Only show the complete form at the end of the quiz
I don't know enough about the Quiz module to say for sure but have you checked out the theme functions available for Quiz?

There is a theme function called theme_quiz_take_summary().
It has a form that it adds if the quiz is set to display_feedback. Maybe it's a setting for the quiz somewhere?

// Get the feedback for all questions. These are included here to provide maximum flexibility for themers
if ($quiz-&gt;display_feedback) {
  $form = drupal_get_form('quiz_report_form', $questions);
  $output .= drupal_render($form);
}


If you want to have your own version of that theme function you should place the whole function in your theme and replace theme_quiz_take_summary() with NAMEOFYOURTHEME_quiz_take_summary().