From 38c76eee05abc147a1ac565dbcac02deb8814b53 Mon Sep 17 00:00:00 2001 From: Chrissy Date: Tue, 25 Feb 2025 13:57:12 -0500 Subject: [PATCH 1/3] adding AC problems for runestone testing --- .../webwork/sample-chapter/sample-chapter.ptx | 349 ++++++++++++++++++ 1 file changed, 349 insertions(+) diff --git a/examples/webwork/sample-chapter/sample-chapter.ptx b/examples/webwork/sample-chapter/sample-chapter.ptx index 17fe57728..7ae48d774 100644 --- a/examples/webwork/sample-chapter/sample-chapter.ptx +++ b/examples/webwork/sample-chapter/sample-chapter.ptx @@ -2582,6 +2582,355 @@ +
+ AC in Runestone Test Problems + + + + Good test problem, scaffolded, dropdown, radio buttons, check that answers restore + + + + + + Lots of dropdowns, using NiceTables, check that answers restore + + + + + + Old Checkbox macro + + + + + + No possible correct answer for dropdown immediately after the first essay box + + + + + + + + + Hardcoded by Alex, risk of being too long + + + + + $v=" approximation is closer to the function for more values of ${BM}x${EM}."; + $radio = RadioButtons(["The cubic$v","The tangent line$v","Both approximate the function equally well."],0); + Context("Interval")->flags->set(tolType,'absolute',tolerance,.25); + $I1=Interval(-.9,.9); + $I3=Interval(-1.7,1.7); + Context("Fraction"); + $f=Fraction(-1,6); + $s=Formula("sin(x)"); + $c=$s->D('x'); + $T3=Formula("x-1/6x^3"); + Context("LimitedNumeric"); + + +

+ Let f(x)=\sin(x) and let T_3(x)=c_0+c_1x+c_2x^2+c_3x^3. + Our goal is to find the values of c_0,\ldots,c_3 that make the sine function and + its derivative values agree with those of the cubic polynomial T_3 at a=0 + and to study the resulting degree 3 approximation of the sine function. +

+ + + + +

+ As in previous work, the derivatives of T_3(x) and their respective values at + a=0 are those shown in the following table. Compute the various derivatives of + f(x)=\sin(x) and evaluate them at a=0 accordingly, recording your + results in the left side of the table. +

+ + + + + + + + f(x)= + \sin(x) + T_3(x)= + c_0+c_1x+c_2x^2+c_3x^3 + + + f'(x)= + + T_3'(x)= + c_1+2c_2x+3c_3x^2 + + + f''(x)= + + T_3''(x)= + 2c_2+6c_3x + + + f'''(x)= + + T_3'''(x)= + 6c_3 + + + f(0)= + + T_3(0)= + c_0 + + + f'(0)= + + T_3'(0)= + c_1 + + + f''(0)= + + T_3''(0)= + 2c_2 + + + f'''(0)= + + T_3'''(0)= + 6c_3 + + + + + + + + + +

+ Now, set T_3(0)=f(0), T_3'(0)=f'(0), T_3''(0)=f''(0), + and T_3'''(0)=f'''(0). This implies c_0={}, + c_1={}, c_2={}, + and c_3={}. +

+

+ Putting it all together, what is the resulting formula for T_3(x)? +

+

+ +

+ + + + + + + +

+ Recall that the tangent line approximation T_1 to f(x)=\sin(x) at + a=0 is T_1(x)=x, as plotted below. + On the same axes, we've plotted the cubic approximation T_3 you found in part (b). +

+ + + \begin{tikzpicture} + \begin{axis}[xmin=-2,xmax=2,xtick={-1,1},minor xtick={-2,-1.75,...,2},ymin=-2,ymax=2,ytick={-1,1},minor ytick={-2,-1.75,...,2},legend style={at={(0.03,0.97)},anchor=north west},domain=-2:2,smooth] + \addplot+{sin(deg(x))}; + \addlegendentry{\(f(x)\)}; + \addplot+{x}; + \addlegendentry{\(T_1(x)\)}; + \addplot+{x-x^3/6}; + \addlegendentry{\(T_3(x)\)}; + \end{axis} + \end{tikzpicture} + + +

+ What do you observe about the approximation T_3 generates compared to the tangent + line approximation T_1? +

+

+ +

+ + + + + + + +

+ Compute f(1)-T_1(1) and f(1)-T_3(1). +

+

+ +

+

+ +

+

+ What do you notice about the size and sign of those differences? +

+ + + + + + + +

+ For about what values of x does it appear that + |f(x)-T_1(x)|\lt0.1? +

+ + + Use interval notation. +

+ +

+

+ For about what values of x does it appear that + |f(x)-T_3(x)|\lt0.1? +

+ Use interval notation. +

+ +

+ + + + + + + + + + + + Runs the risk of being too long, depending on what students enter + +

+ In this problem, the notation "SIMP(2)" is actually what we have called "SIMP(4)" in our previous work. Different authors use different notation, and the author of this WeBWorK exercise chooses to write "SIMP(n)" where we have written "SIMP(2n)". +

+ + + + + + + Shortened version of question above, but told one student everything was wrong + + + + + + Uses old table macros, but parserCheckboxList + + + + + + Uses NiceTables + + + + + + Units Help, once activated and clicked on + + + + + + Check Units being Accepted when MathQuill is being used + + + + + + Click on the HelpLink when activated + + + + + + Weird Error in the Static Rendering + + + + + + My note only said weird... not sure why + + + + + + Problem changes after hitting submit + + + + + + Another problem that changes after hitting submit + + + + + +
+
Deprecations From cf009bb8881187e01052c2d57038b5f4cbb1a81b Mon Sep 17 00:00:00 2001 From: Chrissy Date: Fri, 14 Mar 2025 17:11:38 +0000 Subject: [PATCH 2/3] deleted unncessary comments, added a couple missing labels, fixed indentation --- .../webwork/sample-chapter/sample-chapter.ptx | 668 +++++++++--------- 1 file changed, 324 insertions(+), 344 deletions(-) diff --git a/examples/webwork/sample-chapter/sample-chapter.ptx b/examples/webwork/sample-chapter/sample-chapter.ptx index 7ae48d774..2c4a89783 100644 --- a/examples/webwork/sample-chapter/sample-chapter.ptx +++ b/examples/webwork/sample-chapter/sample-chapter.ptx @@ -2583,351 +2583,331 @@
- AC in Runestone Test Problems + AC in Runestone Test Problems - - - Good test problem, scaffolded, dropdown, radio buttons, check that answers restore - - - - - - Lots of dropdowns, using NiceTables, check that answers restore - - - - - - Old Checkbox macro - - - - - - No possible correct answer for dropdown immediately after the first essay box - - - - - - - - - Hardcoded by Alex, risk of being too long - - - - - $v=" approximation is closer to the function for more values of ${BM}x${EM}."; - $radio = RadioButtons(["The cubic$v","The tangent line$v","Both approximate the function equally well."],0); - Context("Interval")->flags->set(tolType,'absolute',tolerance,.25); - $I1=Interval(-.9,.9); - $I3=Interval(-1.7,1.7); - Context("Fraction"); - $f=Fraction(-1,6); - $s=Formula("sin(x)"); - $c=$s->D('x'); - $T3=Formula("x-1/6x^3"); - Context("LimitedNumeric"); - - -

- Let f(x)=\sin(x) and let T_3(x)=c_0+c_1x+c_2x^2+c_3x^3. - Our goal is to find the values of c_0,\ldots,c_3 that make the sine function and - its derivative values agree with those of the cubic polynomial T_3 at a=0 - and to study the resulting degree 3 approximation of the sine function. -

- - - - -

- As in previous work, the derivatives of T_3(x) and their respective values at - a=0 are those shown in the following table. Compute the various derivatives of - f(x)=\sin(x) and evaluate them at a=0 accordingly, recording your - results in the left side of the table. -

- - - - - - - - f(x)= - \sin(x) - T_3(x)= - c_0+c_1x+c_2x^2+c_3x^3 - - - f'(x)= - - T_3'(x)= - c_1+2c_2x+3c_3x^2 - - - f''(x)= - - T_3''(x)= - 2c_2+6c_3x - - - f'''(x)= - - T_3'''(x)= - 6c_3 - - - f(0)= - - T_3(0)= - c_0 - - - f'(0)= - - T_3'(0)= - c_1 - - - f''(0)= - - T_3''(0)= - 2c_2 - - - f'''(0)= - - T_3'''(0)= - 6c_3 - - - - - - - - - -

- Now, set T_3(0)=f(0), T_3'(0)=f'(0), T_3''(0)=f''(0), - and T_3'''(0)=f'''(0). This implies c_0={}, - c_1={}, c_2={}, - and c_3={}. -

-

- Putting it all together, what is the resulting formula for T_3(x)? -

-

- -

- - - - - - - -

- Recall that the tangent line approximation T_1 to f(x)=\sin(x) at - a=0 is T_1(x)=x, as plotted below. - On the same axes, we've plotted the cubic approximation T_3 you found in part (b). -

- - - \begin{tikzpicture} - \begin{axis}[xmin=-2,xmax=2,xtick={-1,1},minor xtick={-2,-1.75,...,2},ymin=-2,ymax=2,ytick={-1,1},minor ytick={-2,-1.75,...,2},legend style={at={(0.03,0.97)},anchor=north west},domain=-2:2,smooth] - \addplot+{sin(deg(x))}; - \addlegendentry{\(f(x)\)}; - \addplot+{x}; - \addlegendentry{\(T_1(x)\)}; - \addplot+{x-x^3/6}; - \addlegendentry{\(T_3(x)\)}; - \end{axis} - \end{tikzpicture} - - -

- What do you observe about the approximation T_3 generates compared to the tangent - line approximation T_1? -

-

- -

- - - - - - - -

- Compute f(1)-T_1(1) and f(1)-T_3(1). -

-

- -

-

- -

-

- What do you notice about the size and sign of those differences? -

- - - - - - - -

- For about what values of x does it appear that - |f(x)-T_1(x)|\lt0.1? -

- - - Use interval notation. -

- -

-

- For about what values of x does it appear that - |f(x)-T_3(x)|\lt0.1? -

- Use interval notation. -

- -

- - - - - - - - - - - - Runs the risk of being too long, depending on what students enter - -

- In this problem, the notation "SIMP(2)" is actually what we have called "SIMP(4)" in our previous work. Different authors use different notation, and the author of this WeBWorK exercise chooses to write "SIMP(n)" where we have written "SIMP(2n)". -

- - - - - - - Shortened version of question above, but told one student everything was wrong - - - - - - Uses old table macros, but parserCheckboxList - - - - - - Uses NiceTables - - - - - - Units Help, once activated and clicked on - - - - - - Check Units being Accepted when MathQuill is being used - - - - - - Click on the HelpLink when activated - - - - - - Weird Error in the Static Rendering - - - - - - My note only said weird... not sure why - - - - - - Problem changes after hitting submit - - - - - - Another problem that changes after hitting submit - - - - + + Good test problem, scaffolded, dropdown, radio buttons, check that answers restore + + + + + Lots of dropdowns, using NiceTables, check that answers restore + + + + + Old Checkbox macro + + + + + No possible correct answer for dropdown immediately after the first essay box + + + + + Causes (caused?) webwork generation to fail. Weird feedback/color behavior when entering 0 for f(3) or f(5) + + + + + Hardcoded by Alex, risk of being too long, solutions commented out + + + $v=" approximation is closer to the function for more values of ${BM}x${EM}."; + $radio = RadioButtons(["The cubic$v","The tangent line$v","Both approximate the function equally well."],0); + Context("Interval")->flags->set(tolType,'absolute',tolerance,.25); + $I1=Interval(-.9,.9); + $I3=Interval(-1.7,1.7); + Context("Fraction"); + $f=Fraction(-1,6); + $s=Formula("sin(x)"); + $c=$s->D('x'); + $T3=Formula("x-1/6x^3"); + Context("LimitedNumeric"); + + +

+ Let f(x)=\sin(x) and let T_3(x)=c_0+c_1x+c_2x^2+c_3x^3. + Our goal is to find the values of c_0,\ldots,c_3 that make the sine function and + its derivative values agree with those of the cubic polynomial T_3 at a=0 + and to study the resulting degree 3 approximation of the sine function. +

+ + + + +

+ As in previous work, the derivatives of T_3(x) and their respective values at + a=0 are those shown in the following table. Compute the various derivatives of + f(x)=\sin(x) and evaluate them at a=0 accordingly, recording your + results in the left side of the table. +

+ + + + + + + + f(x)= + \sin(x) + T_3(x)= + c_0+c_1x+c_2x^2+c_3x^3 + + + f'(x)= + + T_3'(x)= + c_1+2c_2x+3c_3x^2 + + + f''(x)= + + T_3''(x)= + 2c_2+6c_3x + + + f'''(x)= + + T_3'''(x)= + 6c_3 + + + f(0)= + + T_3(0)= + c_0 + + + f'(0)= + + T_3'(0)= + c_1 + + + f''(0)= + + T_3''(0)= + 2c_2 + + + f'''(0)= + + T_3'''(0)= + 6c_3 + + + + + + + + + +

+ Now, set T_3(0)=f(0), T_3'(0)=f'(0), T_3''(0)=f''(0), + and T_3'''(0)=f'''(0). This implies c_0={}, + c_1={}, c_2={}, + and c_3={}. +

+

+ Putting it all together, what is the resulting formula for T_3(x)? +

+

+ +

+ + + + + + + +

+ Recall that the tangent line approximation T_1 to f(x)=\sin(x) at + a=0 is T_1(x)=x, as plotted below. + On the same axes, we've plotted the cubic approximation T_3 you found in part (b). +

+ + + \begin{tikzpicture} + \begin{axis}[xmin=-2,xmax=2,xtick={-1,1},minor xtick={-2,-1.75,...,2},ymin=-2,ymax=2,ytick={-1,1},minor ytick={-2,-1.75,...,2},legend style={at={(0.03,0.97)},anchor=north west},domain=-2:2,smooth] + \addplot+{sin(deg(x))}; + \addlegendentry{\(f(x)\)}; + \addplot+{x}; + \addlegendentry{\(T_1(x)\)}; + \addplot+{x-x^3/6}; + \addlegendentry{\(T_3(x)\)}; + \end{axis} + \end{tikzpicture} + + +

+ What do you observe about the approximation T_3 generates compared to the tangent + line approximation T_1? +

+

+ +

+ + + + + + + +

+ Compute f(1)-T_1(1) and f(1)-T_3(1). +

+

+ +

+

+ +

+

+ What do you notice about the size and sign of those differences? +

+ + + + + + + +

+ For about what values of x does it appear that + |f(x)-T_1(x)|\lt0.1? +

+ + + Use interval notation. +

+ +

+

+ For about what values of x does it appear that + |f(x)-T_3(x)|\lt0.1? +

+ Use interval notation. +

+ +

+ + + + + + + + + + Runs the risk of being too long, depending on what students enter + +

+ In this problem, the notation "SIMP(2)" is actually what we have called "SIMP(4)" in our previous work. Different authors use different notation, and the author of this WeBWorK exercise chooses to write "SIMP(n)" where we have written "SIMP(2n)". +

+ + + + + + Shortened version of question above, but told one student everything was wrong + + + + + Uses old table macros, but parserCheckboxList + + + + + Uses NiceTables + + + + + Units Help, once activated and clicked on + + + + + Check Units being Accepted when MathQuill is being used + + + + + Click on the HelpLink when activated + + + + + Weird Error in the Static Rendering + + + + + My note only said weird... not sure why + + + + + Problem changes after hitting submit + + + + + Another problem that changes after hitting submit + + + +
From 43e599307389db1ccb755cd910140fc79e3411c6 Mon Sep 17 00:00:00 2001 From: Chrissy Date: Fri, 14 Mar 2025 17:15:12 +0000 Subject: [PATCH 3/3] few more edits --- examples/webwork/sample-chapter/sample-chapter.ptx | 7 +++---- 1 file changed, 3 insertions(+), 4 deletions(-) diff --git a/examples/webwork/sample-chapter/sample-chapter.ptx b/examples/webwork/sample-chapter/sample-chapter.ptx index 2c4a89783..ff2ed3f6a 100644 --- a/examples/webwork/sample-chapter/sample-chapter.ptx +++ b/examples/webwork/sample-chapter/sample-chapter.ptx @@ -2583,7 +2583,7 @@
- AC in Runestone Test Problems + AC in Runestone Test Problems Good test problem, scaffolded, dropdown, radio buttons, check that answers restore @@ -2600,7 +2600,7 @@ - + No possible correct answer for dropdown immediately after the first essay box @@ -2906,10 +2906,9 @@ Another problem that changes after hitting submit - -
+
Deprecations