Among the Jewish students excelling at mainstream schools was 12-year-old Alexandra Evans.
Her A*-grade in maths saw her become one of the youngest pupils in the country to pass a GCSE. Tutored by her father, maths teacher Richard Evans, she started work on the course two years ago and followed in the footsteps of her brother, Jamie, who achieved the same grade at the same age in 2006.
Alexandra, of Arkley, Hertfordshire, said: "It feels really good and I'm very proud of the work I have done with my dad. It was quite challenging but my friends were impressed. I also enjoy Pythagoras' theorem and
trigonometry."
Mr Evans said: "It's incredible fun. Every day we look at a number and work out what its square root is, see whether it's a prime number and so on. The secret is having ten minutes of quality time every day."