diff --git a/core/modules/contact/tests/src/Functional/ContactPersonalTest.php b/core/modules/contact/tests/src/Functional/ContactPersonalTest.php
index 7e6ecad7cd..5f6e8e6ad2 100644
--- a/core/modules/contact/tests/src/Functional/ContactPersonalTest.php
+++ b/core/modules/contact/tests/src/Functional/ContactPersonalTest.php
@@ -6,8 +6,8 @@
 use Drupal\Component\Render\PlainTextOutput;
 use Drupal\Core\Session\AccountInterface;
 use Drupal\Core\Test\AssertMailTrait;
-use Drupal\system\Tests\Cache\AssertPageCacheContextsAndTagsTrait;
 use Drupal\Tests\BrowserTestBase;
+use Drupal\Tests\system\Functional\Cache\AssertPageCacheContextsAndTagsTrait;
 use Drupal\user\RoleInterface;
 
 /**
diff --git a/core/modules/content_translation/tests/src/Functional/ContentTranslationUITestBase.php b/core/modules/content_translation/tests/src/Functional/ContentTranslationUITestBase.php
index e69329cb5f..c755ac4906 100644
--- a/core/modules/content_translation/tests/src/Functional/ContentTranslationUITestBase.php
+++ b/core/modules/content_translation/tests/src/Functional/ContentTranslationUITestBase.php
@@ -11,7 +11,7 @@
 use Drupal\Core\Url;
 use Drupal\language\Entity\ConfigurableLanguage;
 use Drupal\Component\Utility\SafeMarkup;
-use Drupal\system\Tests\Cache\AssertPageCacheContextsAndTagsTrait;
+use Drupal\Tests\system\Functional\Cache\AssertPageCacheContextsAndTagsTrait;
 
 /**
  * Tests the Content Translation UI.
diff --git a/core/modules/history/tests/src/Functional/HistoryTest.php b/core/modules/history/tests/src/Functional/HistoryTest.php
index 6b4708b898..065b9af7aa 100644
--- a/core/modules/history/tests/src/Functional/HistoryTest.php
+++ b/core/modules/history/tests/src/Functional/HistoryTest.php
@@ -4,8 +4,8 @@
 
 use Drupal\Component\Serialization\Json;
 use Drupal\Core\Url;
-use Drupal\system\Tests\Cache\AssertPageCacheContextsAndTagsTrait;
 use Drupal\Tests\BrowserTestBase;
+use Drupal\Tests\system\Functional\Cache\AssertPageCacheContextsAndTagsTrait;
 use GuzzleHttp\Cookie\CookieJar;
 
 /**
diff --git a/core/modules/node/tests/src/Functional/NodeAccessAutoBubblingTest.php b/core/modules/node/tests/src/Functional/NodeAccessAutoBubblingTest.php
index 6af8d8de66..20154553fc 100644
--- a/core/modules/node/tests/src/Functional/NodeAccessAutoBubblingTest.php
+++ b/core/modules/node/tests/src/Functional/NodeAccessAutoBubblingTest.php
@@ -3,7 +3,7 @@
 namespace Drupal\Tests\node\Functional;
 
 use Drupal\Core\Url;
-use Drupal\system\Tests\Cache\AssertPageCacheContextsAndTagsTrait;
+use Drupal\Tests\system\Functional\Cache\AssertPageCacheContextsAndTagsTrait;
 
 /**
  * Tests the node access automatic cacheability bubbling logic.
diff --git a/core/modules/node/tests/src/Functional/NodeBlockFunctionalTest.php b/core/modules/node/tests/src/Functional/NodeBlockFunctionalTest.php
index ad3613d74f..c203c5017a 100644
--- a/core/modules/node/tests/src/Functional/NodeBlockFunctionalTest.php
+++ b/core/modules/node/tests/src/Functional/NodeBlockFunctionalTest.php
@@ -4,7 +4,7 @@
 
 use Drupal\block\Entity\Block;
 use Drupal\Core\EventSubscriber\MainContentViewSubscriber;
-use Drupal\system\Tests\Cache\AssertPageCacheContextsAndTagsTrait;
+use Drupal\Tests\system\Functional\Cache\AssertPageCacheContextsAndTagsTrait;
 use Drupal\user\RoleInterface;
 
 /**
diff --git a/core/modules/page_cache/src/Tests/PageCacheTagsIntegrationTest.php b/core/modules/page_cache/src/Tests/PageCacheTagsIntegrationTest.php
index 6ec8a29cf6..be704d16ed 100644
--- a/core/modules/page_cache/src/Tests/PageCacheTagsIntegrationTest.php
+++ b/core/modules/page_cache/src/Tests/PageCacheTagsIntegrationTest.php
@@ -5,8 +5,8 @@
 use Drupal\Core\EventSubscriber\MainContentViewSubscriber;
 use Drupal\Core\Language\LanguageInterface;
 use Drupal\simpletest\WebTestBase;
-use Drupal\system\Tests\Cache\AssertPageCacheContextsAndTagsTrait;
 use Drupal\node\NodeInterface;
+use Drupal\Tests\system\Functional\Cache\AssertPageCacheContextsAndTagsTrait;
 
 /**
  * Enables the page cache and tests its cache tags in various scenarios.
diff --git a/core/modules/statistics/tests/src/Functional/StatisticsReportsTest.php b/core/modules/statistics/tests/src/Functional/StatisticsReportsTest.php
index edebca166c..0f169238c6 100644
--- a/core/modules/statistics/tests/src/Functional/StatisticsReportsTest.php
+++ b/core/modules/statistics/tests/src/Functional/StatisticsReportsTest.php
@@ -3,7 +3,7 @@
 namespace Drupal\Tests\statistics\Functional;
 
 use Drupal\Core\Cache\Cache;
-use Drupal\system\Tests\Cache\AssertPageCacheContextsAndTagsTrait;
+use Drupal\Tests\system\Functional\Cache\AssertPageCacheContextsAndTagsTrait;
 
 /**
  * Tests display of statistics report blocks.
diff --git a/core/modules/system/src/Tests/Cache/AssertPageCacheContextsAndTagsTrait.php b/core/modules/system/src/Tests/Cache/AssertPageCacheContextsAndTagsTrait.php
index 6bea791e91..8bb3074b7b 100644
--- a/core/modules/system/src/Tests/Cache/AssertPageCacheContextsAndTagsTrait.php
+++ b/core/modules/system/src/Tests/Cache/AssertPageCacheContextsAndTagsTrait.php
@@ -2,6 +2,8 @@
 
 namespace Drupal\system\Tests\Cache;
 
+@trigger_error(__NAMESPACE__ . '\AssertPageCacheContextsAndTagsTrait is deprecated in Drupal 8.4.0 and will be removed before Drupal 9.0.0. Instead, use \Drupal\Tests\system\Functional\Cache\AssertPageCacheContextsAndTagsTrait', E_USER_DEPRECATED);
+
 use Drupal\Core\Cache\Cache;
 use Drupal\Core\Url;
 
@@ -9,6 +11,10 @@
  * Provides test assertions for testing page-level cache contexts & tags.
  *
  * Can be used by test classes that extend \Drupal\simpletest\WebTestBase.
+ *
+ * @deprecated Scheduled for removal in Drupal 9.0.0. Use
+ *  \Drupal\Tests\system\Functional\Cache\AssertPageCacheContextsAndTagsTrait
+ *  instead.
  */
 trait AssertPageCacheContextsAndTagsTrait {
 
diff --git a/core/modules/system/src/Tests/Cache/AssertPageCacheContextsAndTagsTrait.php b/core/modules/system/tests/src/Functional/Cache/AssertPageCacheContextsAndTagsTrait.php
similarity index 98%
copy from core/modules/system/src/Tests/Cache/AssertPageCacheContextsAndTagsTrait.php
copy to core/modules/system/tests/src/Functional/Cache/AssertPageCacheContextsAndTagsTrait.php
index 6bea791e91..667aacb256 100644
--- a/core/modules/system/src/Tests/Cache/AssertPageCacheContextsAndTagsTrait.php
+++ b/core/modules/system/tests/src/Functional/Cache/AssertPageCacheContextsAndTagsTrait.php
@@ -1,6 +1,6 @@
 <?php
 
-namespace Drupal\system\Tests\Cache;
+namespace Drupal\Tests\system\Functional\Cache;
 
 use Drupal\Core\Cache\Cache;
 use Drupal\Core\Url;
@@ -8,7 +8,7 @@
 /**
  * Provides test assertions for testing page-level cache contexts & tags.
  *
- * Can be used by test classes that extend \Drupal\simpletest\WebTestBase.
+ * Can be used by test classes that extend \Drupal\Tests\BrowserTestBase.
  */
 trait AssertPageCacheContextsAndTagsTrait {
 
diff --git a/core/modules/system/src/Tests/Cache/SessionExistsCacheContextTest.php b/core/modules/system/tests/src/Functional/Cache/SessionExistsCacheContextTest.php
similarity index 82%
rename from core/modules/system/src/Tests/Cache/SessionExistsCacheContextTest.php
rename to core/modules/system/tests/src/Functional/Cache/SessionExistsCacheContextTest.php
index 8815bf340f..78fb983a61 100644
--- a/core/modules/system/src/Tests/Cache/SessionExistsCacheContextTest.php
+++ b/core/modules/system/tests/src/Functional/Cache/SessionExistsCacheContextTest.php
@@ -1,16 +1,16 @@
 <?php
 
-namespace Drupal\system\Tests\Cache;
+namespace Drupal\Tests\system\Functional\Cache;
 
 use Drupal\Core\Url;
-use Drupal\simpletest\WebTestBase;
+use Drupal\Tests\BrowserTestBase;
 
 /**
  * Tests the 'session.exists' cache context service.
  *
  * @group Cache
  */
-class SessionExistsCacheContextTest extends WebTestBase {
+class SessionExistsCacheContextTest extends BrowserTestBase {
 
   /**
    * Modules to enable.
@@ -59,8 +59,7 @@ public function testCacheContext() {
    * Asserts whether a session cookie is present on the client or not.
    */
   public function assertSessionCookieOnClient($expected_present) {
-    $non_deleted_cookies = array_filter($this->cookies, function ($item) { return $item['value'] !== 'deleted'; });
-    $this->assertEqual($expected_present, isset($non_deleted_cookies[$this->getSessionName()]), 'Session cookie exists.');
+    $this->assertEqual($expected_present, (bool) $this->getSession()->getCookie($this->getSessionName()), 'Session cookie exists.');
   }
 
 }
diff --git a/core/modules/tracker/tests/src/Functional/TrackerTest.php b/core/modules/tracker/tests/src/Functional/TrackerTest.php
index 17f95ee50d..1a77d95ac8 100644
--- a/core/modules/tracker/tests/src/Functional/TrackerTest.php
+++ b/core/modules/tracker/tests/src/Functional/TrackerTest.php
@@ -9,8 +9,8 @@
 use Drupal\Core\Session\AccountInterface;
 use Drupal\field\Entity\FieldStorageConfig;
 use Drupal\node\Entity\Node;
-use Drupal\system\Tests\Cache\AssertPageCacheContextsAndTagsTrait;
 use Drupal\Tests\BrowserTestBase;
+use Drupal\Tests\system\Functional\Cache\AssertPageCacheContextsAndTagsTrait;
 
 /**
  * Create and delete nodes and check for their display in the tracker listings.
diff --git a/core/modules/views/tests/src/Functional/Handler/FieldWebTest.php b/core/modules/views/tests/src/Functional/Handler/FieldWebTest.php
index 318be3f902..a3646f0c0b 100644
--- a/core/modules/views/tests/src/Functional/Handler/FieldWebTest.php
+++ b/core/modules/views/tests/src/Functional/Handler/FieldWebTest.php
@@ -7,7 +7,7 @@
 use Drupal\Component\Utility\UrlHelper;
 use Drupal\Core\Render\RenderContext;
 use Drupal\Core\Url;
-use Drupal\system\Tests\Cache\AssertPageCacheContextsAndTagsTrait;
+use Drupal\Tests\system\Functional\Cache\AssertPageCacheContextsAndTagsTrait;
 use Drupal\Tests\views\Functional\ViewTestBase;
 use Drupal\views\Views;
 
diff --git a/core/modules/views/tests/src/Functional/Plugin/CacheWebTest.php b/core/modules/views/tests/src/Functional/Plugin/CacheWebTest.php
index 40bf60189c..f8ce5a927f 100644
--- a/core/modules/views/tests/src/Functional/Plugin/CacheWebTest.php
+++ b/core/modules/views/tests/src/Functional/Plugin/CacheWebTest.php
@@ -2,7 +2,7 @@
 
 namespace Drupal\Tests\views\Functional\Plugin;
 
-use Drupal\system\Tests\Cache\AssertPageCacheContextsAndTagsTrait;
+use Drupal\Tests\system\Functional\Cache\AssertPageCacheContextsAndTagsTrait;
 use Drupal\Tests\views\Functional\ViewTestBase;
 use Drupal\views\Plugin\views\display\DisplayPluginBase;
 use Drupal\views\Views;
diff --git a/core/modules/views/tests/src/Functional/Plugin/ContextualFiltersBlockContextTest.php b/core/modules/views/tests/src/Functional/Plugin/ContextualFiltersBlockContextTest.php
index 567e1c930a..215ee2890f 100644
--- a/core/modules/views/tests/src/Functional/Plugin/ContextualFiltersBlockContextTest.php
+++ b/core/modules/views/tests/src/Functional/Plugin/ContextualFiltersBlockContextTest.php
@@ -3,9 +3,9 @@
 namespace Drupal\Tests\views\Functional\Plugin;
 
 use Drupal\Core\Plugin\Context\ContextDefinitionInterface;
+use Drupal\Tests\system\Functional\Cache\AssertPageCacheContextsAndTagsTrait;
 use Drupal\Tests\views\Functional\ViewTestBase;
 use Drupal\views\Tests\ViewTestData;
-use Drupal\system\Tests\Cache\AssertPageCacheContextsAndTagsTrait;
 
 /**
  * A test for contextual filters exposed as block context.
diff --git a/core/modules/views/tests/src/Functional/Plugin/DisplayPageWebTest.php b/core/modules/views/tests/src/Functional/Plugin/DisplayPageWebTest.php
index 3d2aca6639..501d9226ee 100644
--- a/core/modules/views/tests/src/Functional/Plugin/DisplayPageWebTest.php
+++ b/core/modules/views/tests/src/Functional/Plugin/DisplayPageWebTest.php
@@ -2,7 +2,7 @@
 
 namespace Drupal\Tests\views\Functional\Plugin;
 
-use Drupal\system\Tests\Cache\AssertPageCacheContextsAndTagsTrait;
+use Drupal\Tests\system\Functional\Cache\AssertPageCacheContextsAndTagsTrait;
 use Drupal\Tests\views\Functional\ViewTestBase;
 use Drupal\views\Views;
 
diff --git a/core/modules/views/tests/src/Functional/Plugin/ExposedFormTest.php b/core/modules/views/tests/src/Functional/Plugin/ExposedFormTest.php
index 38b7327b4d..134f7b5458 100644
--- a/core/modules/views/tests/src/Functional/Plugin/ExposedFormTest.php
+++ b/core/modules/views/tests/src/Functional/Plugin/ExposedFormTest.php
@@ -4,7 +4,7 @@
 
 use Drupal\Component\Utility\Html;
 use Drupal\entity_test\Entity\EntityTest;
-use Drupal\system\Tests\Cache\AssertPageCacheContextsAndTagsTrait;
+use Drupal\Tests\system\Functional\Cache\AssertPageCacheContextsAndTagsTrait;
 use Drupal\Tests\views\Functional\ViewTestBase;
 use Drupal\views\ViewExecutable;
 use Drupal\views\Views;
diff --git a/core/modules/views/tests/src/Functional/Plugin/PagerTest.php b/core/modules/views/tests/src/Functional/Plugin/PagerTest.php
index eda88916d6..8085256df0 100644
--- a/core/modules/views/tests/src/Functional/Plugin/PagerTest.php
+++ b/core/modules/views/tests/src/Functional/Plugin/PagerTest.php
@@ -2,7 +2,7 @@
 
 namespace Drupal\Tests\views\Functional\Plugin;
 
-use Drupal\system\Tests\Cache\AssertPageCacheContextsAndTagsTrait;
+use Drupal\Tests\system\Functional\Cache\AssertPageCacheContextsAndTagsTrait;
 use Drupal\Tests\views\Functional\ViewTestBase;
 use Drupal\views\Views;
 use Drupal\language\Entity\ConfigurableLanguage;
diff --git a/core/modules/views_ui/tests/src/Functional/DisplayPathTest.php b/core/modules/views_ui/tests/src/Functional/DisplayPathTest.php
index f8e58e719c..af2c4e2a6f 100644
--- a/core/modules/views_ui/tests/src/Functional/DisplayPathTest.php
+++ b/core/modules/views_ui/tests/src/Functional/DisplayPathTest.php
@@ -4,7 +4,7 @@
 
 use Drupal\Core\Menu\MenuTreeParameters;
 use Drupal\menu_link_content\Entity\MenuLinkContent;
-use Drupal\system\Tests\Cache\AssertPageCacheContextsAndTagsTrait;
+use Drupal\Tests\system\Functional\Cache\AssertPageCacheContextsAndTagsTrait;
 
 /**
  * Tests the UI of generic display path plugin.
@@ -13,6 +13,7 @@
  * @see \Drupal\views\Plugin\views\display\PathPluginBase
  */
 class DisplayPathTest extends UITestBase {
+
   use AssertPageCacheContextsAndTagsTrait;
 
   protected function setUp($import_test_views = TRUE) {