In our experience, the students who do best in the course are those who turn in the problem sets and participate actively in the tutorials. If you are interested in making the most of them, here is some advice.
Problem sets are a good opportunity to
In quantitative questions (i.e., numerical calculations), getting the numbers right is much less important than explaining your reasoning. The "right answer" will not receive full credit unless you show how you arrived at that answer. And even without a final answer, you can still get some credit by describing what you tried, and where and why you got stuck. This also makes it easier to address difficulties when we go through the problems in class.
In qualitative questions, pretend you are a teacher and aim to make your text understandable to any other astronomy student who might read it. Use the chance to develop your own knowledge of the topic.
Whenever appropriate, use words, formulas and diagrams to make your explanations clearer.
General strategy:
What information do you need in order to obtain the answer? Review the relevant topics and try to outline the steps before looking up equations and beginning your calculations.
Did everyone solve the problem on their own? If not, see if you can identify the reason. Maybe someone else can help explain a difficult concept or suggest what to try. On the other hand, if everyone already solved the problem, it could be useful to compare strategies and see if there are different ways of doing the problem.
This is a very important point. It is good to talk with other students about how to approach the different problems, but when you actually write down your answers (or at least describe your attempts to find an answer), you should do this on your own. To get a good grade, your problem sets should be in your own words and not copied from a text, book or other student.
One aim of the tutorials is for students to review and understand better what was presented in the lectures. So, before each tutorial, please take time to go through the material that was covered since the last tutorial. Summarize the main points for yourself. Are some ideas unclear or difficult to understand? See if you can learn more with the help of your class notes or a book in the library. Do you understand now? If so, write down a few notes about it so you can present it to the other students in class. If not, formulate a question to ask in class...you are probably not the only one who was wondering about that!
A second aim of the tutorials is to understand how the problem sets can be solved. You should come prepared to show, on the blackboard, how you worked out any given problem in the problem set. But please remember that you are not expected to do everything perfectly! The purpose is to practice discussing physics in a group, and we will all learn more if people bring up points they are not sure about, so we can try to figure them out together.
In order to get a good grade for class participation, you should present some thoughts on a relevant topic, show how you did (at least part of) a problem on the blackboard, or ask and answer several questions during every tutorial session.