We investigate a personal response system (PRS) pedagogy for lecture halls that encourages active engagement yet lowers barriers for implementation by eliminating the need to address student requests to make up questions because students must answer (not necessarily correctly) only more than half (greater than or equal 50%) of PRS questions to earn course credit. We analyze over 3000 students in the same introductory undergraduate science course over a 13-year period. Students who earn an A answer more questions throughout the course (between 76 and 87%, on average) than B students, who answer more than C students, but this pattern is also explained by prior GPA. In addition, while PRS response rate is positively correlated with student total exam score, the slope of this relationship also depends on the type of student. It is larger for students with higher prior GPAs (a 2.5% increase in exam score for every 10% increase in PRS response rate for A students), and there is no overall significant effect for students with a D prior GPA. However, there are years that exam scores increase with PRS response rate for D students, implying that all students can benefit if they engage cognitively as well as behaviorally. Finally, since non-first-year students typically score better on exams (despite using the PRS less frequently), this PRS pedagogy can be especially helpful for new college students.