All Type 2 (一段) verbs end in -iru and -eru.
The converse is not true i.e. verbs that end in -iru and -eru may also be Type 1 (五段).
The conjugation for polite form for Type 2 (一段) is quite straightforward.
- Remove る, append ます
The conjugation for polite form for Type 1 (五段):
- Change final sound to the corresponding one that ends in -i, then append ます
I think the confusion is when the polite form is taken to be the starting point, and it gets "reverse conjugated" to obtain the dictionary form. In my opinion, it is much more systematic to start from the dictionary form.
変える and 帰る are both かえる. I suppose your method of "remove ます + る" test for 一段 works sufficiently well.
I'm asking because this packet I got tells me to remember the dictionary and past forms, but I don't see how this is helpful.
It is "helpful" because the past form is not built from the polite form, but from the dictionary form. You need to know the dictionary form in order to conjugate to the past form. Your course probably taught you the polite form first, so now the thought process you are going to use is probably:
- polite form→dictionary form→past form
When it is actually:
- dictionary form→polite form
- dictionary form→past form