Testing non-scope functions in Angular Controller with Jasmine

Jasmine is one of the most widely used testing frameworks to unit-test javascript code in BDD manner. I tried to use it for AngularJS components testing. AngularJS documentation provides the following sample code

describe('PasswordController', function() {
  beforeEach(module('app'));
  var $controller;

  beforeEach(inject(function(_$controller_){
    $controller = _$controller_;
  }));

  describe('$scope.grade', function() {
    it('sets the strength to "strong" if the password length is >8 chars', function() {
      var $scope = {};
      var controller = $controller('PasswordController', { $scope: $scope });
      $scope.password = 'longerthaneightchars';
      $scope.grade();
      expect($scope.strength).toEqual('strong');
    });
  });
});

So the code above uses angular mock library and via dependency injection processes a scope through a controller. Now I have a scope object with functions and objects my controller assigned to it. I can test it well. Happy.

Now the interesting part is if I want to test the functions which are not linked to the scope. For example, the doSomethingVeryCoolThatNeedsTesting function below

angular.module('app', [])
.controller('PasswordController', function PasswordController($scope) {
  $scope.password = '';
  $scope.grade = function() {
    var size = $scope.password.length;
    if (size > 8) {
      $scope.strength = 'strong';
    } else if (size > 3) {
      $scope.strength = 'medium';
    } else {
      $scope.strength = 'weak';
    }

   function doSomethingVeryCoolThatNeedsTesting() {
    ....  
   }

  };
});

It seems that whenever I use $controller('PasswordController', { $scope: $scope }); it returns a populated $scope object and undefined controller object.

TL;DR

Is there a way I can test Angular Controller functions which are not linked to the scope?