In this skill, we focus a bit more on adjectives and their case forms
As a "problem" in a Math class, «задача» is more frequent. Other than that, «задача» may be a problem, a task, an objective—while «задание» is a task assigned by someone else (again, unless it's an exercise you randomly encountered in your textbook).
When you want to express "the most" strong degree of some quality, Russian will almost always use an analytical form. Just add the adjective «самый» in front:
There are one-word forms for many adjectives, though few of them are popular. Here are the synthetic forms, to give you an idea:
наи-prefixed versions should be used with extreme care since they will almost always sound too fancy for spoken language and too emotional for academic writing. Still, a few of most popular may be just the right thing in written style (eg. наилучший, наихудший, наисложнейший).