Only display certain items in AngularJS

I am a newbie to AngularJS and Ionic framework and using the basic Starter Tabs Ionic template, I want to be able to "Favourite/Bookmark" some items and display them on a different tab.

My books.js structure is as follow:

.factory('Books', function() {

  // books data
  var books = [{
    id: 0,
    title: 'Sample Title',
    author: 'Sample Author',
    category: 'Horor, Fiction',
    cover: '/cover.jpeg',
    details: 'some details about the book',
    chapters: [
      {
        id : 1,
        name: 'Chapter 1',
        filename: 'chapter1.html',
      },
      {
        id : 2,
        name: 'Chapter 2',
        filename: 'Chapter2.html',
      }
    ]
  }
  .....  
  return {
    all: function() {
      return books;
    },
    // remove a book from the list
    remove: function(book) {
      books.splice(books.indexOf(book), 1);
    },

Now, if I want to be able to add that book to a list, should I create a new array? or does angularJS provide some sort of library which can store that data without actually creating a new list?

I am really not sure how to approach this problem.

Update # 1: After looking at Andy's example, I have made the following modifications to the controllers.js

.controller('DashCtrl', function($scope, Books) {

  $scope.books = Books.all();
  $scope.remove = function(book) {
    Books.remove(book);
  };
  $scope.markFavorite = function(book) {
    Books.isFavorite = true;
  };
  $scope.unmarkFavorite = function(book) {
    Books.isFavorite = false;
  };    
})

and the buttons : 

<ion-option-button class="button-assertive" ng-click="remove(book)">
    Delete
</ion-option-button>
<ion-option-button class="button-positive" ng-click="markFavorite(book)">
    Fav
</ion-option-button>

but using the following ng-repeat: 

ng-repeat="book in books | filter:{isFavorite:true}"

I can't list favorite books.

Here's an example:

var app = angular.module('plunker', []);

app.controller('MainCtrl', function($scope) {
  $scope.books = [
    { title: 'Sample Title' },
    { title: 'Sample Title 2' },
    { title: 'Sample Title 3' },
    { title: 'Sample Title 4' }
  ];

  $scope.markFavorite = function(book) {
    book.isFavorite = true;
  };

  $scope.unmarkFavorite = function(book) {
    book.isFavorite = false;
  };

});

The view:

  <body ng-controller="MainCtrl">

    <p>All books</p>    
    <ul>
      <li ng-repeat="book in books"><button ng-click="markFavorite(book)">{{book.title}}</button></li>
    </ul>

    <p>Favorite books</p>    
    <ul>
      <li ng-repeat="book in books | filter:{isFavorite:true}"><button ng-click="unmarkFavorite(book)">{{book.title}}</button></li>
    </ul>

  </body>

Here's a Plunker.