diff --git a/wagtail/contrib/postgres_search/tests/test_backend.py b/wagtail/contrib/postgres_search/tests/test_backend.py
index 1f56f8936..d4a05e429 100644
--- a/wagtail/contrib/postgres_search/tests/test_backend.py
+++ b/wagtail/contrib/postgres_search/tests/test_backend.py
@@ -3,12 +3,12 @@ import unittest
 
 from django.test import TestCase
 
-from wagtail.search.tests.test_backends import BackendTests
+from wagtail.search.tests.test_backends import QueryAPITestMixin, BackendTests
 
 from ..utils import BOOSTS_WEIGHTS, WEIGHTS_VALUES, determine_boosts_weights, get_weight
 
 
-class TestPostgresSearchBackend(BackendTests, TestCase):
+class TestPostgresSearchBackend(QueryAPITestMixin, BackendTests, TestCase):
     backend_path = 'wagtail.contrib.postgres_search.backend'
 
     def test_weights(self):
diff --git a/wagtail/search/tests/elasticsearch_common_tests.py b/wagtail/search/tests/elasticsearch_common_tests.py
index a9fbe738b..034d502e2 100644
--- a/wagtail/search/tests/elasticsearch_common_tests.py
+++ b/wagtail/search/tests/elasticsearch_common_tests.py
@@ -177,41 +177,3 @@ class ElasticsearchCommonSearchBackendTests(BackendTests):
     @unittest.expectedFailure
     def test_delete(self):
         super().test_delete()
-
-    #
-    # Basic query classes
-    #
-
-    # Not implemented yet
-    @unittest.expectedFailure
-    def test_term(self):
-        super().test_term()
-
-    # Not implemented yet
-    @unittest.expectedFailure
-    def test_and(self):
-        super().test_and()
-
-    # Not implemented yet
-    @unittest.expectedFailure
-    def test_or(self):
-        super().test_or()
-
-    # Not implemented yet
-    @unittest.expectedFailure
-    def test_not(self):
-        super().test_not()
-
-    # Not implemented yet
-    @unittest.expectedFailure
-    def test_operators_combination(self):
-        super().test_operators_combination()
-
-    #
-    # Shortcut query classes
-    #
-
-    # Not implemented yet
-    @unittest.expectedFailure
-    def test_filter_query(self):
-        super().test_filter_query()
diff --git a/wagtail/search/tests/test_backends.py b/wagtail/search/tests/test_backends.py
index 97316c461..d27754adf 100644
--- a/wagtail/search/tests/test_backends.py
+++ b/wagtail/search/tests/test_backends.py
@@ -428,6 +428,8 @@ class BackendTests(WagtailTestUtils):
             "The Fellowship of the Ring"
         ])
 
+
+class QueryAPITestMixin:
     #
     # Basic query classes
     #
diff --git a/wagtail/search/tests/test_db_backend.py b/wagtail/search/tests/test_db_backend.py
index 40953d9e7..9f4c86d58 100644
--- a/wagtail/search/tests/test_db_backend.py
+++ b/wagtail/search/tests/test_db_backend.py
@@ -2,10 +2,10 @@ import unittest
 
 from django.test import TestCase
 
-from .test_backends import BackendTests
+from .test_backends import BackendTests, QueryAPITestMixin
 
 
-class TestDBBackend(BackendTests, TestCase):
+class TestDBBackend(QueryAPITestMixin, BackendTests, TestCase):
     backend_path = 'wagtail.search.backends.db'
 
     # Doesn't support ranking