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In recent years, significant numbers of academics from the science and health disciplines at our institution have found that their students lack the appropriate 'mathematical' background to cope with first-year science subjects. Consequently, failure rates are on the increase in these subjects. The mathematical background of students entering university has been found to be a problem in other universities in Australia, as well as in the UK, Ireland and the US. In this report, the authors analyse data on current students' performance and present suggestions for addressing the problems found. The performance of first-year students in four different mathematics and mathematically related subjects is compared to the level of their secondary school mathematics and performance, and to their tertiary entrance score. We conclude that a student's secondary school mathematics background, not their tertiary entrance score, has a dramatic effect on pass rates. On the basis of our findings, a way forward is suggested. [ABSTRACT FROM AUTHOR]