The authors present the results of a study investigating how evolution of Ca-rich precipitates (Ca₂CuO₃) in melt-quenched Bi₂Sr₂Ca_1.2Cu₂O_x affects the superconducting transition temperature (T_c) and the transport critical current density (J_c). An excess of 20 at.% Ca raised the transition temperature at zero resistance (T_c,zero) and the transport critical current density (J_c) of the melt-quenched material to (85.6+or-0.8) K and (18.9+or-0.5) A cm^-2 at 77 K respectively, compared with (80.2+or-0.6) K and (10.2+or-0.7) A cm^-2 at 70 K for melt-quenched material of stoichiometric composition, with both materials annealed at 840 degrees C for 100 h. The formation of Ca-rich precipitates (Ca₂CuO₃) in melt-quenched material with excess Ca was studied with the help of a scanning electron microscope. As the time of anneal at 840 degrees C was increased from 1 min to 150 h, the volume fraction and the average size of Ca₂CuO₃ precipitates initially increased, reaching maximum values of 27.2% and 1.08 mu m, respectively, at 30 min of annealing, and then started to decrease. However, as the annealing time was increased from 30 min to 150 h, T_c,zero increased from (35.0+or-0.5) to (85.0+or-0.8) K and the transport critical current density (J_c0) extrapolated at absolute zero temperature increased from (2.1+or-0.4) to (107.0+or-3.3) A cm^-2. It is thought that dissolution of Ca₂CuO₃ precipitates converts Bi₂Sr₂CuO_x (2201) phase at the grain boundaries to superconducting Bi₂Sr₂CaCu₂O_x (2212) phase, thereby reducing the weak link at the interfaces.