How to grant User Points after Quiz questions are answered correctly?
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:

{ "rules_send_results_at_the_end_of_a_quiz" : {
    "LABEL" : "Send quiz results at the end of a quiz",
    "PLUGIN" : "reaction rule",
    "ACTIVE" : false,
    "OWNER" : "rules",
    "TAGS" : [ "quiz" ],
    "REQUIRES" : [ "rules", "entity" ],
    "ON" : { "quiz_result_update" : [] },
    "IF" : [
      { "data_is" : { "data" : [ "quiz-result-unchanged:is-evaluated" ], "value" : "0" } },
      { "data_is" : { "data" : [ "quiz-result:is-evaluated" ], "value" : "1" } }
    ],
    "DO" : [
      { "mail" : {
          "to" : [ "quiz-result:uid:mail" ],
          "subject" : "[site:name]: Your results for [quiz-result:nid:title]",
          "message" : "[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]",
          "language" : [ "" ]
        }
      },
      { "mail" : {
          "to" : [ "quiz-result:nid:author:mail" ],
          "subject" : "[site:name]: [quiz-result:uid:name]\u0027s results for [quiz-result:nid:title]",
          "message" : "[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",
          "language" : [ "" ]
        }
      }
    ]
  }
}


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 Rules Action to grant an amount of User Points that you may want to be related to [quiz-result:score] (note that this token is also shown in the Rules example above (within the Rules Action).

If you're not familiar with how to use Rules to grant user points, then have a look at the answer to "How to grant userpoints only for modifying nodes last changed at least 20 days ago?" (which also includes a Rules example to make that happen).

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.