Problems using jQuery validate to submit a form without page refresh

Question

I am creating a quiz in business catalyst and having some issues with my scripts.

I am trying to submit a form and then return the results of the form via the jquery validate and post functions. I keep getting an error saying that I have an uncaught TypeError:undefined is not a function. I'm not really sure what's going wrong with the code. I've tried with and without no Conflict and stripped away all of my excess coding and scripts and I still cannot figure out what I am doing wrong.

Any and all help understanding why it's not working is appreciated. Thank you!

Here is my code:

var returnResults = function() {
        $.post('Default.aspx?CCID=19627&FID=214659&ExcludeBoolFalse=True&PageID=11898769&ID=/quiz-survey-results', {'CAT_Custom_1': '{module_emailaddress}','CAT_Custom_206': '{tag_itemid}'}, function(data) {
            $("#quizResults").html(data);
        });
    };

    $(document).ready(function() {
        $('#qsForm').validate({
            submitHandler: function(form) {
                showAnswers();
                scoreQuiz();
                changeName();
                $(form).ajaxSubmit({  /** I've also used the form ID in place of the variable 'form'. */
                    type: 'POST',
                    url: $(this).attr('action'),
                    data: $(this).serialize(),
                    success: function() {
                        $('#quizSurveyDiv').hide('slow');
                        alert('Success!');
                        returnResults();
                    }
                });
            }
        });
    });