Math Expression Input Problems

Math Expression Input Problems#

Tags: educator reference

The math expression input problem type is a core problem type that can be added to any course. At a minimum, math expression problems include a question or prompt and a response field for a numeric answer.

For more information about the core problem types, see Working with Problem Components.

Overview#

In math expression input problems, learners enter text that represents a mathematical expression. The text is converted to a symbolic expression that appears below the response field. Unlike numerical input problems, which only allow integers and a few select constants, math expression input problems can include unknown variables and more complicated symbolic expressions.

For more information about how learners enter expressions, see Math Formatting in the Open edX Learner’s Guide.

Note

You can make a calculator tool available to your learners on every unit page. For more information, see Calculator Tool.

For math expression input problems, the grader uses numerical sampling to determine whether a learner’s response matches the math expression that you provide, to a specified numerical tolerance. You specify the allowed variables in the expression as well as the range of values for each variable.

When you create a math expression input problem in Studio, you use MathJax to format text strings into “beautiful math.” For more information about how to use MathJax in Studio, see MathJax for Mathematics.

Note

Math expression input problems currently cannot include negative numbers raised to fractional powers, such as (-1)^(1/2). Math expression input problems can include complex numbers raised to fractional powers, or positive non-complex numbers raised to fractional powers.

Example Math Expression Input Problem#

In the LMS, learners enter a value into a response field to complete a math expression input problem. The following example shows a completed math expression input problem that contains two questions.

A problem shown in the LMS that requests the symbolic expressions for displacement and for elongation of a blade. Both questions were answered correctly. The solutions are not shown.

The open learning XML (OLX) markup for this example math expression input problem follows.

<problem>
  <formularesponse inline="1" type="cs" samples="R,omega,E,rho,L@0.1,0.1,0.1,0.1,0.1:10,10,10,10,10#10" answer="(rho*omega^2*L^2)/E*((11*L)/48 +(3*R)/8)">
    <label>Find a symbolic expression for the displacement of the blade mid-section, \( u_{x}(L/2) \), in terms of \(R\), \(L\), \(\rho\), \(\omega\), and \(E\).</label>
    <description>\(u_x(L/2) = \)</description>
    <responseparam type="tolerance" default="1%"/>
    <textline inline="1" math="1"/>
    <solution>
      <div class="worked-solution">
        <p><b>Obtaining the displacement at the mid-section \( u_{x}(x = L / 2)\):</b></p><p>According to the definition of strain,</p>
        \[ \frac {du_{x}(x)} {dx} = \epsilon_a(x).\]
        <p>Therefore, we can obtain the displacement field as</p>
        \[ u_x(x) = u_x(0) + \int_0^x \epsilon_a (x') dx' = u_x(0) + \left[ \frac{\rho \omega^2}{E} \left(\frac{L^2x'}{2} - \frac{(x')^3}{6} + RLx' - \frac{R(x')^2}{2} \right) \right]_0^x\]
        <p>Since the bar is fixed at x=0, therefore \(u_x(0)=0\). Hence we obtain</p>
        \[\Rightarrow u_x(x) = \frac{\rho\omega^2}{E} \left( \frac{L^2x}{2} - \frac{x^3}{6} + RLx - \frac{Rx^2}{2} \right).\]
        <p>The displacement of the bar at \(x=L/2\) is </p>
        \[u_{x}(L/2) = \frac {\rho\omega^2L^2}{E} \left( \frac {11L}{48} + \frac {3R}{8} \right).\]
      </div>
    </solution>
  </formularesponse>

  <formularesponse inline="1" type="cs" samples="R,omega,E,rho,L@0.1,0.1,0.1,0.1,0.1:10,10,10,10,10#10" answer="(rho*omega^2)/E*(L^3/3 + (R*L^2)/2)">
    <label>Find a symbolic expression for the blade elongation \( \delta \) in terms of \(R\), \(L\), \(\rho\), \(\omega\), and \(E\).</label>
    <description>\(\delta = \)</description>
    <responseparam type="tolerance" default="1%"/>
    <textline inline="1" math="1"/>
    <solution>
      <div class="worked-solution">
        \[  \delta = \frac {\rho \omega^2}{E} \left( \frac {L^3} {3} + \frac { RL^2} {2} \right) \]
        <p><b>Obtaining the total elongation of the blade  \( \delta \):</b></p>
        <p>The strain field in the bar is</p>
        \[  \epsilon_a(x) = \frac {\mathcal{N}(x)}{EA} = \frac {\rho \omega^2 \left( \frac {L^2 - x^2}{2} + R\left(L-x\right)\right)}{E}. \]
        <p>We can now calculate the elongation of the bar as the following.</p>
        \[ \delta = \int_0^L \epsilon_{a}(x)dx = \int_0^L \frac {\rho \omega^2}{E} \left( \frac {L^2 - x^2}{2} + R\left(L-x\right)\right)dx. \]
        \[ \Rightarrow \delta= \left[ \frac { \rho \omega^2}{E} \left( \frac {L^2x}{2}  - \frac {x^3}{6} + RLx - \frac {Rx^2}{2} \right)\right]_0^L.\]
        \[ \Rightarrow \delta = \frac {\rho \omega^2}{E} \left( \frac {L^3}{2} - \frac{L^3}{6} + RL^2 - \frac {RL^2}{2} \right).\]
        \[\Rightarrow \delta= \frac {\rho \omega^2}{E} \left( \frac {L^3}{3} + \frac {RL^2}{2} \right). \]
      </div>
    </solution>
  </formularesponse>
</problem>