Edit in JSFiddle

angular.module('MyModule', [])
    .controller('MyController', function ($scope) {
        
    $scope.mytext = "Hello World"; //default   
    $scope.myfunction = function (data) {
        alert("---" + data);
    };
        
        $scope.$watch('text', function(newValue, oldValue) {
          console.log(newValue);
          console.log(oldValue);
        });
});

window.onload = function () {
   //get ng scope by elem id
    var ngScope =  angular.element(document.getElementById('span')).scope();
    //trigger ng-function by jQuery
   ngScope.myfunction('test');
   
    //change mytext parameter
   ngScope.mytext = 'Hello World 2';
    
   //update mytext to angular world with $apply function 
   ngScope.$apply(function(){
       
        
    });
}

<div id="span" ng-app='MyModule' ng-controller="MyController">
    {{mytext}}
</div>