diff --git a/common/lib/capa/capa/tests/test_responsetypes.py b/common/lib/capa/capa/tests/test_responsetypes.py
index bf64d3cc69..ab21a845eb 100644
--- a/common/lib/capa/capa/tests/test_responsetypes.py
+++ b/common/lib/capa/capa/tests/test_responsetypes.py
@@ -33,10 +33,16 @@ class ResponseTest(unittest.TestCase):
         xml = self.xml_factory.build_xml(**kwargs)
         return lcp.LoncapaProblem(xml, '1', system=test_system)
 
-    def assert_grade(self, problem, submission, expected_correctness):
+    def assert_grade(self, problem, submission, expected_correctness, msg=None):
         input_dict = {'1_2_1': submission}
         correct_map = problem.grade_answers(input_dict)
-        self.assertEquals(correct_map.get_correctness('1_2_1'), expected_correctness)
+        if msg is None:
+            self.assertEquals(correct_map.get_correctness('1_2_1'), expected_correctness)
+        else:
+            if correct_map.get_correctness('1_2_1')!= expected_correctness:
+                print submission
+                print correct_map
+            self.assertEquals(correct_map.get_correctness('1_2_1'), expected_correctness, msg)
 
     def assert_answer_format(self, problem):
         answers = problem.get_question_answers()
@@ -358,6 +364,84 @@ class FormulaResponseTest(ResponseTest):
         self.assert_grade(problem, '3*x', 'incorrect')
 
 
+    def test_parallel_resistors(self):
+        """Test parallel resistors"""
+        sample_dict = {'R1': (10,10), 'R2': (2,2), 'R3': (5,5), 'R4': (1,1)}
+
+        # Test problem
+        problem = self.build_problem(sample_dict=sample_dict,
+                                     num_samples=10,
+                                     tolerance=0.01,
+                                     answer="R1||R2")
+        # Expect answer to be marked correct
+        input_formula = "R1||R2"
+        self.assert_grade(problem, input_formula, "correct")
+
+        # Expect random number to be marked incorrect
+        input_formula = "13"
+        self.assert_grade(problem, input_formula, "incorrect")
+
+        # Expect incorrect answer marked incorrect
+        input_formula = "R3||R4"
+        self.assert_grade(problem, input_formula, "incorrect")
+
+    def test_default_variables(self):
+        """Test the default variables provided in common/lib/capa/capa/calc.py"""
+        # which are: j (complex number), e, pi, k, c, T, q
+
+        # Sample x in the range [-10,10]
+        sample_dict = {'x': (-10, 10)}
+        default_variables = [('j', 2, 3), ('e', 2, 3), ('pi', 2, 3), ('c', 2, 3), ('T', 2, 3), 
+                             ('k', 2*10**23, 3*10**23), # note k = scipy.constants.k = 1.3806488e-23
+                             ('q', 2*10**19, 3*10**19)] # note k = scipy.constants.e = 1.602176565e-19
+        for (var, cscalar, iscalar) in default_variables:
+            # The expected solution is numerically equivalent to cscalar*var
+            correct = '{0}*x*{1}'.format(cscalar, var)
+            incorrect = '{0}*x*{1}'.format(iscalar, var)
+            problem = self.build_problem(sample_dict=sample_dict,
+                                         num_samples=10,
+                                         tolerance=0.01,
+                                         answer=correct)
+            # Expect that the inputs are graded correctly
+            
+            self.assert_grade(problem, correct, 'correct', 
+                              msg="Failed on variable {0}; the given, correct answer was {1} but graded 'incorrect'".format(var, correct))
+            self.assert_grade(problem, incorrect, 'incorrect', 
+                              msg="Failed on variable {0}; the given, incorrect answer was {1} but graded 'correct'".format(var, incorrect))
+
+    def test_default_functions(self):
+        """Test the default functions provided in common/lib/capa/capa/calc.py"""
+        # which are: sin, cos, tan, sqrt, log10, log2, ln, 
+        # arccos, arcsin, arctan, abs,
+        # fact, factorial
+
+        # Sample x in the range [-10,10]
+        import random
+        w = random.randint(3, 10)
+        sample_dict = {'x': (-10, 10), 'y': (1, 10), 'z':(-1, 1), 'w':(w,w)}
+        default_functions = [('sin', 2, 3, 'x'), ('cos', 2, 3, 'x'), ('tan', 2, 3, 'x'), ('sqrt', 2, 3, 'y'), ('log10', 2, 3, 'y'), 
+                             ('log2', 2, 3, 'y'), ('ln', 2, 3, 'y'), ('arccos', 2, 3, 'z'), ('arcsin', 2, 3, 'z'), ('arctan', 2, 3, 'x'), 
+                             ('abs', 2, 3, 'x'), ('fact', 2, 3, 'w'), ('factorial', 2, 3, 'w'),]
+        for (func, cscalar, iscalar, var) in default_functions:
+            print 'func is: {0}'.format(func)
+            # The expected solution is numerically equivalent to cscalar*func(var)
+            correct = '{0}*{1}({2})'.format(cscalar, func, var)
+            incorrect = '{0}*{1}({2})'.format(iscalar, func, var)
+            problem = self.build_problem(sample_dict=sample_dict,
+                                         num_samples=10,
+                                         tolerance=0.01,
+                                         answer=correct)
+            # Expect that the inputs are graded correctly
+            
+            self.assert_grade(problem, correct, 'correct', 
+                              msg="Failed on function {0}; the given, correct answer was {1} but graded 'incorrect'".format(func, correct))
+            self.assert_grade(problem, incorrect, 'incorrect', 
+                              msg="Failed on function {0}; the given, incorrect answer was {1} but graded 'correct'".format(func, incorrect))
+
+
+
+
+
 class StringResponseTest(ResponseTest):
     from response_xml_factory import StringResponseXMLFactory
     xml_factory_class = StringResponseXMLFactory