Testing for upper level coast guard exams can be stressful.


So, for the curious or the candidate, we will be exploring several of the trickier math problems found in these exams in the next few posts.

There are basically three types of problems in these exams, domain knowledge, methodology, and math. That is my own classification system, so allow me to explain:


These are those questions that require you memorizing the pertinent equations and properly solving them. Often this will involve some methodology as well, when you have to find a part of the answer in the reference materials. In the next couple of posts we will tackle how to solve a few of these types of questions. I would love to share a how-to for every type of math problem in the exams and maybe one day I will, but this start will focus on those that aren’t well represented online in the free references that I found. Namely the celestial problems from the upper level near coastal exams.

Domain knowledge questions are those where you cannot find the answer in the resources available to you in the testing room, but test your familiarity with maritime practices and terminology. The best example of these problems would be the deck general exams. They ask questions about the breaking strength of certain types of lines, crane operations, a whole gamut of subjects. The scope of the questions is what makes these tough, unless you deal with crude oil transport, those specific questions are probably out of your wheelhouse, pun intended. For these problems, I have a couple of suggestions that will cover all those obscure subjects without forking out thousands to a maritime training school. The Merchant Marine Officers Handbook – This book covers most of these questions, although I’d give it 5/5 for a snoozefest of a cover to cover read. Great reference for when you want to look something up though. American Merchant Seamans Manual – This one is more of a practical how to book. Be warned though that it covers the state of the art from the 1980’s, even in the 7th revised edition. Between these two books, you will find the answers to (almost) all the domain knowledge questions you could ever hope for.

Methodology questions test your ability to find an answer and could be subset further into plotting and reference questions. Plotting questions are those where you literally plot something out on the chart or a radar plotting sheet to derive an answer, Navigation: chart plot being the obvious example of an exam here. They want to know you recognize how to find the answer and can accurately plot it out. Sometimes, the answers in the USCG exams will not match up with the answer you derive, DON’T PANIC in these cases. Simply select the closest answer, many of the coast guard exams do not have an actual correct answer for some reason. Many of these questions can be answered mathematically using trigonometry, if you really want to be sure that the answer is just close to an option. One word of advice is when you come across these questions and it is a set and drift problem, rely on DRIFT, the set is off by as much as 10 degrees in some “correct” answers on the exams. While we are on the subject, all the USCG calculations use 6080 feet per nautical mile, so when you do the math using the actual value of 6076 feet per mile, you won’t come up with an exact answer, again select the closest. I digress, so lets look at the reference questions. These are those questions that involve looking up the answer in the reference materials provided, like CFR questions in the deck safety and environmental protection exams. The goal here is test whether you know where to find the answer and how to navigate the various reference tables etc. Practice is the key to these problems, simply spend some time looking through the reference materials that will be available to you, they can almost all be found for free online. Practice plotting out time abeam problems, set and drift, working with paper charts. These were everyday skills ten years ago, but with ECDIS and ARPA being so prevalent now, most of us don’t get to use those paper plotting skills much anymore.

Breaking down which type of question I was faced with helped me.

I would then know whether to grab scratch paper, a reference book, or a plotting sheet and my plotting tools. From there, it is (hopefully) a clear-cut path forward. Some questions can be solved through plotting or looking up in the reference, or mathematically, these will depend on which methods you are the most comfortable with. Probably the best example would be distance when abeam from two bearings. You could look it up in the green Bowditch, solve with trigonometry, or as I would, simply plot it out on a radar sheet. Whatever method is your strong suit, classifying problems helped me study and when taking the exams. It helps you recognize that which must be memorized, and what can be found while you’re in the exam.

So, that being said, I hope you enjoy these next few posts about how to solve some of the navigational problems found in the exams.

USCG Exam Solutions: Compass Error by Azimuth

USCG Exam solutions: Compass Error by Amplitude



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