diff --git a/backup/moodle2/restore_stepslib.php b/backup/moodle2/restore_stepslib.php
index 529645f9bf8..7e4b7aac6ac 100644
--- a/backup/moodle2/restore_stepslib.php
+++ b/backup/moodle2/restore_stepslib.php
@@ -4446,6 +4446,12 @@ class restore_create_categories_and_questions extends restore_structure_step {
 
         // With newitemid = 0, let's create the question
         if (!$questionmapping->newitemid) {
+            if ($data->qtype === 'random') {
+                // Ensure that this newly created question is considered by
+                // \qtype_random\task\remove_unused_questions.
+                $data->hidden = 0;
+            }
+
             $newitemid = $DB->insert_record('question', $data);
             $this->set_mapping('question', $oldid, $newitemid);
             // Also annotate them as question_created, we need
diff --git a/question/type/random/classes/task/remove_unused_questions.php b/question/type/random/classes/task/remove_unused_questions.php
new file mode 100644
index 00000000000..08844f8ffa0
--- /dev/null
+++ b/question/type/random/classes/task/remove_unused_questions.php
@@ -0,0 +1,69 @@
+<?php
+// This file is part of Moodle - http://moodle.org/
+//
+// Moodle is free software: you can redistribute it and/or modify
+// it under the terms of the GNU General Public License as published by
+// the Free Software Foundation, either version 3 of the License, or
+// (at your option) any later version.
+//
+// Moodle is distributed in the hope that it will be useful,
+// but WITHOUT ANY WARRANTY; without even the implied warranty of
+// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+// GNU General Public License for more details.
+//
+// You should have received a copy of the GNU General Public License
+// along with Moodle.  If not, see <http://www.gnu.org/licenses/>.
+
+/**
+ * A scheduled task to remove unneeded random questions.
+ *
+ * @package   qtype_random
+ * @category  task
+ * @copyright 2018 Bo Pierce <email.bO.pierce@gmail.com>
+ * @license   http://www.gnu.org/copyleft/gpl.html GNU GPL v3 or later
+ */
+
+namespace qtype_random\task;
+
+defined('MOODLE_INTERNAL') || die();
+
+
+/**
+ * A scheduled task to remove unneeded random questions.
+ *
+ * @copyright 2018 Bo Pierce <email.bO.pierce@gmail.com>
+ * @license   http://www.gnu.org/copyleft/gpl.html GNU GPL v3 or later
+ */
+class remove_unused_questions extends \core\task\scheduled_task {
+
+    public function get_name() {
+        return get_string('taskunusedrandomscleanup', 'qtype_random');
+    }
+
+    public function execute() {
+        global $DB, $CFG;
+        require_once($CFG->libdir . '/questionlib.php');
+
+        // Find potentially unused random questions (up to 10000).
+        // Note, because we call question_delete_question below,
+        // the question will not actually be deleted if something else
+        // is using them, but nothing else in Moodle core uses qtype_random,
+        // and not many third-party plugins do.
+        $unusedrandomids = $DB->get_records_sql("
+                SELECT q.id, 1
+                  FROM {question} q
+             LEFT JOIN {quiz_slots} qslots ON q.id = qslots.questionid
+                 WHERE qslots.questionid IS NULL
+                   AND q.qtype = ? AND hidden = ?", ['random', 0], 0, 10000);
+
+        $count = 0;
+        foreach ($unusedrandomids as $unusedrandomid => $notused) {
+            question_delete_question($unusedrandomid);
+            // In case the question was not actually deleted (because it was in use somehow
+            // mark it as hidden so the query above will not return it again.
+            $DB->set_field('question', 'hidden', 1, ['id' => $unusedrandomid]);
+            $count += 1;
+        }
+        mtrace('Cleaned up ' . $count . ' unused random questions.');
+    }
+}
diff --git a/question/type/random/db/tasks.php b/question/type/random/db/tasks.php
new file mode 100644
index 00000000000..e6298dcd781
--- /dev/null
+++ b/question/type/random/db/tasks.php
@@ -0,0 +1,38 @@
+<?php
+// This file is part of Moodle - http://moodle.org/
+//
+// Moodle is free software: you can redistribute it and/or modify
+// it under the terms of the GNU General Public License as published by
+// the Free Software Foundation, either version 3 of the License, or
+// (at your option) any later version.
+//
+// Moodle is distributed in the hope that it will be useful,
+// but WITHOUT ANY WARRANTY; without even the implied warranty of
+// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+// GNU General Public License for more details.
+//
+// You should have received a copy of the GNU General Public License
+// along with Moodle.  If not, see <http://www.gnu.org/licenses/>.
+
+/**
+ * Definition of question/type/random scheduled tasks.
+ *
+ * @package   qtype_random
+ * @category  task
+ * @copyright 2018 Bo Pierce <email.bO.pierce@gmail.com>
+ * @license   http://www.gnu.org/copyleft/gpl.html GNU GPL v3 or later
+ */
+
+defined('MOODLE_INTERNAL') || die();
+
+$tasks = array(
+    array(
+        'classname' => 'qtype_random\task\remove_unused_questions',
+        'blocking' => 0,
+        'minute' => 'R',
+        'hour' => '*',
+        'day' => '*',
+        'month' => '*',
+        'dayofweek' => '*'
+    )
+);
diff --git a/question/type/random/lang/en/qtype_random.php b/question/type/random/lang/en/qtype_random.php
index d411e463100..f6b76048deb 100644
--- a/question/type/random/lang/en/qtype_random.php
+++ b/question/type/random/lang/en/qtype_random.php
@@ -33,3 +33,4 @@ $string['randomqname'] = 'Random ({$a})';
 $string['randomqplusname'] = 'Random ({$a} and subcategories)';
 $string['selectedby'] = '{$a->questionname} selected by {$a->randomname}';
 $string['selectmanualquestions'] = 'Random questions can use manually graded questions';
+$string['taskunusedrandomscleanup'] = 'Remove unused random questions';
diff --git a/question/type/random/tests/cleanup_task_test.php b/question/type/random/tests/cleanup_task_test.php
new file mode 100644
index 00000000000..a8f43b0b5e2
--- /dev/null
+++ b/question/type/random/tests/cleanup_task_test.php
@@ -0,0 +1,70 @@
+<?php
+// This file is part of Moodle - http://moodle.org/
+//
+// Moodle is free software: you can redistribute it and/or modify
+// it under the terms of the GNU General Public License as published by
+// the Free Software Foundation, either version 3 of the License, or
+// (at your option) any later version.
+//
+// Moodle is distributed in the hope that it will be useful,
+// but WITHOUT ANY WARRANTY; without even the implied warranty of
+// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+// GNU General Public License for more details.
+//
+// You should have received a copy of the GNU General Public License
+// along with Moodle.  If not, see <http://www.gnu.org/licenses/>.
+
+/**
+ * Tests of the scheduled task for cleaning up random questions.
+ *
+ * @package    qtype_random
+ * @copyright  2018 The Open University
+ * @license    http://www.gnu.org/copyleft/gpl.html GNU GPL v3 or later
+ */
+
+
+defined('MOODLE_INTERNAL') || die();
+
+global $CFG;
+require_once($CFG->dirroot . '/mod/quiz/locallib.php');
+
+
+/**
+ * Tests of the scheduled task for cleaning up random questions.
+ *
+ * @copyright  2018 The Open University
+ * @license    http://www.gnu.org/copyleft/gpl.html GNU GPL v3 or later
+ */
+class qtype_random_cleanup_task_testcase extends advanced_testcase {
+
+    public function test_cleanup_task_removes_unused_question() {
+        global $DB;
+        $this->resetAfterTest();
+        $this->setAdminUser();
+
+        $generator = $this->getDataGenerator();
+        $questiongenerator = $generator->get_plugin_generator('core_question');
+        $quizgenerator = $generator->get_plugin_generator('mod_quiz');
+        $cat = $questiongenerator->create_question_category();
+        $quiz = $quizgenerator->create_instance(['course' => SITEID]);
+
+        // Add two random questions.
+        quiz_add_random_questions($quiz, 0, $cat->id, 2, false);
+        $quizslots = $DB->get_records('quiz_slots', ['quizid' => $quiz->id],
+                'slot', 'slot, id, questionid');
+
+        // Now remove the second from the quiz. (Do it manually,
+        // because the API cleans up the random question, but we are trying to
+        // create an orphaned random question.)
+        $DB->delete_records('quiz_slots', array('id' => $quizslots[2]->id));
+
+        // Run the scheduled task.
+        $task = new \qtype_random\task\remove_unused_questions();
+        $this->expectOutputString("Cleaned up 1 unused random questions.\n");
+        $task->execute();
+
+        // Verify.
+        $this->assertTrue($DB->record_exists('question', ['id' => $quizslots[1]->questionid]));
+        $this->assertFalse($DB->record_exists('question', ['id' => $quizslots[2]->questionid]));
+    }
+}
diff --git a/question/type/random/version.php b/question/type/random/version.php
index 77ca68c8332..611212b1693 100644
--- a/question/type/random/version.php
+++ b/question/type/random/version.php
@@ -26,7 +26,7 @@
 defined('MOODLE_INTERNAL') || die();
 
 $plugin->component = 'qtype_random';
-$plugin->version   = 2017111300;
+$plugin->version   = 2017111301;
 
 $plugin->requires  = 2017110800;