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Magister Educationis - MEd / Algebraic graphs are a difficult topic for most secondary school mathematics learners. My experience as a Mathematics teacher in the Further Education and Training Phase (FET) is that learners solve problems involving graphs with difficulty. Consequently, the purpose of this research was to investigate learners’ ways of working with algebraic graphs in high-stakes examinations including their errors and misconceptions in this respect. The investigation carried out to identify learners’ errors and misconceptions is based on the analysis of 444 scripts from the 2012 grade 12 final Mathematics examination. More specifically, the study aimed to investigate the ways learners used to solve questions related to graphs in this examination. The focus of the study was the algebraic graphs tested in Paper 1 of the National Senior Certificate (NSC) examination with an emphasis on the identification of errors exhibited in the learners’ scripts. The study adopted a qualitative approach using documentary analysis methodology. As data, the study used the scripts of the final grade 12 Mathematics examinations of schools participating in a project for the improvement of Mathematics based at the University of the Western Cape (UWC). The analysis of learners’ scripts reveals that learners make many errors when they work with algebraic graphs. These errors that have been found in this investigation were coordinate, intercept, domain and range, asymptote, identification, drawing and function errors. Additional errors which were identified are transformation and inverse errors.