Remember, the order in which you complete problems on an exam is not important. Subsequent passes through the test will allow you the time to work the intermediate and finally most difficult problems. Never spend too much time on any one problem since you then squander valuable time that could be better spent on other problems. If your test is multiple choice, never leave a question blank unless you will be penalized for wrong answers. If you do not know how to solve a problem directly, use your best logic to eliminate as many of the choices you can and then make an educated guess between the remaining options.
Students sometimes work backwards from the responses when they have no other way to proceed.
Never feel intimidated that other students are leaving the test before you are. As long as there is still time left on the clock, chances are valuable tasks remain for you to complete. This is particularly good advice for students whose instructors give partial credit. As you are brainstorming a difficult problem on an exam, use your scratch paper as a drawing board where you can sketch drawings, start formulas, etc. This visual process will often lead a student toward a viable solution, as well as generate possible partial credit points along the way.