.. raw:: latex
  
      \newpage %


==========================
APPENDIX E: Problem Types
==========================

Option Response
===============

The Option Response input type allows the student to choose from a collection of
answer options, presented as a drop-down list.

Option Response is structurally similar to Multiple Choice. Some conceptual
differences between the two include the following.

* The Multiple Choice radio button format makes it easier for students to read very long response options.

* The Option Response drop-down input format makes it more likely for students to think of an answer and then search for it, rather than relying purely on recognition to answer the question. The Multiple Choice format is more explicit and visual. This makes it a more appropriate choice for presenting tricky or complicated answer options which are intended to get the student to pause and think.

Sample Problem:

.. image:: ../images/image287.png
    :width: 600  

**Problem Code:**

.. code-block:: xml

  <problem>

   <p>Option Response is most similar to __________.</p>

    <optionresponse>
     <optioninput
       options="('Multiple Choice','String Response',
                'Numerical Response','External Response',
                'Image Response')"
      correct="Multiple Choice"/>1
    </optionresponse>

   <solution>
     <div class="detailed-solution">
       <p>Explanation</p>
        <p>Like Option Response, Multiple Choice also allows students to select
       from a variety of pre-written responses.</p>
     </div>
    </solution>
  </problem>




**Template**

.. code-block:: xml

  <problem>

    <optionresponse>
     options="('A','B')"
      correct="A"/>
    </optionresponse>

    <solution>
      <div class="detailed-solution">
      </div>
    </solution>
  </problem> 



**XML Attribute Information**

<optionresponse>


  .. image:: ../images/option_response1.png


<optioninput>

  .. image:: ../images/optionresponse2.png


.. raw:: latex
  
      \newpage %


Multiple Choice 
===============


The Multiple Choice input type allows the student to select at most one choice
from a collection of answer choices, presented as a list of radio buttons.

A Multiple Choice problem can have more than one correct answer, depending on
how many choices are marked as correct in the underlying XML. If all choices are
marked as incorrect, there is no correct response.

Multiple Choice is structurally similar to Option Response. Some conceptual
differences between the two include the following.

• The Multiple Choice radio button format makes it easier for students to read very long response options.

• The Option Response drop-down input format makes it more likely for students to think of an answer and then search for it, rather than relying purely on recognition to answer the question.

• The Multiple Choice format is more explicit and visual. This makes it a more appropriate choice for presenting tricky or complicated answer options which areintended to get the student to pause and think. 

Sample Problem:

.. image:: ../images/image289.png
 :width: 600  

**Problem Code:** 

.. code-block:: xml

  <problem>
  <p><b>Example Problem</b></p>
  <p>How many correct responses can a Multiple Choice question have?</p>
      <multiplechoiceresponse>
     <choicegroup type="MultipleChoice">
        <choice correct="false" name="one">Only one</choice>
        <choice correct="false" name="zeroone">Only zero or one</choice>
        <choice correct="true" name="zeromore">Zero or more</choice>
        <choice correct="false" name="onemore">Only one or more</choice>
        <choice correct="false" name="noone">Nobody knows</choice>
        <choice correct="true" name="someone">Somebody might know :)</choice>
    </choicegroup>
    </multiplechoiceresponse>
  <solution>
        <div class="detailed-solution">
          <p>Explanation</p>
            <p>It depends on how many choices are marked as correct in the underlying XML.</p>                  
  <p>Note that if all choices are marked as incorrect, there is no
          correct response.</p>
        </div>
    </solution>
  </problem>


**Template** 

.. code-block:: xml

  <problem>

  <multiplechoiceresponse>
    <choicegroup type="MultipleChoice">
      <choice correct="false" name="a">A</choice>
      <choice correct="true" name="b">B</choice>
    </choicegroup>
  </multiplechoiceresponse>

  <solution>
    <div class="detailed-solution">

    </div>
  </solution>
  </problem>


**XML Attribute Information**


<multiplechoiceresponse>

.. image:: ../images/multipleresponse.png


<choicegroup>

  .. image:: ../images/multipleresponse2.png


<choice>

  .. image:: ../images/multipleresponse3.png


.. raw:: latex
  
      \newpage %


Checkbox
========

The Checkbox input type allows the student to select zero or more choices from a
collection of answer choices, presented as a list of checkboxes.

Remark: Questions with one Checkbox input type have exactly one correct
response. All the choices marked as correct="true" have to be selected for the
submitted answer (i.e. the response) to be considered correct.

In particular, the response of no boxes checked off could be the single correct
response, and a Checkbox question, unlike a Multiple Choice question, cannot
have zero correct responses.

Sample Problem:

.. image:: ../images/image290.png
 :width: 600  


**Problem Code:**

.. code-block:: xml

  <problem>
  <startouttext/>
    <p>How many correct responses can a Checkbox question have?</p>

  <choiceresponse>
  <checkboxgroup>
  <choice correct="false"><text>Zero</text></choice>
  <choice correct="true"><text>One</text></choice>
  <choice correct="false"><text>Two or more</text></choice>
  <choice correct="false"><text>Nobody knows</text></choice>
  <choice correct="true"><text>Somebody might know :)</text></choice>
  </checkboxgroup>
  </choiceresponse>
  </problem>


**Template**

.. code-block:: xml

  <problem>

  <choiceresponse>
  <checkboxgroup>
  <choice correct="false"><text>Zero</text></choice>
  <choice correct="true"><text>One</text></choice>
  </checkboxgroup>
  </choiceresponse>
  </problem>

.. raw:: latex
  
     \newpage %


String Response
===============

The String Response input type provides an input box in which the student can
enter a line of text, which is then checked against a specified expected answer.

A String Response input does not provide any answer suggestions, so it can be a
good way to get the students to engage with the material more deeply in a
sequence and look up, figure out, or remember the correct answer themselves.

Note that a student's answer in a String Response is marked as correct if it
matches every character of the expected answer. This can be a problem with
international spelling, dates, or anything where the format of the answer is not
clear.

Sample Problem:

.. image:: ../images/image291.png
 :width: 600   

**Problem Code:**

.. code-block:: xml

  <problem>
    <p><b>Example Problem</b></p>
    <p>What is the name of this unit? (What response type is this?)</p>
    <stringresponse answer="String Response" type="ci">
      <textline size="20"/>
    </stringresponse>
    <solution>
      <div class="detailed-solution">
        <p>Explanation</p>
        <p>The name of this unit is "String Response," written without the punctuation.</p>
        <p>Arbitrary capitalization is accepted.</p>
      </div>
    </solution>
  </problem>

**Template**

.. code-block:: xml

  <problem>
    <stringresponse answer="REPLACE_THIS" type="ci">
      <textline size="20"/>
    </stringresponse>
    <solution>
      <div class="detailed-solution">
      </div>
    </solution>
  </problem>

**XML Attribute Information**

<stringresponse>

  .. image:: ../images/stringresponse.png

<textline>

  .. image:: ../images/stringresponse2.png


.. raw:: latex
  
      \newpage %


Numerical Response
==================

The Numerical Response input type accepts a line of text input from the student
and evaluates the input for correctness based on its numerical value. The input
is allowed to be a number or a mathematical expression in a fixed syntax.

The answer is correct if it is within a specified numerical tolerance of the
expected answer.

The expected answer can be specified explicitly or precomputed by a Python
script.

Sample Problem:

.. image:: ../images/image292.png
 :width: 600   


**Problem Code**:

.. code-block:: xml

  <problem>
    <p><b>Example Problem</b></p>

  <p>What base is the decimal numeral system in?
      <numericalresponse answer="10">
          <textline />
      </numericalresponse>
  </p>

    <p>What is the value of the standard gravity constant <i>g</i>, measured in m/s<sup>2</sup>? Give your answer to at least two decimal places.
    <numericalresponse answer="9.80665">
      <responseparam type="tolerance" default="0.01" />
        <textline />
    </numericalresponse>
  </p>

  <!-- Use python script spacing. The following should not be indented! -->
  <script type="loncapa/python">
  computed_response = math.sqrt(math.fsum([math.pow(math.pi,2), math.pow(math.e,2)]))
  </script>
    
  <p>What is the distance in the plane between the points (pi, 0) and (0, e)? You can type math.
      <numericalresponse answer="$computed_response">
          <responseparam type="tolerance" default="0.0001" />
          <textline math="1" />
      </numericalresponse>
  </p>
  <solution>
    <div class="detailed-solution">
      <p>Explanation</p>
      <p>The decimal numerical system is base ten.</p>
      <p>The standard gravity constant is defined to be precisely 9.80665 m/s<sup>2</sup>.
      This is 9.80 to two decimal places. Entering 9.8 also works.</p>
      <p>By the distance formula, the distance between two points in the plane is
         the square root of the sum of the squares of the differences of each coordinate.
        Even though an exact numerical value is checked in this case, the
        easiest way to enter this answer is to type
        <code>sqrt(pi^2+e^2)</code> into the editor. 
        Other answers like <code>sqrt((pi-0)^2+(0-e)^2)</code> also work.
      </p>
    </div>
  </solution>
  </problem>

**Templates**

Exact values

.. code-block:: xml

  <problem>

    <numericalresponse answer="10">
      <textline />
    </numericalresponse>

    <solution>
    <div class="detailed-solution">

    </div>
  </solution>
  </problem>

Answers with decimal precision

.. code-block:: xml

  <problem>

    <numericalresponse answer="9.80665">
      <responseparam type="tolerance" default="0.01" />
        <textline />
    </numericalresponse>

    <solution>
    <div class="detailed-solution">

    </div>
  </solution>
  </problem>

Answers with percentage precision

.. code-block:: xml

  <problem>

    <numericalresponse answer="100">
      <responseparam type="tolerance" default="10%" />
        <textline />
    </numericalresponse>

    <solution>
    <div class="detailed-solution">

    </div>
  </solution>
  </problem>

Answers with a live math interpretation popup display

.. code-block:: xml

  <problem>

    <numericalresponse answer="3.14159">
      <responseparam type="tolerance" default="0.00001" />
      <textline math="1" />
    </numericalresponse>

    <solution>
    <div class="detailed-solution">

    </div>
  </solution>
  </problem>

Answers with scripts

.. code-block:: xml

  <problem>

  <!-- Use python script spacing. The following should not be indented! -->
  <script type="loncapa/python">
  computed_response = math.sqrt(math.fsum([math.pow(math.pi,2), math.pow(math.e,2)]))
  </script>

    <numericalresponse answer="$computed_response">
      <responseparam type="tolerance" default="0.0001" />
      <textline math="1" />
    </numericalresponse>

    <solution>
    <div class="detailed-solution">

    </div>
  </solution>
  </problem>


XML Attribute Information

<script>

  .. image:: ../images/numericalresponse.png

<numericalresponse>


  .. image:: ../images/numericalresponse2.png

<responseparam>

  .. image:: ../images/numericalresponse4.png

<textline>

  .. image:: ../images/numericalresponse5.png


.. raw:: latex
  
      \newpage %



Formula Response
================

The Formula Response input type accepts a line of text representing a
mathematical expression from the student and evaluates the input for equivalence
to a mathematical expression provided by the grader. Correctness is based on
numerical sampling of the symbolic expressions.

The answer is correct if both the student-provided response and the grader's
mathematical expression are equivalent to specified numerical tolerance, over a
specified range of values for each variable.

This kind of response type can handle symbolic expressions. However, it places
an extra burden on the problem author to specify the allowed variables in the
expression and the numerical ranges over which the variables must be sampled in
order to test for correctness.

Sample Problem:

.. image:: ../images/image293.png
 :width: 600   

**Problem Code**:

.. code-block:: xml

  <problem>
    <p><b>Example Problem</b></p>
    <p>This is a short introduction to the Formula Response editor.</p>

    <p>Write an expression for the product of R_1, R_2, and the inverse of R_3.</p>
    <formularesponse type="ci" samples="R_1,R_2,R_3@1,2,3:3,4,5#10" answer="$VoVi">
      <responseparam type="tolerance" default="0.00001"/> 
      <textline size="40" math="1" />
    </formularesponse>

    <p>Let <i>c</i> denote the speed of light. What is the relativistic energy <i>E</i> of an object of mass <i>m</i>?</p>
  <script type="loncapa/python">
  VoVi = "(R_1*R_2)/R_3"
  </script>
  <formularesponse type="cs" samples="m,c@1,2:3,4#10" answer="m*c^2">
      <responseparam type="tolerance" default="0.00001"/> 
    <text><i>E</i> =</text> <textline size="40" math="1" />    
  </formularesponse>

    <p>Let <i>x</i> be a variable, and let <i>n</i> be an arbitrary constant. What is the derivative of <i>x<sup>n</sup></i>?</p>
  <script type="loncapa/python">
  derivative = "n*x^(n-1)"
  </script>
  <formularesponse type="ci" samples="x,n@1,2:3,4#10" answer="$derivative">
    <responseparam type="tolerance" default="0.00001"/> 
    <textline size="40" math="1" />    
  </formularesponse>

    <solution>
      <div class="detailed-solution">
        <p>Explanation</p>
        <p>Use standard arithmetic operation symbols and indicate multiplication explicitly.</p>
        <p>Use the symbol <tt>^</tt> to raise to a power.</p>
        <p>Use parentheses to specify order of operations.</p>
      </div>
    </solution>
  </problem>
  Template
  <problem>

  <script type="loncapa/python">
  answer_value = "n*x^(n-1)"
  </script>
  <formularesponse type="ci" samples="x,n@1,2:3,4#10" answer="$answer_value">
    <responseparam type="tolerance" default="0.00001"/> 
    <textline size="40" math="1" />    
  </formularesponse>

    <solution>
      <div class="detailed-solution">

      </div>
    </solution>
  </problem>


XML Attribute Information

<script>


  .. image:: ../images/formularesponse.png


<formularesponse>


  .. image:: ../images/formularesponse3.png

<responseparam>


  .. image:: ../images/formularesponse6.png


.. raw:: latex
  
      \newpage %


Image Response
==============

The Image Response input type presents an image and accepts clicks on the image as an answer.
Images have to be uploaded to the courseware Assets directory. Response clicks are marked as correct if they are within a certain specified sub rectangle of the image canvas.

*Note The Mozilla Firefox browser is currently not supported for this problem type.*

Sample Problem:

.. image:: ../images/image294.png
 :width: 600   


**Problem Code**:

.. code-block:: xml

  <problem>
    <p><b>Example Problem</b></p>
  <startouttext/>
      <p>You are given three shapes. Click on the triangle.</p>
      <endouttext/>
      <imageresponse>
      <imageinput src="/c4x/edX/edX101/asset/threeshapes.png" width="220" height="150" rectangle="(80,40)-(130,90)" />
      </imageresponse>
  </problem>
  Template
  <problem>
      <imageresponse>
      <imageinput src="Path_to_Image_File.png" width="220" height="150" rectangle="(80,40)-(130,90)" />
      </imageresponse> 
  </problem>

XML Attribute Information


<imageresponse>

  .. image:: ../images/imageresponse1.png

<imageinput>

  .. image:: ../images/imageresponse2.png

.. raw:: latex
  
      \newpage %


Custom Response
===============

A Custom Response input type accepts one or more lines of text input from the student and evaluate the inputs for correctness using an embedded Python script.

Sample Problem:

.. image:: ../images/image295.png
 :width: 600  


**Problem Code**:

.. code-block:: xml

  <problem>
    <p><b>Example Problem</b></p>
  <script type="loncapa/python">

  def test_add_to_ten(expect,ans):
    try:
      a1=int(ans[0])
      a2=int(ans[1])
    except ValueError:
      a1=0
      a2=0
    return (a1+a2)==10

  def test_add(expect,ans):
    try:
      a1=float(ans[0])
      a2=float(ans[1])
    except ValueError:
      a1=0
      a2=0
    return (a1+a2)== float(expect)
  </script>

    <p>This question consists of two parts. </p>
  <p>First, enter two integers which sum to 10. </p>
  <customresponse cfn="test_add_to_ten">
          <textline size="40" /><br/>
          <textline size="40" />
  </customresponse>

    <p>Now enter two (finite) decimals which sum to 20.</p>
  <customresponse cfn="test_add" expect="20">
          <textline size="40" /><br/>
          <textline size="40" />
  </customresponse>

      <solution>
          <div class="detailed-solution">
              <p>Explanation</p>
            <p>For the first part, any two numbers of the form <i>n</i>
              and <i>10-n</i>, where <i>n</i> is any integer, will work. 
              One possible answer would be the pair 0 and 10.
            </p>
            <p>For the second part, any pair <i>x</i> and <i>20-x</i> will work, where <i>x</i> is any real number with a finite decimal representation. Both inputs have to be entered either in standard decimal notation or in scientific exponential notation. One possible answer would be the pair 0.5 and 19.5. Another way to write this would be 5e-1 and 1.95e1.
            </p>
          </div>
      </solution>
  </problem>

**Templates**

*With displayed suggested correct answers*

.. code-block:: xml

  <problem>

  <script type="loncapa/python">
  def test_add(expect,ans):
    a1=float(ans[0])
    a2=float(ans[1])
    return (a1+a2)== float(expect)
  </script>


  <p>Enter two real numbers which sum to 20: </p>
  <customresponse cfn="test_add" expect="20">
          <textline size="40" correct_answer="11"/><br/>
          <textline size="40" correct_answer="9"/>
  </customresponse>

      <solution>
          <div class="detailed-solution">
          </div>
      </solution>
  </problem>


**Templates**

*With NO suggested correct answers*


.. code-block:: xml

  <problem>

  <script type="loncapa/python">
  def test_add(expect,ans):
    a1=float(ans[0])
    a2=float(ans[1])
    return (a1+a2)== float(expect)
  </script>


  <p>Enter two real numbers which sum to 20: </p>
  <customresponse cfn="test_add" expect="20">
          <textline size="40" /><br/>
          <textline size="40" />
  </customresponse>

      <solution>
          <div class="detailed-solution">
          </div>
      </solution>
  </problem>


.. raw:: latex
  
      \newpage %

Chemical Equation Response
==========================

The Chemical Equation Response input type is a special type of Custom Response
that allows the student to enter chemical equations as answers. 

Sample Problem:

.. image:: ../images/image296.png
 :width: 600   

**Problem Code**:

.. code-block:: xml

  <problem>
    <p><b>Example Problem</b></p>
    <startouttext/>
    <p>Some problems may ask for a particular chemical equation. Practice by writing out the following reaction in the box below.</p>
    <center>\( \text{H}_2\text{SO}_4 \longrightarrow \text{ H}^+ + \text{ HSO}_4^-\)</center>
    <br/>
    <customresponse>
      <chemicalequationinput size="50"/>
      <answer type="loncapa/python">

  if chemcalc.chemical_equations_equal(submission[0], 'H2SO4 -> H^+ + HSO4^-'): 
      correct = ['correct']
  else:
      correct = ['incorrect']

  </answer>
    </customresponse>
    <p> Some tips:<ul><li>Only real element symbols are permitted.</li><li>Subscripts are entered with plain text.</li><li>Superscripts are indicated with a caret (^).</li><li>The reaction arrow (\(\longrightarrow\)) is indicated with "->".</li></ul>
     So, you can enter "H2SO4 -> H^+ + HSO4^-".</p>
    <endouttext/>
  </problem> 

h
.. raw:: latex
  
      \newpage %

Schematic Response
==================

The Schematic Response input type provides an interactive grid on which the
student can construct a schematic answer, such as a circuit. 

Sample Problem:

.. image:: ../images/image297.png
 :width: 600 

.. image:: ../images/image298.png
 :width: 600   

.. image:: ../images/image299.png
 :width: 600   

**Problem Code**:

.. code-block:: xml


    <problem>
      Make a voltage divider that splits the provided voltage evenly.

    <schematicresponse>
    <center>
    <schematic height="500" width="600" parts="g,r" analyses="dc"
    initial_value="[["v",[168,144,0],{"value":"dc(1)","_json_":0},["1","0"]],["r",[296,120,0],{"r":"1","_json_":1},["1","output"]],["L",[296,168,3],{"label":"output","_json_":2},["output"]],["w",[296,216,168,216]],["w",[168,216,168,192]],["w",[168,144,168,120]],["w",[168,120,296,120]],["g",[168,216,0],{"_json_":7},["0"]],["view",-67.49999999999994,-78.49999999999994,1.6000000000000003,"50","10","1G",null,"100","1","1000"]]"
    />
    </center>
    <answer type="loncapa/python">
    dc_value = "dc analysis not found"
    for response in submission[0]:
      if response[0] == 'dc':
          for node in response[1:]:
              dc_value = node['output']

    if dc_value == .5:
      correct = ['correct']
    else:
      correct = ['incorrect']

    </answer>
    </schematicresponse>
    <schematicresponse>
    <p>Make a high pass filter.</p>
    <center>
    <schematic height="500" width="600" parts="g,r,s,c" analyses="ac"
    submit_analyses="{"ac":[["NodeA",1,9]]}"
    initial_value="[["v",[160,152,0],{"name":"v1","value":"sin(0,1,1,0,0)","_json_":0},["1","0"]],["w",[160,200,240,200]],["g",[160,200,0],{"_json_":2},["0"]],["L",[240,152,3],{"label":"NodeA","_json_":3},["NodeA"]],["s",[240,152,0],{"color":"cyan","offset":"0","_json_":4},["NodeA"]],["view",64.55878906250004,54.114697265625054,2.5000000000000004,"50","10","1G",null,"100","1","1000"]]"/>
    </center>
    <answer type="loncapa/python">
    ac_values = None
    for response in submission[0]:
      if response[0] == 'ac':
          for node in response[1:]:
              ac_values = node['NodeA']
    print "the ac analysis value:", ac_values
    if ac_values == None:
      correct = ['incorrect']
    elif ac_values[0][1] < ac_values[1][1]:
      correct = ['correct']
    else:
      correct = ['incorrect']
    </answer>
    </schematicresponse>

        <solution>
            <div class="detailed-solution">
                <p>Explanation</p>
                <p>A voltage divider that evenly divides the input voltage can be formed with two identically valued resistors, with the sampled voltage taken in between the two.</p>
                <p><img src="/c4x/edX/edX101/asset/images_voltage_divider.png"/></p>
                <p>A simple high-pass filter without any further constaints can be formed by simply putting a resister in series with a capacitor. The actual values of the components do not really matter in order to meet the constraints of the problem.</p>
                <p><img src="/c4x/edX/edX101/asset/images_high_pass_filter.png"/></p>
            </div>
        </solution>
    </problem>
