Dario Iacoponi, 15, shot himself in the head with his father's shotgun. He was found slumped in a room at his family's home in west London in November.

He had already passed six GCSEs at A grades a year early at the London Oratory school, whose pupils include the prime minister's sons Euan, 14, and Nicky, 12.

But although the teenager, who wanted to study law in the United States, seemed to have everything to live for, his diaries revealed a darker side, the coroner said.

West London coroners' court in Fulham, London, was told that Dario had considered taking his own life during the last two months of his life.

'He did not fear death'

Coroner Dr John Burton said he had weighed up the pros and cons in his diary and "came down on the side of suicide".

Dr Burton said: "He did not fear death.

"He decided on balance that life is not good and points out that the mathematics he has used are indisputable, and that is his last entry. It was a considered process."

Police recovered five diaries covering the last year of Dario's life. Dr Burton said there was no reference in them to any bullying at school. They will be returned to his parents.

The inquest heard how Dario, an only child, had used his father's shotgun to shoot himself in the head, pulling the trigger with a wooden spoon using his feet.

He had taken just one cartridge for the gun, which he had secretly learnt to use.