form.

But, as Ben Williams pointed out, A-levels are not for everyone. “I don’t really fit in well in a school environment. I did some work experience at a hairdressers and really enjoyed it,” he said.

Williams, 16, who received hugs from several of his friends after he showed them his grades, will start work as an apprentice hairdresser in the city this autumn.

He achieved three 7s (As) in nine GCSEs. “To be honest, I don’t really stress and I’ve been calm throughout it, but my grades are much better than I was expecting,” he said.