diff --git a/pandas/tests/extension/base/methods.py b/pandas/tests/extension/base/methods.py
index 472e783c977f0..7e7f1f1a6e025 100644
--- a/pandas/tests/extension/base/methods.py
+++ b/pandas/tests/extension/base/methods.py
@@ -394,7 +394,7 @@ def test_hash_pandas_object_works(self, data, as_frame):
 
     def test_searchsorted(self, data_for_sorting, as_series):
         b, c, a = data_for_sorting
-        arr = type(data_for_sorting)._from_sequence([a, b, c])
+        arr = data_for_sorting.take([2, 0, 1])  # to get [a, b, c]
 
         if as_series:
             arr = pd.Series(arr)
diff --git a/pandas/tests/extension/test_categorical.py b/pandas/tests/extension/test_categorical.py
index e38de67071f15..9cea274a118c0 100644
--- a/pandas/tests/extension/test_categorical.py
+++ b/pandas/tests/extension/test_categorical.py
@@ -175,10 +175,6 @@ def test_combine_add(self, data_repeated):
     def test_fillna_length_mismatch(self, data_missing):
         super().test_fillna_length_mismatch(data_missing)
 
-    def test_searchsorted(self, data_for_sorting):
-        if not data_for_sorting.ordered:
-            raise pytest.skip(reason="searchsorted requires ordered data.")
-
 
 class TestCasting(base.BaseCastingTests):
     @pytest.mark.parametrize("cls", [Categorical, CategoricalIndex])
@@ -229,21 +225,26 @@ def test_consistent_casting(self, dtype, expected):
 
 
 class TestArithmeticOps(base.BaseArithmeticOpsTests):
-    def test_arith_frame_with_scalar(self, data, all_arithmetic_operators):
+    def test_arith_frame_with_scalar(self, data, all_arithmetic_operators, request):
         # frame & scalar
         op_name = all_arithmetic_operators
-        if op_name != "__rmod__":
-            super().test_arith_frame_with_scalar(data, all_arithmetic_operators)
-        else:
-            pytest.skip("rmod never called when string is first argument")
-
-    def test_arith_series_with_scalar(self, data, all_arithmetic_operators):
-
+        if op_name == "__rmod__":
+            request.node.add_marker(
+                pytest.mark.xfail(
+                    reason="rmod never called when string is first argument"
+                )
+            )
+        super().test_arith_frame_with_scalar(data, op_name)
+
+    def test_arith_series_with_scalar(self, data, all_arithmetic_operators, request):
         op_name = all_arithmetic_operators
-        if op_name != "__rmod__":
-            super().test_arith_series_with_scalar(data, op_name)
-        else:
-            pytest.skip("rmod never called when string is first argument")
+        if op_name == "__rmod__":
+            request.node.add_marker(
+                pytest.mark.xfail(
+                    reason="rmod never called when string is first argument"
+                )
+            )
+        super().test_arith_series_with_scalar(data, op_name)
 
     def test_add_series_with_extension_array(self, data):
         ser = pd.Series(data)