By empirical demonstration, this study extends the assessments of BRICS countries (Brazil, Russia, India, China and South Africa) in performing science and technology in previous studies by exploring their cumulative patterns of science and technology (proxied by publications and patents respectively). Projections of cumulative production in science and technology are made using logistic growth function. Our analyses show that - though having different growth trajectories in science production - the BRICS countries exhibit similar patterns in pursuing technology. This embodies the strong commitment of BRICS to improve their technological capabilities in the process of industrial development. Inspired by the Relative Impact Index (RII) proposed by Nesta and Patel, we propose the Relative Science Impact Index (RSII) to evaluate the relative impact of science and technology on the process of technological catching-up in emerging economies and examine the co-evolution between science-based patents and patent citations. Our correlation analysis between forward citation and RSII marks some distinctive pursuits of BRICS countries in science-based patenting activities.