How to perform a redirect after completing a Quiz?
If using Quiz 7.x-5.x
Assuming you're using the 7.x-5.x-rc3 version of the Quiz module, you can take advantage of integration with the Rules module that this new release comes with.
To do so, have a look at the delivered rule, which looks like so:
{ &quot;rules_send_results_at_the_end_of_a_quiz&quot; : {
    &quot;LABEL&quot; : &quot;Send quiz results at the end of a quiz&quot;,
    &quot;PLUGIN&quot; : &quot;reaction rule&quot;,
    &quot;ACTIVE&quot; : false,
    &quot;OWNER&quot; : &quot;rules&quot;,
    &quot;TAGS&quot; : [ &quot;quiz&quot; ],
    &quot;REQUIRES&quot; : [ &quot;rules&quot;, &quot;entity&quot; ],
    &quot;ON&quot; : { &quot;quiz_result_update&quot; : [] },
    &quot;IF&quot; : [
      { &quot;data_is&quot; : { &quot;data&quot; : [ &quot;quiz-result-unchanged:is-evaluated&quot; ], &quot;value&quot; : &quot;0&quot; } },
      { &quot;data_is&quot; : { &quot;data&quot; : [ &quot;quiz-result:is-evaluated&quot; ], &quot;value&quot; : &quot;1&quot; } }
    ],
    &quot;DO&quot; : [
      { &quot;mail&quot; : {
          &quot;to&quot; : [ &quot;quiz-result:uid:mail&quot; ],
          &quot;subject&quot; : &quot;[site:name]: Your results for [quiz-result:nid:title]&quot;,
          &quot;message&quot; : &quot;[quiz-result:uid:name],\r\n\r\nYou finished the quiz [quiz-result:nid:title] on [quiz-result:time-start]\r\n\r\nYour score: [quiz-result:score]%\r\n\r\nYou can access the result here: [site:url]node\/[quiz-result:nid:nid]\/quiz-results\/[quiz-result:result-id]&quot;,
          &quot;language&quot; : [ &quot;&quot; ]
        }
      },
      { &quot;mail&quot; : {
          &quot;to&quot; : [ &quot;quiz-result:nid:author:mail&quot; ],
          &quot;subject&quot; : &quot;[site:name]: [quiz-result:uid:name]\u0027s results for [quiz-result:nid:title]&quot;,
          &quot;message&quot; : &quot;[quiz-result:nid:author:name],\r\n\r\n[quiz-result:uid:name] finished the quiz [quiz-result:nid:title] on [quiz-result:time-start]\r\n\r\nTheir score: [quiz-result:score]%\r\n\r\nYou can access the result here: [site:url]node\/[quiz-result:nid:nid]\/quiz\/results\/[quiz-result:result-id]\/view&quot;,
          &quot;language&quot; : [ &quot;&quot; ]
        }
      }
    ]
  }
}

After you enable Rules (and Rules UI, a submodule of it), just clone the above rule (using the Rules UI) and replace both Rules Actions with a basic &quot;redirect&quot; (a typical Rules Action) that fits your needs.
If using Quiz 7.x-4.x
For the 7.x-4.x version of the Quiz module, you may want to try the patch from fago (aka the Rules maestro ...), attached to issue # 1300420, which has a description like so (note the last phrase in it ...):

... adds basic rules integration to quiz. It includes an event when users have finished taking a quiz, a condition to check whether a user has passed a certain quiz and an action to clear quiz results for a user.
Patch works for me.