Questions can be added to a new Quiz through the question bank. Questions may be searched for by either by the quiz(zes) or by the course(s) that they are included in.
Create a Quiz.
After creating the quiz, click the "Edit questions" link.
Click the "Questions by Quiz" tab or the "Questions by Course" tab (7.6+).
Adjust the filters to limit the list of questions.
Check the box next to the questions to add to the Quiz.
Click the "Add questions to quiz" button.
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The selected questions are now in the Quiz.