This paper examines two neglected critical issues of the effective utilization of Computer Algebra System (CAS). By using a number of examples from an upper secondary mathematics education, these issues deal with the instrumentalization of CAS, and support to students when solving tasks by CAS (i.e. CAS-based task design). Regarding this instrumentalization, the paper considers the extent to which it can be done with CAS tools at present, and discusses several critical issues in doing so with respect to tool, task and designer (learner). Concerning this support, the paper calls for a detailed task design that also includes the issues of acceptable solutions and scaffolding offered, which should be, in some detail, clarified and given in examination materials. Several challenges relating to the two critical issues are considered.