Research has demonstrated the positive impact of active learning on students' learning outcomes, particularly in science, technology, engineering and mathematics (STEM) fields. However, few studies have explored the impact of active learning via problem-based collaborative games in large mathematics classes in the context of Asian tertiary education. This study assesses the effects of active learning on students' learning outcomes using class test scores and the calculus concept inventory (CCI) to test the conceptual understanding of the basic principles of differential calculus, in a first year calculus course in Hong Kong. Three hypotheses were tested to determine the effects of game-based collaborative learning on learning mathematics among students. Active learning through a problem-based collaborative learning methodology was employed, using Kahoot!, a game-based learning platform. Results supported all three hypotheses, demonstrating a statistically significant increase in students' conceptual understanding and examination performance, based upon their individual perceptions of active engagement and time spent in active learning. Our results indicated that active learning "levels the playing field", in the sense that students with less pre-requisite background knowledge, using a problem-based collaborative learning methodology, were relatively more inclined to catch up or even exceed the performance of students with a stronger prerequisite background knowledge, at the end of the course.