How many times has the last dalek been used on the TV snow Doctor Who when introducing a Dalek and exactly how many more times do they plan on using this phrase?

Answer 1

They used it a few times. The phrase is based on limited information - the Doctor believed they were extinct, but a few had escaped destruction by accident or by design.

In "Dalek", one lone soldier dalek had fallen through time and had been acquired by a curio collector. Initially battered and powerless, it escaped and repaired itself, but committed suicide.

In "Bad Wolf", the Doctor learned that the Dalek Emperor himself had survived the time war, his ship falling through time. He was able to re-establish the race using cells cultivated from humans, but all of them were turned to dust by Rose, as Bad Wolf.

In "The Army of Ghosts", four special daleks, the Cult of Skaro, were revealed to have been hiding in a Void Ship, unaffected by the passage of time. They had brought with them a 'Genesis Ark' which was actually a prison ship for captured daleks, which they managed to release. However all of these were sucked into the void, though the Cult of Skaro managed to escape.

In "Daleks in Manhattan", the Cult of Skaro resurface. Three are killed in the events of the following episode "Evolution of the Daleks", the last, Jast, escapes yet again.

In "The Stolen Earth", a Dalek force including their original creator Davros, is stealing planets in order to create a specific configuration of their gravitational fields, as part of the plans for a 'reality bomb' to destroy the universe, themselves excluded. These Daleks are here because of Jast, melted and maddened, he fell into the Time War and brought them out to a different time. In the following episode, "Journey's End", they are wiped out by an alternate form of the 10th Doctor, though Davros' ultimate fate is uncertain.

Lastly, in "Victory of the Daleks", survivors from "Journey's End" try to activate a Progenitor device to create more Daleks. Since they themselves were grown from Davros' cells, the device does not recognise them as true Daleks, thus they require the Doctor's 'testimony' to activate it. The device creates new Daleks, the New Paradigm, who destroy the old Daleks, they die willingly. These New Paradigm daleks escape as the Doctor's attention is forced elsewhere.

After this, the Daleks have re-established themselves as a race, and as the Doctor notes, have seemingly abandoned their usual policies of single-minded destruction and racial purity into something almost approaching tolerance, solely out of fear of him.