diff --git a/python/gtsam/tests/test_Utilities.py b/python/gtsam/tests/test_Utilities.py
index ef53660bf..851684f12 100644
--- a/python/gtsam/tests/test_Utilities.py
+++ b/python/gtsam/tests/test_Utilities.py
@@ -103,6 +103,94 @@ class TestUtilites(GtsamTestCase):
         np.testing.assert_allclose(gtsam.utilities.extractPose3(initial),
                                    pose3.reshape(-1, 12))
 
+    def test_perturbPoint2(self):
+        """Test perturbPoint2."""
+        values = gtsam.Values()
+        values.insert(0, gtsam.Pose3())
+        values.insert(1, gtsam.Point2(1, 1))
+        gtsam.utilities.perturbPoint2(values, 1.0)
+        self.assertTrue(
+            not np.allclose(values.atPoint2(1), gtsam.Point2(1, 1)))
+
+    def test_perturbPose2(self):
+        """Test perturbPose2."""
+        values = gtsam.Values()
+        values.insert(0, gtsam.Pose2())
+        values.insert(1, gtsam.Point2(1, 1))
+        gtsam.utilities.perturbPose2(values, 1, 1)
+        self.assertTrue(values.atPose2(0) != gtsam.Pose2())
+
+    def test_perturbPoint3(self):
+        """Test perturbPoint3."""
+        values = gtsam.Values()
+        point3 = gtsam.Point3(0, 0, 0)
+        values.insert(0, gtsam.Pose2())
+        values.insert(1, point3)
+        gtsam.utilities.perturbPoint3(values, 1)
+        self.assertTrue(not np.allclose(values.atPoint3(1), point3))
+
+    def test_insertBackprojections(self):
+        """Test insertBackprojections."""
+        values = gtsam.Values()
+        cam = gtsam.PinholeCameraCal3_S2()
+        gtsam.utilities.insertBackprojections(
+            values, cam, [0, 1, 2], np.asarray([[20, 30, 40], [20, 30, 40]]),
+            10)
+        np.testing.assert_allclose(values.atPoint3(0),
+                                   gtsam.Point3(200, 200, 10))
+
+    def test_insertProjectionFactors(self):
+        """Test insertProjectionFactors."""
+        graph = gtsam.NonlinearFactorGraph()
+        gtsam.utilities.insertProjectionFactors(
+            graph, 0, [0, 1], np.asarray([[20, 30], [20, 30]]),
+            gtsam.noiseModel.Isotropic.Sigma(2, 0.1), gtsam.Cal3_S2())
+        self.assertEqual(graph.size(), 2)
+
+        graph = gtsam.NonlinearFactorGraph()
+        gtsam.utilities.insertProjectionFactors(
+            graph, 0, [0, 1], np.asarray([[20, 30], [20, 30]]),
+            gtsam.noiseModel.Isotropic.Sigma(2, 0.1), gtsam.Cal3_S2(),
+            gtsam.Pose3(gtsam.Rot3(), gtsam.Point3(1, 0, 0)))
+        self.assertEqual(graph.size(), 2)
+
+    def test_reprojectionErrors(self):
+        """Test reprojectionErrors."""
+        pixels = np.asarray([[20, 30], [20, 30]])
+        I = [1, 2]
+        K = gtsam.Cal3_S2()
+        graph = gtsam.NonlinearFactorGraph()
+        gtsam.utilities.insertProjectionFactors(
+            graph, 0, I, pixels, gtsam.noiseModel.Isotropic.Sigma(2, 0.1), K)
+        values = gtsam.Values()
+        values.insert(0, gtsam.Pose3())
+        cam = gtsam.PinholeCameraCal3_S2(gtsam.Pose3(), K)
+        gtsam.utilities.insertBackprojections(values, cam, I, pixels, 10)
+        errors = gtsam.utilities.reprojectionErrors(graph, values)
+        np.testing.assert_allclose(errors, np.zeros((2, 2)))
+
+    def test_localToWorld(self):
+        """Test localToWorld."""
+        local = gtsam.Values()
+        local.insert(0, gtsam.Point2(10, 10))
+        local.insert(1, gtsam.Pose2(6, 11, 0.0))
+        base = gtsam.Pose2(1, 0, 0)
+        world = gtsam.utilities.localToWorld(local, base)
+
+        expected_point2 = gtsam.Point2(11, 10)
+        expected_pose2 = gtsam.Pose2(7, 11, 0)
+        np.testing.assert_allclose(world.atPoint2(0), expected_point2)
+        np.testing.assert_allclose(
+            world.atPose2(1).matrix(), expected_pose2.matrix())
+
+        user_keys = [1]
+        world = gtsam.utilities.localToWorld(local, base, user_keys)
+        np.testing.assert_allclose(
+            world.atPose2(1).matrix(), expected_pose2.matrix())
+
+        # Raise error since 0 is not in user_keys
+        self.assertRaises(RuntimeError, world.atPoint2, 0)
+
 
 if __name__ == "__main__":
     unittest.main()