A systematic study of the mathematical competence of all first‐year engineering undergraduates at Plymouth Polytechnic is described. Fundamental and widespread deficiencies are identified in such topics as handling inequalities, the algebraic manipulation of indices, and factorization of quadratics. In attempting to remedy a situation which appears to be deteriorating year by year, a self‐instructional remedial course has been designed. Evidence is cited that the course has been generally well received by the first group of students, and that it has contributed to the alleviation of some deficiencies. Other institutions are invited to participate in the further monitoring of student competence and the development of remedial material.