In the summer term of 1929 they were doing only the dull revision work for the Higher School Certificate, but even this was coloured by romance since 'As always it was my great ambition to do as well as Chris. I was always as well supplied with ideas as he, but have not the same thoroughness in carrying them out.' Alan had never before taken any notice of naggings to take care over details and style, since he had worked for himself, by himself. But now perhaps he recognised that what was good enough for Christopher Morcom was good enough for him, and that he should train himself to communicate in the way that the system required. He had not yet acquired the necessary skill. Andrews observed that he was 'at last trying to improve his style in written work, ' but Eperson, writing that his work for the Higher Certificate showed 'distinct promise', re-emphasised the need to 'put a neat and tidy solution on paper.' The examiner for the mathematics of the Higher Certificate24 commented that:

A.M. Turing showed an unusual aptitude for noticing the less obvious points to be discussed or avoided in certain questions and for discovering methods which would at once shorten or illumine the solutions. But he appeared to lack the patience necessary for careful computation of algebraic verification, and his handwriting was so bad that he lost marks frequently – sometimes because his work was definitely illegible, and sometimes because his misreading his own writing led him into mistakes. His mathematical ability was not of a standard to compensate entirely for the cumulative effects of these faults.

Alan obtained 1033 marks in the mathematics papers, compared with Christopher's 1436.

The Morcoms were a wealthy, vigorous scientific and artistic family, with a base in a Midlands engineering firm.

They had developed a Jacobean dwelling near Bromsgrove in Worcestershire into a large country house, the Clock House, where they lived in some style. Christopher's grandfather had been an entrepreneur in stationary steam engines, and the Birmingham company of Belliss and Morcom, of which his father, Colonel Reginald Morcom, had recently become chairman, now also built steam turbines and air compressors. Christopher's mother was the daughter of Sir Joseph Swan, who starting from a very ordinary background had become in 1879 the inventor, independently of Edison, of the electric light. Colonel Morcom retained an active interest in scientific research, while Mrs Morcom matched his energy in her own pursuits. At the Clock House she ran a goat farm; she bought and renovated cottages in the neighbouring village of Catshill; she was out every day on some project or county duty. She had studied in London at the Slade School of Art, and in 1928 returned there, taking a flat and a studio near Victoria, and producing sculpture of force and style. It was typical of her flair and zest that when back at the Slade she still pretended to be 'Miss Swan', but then invited other art students back to the Clock House, involving herself in absurd disguises when she doubled as Mrs Morcom.