First Step - Admit it. If you see an explanation to a problem, and "get it" - do you move on? NOT the right approach! The only thing that counts is if you can START a problem all on your own and finish it correctly all the way through. If you get a HW question wrong, the best thing to do is find a similar question and try that, and do this until you are consistently getting that material or question type right. You want to make sure you can find the "solution logic" without any hints or helps. Understanding an explanation, or following along, is completely different from doing it on your own. Don't fall for fooling yourself! And please don't try to fool your tutor by not mentioning HW questions you understood once you saw the answer. If you really understood it, that's fine - but you are not getting at the real issue - addressing why you fall victim to the careless error. You may not realize how much careless errors are stealing from your score, and it will not be overcome unless specifically addressed.
Second Step - WRITE! WRITE! WRITE! Mental math errors can steal huge points. And you also don't see assumption errors or an inconsistency in units unless you write it out. Use your own shorthand to write the info given, the intermediate calculations,... - all the way to the answer. It really doesn't take much time and not that much energy! I'm not sure why so many students are adverse to actually pushing the pencil, but those who do write things down consistently score higher. You also save time at the end because you can't check your work, and catch an error(!), without totally redoing the problem unless you have something written down from the first time around!
Third Step - check your work, as you go, and when you are through. Ask yourself - did I copy the information right? Are my assumptions valid? Are the intermediate calculations correct? Look at equations you write backwards and forwards to catch the "careless error". Check if the "units match" on both sides of the equation. Lastly, ask - does the answer makes sense? Should the answer be larger or smaller than what I started with? Questions like this will help you catch the "careless errors" and raise your score.
Test Anxiety is a real issue, that often needs addressing all on it's own. But, if some of the anxiety is coming from a history of underperforming on tests, and that is due to a multitude of careless errors, you can conquer those with some simple steps. Develop the habits of writing and checking. Your goal is to get it right, by yourself, cold. If it really is just "careless errors", you can avoid them with good habits. The confidence you gain by consistently higher scores, may lessen your anxiety on the next test.
I can help you with this, and provide more tips and techniques for combatting specific careless errors. I can also help you strengthen subject matter, which builds confidence. Separately, I address test anxiety issues with a variety of exercises and techniques that have proven helpful. Contact me for more information.