Three new OPL problems and one bug fix

Contrib/UMN-Morris/MSAF/derivative_rules.pg

@@ -0,0 +1,140 @@
+# DESCRIPTION
+# A scaffolded problem where students apply derivative rules one step at a time.
+# ENDDESCRIPTION
+
+## KEYWORDS('derivative, differentiation, derivative rules')
+## TitleText1('Derivative Rules Problem')
+## DBsubject(Calculus - single variable)
+## DBchapter(Differentiation)
+## DBsection(Derivatives of polynomials and power functions)
+## MO(1)
+## Level(2)
+## Static(1)
+## Language(en)
+## Author('Chenfei Peng, Mercredi Chasman')
+## Institution('UMinnMorris, 12/13/2024')
+## TitleText1(Calculus)
+## EditionText1(6e)
+## AuthorText1(Stewart)
+## Section1(3.1)
+
+DOCUMENT();
+loadMacros(
+  "PGstandard.pl",
+  "MathObjects.pl",   
+  "PGML.pl",
+  "PGcourse.pl",
+  'scaffold.pl',
+  'parserPopUp.pl',
+);
+
+$showPartialCorrectAnswers = 1;
+
+# Define popup options for each step of the derivative process
+$popup1 = PopUp([ '?', 'FOIL', 'Sum/difference Rule', 'Power Rule', 'Constant Rule', 'Constant Multiple Rule', 
+'Simplify', 'Distribute/expand', 'Product Rule', 'Factor'], 'Distribute/expand');
+$popup2 = PopUp([ '?', 'FOIL', 'Sum/difference Rule', 'Power Rule', 'Constant Rule', 'Constant Multiple Rule', 
+'Simplify', 'Distribute/expand', 'Product Rule', 'Factor'], 'Sum/difference Rule');
+$popup3 = PopUp([ '?', 'FOIL', 'Sum/difference Rule', 'Power Rule', 'Constant Rule', 'Constant Multiple Rule', 
+'Simplify', 'Distribute/expand', 'Product Rule', 'Factor'], 'Constant Multiple Rule');
+$popup4 = PopUp([ '?', 'FOIL', 'Sum/difference Rule', 'Power Rule', 'Constant Rule', 'Constant Multiple Rule', 
+'Simplify', 'Distribute/expand', 'Product Rule', 'Factor'], 'Power Rule');
+$popup5 = PopUp([ '?', 'FOIL', 'Sum/difference Rule', 'Power Rule', 'Constant Rule', 'Constant Multiple Rule', 
+'Simplify', 'Distribute/expand', 'Product Rule', 'Factor'], 'Simplify');
+
+Context("Numeric");
+$f=Formula("35x^4 - 44x^3 + 24x^2");
+BEGIN_PGML
+Evaluate the following derivative without using the Product Rule, Quotient Rule, or Chain Rule. Use only one derivative rule at a time and order terms in descending expression order.  Answer blanks should be filled with mathematical expressions, numbers, or mathematical symbols [`+,-,*,/,^`] as appropriate.
+END_PGML
+
+Scaffold::Begin(
+    can_open => "when_previous_correct",
+    is_open  => "correct_or_first_incorrect"
+);
+
+Section::Begin('Step 1');
+
+BEGIN_PGML
+
+[``
+\frac{d}{dx} \Big[ x^3(7x^2 - 11x + 8) \Big] = \frac{d}{dx} \Big[ ``] [__]{7x^5} - [__]{11x^4} + [__]{8x^3} [`` \Big]
+``]
+
+*Which rule applies here?*
+[________]{$popup1}
+END_PGML
+
+Section::End();
+
+Section::Begin('Step 2');
+
+BEGIN_PGML
+
+[``
+= \frac{d}{dx} \Big[ ``] [__]{7x^5} [`` \Big] - \frac{d}{dx} \Big[ ``] [__]{11x^4} [`` \Big] + \frac{d}{dx} \Big[ ``] [__]{8x^3} [`` \Big]
+``]
+
+*Which rule applies here?*
+[________]{$popup2}
+END_PGML
+
+Section::End();
+
+Section::Begin('Step 3');
+
+BEGIN_PGML
+
+[``
+= 7\frac{d}{dx} \Big[ ``] [__]{Formula("x^5")} [`` \Big] - 11\frac{d}{dx} \Big[ ``] [__]{Formula("x^4")} [`` \Big] + 8\frac{d}{dx} \Big[ ``] [__]{Formula("x^3")} [`` \Big]
+``]
+
+*Which rule applies here?*
+[________]{$popup3}
+END_PGML
+
+Section::End();
+
+Section::Begin('Step 4');
+
+BEGIN_PGML
+
+[``
+= 7 \Big( ``] [__]{5x^4} [`` \Big) - 11 \Big( ``] [__]{4x^3} [`` \Big) + 8 \Big( ``] [__]{3x^2} [`` \Big)
+``]
+
+*Which rule applies here?*
+[________]{$popup4}
+END_PGML
+
+Section::End();
+
+Section::Begin('Step 5');
+
+BEGIN_PGML
+Finally, simplify:
+
+[``
+= ``] [__]{$f}
+
+
+END_PGML
+
+Section::End();
+
+Scaffold::End();
+
+BEGIN_PGML_SOLUTION
+In this solution, we apply the following derivative rules step by step to compute the derivative .
+
+- **Step 1**: We **Distribute/Expand** the product to put it in a form we can differentiate.
+- **Step 2**: We use the **Sum/Difference Rule** to break the derivative into individual terms.
+- **Step 3**: We apply the **Constant Multiple Rule**, which allows us to pull out constants from the derivatives.
+- **Step 4**: We then apply the **Power Rule** to differentiate each power x^n.
+- **Step 5**: Finally, we **Simplify** the expression to get the final result.
+
+Final result:  35x^4 - 44x^3 + 24x^2 
+END_PGML_SOLUTION
+
+
+ENDDOCUMENT();

Contrib/UMN-Morris/MSAF/limitlaws.pg

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+# DESCRIPTION
+# A scaffolded problem where students use one limit law or operation at a time to compute a limit.
+# ENDDESCRIPTION
+
+## DBsubject(Calculus - single variable)
+## DBchapter(Limits and continuity)
+## DBsection(Rules of limits - basic)
+## KEYWORDS('calculus','limits','Limit')
+## Level(2)
+## MO(1)
+## Static(1)
+## Language(en)
+## TitleText1('Calculus')
+## EditionText1('6')
+## AuthorText1('Stewart')
+## Section1('2.3')
+## Problem1('')
+## Author('Chenfei Peng, Mercredi Chasman')
+## Institution('UMinnMorris, 12/13/2024')
+
+
+DOCUMENT();
+loadMacros(
+  "PGstandard.pl",
+  "MathObjects.pl",   
+  "PGML.pl",
+  "PGcourse.pl",
+  'scaffold.pl',
+  'parserPopUp.pl',
+);
+
+$showPartialCorrectAnswers = 1;
+$popup1 = PopUp([ '?', 'Sum/difference law', 'Constant Multiple Law', 'Constant Law', 'Power Law',
+'Quotient Law', 'Product Law', 'Linear Law'], 'Sum/difference law');
+$popup2 = PopUp([ '?', 'Sum/difference law', 'Constant Multiple Law', 'Constant Law', 'Power Law',
+'Quotient Law', 'Product Law', 'Linear Law'], 'Constant Multiple Law');
+$popup3 = PopUp([ '?', 'Sum/difference law', 'Constant Multiple Law', 'Constant Law', 'Power Law',
+'Quotient Law', 'Product Law', 'Linear Law'], 'Power Law');
+$popup4 = PopUp([ '?', 'Sum/difference law', 'Constant Multiple Law', 'Constant Law', 'Power Law',
+'Quotient Law', 'Product Law', 'Linear Law'], 'Linear Law');
+
+
+Context("Numeric");
+
+BEGIN_PGML
+Use limit laws to compute the following limit. Use only one rule at a time. Answer blanks should be filled with mathematical expressions, numbers, or mathematical symbols [`+,-,*,/,^`] as appropriate.
+END_PGML
+
+Scaffold::Begin(
+    can_open => "when_previous_correct",
+    is_open  => "correct_or_first_incorrect"
+);
+
+Section::Begin('Step 1');
+
+BEGIN_PGML
+[``
+\lim_{x \to 3} \Big[7x^2 + 11x \Big] = \lim_{x \to 3}\Big[ ``] [___]{7x^2} [``\Big]``]      [___]{str_cmp("+")}       [``\lim_{x \to 3}\Big[ ``] [_]{11x} [``\Big]``]
+
+*Which limit law applies here?*
+[________]{$popup1}
+END_PGML
+
+Section::End();
+
+Section::Begin('Step 2');
+BEGIN_PGML
+
+[``
+= ``] [___]{7} [`` \lim_{x \to 3}\Big[ ``] [___]{Formula("x^2")} [``\Big]``] + [_]{11} [``\lim_{x \to 3}\Big[ ``] [_]{x} [``\Big]``]
+
+*Which limit law applies here?*
+[________]{$popup2}
+END_PGML
+Section::End();
+
+Section::Begin('Step 3');
+BEGIN_PGML
+
+[``
+= 7 ( \lim_{x \to 3} \Big[ ``] [___]{x} [``\Big] )^2 + 11 \lim_{x \to 3} \Big[ ``] [_]{x} [``\Big]``]
+
+*Which limit law applies here?*
+[________]{$popup3}
+END_PGML
+Section::End();
+
+Section::Begin('Step 4');
+BEGIN_PGML
+
+[`` = 7 ( ``] [___]{3} [`` )^2 + 11 ( ``] [___]{3} [`` ) ``]
+
+*Which limit law applies here?*
+[________]{$popup4}
+END_PGML
+Section::End();
+
+Section::Begin('Step 5');
+BEGIN_PGML
+
+[`` = ``] [___]{96}
+
+END_PGML
+Section::End();
+
+Scaffold::End();
+
+
+BEGIN_PGML_SOLUTION
+In this solution, we apply the limit laws step by step to simplify the expression and find the value of the limit.
+
+- **Step 1**: Apply the **Sum/Difference Law** to split the limit.
+- **Step 2**: Apply the **Constant Multiple Law** to factor out the constants.
+- **Step 3**: Use the **Power Law** to deal with the powers of \( x \).
+- **Step 4**: Evaluate the limits by substitution.
+- **Step 5**: Combine the results to get the final answer.
+
+Final result: 96.
+END_PGML_SOLUTION
+
+ENDDOCUMENT();