Silicon carbide (SiC) has already found useful applications in high-power electronic devices and light-emitting diodes (LEDs). Interestingly, SiC is a suitable substrate for growing monolayer epitaxial graphene and GaN-based devices. Therefore, it provides the opportunity for integration of high-power devices, LEDs, atomically thin electronics, and high-frequency devices, all of which can be prepared on the same SiC substrate. In this paper, we concentrate on detailed measurements on ultralow-density p-type monolayer epitaxial graphene, which has yet to be extensively studied. The measured resistivity ρxx shows insulating behavior in the sense that ρxx decreases with increasing temperature T over a wide range of T (1.5 K ≤ T ≤ 300 K). The crossover from negative magnetoresistivity (MR) to positive magnetoresistivity at T = 40 K in the low-field regime is ascribed to a transition from low-T quantum transport to high-T classical transport. For T ≥ 120 K, the measured positive MR ratio [ρxx(B) − ρxx(B = 0)]/ρxx(B = 0) at B = 2 T decreases with increasing T, but the positive MR persists up to room temperature. Our experimental results suggest that the large MR ratio (~100% at B = 9 T) is an intrinsic property of ultralow-charge-density graphene, regardless of the carrier type. This effect may find applications in magnetic sensors and magnetoresistance devices.