We present a study of the ultra-faint Milky Way dwarf satellite galaxy Tucana II using deep photometry from the 1.3m SkyMapper telescope at Siding Spring Observatory, Australia. The SkyMapper filter-set contains a metallicity-sensitive intermediate-band $v$ filter covering the prominent Ca II K feature at 3933.7A. When combined with photometry from the SkyMapper $u, g$, and $i$ filters, we demonstrate that $v$ band photometry can be used to obtain stellar metallicities with a precision of $sim0.20$dex when [Fe/H] $> -2.5$, and $sim0.34$dex when [Fe/H] $< -2.5$. Since the $u$ and $v$ filters bracket the Balmer Jump at 3646A, we also find that the filter-set can be used to derive surface gravities. We thus derive photometric metallicities and surface gravities for all stars down to a magnitude of $gsim20$ within $sim$75 arcminutes of Tucana II. Photometric metallicity and surface gravity cuts remove nearly all foreground contamination. By incorporating Gaia proper motions, we derive quantitative membership probabilities which recover all known members on the red giant branch of Tucana II. Additionally, we identify multiple likely new members in the center of the system and candidate members several half-light radii from the center of the system. Finally, we present a metallicity distribution function derived from the photometric metallicities of likely Tucana II members. This result demonstrates the utility of wide-field imaging with the SkyMapper filter-set in studying UFDs, and in general, low surface brightness populations of metal-poor stars. Upcoming work will clarify the membership status of several distant stars identified as candidate members of Tucana II.
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