Given could be used on its own (in your sentence) because the pre- you suggest is superfluous. Given on its own implies that it has already been mentioned.
To support this with a source, take one of the definitions listed by Oxford Dictionary Online:
Specified or stated.
They also provide some example sentences, one of them is:
‘His observations of the defenders dictates which play to use in a given situation.’
A more technical use can be found in The Encyclopaedia Britannica : a dictionary of arts, sciences, literature and general information, on page 117 (emphasis is mine):
To interpolate a series is to interpose among its terms others which shall be subject to the same law, or which shall be formed in the same manner as the original terms of the series; or, in other words, it is to find the value of one or more terms by means of others which are given, and which may be either at equal or unequal intervals from one another, the places of the given terms as well as of those sought being supposed known.
1 "Given | Definition of given in English by Oxford Dictionaries." Oxford Dictionaries | English. Accessed May 09, 2018. https://en.oxforddictionaries.com/definition/given.
2 Stewart, Dugald, and Macvey Napier. Encyclopaedia Britannica, Or, Dictionary of Arts, Sciences, and General Literature ...: Including the Late Supplement, a General Index and Numerous Engravings. Vol. 20. Edinburgh: A. & C. Black, 1842.