While many students are underprepared for higher education, especially in mathematics-heavy disciplines such as engineering, universities are also underprepared for the students they admit. This has resulted in low graduation and high dropout rates in engineering programs globally. In the USA, only around 30% of students who enter an engineering qualification graduate in the expected time and fewer than 60% graduate within regulation time plus two years. To this end, we seek to answer the question: "How does students' mathematics ability upon entry into university affect graduation and dropout rates in engineering study?" We determine mathematics ability using two assessments employed in the South African context – one a statutory school-leaving assessment and the other an optional higher education admission assessment. Academic performance (graduation and dropout) in engineering study is assessed at the end of first year and again at the end of four and six years, for the same cohort of students. A sample of 525 students is selected, amongst which 23.2% dropped out at the end of first year and 30.9% dropped out at the end of four years. While only 26.5% graduated in regulation time (4 years), 60.4% graduated in regulation time plus two years (6 years). With regard to whether mathematics ability offers insight into this poor performance, we find a strong correlation between both mathematics assessments and performance in engineering study. This information can be used to inform the ways in which curriculum development and teaching and learning should be responsive to students admitted into engineering programs of study, both within South Africa and internationally.