Practice Problems for Exam 1 (with answers)

You can use these questions as a guide to practice for the exam. Recall that if you want even more question you can re-do questions from your quizzes, lectures, homework, and worksheets. If you need more than that, you also have questions in your books and questions from the discussion section.

A couple of guidelines:

• You can use these questions as either assessment or evaluative.
• If you plan to use these questions as an “assessment,” I recommend you not study, take these questions, and then go back to exploring those topics in which you feel weaker.
• If you plan to use these questions as "evaluative," I recommend also timing yourself. Since the exam is a time-constrained exercise, it's good also to practice questions with a time constraint.
• We note that some answers are meant to be didactical (teaching moments) rather than answers that get straight to the point.
• Some questions will say, "Show your work," but in the answers, we show numbers. One would want to show the process; the answer is to check if you use the proper method.
• It would be best to try not to learn all types of questions, as this will train you to answer a particular question rather than "any question."
• Recall that these exercises are not exhaustive of all the concepts we’ve seen in class!
• Doing a bunch of questions could be useful, but it could also be not beneficial if you are not training your brain to think carefully. For example, a better way of using tools like this is to first write answers for all without looking at the right answer. Second, discuss the answers with a peer. Finding someone who disagrees with your answer is particularly helpful. Discussing how to approach a question (without looking at the right answer) is a useful exercise that the brain can take advantage of to make things “click.” Finally, have someone grade you and give you a grade without them telling you what you got wrong or right. Then, re-take it or re-do the exercise and have them grade it again until you get 100%. In short, the ideal case is when one never looks at the right answer. This is because learning only happens when your brain is trying to find an answer, and learning sometimes “stops” when you see the answer, so as soon as you see an answer to something you are likely to stop your learning.
• Notice that when doing any work assignment, especially in a non-school setting, one doesn’t know the “right answer.” You only know how you think you would approach it, and that’s exactly what we are after. So overall, the key is to see the “right answer” as the last thing you do.
• When you have a question that has multiple-choice options (like in the quizzes), go through each option and think about why it’s right or wrong or what you could change it to to make it right.
• “Trivial mistakes.” Sometimes, we look at an answer, realize we made a mistake, and categorize it as a “silly mistake.” Sometimes, this makes sense, but we must be careful about what we categorize as a “silly mistake” and not do anything about it. You want to ask yourself, “How could I change my process to guarantee that this doesn’t happen again?”. For example, if the pilot industry were comfortable with “silly mistakes,” we’d be in a pickle. Their approach is to create a set of “checklists” to ensure the likelihood of making a silly mistake is zero. What does that mean for RMDA? For example, let’s say your silly mistake is “wrong units,” so something that you want to add to your process is “check in what units should be the final answer” as part of the process; you can add that step, maybe at the end. The takeaway from this tip should be: “How could I change my process to guarantee that this doesn’t happen again?”.
• Change the scenarios: You can create more questions out of these questions. For example, change some numbers and re-do problems. Maybe change the Y to other units; how do the results change? Ask yourself: What other questions could we ask given this setting? etc. The practice of making your brain think about other potential questions is the “studying” itself.