If you are not using Google Classroom yet, this might be a reason to give it a try. Google Classroom now gives you the ability to create a quiz and assign it in locked mode. Locked mode in Quizzes in Google Forms is a new way to keep students focused and distraction-free during tests and quizzes by locking the ability for them to exit the quiz and open a browser window. You can create new quizzes directly from within Google Classroom under the Classwork tab or you can use existing quizzes and simply turn on the locked mode feature.
Here are a couple of tutorials to help you get started:
Please note that this program is still in “beta” and it may still contain some bugs or glitches. If you encounter a situation where a student is able to escape the locked mode and open a browser window, please send feedback using this form.