Can a student that studied only the Core curriculum for IGCSE Mathematics 0580 still opt to study Mathematics at AS & A Level?

We do not set entry requirements for our examinations. As a centre, you may set your own requirements for candidates who would like to enter for our examinations. Cambridge Mathematics 0580 extended curriculum is only a recommendation but not required. However, on page 17, Prior Knowledge section of the Cambridge International AS & A Level mathematics 9709 syllabus here content of the extended curriculum will be assumed knowledge.