The University of Auckland offers a one-year pre-degree Tertiary Foundation Certificate (TFC) Programme, for up to 200 students who are under-prepared for university study. The students may come straight from school without having gained a university entrance qualification, or they may be students returning to education who lack the confidence to begin degree studies. This paper describes the features of the compulsory mathematics courses offered in the TFC programme. It provides evidence of the effectiveness of these courses, as gauged from written responses in student reflections during the year, and from results in ex-TFC students' subsequent Stage One studies in mathematics. (Contains 7 tables.)