How to write tests for classes with inheritance

I have a project written in Angular 1.3 that have services that inherit each other. There is a BaseApiService, which is a parent class and it implements a lot of functionality related to API calls. It looks like that:

.factory('BaseApiService', function ($resource, apiHost, apiUrl, WebSocketService, $q, $timeout) {

  //initializer
  return function (resourceName, options) {
    options = angular.extend({}, {
      resourceUrl: resourceName + '/:id',
      resourceParams: {id: '@id'},
      resourceMethods: {
        'get':    {method:'GET'},
        'update': {method:'PUT'},
        'save':   {method:'POST'},
        'all':    {method:'GET', isArray:true},
        'remove': {method:'DELETE'},
        'delete': {method:'DELETE'}
      }
    }, options);


    this.loadCache = function () {
      //...
    };

    this.new = function () {
      //...
    };

    this.get = function (id) {
      //...
    };

    this.getBy = function (propertyName, value) {
      //...
    };

    this.all = function (params) {
      //...
    };

    //lots of other methods here

Then there are multiple children classes that implement access to the specific API end-points. They are done like that:

.factory('HandymanTasks', function(BaseApiService, $q){

  var service = new BaseApiService('handyman_tasks');

  angular.extend(service, {
    getByRoomId: function(room_id){
      return service.getBy('room_id', room_id);
    },
    capturePhoto: function() {
      //...
    }
  });

  return service;
});

Children services for the most part use parent's methods and only add a few of their own. Parent class is only instantiated for the sake of inheritance, it isn't used on it's own. My question is: how to properly write tests in this scenario? I need to ensure the all the API access functions work in all the children classes. My ideas are:

• Write a helper that tests all the API access functions (that are implemented in the parent) and then call it in tests for all children classes;
• Test API calls in the parent class, assume that they work in children classes, since I know that they are always inherited. Test only for their own functions in children classes;
• Test that children have all the methods of the parents defined, assume that they work properly, because the parent class is covered by tests;

Basically, I just want to ensure that all the functionality of the children classes work properly, but don't have too much copy-pasted/very similar tests in a test suit for each class.