Insert into DB and AJAX

Question

So I have 3 forms on a page, and depending on which form is submitted - something is entered into the DB. Now, this code works perfectly, if I include it all on the same page, but of course, it requires a refresh, so I am looking to implement AJAX. Now, I've moved the insert php code onto a new page, and am looking for some help with building an AJAX call to pass the data to the php page, which will proceed to insert the right data.

Essentially:

1. There are three forms, one for each activity type.
2. Depending on which form is submitted, some different data is entered into the DB
3. Need help with building an AJAX call to figure out which form was submitted, pass the data to the next page succesfully so the PHP code can insert into DB.

4. I will rewrite the SQL using PDO, so please ignore that in the current code.

   <form id="form1"  method="post">
   <input type="submit" id="activity1" name="activity1" class="btn btn-info span3 mhm" value="<?php echo htmlspecialchars($type1);?>">
   </form>
   
   <form id="form2" action="registerresults.php" method="post">
     <input type="submit" id="activity2" name="activity2" class="btn btn-info span3 mhm" value="<?php echo htmlspecialchars($type2);?>">
   </form>
   
   <form id="form3" action="registerresults.php" method="post">
     <input type="submit" id="activity3" name="activity3" class="btn btn-info span3 mhm" value="<?php echo htmlspecialchars($type3);?>">
   </form>
   

   //registerresults.php - Inserts into DB

        $id = $_SESSION['id'];
        $competitionId = $_GET['competitionId'];
        $organisationId = $_SESSION['organisationId'];
   
   
       if (isset($_POST['activity1']) && !empty($_POST['activity1']))
       {
           //insert new points into database
           $today = date("Y-m-d h:i:s");
           $insertCall = mysql_query("INSERT INTO `entries` (`userid`, `competitionId`, `activity_type`, `activity_id`, `points`, `date`) VALUES ('$id', '$competitionId', '$type1', '1', '$weighting1', '$today');");
   
       }
   
       if (isset($_POST['activity2']) && !empty($_POST['activity2']))
       {
           $today = date("Y-m-d h:i:s");
           $insertCall = mysql_query("INSERT INTO `entries` (`userid`, `competitionId`, `activity_type`, `activity_id`, `points`, `date`) VALUES ('$id', '$competitionId', '$type2', '2', '$weighting2', '$today');");
   
       }
   
       if (isset($_POST['activity3']) && !empty($_POST['activity3']))
       {
           $today = date("Y-m-d h:i:s");
           $insertCall = mysql_query("INSERT INTO `entries` (`userid`, `competitionId`, `activity_type`, `activity_id`, `points`, `date`) VALUES ('$id', '$competitionId', '$type3', '3', '$weighting3', '$today');");
   
       }
   ?>