Using CAS for writing questions

Computer Algebra Systems (CAS) are very powerful tools for mathematics but they are underused in the classroom probably because they aren't allowed in examinations (at least in the English school system).  This lack of use by students means that teachers often overlook how useful they could be for themselves.

One time-saving use for teachers is writing questions with certain properties.  For example if you know you want a cubic with a repeated root you could multiply out appropriate brackets by hand, or you could use CAS to do it:

Similarly you may want a quadratic with specific complex roots:

Most CAS engines also feature calculus tools too so you could use the integration function to find a function with a specific derivative:

In addition to using CAS to write questions teachers can also use to check students' answers.

There are many CAS tools available.  The three that I have used here are:

• TI-nspire http://education.ti.com/html/nspire_uk/  (this is available as a CAS and non-CAS version - students will likely want to buy the non-CAS version so they can use it in exams but teachers are advised to buy the CAS version)
• Microsoft Mathematics http://www.microsoft.com/education/products/student/math/ (free download)
• Maxima http://maxima.sourceforge.net/ (open-source, free download)