The Alpha Particle X-ray spectrometer (APXS) on board the Curiosity rover at the Kimberley location within Gale crater, Mars, analyzed basaltic sandstones that are characterized by potassium enrichments of 2 to 8 times estimates for average Martian crust. They are the most potassic rocks sampled on Mars to date. They exhibit elevated Fe, Mg, Mn and Zn and depleted Na, Al, and Si. These compositional characteristics are common to other potassic sedimentary rocks analyzed by APXS at Gale but distinct from other landing sites and Martian meteorites. CheMin and APXS analysis of a drilled sample indicate mineralogy dominated by sanidine, Ca-rich and Ca-poor clinopyroxene, magnetite, olivine, and andesine. The anhydrous mineralogy of the Kimberley sample, and the normative mineralogy derived from APXS of other Bathurst class rocks, together indicate provenance from one or more potassium-rich magmatic or impact-generated source rocks on the rim of Gale crater or beyond. Elevated Zn, Ge, and Cu suggest that a localized area of the source region(s) experienced hydrothermal alteration, which was subsequently eroded, dispersed, and diluted throughout the unaltered sediment during transport and deposition. The identification of the basaltic, high potassium Bathurst class and other distinct rock compositional classes by the APXS, attests to the diverse chemistry of crustal rocks within and in the vicinity of Gale crater. We conclude that weathering, transport, and diagenesis of the sediment did not occur in a warm and wet environment, but instead under relatively cold and wet conditions, perhaps more fitting with processes typical of glacial/periglacial environments.