I took the Numerical and Applied Math qualifiers. Here are posted some of the solutions I wrote.
However, you should know that these solutions may contain many mistakes!
Some common suggestions when preparing for one of these exams:

Read the syllabus! (Probably the most important thing besides actually studying)

Review the material covered in class.

Before looking at the solution, always try the problem on your own.

If you cannot figure it out, review that particular topic in a book or your notes.

If everything else fails look at the solution.

Don't spend too much time on a single problem. The key is to work out as many exercises as you can.

Form a team to study with! Thanks to the help of my friends Saulo and Nuwan the summer was so much more enjoyable.