discrete math ii/C960 pre-OA study log
the goblin believes that an account of what items were studied, along with a daily reflection, would be beneficial to understanding what needs to be done.
I kept a log from Thursday to Friday, so two days, of what I studied for my discrete math exam. Iâll keep at the top my experience with the exam itself, and have the log posted below.
Thoughts on the Exam
Throughout the exam, I felt like I was taking my AP Calc BC exam from back in 2017. The questions looked overwhelming sometimes, and on about five or six of them, I ended up just making a good guess. Ended with seven minutes left on the clock.
Some items, it looked like they were hard, but in reality, they just looked hard. For what I couldnât solve directly, I looked at the answer and tried reasoning them out. One of the questions, it got very long and I spent 10 of my precious 30 minutes left trying to solve it. đ (The exam had plenty of time, I believe. I just stared at the whiteboard scratching my head trying to solve it. And I used almost the entire side of a whiteboard to do so.)
I gave myself a few tips; these are just general test-taking tips I wrote down:
Do things right the first time, but should it take longer than expected, skip it and come back to it later after answering other questions you can answer comfortably.
I bookmark all the questions Iâm certain about, but if I answer it with confidence, I donât look at it again.
Take your time! Dissect and understand the questionsâ parts. Many tend to have multiple parts that you need to break the problem down into.
There is a right answer; if your answer that you come up with on your whiteboard and calculator donât match up with any of the choices, try to reverse-engineer the answersâprovided that you have the time to do so. What this means for me is to essentially use induction on the answers and see if there was a way to get to them. If I find a way to get to them, I just choose that answer.
In addition, if you feel like your answer on the whiteboard is correct but itâs not an answer choice, consider what your answer means. All roads are valid for getting to places, but you also have to know what your destination is.
Zoom out, but read the entire question before answering. This goes along with the âtake your timeâ point. Figure out what formulas and algorithms youâll need to do first, and then pick out the details in the question to answer it.
Keep your work neat/easy to follow. The easier you can read what you have on your whiteboard, the better. If you think you made a mistake, itâs easier to trace back your steps and check what you may have done wrong.
As I mention in the study log: I assume a 70-75% is a pass for most of the classes (I take a look at my attempt after the PA), so I try to feel confident on 70-75% of my questions. Once thatâs done, I go back to my troublesome questions and answer them. And then, when there is no time left, I begin making reasonable guesses and submit the exam.
Study Log for Exam Prep
2022.12.29 â Thursday
Working on counting techniques today, going through the end-of-chapter/lesson exercises. In the Zybook, these are not interactive but they have an answer, usually with an explanation.
Counting was a topic that was scored low, which I believe is due to the fact that many of the questions are word problems. I have to decipher these first, but I if do not put it into the formulas correctly, I get the question wrong.
So to remediate that, I am doing many of the harder word problems as I can. For counting, Iâve done about nineteen, most of which are multipart problems.
In addition to counting, Iâm reviewing the discrete probability section. Although I wouldâve assumed that Iâd be okay since I took statistics, I guess that I am not. On reddit, lots people said that the counting and probability units go hand in hand, so I could understand why that, if I did not do good in counting, then I would not do good in probability (but not the other way around, since there is no mention of probability in the counting section).
Once again, it being heavy in word problems throws me off. They also require me to break down problems into subproblems, and sometimes, when I think that the next part will require an answer from a previous part, it actually wonât! Isnât that fun?
Tomorrow, Iâll review conditional probability, expected value, and Bayesâ theorem. It is just sometimes difficult for me to translate the word problems and plug in the values into the formulas. However, the thing is with the textbook, they are not multiple choice, so I have to develop my own answer.
I say this because, should I have multiple choice, I can always reverse engineer the answers after honing it down to the most likely ones.
Tomorrow in addition to that, Iâll check out recursion in the context of reading pseudocode, since I think that was my weakness. Unfortunately, I donât recall seeing any actual pseudocode outside of maybe the algorithms section, and algorithms for when there are repeated steps in the different skills learned in the course.
I will take the test on Saturday. On my last test, I am to get 75-80% of the questions right, which I calculate according to how many are on the OA. For example, if an OA has 80 questions (perhaps in another course), then I will aim to have at least 60 to 64 questions that I am confident about and do not need to hesitate reviewing. I think the passing percentage is around 70%, so I think that it is a good âbuffer zoneâ, in the event that I have a false confidence one a question or two.
I am confident with the number theory unit since itâs straightforward, even though it may look like itâs a lot of steps. There are no silly word problems I must decipher.
Algorithms, I need to review the time complexities since I mix up what it means for a function to be of another function (as time complexity representations). I will seek additional resources for this.
Recursion/induction is actually my preferred way of reasoning, assuming a case to begin with instead of finding the truth of a case.
Computation models are surprisingly easy. I hope to get a 100% on that section on my exam so I have more padding on my score.
2022.12.30 â Friday
My main issue still remains to be picking out the details from a word problem to find out what each event in probability entails. Sometimes, finding the size of those events is not intuitive either, so I ended up having to look at the solution, which I understood afterwards.
I will probably skip random variables/expected value, since the topic itself is easy to understand. Iâll just write down the gist of those two topics and how they relate to each other, with my own examples.
In addition, I will later jot down reminders to keep in mind for the exam. I sometimes âfreezeâ upon seeing a problem since the method to do it may not appear obvious.
Going through the worksheets once more and doing the lesson exercises did help though, giving me exposure to the various ways problems can be worded. Thatâs how I passed my stats class in community college: since it was online and questions were randomly generated, the format was generally the same but the numbers/what youâre asked to solve for differs. Iâd practice for 2-3 hours a day on those and I did well on the test when it came time.
Most likely, the next course will be Computer Architecture, so Iâm gonna take a look at the course planning tool for that to see what itâs all about.
I did, and Iâve learned I know very little. But it seems like itâs mostly vocab, so going through the course will help, definitely.
Other Notes
I read the Zybook âcover to coverâ, with notes on each section. After doing the practice assessment, I went back to the sections I had trouble on to work through the end-of-lesson problems.
I watched the videos the CI made, and did the worksheets. These help a lot since they cover things that arenât in the book but are on the test.
The probability section did cover some material I had learned in statistics class back in 2020, at my community college, but I think it expanded on certain topics a lot more.
I donât believe I really used any other outside resources. I worked through a couple modulo congruence problems on Khan Academy (literally, like three problems). That excludes some posts on Reddit about this class though; those gave helpful tips on what other students had to focus on during their test.
My Own Suggestions
Jot down key words and formulas, and the steps in algorithms/procedures in your notes. Do all the participation activities, challenges as you write your notes. (I used OneNote for notetaking, and a graphics tablet to handwrite my notes. It took a fairly long time.)
You could perhaps progress through several lessons a day. Try doing a problem from each exercise lesson block, though. They are harder than the challenge/participation problems but itâs similar to whatâs on the test.
So you could do maybe three lessons in a day, do the participation/challenge questions, and work on the hardest exercise question from each lesson. Read through the explanation and see how the book did it.
Do the worksheets after each unit/competency completed, and when comparing your answers to the answer sheet, attain understanding of why the answers are like that. Once youâre finished with the book, you should be able to do it again with less struggle (at least thatâs how it was for me, since the knowledge has âseepedâ into my head the second time around).
It was definitely a challenging class, but nothing super hard!
Tomorrow is the New Year, so I will then have 120 days left to do as many classes I can in my first term. Iâll work on AWS material and check out the Computer Architecture tips on Reddit and such. Iâll probably start that course in a couple days.
Until next time,
~ Your pet goblin.