The MCOM (Mathematics Comprehension) test is a Test of Academic Potential (TAP) that attempts to assess a student's ability to engage with and respond to teaching. The test is in some ways similar to a comprehension test in a language course, but on a mathematical topic; hence the name.
There are usually two sections. In each section a topic that is not taught in Mathematics courses at school is introduced. At regular intervals in the text, questions on the material that have been introduced are asked, and after some questions feedback is given that alerts the writer to possible misconceptions.
The questions range from straightforward questions on the concepts introduced to more challenging questions that require deeper understanding. In this way the test attempts to mimic the classroom situation and in this way to assess the student's ability to be engage with new material.
The topics are chosen in such a way that the test relies only marginally on school mathematics, in an attempt to minimise the effect of prior learning. There is therefore also no need to prepare for this test.