As of July 2015, samples of gun safety exams are online at the International Hunter Education Association, Project Childsafe and Best Handgun Training. IHEA presents a 10-question quiz about firearms.
At the end of the IHEA quiz, clicking on the Check Answers button displays the quiz results. If any answers are wrong, a link leads to a hint for the correct answer.
Project Childsafe's website has links to two quizzes. The first covers both facts and myths about firearm safety, while the second covers hunting concerns.
Best Handgun Training links to the Handgun Safety Certificate study guide from the California Department of Justice. This manual has self-tests in several safety areas, including basic rules, handguns and children, and firearm laws.