The article analyzes the influence of selected factors on the activity rate of cement binder containing 50% of ground granulated blast furnace slag in its composition. These factors are the chemical and mineral composition of Portland cement CEM I, the degree of grinding of granulated blast furnace slag and Portland cement, and the water/binder ratio. This slag content is characteristic for blast furnace cement CEM III/A. In addition to the application effects, this type of cement is a low-carbon binder (there is a reduction of CO ₂ emissions by about 45% compared to Portland cement CEM I). The use of this type of cement in the composition of concrete enables the obtaining of concrete with a very small carbon footprint. Based on the results of our own research, it was found that such a high proportion of ground granulated blast furnace slag in the binder composition leads to a significant reduction in the early compressive strength of standard mortars (after two and seven days of setting). This results in a significant reduction in the use of these types of binders (cements) in selected areas of construction, e.g. prefabrication and high-strength concrete. Analyzing the obtained results of their own research, the authors concluded that the early strength of these types of binders can be significantly improved by increasing the specific surface area (degree of grinding) of Portland cement CEM I and lowering the water/slag ratio (w/s, where: s = cement + slag). The proposed material and technological modifications also enable the obtaining of higher compressive strength at all tested dates. The strength of the standard (after twenty-eight days and over longer periods) is comparable to or higher than that of Portland cement CEM I.