The first V Rc Ic bands light curves of MQ UMa are presented and analyzed using the Wilson-Devinney (W-D) program. It is discovered that MQ UMa is an A-subtype contact binary with a high fill-out (f=82 %) and a low mass ratio (q = 0:195), which indicates that it is in the late evolutionary stage of latetype tidal-locked binary stars. The mass of the primary and secondary stars are estimated and the evolutionary status of the two components are placed in the H-R diagram. The W-D solutions also indicates that MQ UMa may be a triple system with an F5V type additional component. A sample of sixteen high fillout, low mass ratio overcontact binaries are collected and their possible evolution scenarios are discussed. Using the five times of light minimum recently observed together with those collected from literatures, the authors find that the observedcalculate (O-C) curve exhibits a cyclic period variation. The cyclic period change also reveals the presence of a tertiary component, which may play an important role in the formation and evolution of this binary system by drawing angular momentum from the central system.
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