Question corpus
Explore imported STACK questions and their current support
Use the teacher track to choose and try a question. The developer track keeps replay details and adaptation issues together.
For teachers
These are 35 unchanged STACK XML questions from the upstream library. The 23 questions whose authored tests passed on every replayed seed have interactive cards. Each question has a local XML download and an observed result. One additional presentation teaching copy shows a matrix question whose original HTML is unsupported. Other originals remain available with the observed mismatch or unsupported feature shown explicitly.
In this snapshot, 23 pass their author tests, 1 has a test mismatch, and 11 cannot be fully checked here. The replay record gives the tested variants and exact results.
The worked matrix examples include determinant, basis and positive-definiteness tasks. They all use predicates in the shared matrix library. These authored examples are separate from the unchanged exports and their baseline counts. See Python answer tests.
Browse all 35
| Question | Topic | Adapter status | Original XML |
|---|---|---|---|
| AlgMap-1.5 | Algebra Refresher / 01 Combinations of arithmetic operations | Passed authored tests | Download |
| AlgMap-1.6 | Algebra Refresher / 01 Combinations of arithmetic operations | Passed authored tests | Download |
| AlgMap-2.1 | Algebra Refresher / 02 Factorisation of whole numbers | Passed authored tests | Download |
| AlgMap-2.5 | Algebra Refresher / 02 Factorisation of whole numbers | Passed authored tests | Download |
| AlgMap-3.1 | Algebra Refresher / 03 Addition and subtraction of fractions | Cannot import this question | Download |
| AlgMap-3.3 | Algebra Refresher / 03 Addition and subtraction of fractions | Cannot prepare this variant | Download |
| AlgMap-4.1 | Algebra Refresher / 04 Multiplication and division of fractions | Passed authored tests | Download |
| AlgMap-4.13 | Algebra Refresher / 04 Multiplication and division of fractions | Passed authored tests | Download |
| AlgMap-5.1 | Algebra Refresher / 05 Combinations of arithmetic operations on fractions | Cannot prepare this variant | Download |
| AlgMap-6.4 | Algebra Refresher / 06 Simplifying algebraic expressions | Passed authored tests | Download |
| AlgMap-6.7 | Algebra Refresher / 06 Simplifying algebraic expressions | Passed authored tests | Download |
| AlgMap-7.1 | Algebra Refresher / 07 Removing brackets | Passed authored tests | Download |
| AlgMap-7.10 | Algebra Refresher / 07 Removing brackets | Cannot prepare this variant | Download |
| AlgMap-8.5 | Algebra Refresher / 08 Algebraic fractions | Passed authored tests | Download |
| AlgMap-8.10 | Algebra Refresher / 08 Algebraic fractions | Original scoring-tree issue | Download |
| AlgMap-9.1 | Algebra Refresher / 09 Linear equations | Passed authored tests | Download |
| AlgMap-9.6 | Algebra Refresher / 09 Linear equations | Passed authored tests | Download |
| AlgMap-10.1 | Algebra Refresher / 10 Expressions single term common factors | Passed authored tests | Download |
| AlgMap-11.1 | Algebra Refresher / 11 Rearranging algebraic formulae | Passed authored tests | Download |
| AlgMap-11.8 | Algebra Refresher / 11 Rearranging algebraic formulae | Passed authored tests | Download |
| AlgMap-12.1 | Algebra Refresher / 12 Simultaneous linear equations | Cannot prepare this variant | Download |
| AlgMap-13.1 | Algebra Refresher / 13 Factorising algebraic expressions | Passed authored tests | Download |
| AlgMap-14.1 | Algebra Refresher / 14 Algebraic fractions involving factorising | Passed authored tests | Download |
| AlgMap-15.1 | Algebra Refresher / 15 Quadratic equations | Cannot prepare this variant | Download |
| Complex_Convert_1 | Topics / Complex Numbers | Passed authored tests | Download |
| Limits_1 | Topics / Limits | Cannot import this question | Download |
| Logs_1 | Topics / Logs and Exponentials | Passed authored tests | Download |
| Matrices_find det 2*2 | Topics / LinearAlgebra / Matrix Calculations | Cannot prepare this variant | Download |
| Inequality_1 | Topics / Inequalities | Cannot prepare this variant | Download |
| Numerical input (min sf) | Features / input type sample questions | Cannot import this question | Download |
| LinearAlgebra_elementary_1 | Linear algebra / Matrix input | Passed authored tests | Download |
| LinearAlgebra_elementary_2 | Linear algebra / Matrix input | Passed authored tests | Download |
| LinearAlgebra_elementary_3 | Linear algebra / Matrix input | Passed authored tests | Download |
| LinearAlgebra_elementary_4 | Linear algebra / Matrix input | Passed authored tests | Download |
| 7.3.26 (Write sim. eqns. with matrices) | Introductory Mathematics / Matrix equations | Cannot prepare this variant | Download |
Five matrix-input problems
The four elementary-row-operation problems below run directly from unchanged official exports: row 2 plus a multiple of row 3, row 1 plus a multiple of row 3, row 2 plus a multiple of row 1, and row 1 minus a multiple of row 2. Together their original tests pass all 24 recorded seed/case combinations. Each uses a fixed 3 by 3 matrix editor and whole-matrix algebraic equivalence; no automatic cell partial credit is added.
The fifth asks learners to write a system of three linear equations as a coefficient matrix and a column vector. Its original XML is preserved unchanged and remains blocked by an unsupported inline HTML style. This explicitly attributed presentation teaching copy removes that style and closes its list; variables, answers, PRT and authored qtest are unchanged. Its original qtest passed on the recorded Moodle seeds; the SymPy proposals below run their own qtests. This is a presentation adaptation, not evidence that the original export runs unchanged.
Write the following system of linear equations as a matrix equation. \[ \begin{align*} &{2}x;_1 + {5}x_2 + {1}x_3 = {4} \\ &{3}x;_1 + {1}x_2 + {4}x_3 = {2} \\ &{4}x;_1 + {4}x_2 + {4}x_3 = {8} \end{align*} \]
- \(\begin{bmatrix} x_1 \\ x_2 \\ x_3 \end{bmatrix} = \)
Show source
```{.stack-question}
#| file: questions/corrected/7-3-26-(Write-sim-eqns-with-matrices).xml
#| question: 7.3.26 (Write sim. eqns. with matrices) (presentation teaching copy)
#| label: corpus-matrix-system
#| review: true
```Show STACK source
<?xml version="1.0" encoding="UTF-8"?>
<quiz>
<question type="stack">
<name>
<text>7.3.26 (Write sim. eqns. with matrices) (presentation teaching copy)</text>
</name>
<questiontext format="moodle_auto_format">
<text><![CDATA[<p>Write the following system of linear equations as a matrix equation.
\[
\begin{align*}
&{@a1@}x_1 + {@a2@}x_2 + {@a3@}x_3 = {@b1@}
\\
&{@a4@}x_1 + {@a5@}x_2 + {@a6@}x_3 = {@b2@}
\\
&{@a7@}x_1 + {@a8@}x_2 + {@a9@}x_3 = {@b3@}
\end{align*}
\]</p>
<ul>
<li>
[[input:ans1]] [[validation:ans1]] \(\begin{bmatrix}
x_1
\\
x_2
\\
x_3
\end{bmatrix} = \)[[input:ans2]] [[validation:ans2]]
</li></ul>]]></text>
</questiontext>
<generalfeedback format="moodle_auto_format">
<text><![CDATA[<p>We can use matrices to write this equation in the form \(A \mathbf{x} = \mathbf{b}\). So the coefficients of each \(x_i\) are the entries of the matrix \(A\) and the entries of the vector \(\mathbf{b}\) are the values on the right hand side of the equals sign. So we have
\[
{@ta1@} \begin{bmatrix}
x_1
\\
x_2
\\
x_3
\end{bmatrix} = {@ta2@}.
\]</p>]]></text>
</generalfeedback>
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<idnumber/>
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<text>2020081700</text>
</stackversion>
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<text>a1: 1+rand(5);
a2: 1+rand(5);
a3: 1+rand(5);
a4: 1+rand(5);
a5: 1+rand(5);
a6: 1+rand(5);
a7: 1+rand(5);
a8: 1+rand(5);
a9: 1+rand(5);
b1: 1+rand(10);
b2: 1+rand(10);
b3: 1+rand(10);
ta1: matrix([a1,a2,a3],[a4,a5,a6],[a7,a8,a9]);
ta2: matrix([b1],[b2],[b3]);</text>
</questionvariables>
<specificfeedback format="html">
<text>[[feedback:prt1]]</text>
</specificfeedback>
<questionnote format="moodle_auto_format">
<text>\({@ta1@} \begin{bmatrix}
x_1
\\
x_2
\\
x_3
\end{bmatrix} {@ta2@}\)</text>
</questionnote>
<questiondescription format="moodle_auto_format">
<text/>
</questiondescription>
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<scientificnotation>*10</scientificnotation>
<multiplicationsign>dot</multiplicationsign>
<sqrtsign>1</sqrtsign>
<complexno>i</complexno>
<inversetrig>cos-1</inversetrig>
<logicsymbol>lang</logicsymbol>
<matrixparens>[</matrixparens>
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<metadata>
{"author":[{"firstName":"","lastName":"","institution":"Unknown - Legacy question","year":"2025"}],"language":["en"],"isPartOf":"STACK Library","license":"cc-sa-4.0","additional":{"UoE":{"Notes":"This is automatically generated metadata."}},"freeform":{}}
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</feedbackvariables>
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<text/>
</falsefeedback>
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<answertest>AlgEquiv</answertest>
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<text/>
</truefeedback>
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<falseanswernote>prt1-2-F</falseanswernote>
<falsefeedback format="html">
<text/>
</falsefeedback>
</node>
</prt>
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<qtest>
<testcase>1</testcase>
<description/>
<testinput>
<name>ans1</name>
<value>ta1</value>
</testinput>
<testinput>
<name>ans2</name>
<value>ta2</value>
</testinput>
<expected>
<name>prt1</name>
<expectedscore>1.0000000</expectedscore>
<expectedpenalty>0.0000000</expectedpenalty>
<expectedanswernote>prt1-2-T</expectedanswernote>
</expected>
</qtest>
</question>
</quiz>
Download presentation teaching XML · Adaptation and licensing
Ready to try
These 23 cards use independently generated SymPy variants of each question. Press Validate answers, then Check answer. Run question tests checks the displayed variant against the question’s authored cases. Three cards use corrected teaching copies for mathematical or grading defects in the originals. Each original remains downloadable; the baseline records every tested variant.
AlgMap-1.5
Algebra Refresher / 01 Combinations of arithmetic operations · 1 answer field · 2 author tests.
Corrected teaching copy: The worked explanation now uses multiplication in the exponent product rule, rather than the incorrect addition rule. The original XML is preserved unchanged; this card and its source panels use the corrected copy linked below.
Simplify the algebraic expression \[{c^{3} \cdot c^{6}}.\] Be sure to leave your answer in the form: \(x^y\).
Show source
```{.stack-question}
#| file: questions/corrected/AlgMap-1-5.xml
#| question: AlgMap-1.5 (corrected teaching copy)
#| label: corpus-algmap-1-5
#| review: true
```Show STACK source
<?xml version="1.0" encoding="UTF-8"?>
<!-- Teaching correction by CTM, 2026-10-16. Derived from the pinned STACK
corpus/AlgMap-1-5.xml export; CC BY-SA 4.0. Original authors and source:
../corpus/manifest.json. The original export is preserved unchanged. -->
<quiz>
<question type="stack">
<name>
<text>AlgMap-1.5 (corrected teaching copy)</text>
</name>
<questiontext format="html">
<text><![CDATA[<p>Simplify the algebraic expression \[{@c^a*c^b@}.\] Be sure to leave your answer in the form: \(x^y\). <br /> <br /> [[input:ans]] [[validation:ans]]</p>]]></text>
</questiontext>
<generalfeedback format="html">
<text><![CDATA[<p>Remember the product rule, \(c^a\cdot c^b=c^{a+b}\). <br /> <br /> In this example: \[c^{@a@}\cdot c^{@b@}=c^{@ev(a+b,simp)@}.\]</p>]]></text>
</generalfeedback>
<defaultgrade>1</defaultgrade>
<penalty>0.1</penalty>
<hidden>0</hidden>
<idnumber/>
<stackversion>
<text/>
</stackversion>
<questionvariables>
<text>a:ev(rand(6)+2,simp);
b:ev(rand(6)+2,simp);
p:(ev(c^a,simp)*ev(c^b,simp));
ta:ev(c^(a+b),simp);</text>
</questionvariables>
<specificfeedback format="html">
<text><![CDATA[<p>[[feedback:prt1]]</p>]]></text>
</specificfeedback>
<questionnote format="moodle_auto_format">
<text>\( {@c^a*c^b@} = {@ta@} \).</text>
</questionnote>
<questiondescription format="moodle_auto_format">
<text/>
</questiondescription>
<questionsimplify>0</questionsimplify>
<assumepositive>0</assumepositive>
<assumereal>0</assumereal>
<scientificnotation>*10</scientificnotation>
<multiplicationsign>dot</multiplicationsign>
<sqrtsign>1</sqrtsign>
<complexno>i</complexno>
<inversetrig>cos-1</inversetrig>
<logicsymbol>lang</logicsymbol>
<matrixparens>[</matrixparens>
<isbroken>0</isbroken>
<prescribedmetadata/>
<metadata>
{"author":[{"firstName":"Tony","lastName":"Barnard","institution":"","year":"1999"}],"language":["en"],"isPartOf":"STACK Library - Algebra Refresher","license":"cc-sa-4.0","additional":{"UoE":{"Notes":"This is automatically generated metadata."}},"freeform":{}}
</metadata>
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<type>algebraic</type>
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<options/>
</input>
<prt>
<name>prt1</name>
<value>1.0000000</value>
<autosimplify>0</autosimplify>
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<text/>
</feedbackvariables>
<node>
<name>0</name>
<description/>
<answertest>EqualComAss</answertest>
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<truescore>1.0000000</truescore>
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<trueanswernote>1-0-T </trueanswernote>
<truefeedback format="html">
<text/>
</truefeedback>
<falsescoremode>=</falsescoremode>
<falsescore>0.0000000</falsescore>
<falsepenalty/>
<falsenextnode>1</falsenextnode>
<falseanswernote>1-0-F </falseanswernote>
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<text/>
</falsefeedback>
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<node>
<name>1</name>
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<answertest>AlgEquiv</answertest>
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<truepenalty/>
<truenextnode>-1</truenextnode>
<trueanswernote>1-1-T </trueanswernote>
<truefeedback format="html">
<text><![CDATA[<p>Your answer is equivalent to the correct answer but you haven't fully simplified.</p>]]></text>
</truefeedback>
<falsescoremode>=</falsescoremode>
<falsescore>0.0000000</falsescore>
<falsepenalty/>
<falsenextnode>-1</falsenextnode>
<falseanswernote>1-1-F </falseanswernote>
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<text/>
</falsefeedback>
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</prt>
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<name>ans</name>
<value>ta</value>
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<expectedscore>1.0000000</expectedscore>
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<expectedanswernote>1-0-T</expectedanswernote>
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<qtest>
<testcase>2</testcase>
<description/>
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<name>ans</name>
<value>p</value>
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<expected>
<name>prt1</name>
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<expectedanswernote>1-1-T </expectedanswernote>
</expected>
</qtest>
</question>
</quiz>
AlgMap-1.6
Algebra Refresher / 01 Combinations of arithmetic operations · 1 answer field · 2 author tests.
\({\left( {2}^{2} \right)}^{4}\) can be expressed in the form:
\[{2}^x.\] Find the value of \(x\).
\(x\) =
Show source
```{.stack-question}
#| file: questions/corpus/AlgMap-1-6.xml
#| question: AlgMap-1.6
#| label: corpus-algmap-1-6
#| review: true
```Show STACK source
<?xml version="1.0" encoding="UTF-8"?>
<quiz>
<question type="stack">
<name>
<text>AlgMap-1.6</text>
</name>
<questiontext format="html">
<text><![CDATA[<p>\({\left( {@c@}^{@a@} \right)}^{@b@}\) can be expressed in the form: <br /> \[{@c@}^x.\] Find the value of \(x\). <br /> <br /> \(x\) = [[input:ans]] [[validation:ans]]</p>]]></text>
</questiontext>
<generalfeedback format="html">
<text><![CDATA[<p>Remember the rule that \(\left( c^a \right)^b=c^{ab}\). In this example \(\left({@c@}^{@a@} \right)^{@b@}\) = \({@c@}^{{@a@}\cdot{@b@}}\). Therefore: \[x = {@a@} \cdot {@b@} = {@ta@}.\]</p>]]></text>
</generalfeedback>
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<penalty>0.1</penalty>
<hidden>0</hidden>
<idnumber/>
<stackversion>
<text/>
</stackversion>
<questionvariables>
<text>a:rand(3)+2;
b:rand(3)+2;
c:rand(2)+2;
ta:(a*b);</text>
</questionvariables>
<specificfeedback format="html">
<text><![CDATA[<p>[[feedback:prt1]]</p>]]></text>
</specificfeedback>
<questionnote format="moodle_auto_format">
<text>\({\left( {@c@}^{@a@} \right)}^{@b@} = {@c@}^{@a*b@}. \)</text>
</questionnote>
<questiondescription format="moodle_auto_format">
<text/>
</questiondescription>
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<scientificnotation>*10</scientificnotation>
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<sqrtsign>1</sqrtsign>
<complexno>i</complexno>
<inversetrig>cos-1</inversetrig>
<logicsymbol>lang</logicsymbol>
<matrixparens>[</matrixparens>
<isbroken>0</isbroken>
<prescribedmetadata/>
<metadata>
{"author":[{"firstName":"Tony","lastName":"Barnard","institution":"","year":"1999"}],"language":["en"],"isPartOf":"STACK Library - Algebra Refresher","license":"cc-sa-4.0","additional":{"UoE":{"Notes":"This is automatically generated metadata."}},"freeform":{}}
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</input>
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<truescore>1.0000000</truescore>
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<truenextnode>-1</truenextnode>
<trueanswernote>1-0-T </trueanswernote>
<truefeedback format="html">
<text/>
</truefeedback>
<falsescoremode>=</falsescoremode>
<falsescore>0.0000000</falsescore>
<falsepenalty/>
<falsenextnode>-1</falsenextnode>
<falseanswernote>1-0-F </falseanswernote>
<falsefeedback format="html">
<text/>
</falsefeedback>
</node>
</prt>
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<expectedscore>1.0000000</expectedscore>
<expectedpenalty>0.0000000</expectedpenalty>
<expectedanswernote>1-0-T</expectedanswernote>
</expected>
</qtest>
<qtest>
<testcase>2</testcase>
<description/>
<testinput>
<name>ans</name>
<value>ans+1</value>
</testinput>
<expected>
<name>prt1</name>
<expectedscore>0.0000000</expectedscore>
<expectedpenalty>0.1000000</expectedpenalty>
<expectedanswernote>1-0-F</expectedanswernote>
</expected>
</qtest>
</question>
</quiz>
AlgMap-2.1
Algebra Refresher / 02 Factorisation of whole numbers · 1 answer field · 2 author tests.
Factorise \({60}\) into primes:
Write your answer as powers of primes, e.g. \(p_1^{n_1}\times\cdots\).
Show source
```{.stack-question}
#| file: questions/corpus/AlgMap-2-1.xml
#| question: AlgMap-2.1
#| label: corpus-algmap-2-1
#| review: true
```Show STACK source
<?xml version="1.0" encoding="UTF-8"?>
<quiz>
<question type="stack">
<name>
<text>AlgMap-2.1</text>
</name>
<questiontext format="html">
<text><![CDATA[<p>Factorise \({@n@}\) into primes: <br /> Write your answer as powers of primes, e.g. \(p_1^{n_1}\times\cdots\). <br /> [[input:ans]] [[validation:ans]]</p>]]></text>
</questiontext>
<generalfeedback format="html">
<text><![CDATA[<p>To factorise a number, \(n\) into primes the best trick is to divide by the smallest prime, \(2\). If the resulting value, \(m\), is an integer then we write it as \(2 \cdot m\). If not, then we try the next largest prime, \(3\), and repeat the process until we have obtained a product of the form \[p_1 \cdot p_2 \cdot ... \cdot 1, \] where p are prime numbers. In this particular example: \[ {@n@} = {@ta@}. \]</p>]]></text>
</generalfeedback>
<defaultgrade>1</defaultgrade>
<penalty>0.1</penalty>
<hidden>0</hidden>
<idnumber/>
<stackversion>
<text/>
</stackversion>
<questionvariables>
<text>n:ev(2^((rand(2)+2))*3^(rand(2)+1)*5^(rand(2))*7^(rand(2)),simp);
ta:factor(n);</text>
</questionvariables>
<specificfeedback format="html">
<text><![CDATA[<p>[[feedback:prt1]]</p>]]></text>
</specificfeedback>
<questionnote format="moodle_auto_format">
<text>{@n@} = {@ta@}</text>
</questionnote>
<questiondescription format="moodle_auto_format">
<text/>
</questiondescription>
<questionsimplify>0</questionsimplify>
<assumepositive>0</assumepositive>
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<scientificnotation>*10</scientificnotation>
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<metadata>
{"author":[{"firstName":"Tony","lastName":"Barnard","institution":"","year":"1999"}],"language":["en"],"isPartOf":"STACK Library - Algebra Refresher","license":"cc-sa-4.0","additional":{"UoE":{"Notes":"This is automatically generated metadata."}},"freeform":{}}
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<truescore>1.0000000</truescore>
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<trueanswernote>1-0-T </trueanswernote>
<truefeedback format="html">
<text/>
</truefeedback>
<falsescoremode>=</falsescoremode>
<falsescore>0.0000000</falsescore>
<falsepenalty/>
<falsenextnode>1</falsenextnode>
<falseanswernote>1-0-F </falseanswernote>
<falsefeedback format="html">
<text/>
</falsefeedback>
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<node>
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<answertest>AlgEquiv</answertest>
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<truepenalty/>
<truenextnode>-1</truenextnode>
<trueanswernote>1-1-T </trueanswernote>
<truefeedback format="html">
<text><![CDATA[<p>Your answer is equivalent to the correct answer but not fully factored.</p>]]></text>
</truefeedback>
<falsescoremode>=</falsescoremode>
<falsescore>0.0000000</falsescore>
<falsepenalty/>
<falsenextnode>-1</falsenextnode>
<falseanswernote>1-1-F </falseanswernote>
<falsefeedback format="html">
<text/>
</falsefeedback>
</node>
</prt>
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<expectedscore>1.0000000</expectedscore>
<expectedpenalty>0.0000000</expectedpenalty>
<expectedanswernote>1-0-T</expectedanswernote>
</expected>
</qtest>
<qtest>
<testcase>2</testcase>
<description/>
<testinput>
<name>ans</name>
<value>n</value>
</testinput>
<expected>
<name>prt1</name>
<expectedscore>0.0000000</expectedscore>
<expectedpenalty>0.1000000</expectedpenalty>
<expectedanswernote>1-1-T </expectedanswernote>
</expected>
</qtest>
</question>
</quiz>
AlgMap-2.5
Algebra Refresher / 02 Factorisation of whole numbers · 1 answer field · 2 author tests.
Corrected teaching copy: A reduced answer with the wrong value can receive full credit. This defect belongs to the original response tree. The corrected card checks value equivalence before lowest-terms form and adds a wrong-value author test. The original XML is preserved unchanged; this card and its source panels use the corrected copy linked below.
Reduce the following fraction to its lowest terms: \[\frac{15}{30}.\]
Show source
```{.stack-question}
#| file: questions/corrected/AlgMap-2-5.xml
#| question: AlgMap-2.5 (corrected teaching copy)
#| label: corpus-algmap-2-5
#| review: true
```Show STACK source
<?xml version="1.0" encoding="UTF-8"?>
<!-- Teaching correction by CTM, 2026-10-16. Derived from the pinned STACK
corpus/AlgMap-2-5.xml export; CC BY-SA 4.0. Original authors and source:
../corpus/manifest.json. The original export is preserved unchanged. -->
<quiz>
<question type="stack">
<name>
<text>AlgMap-2.5 (corrected teaching copy)</text>
</name>
<questiontext format="html">
<text><![CDATA[<p>Reduce the following fraction to its lowest terms: \[\frac{@ev(a*c,simp)@}{@ev(b*c,simp)@}.\] <br /> [[input:ans]] [[validation:ans]]</p>]]></text>
</questiontext>
<generalfeedback format="html">
<text><![CDATA[<p>Factorise the numerator and the denominator into prime factors, then cancel matching factors. In this example: <br /> \[ \frac{@factor(a*c)@}{@factor(b*c)@} = {@ta@}. \]</p>]]></text>
</generalfeedback>
<defaultgrade>1</defaultgrade>
<penalty>0.1</penalty>
<hidden>0</hidden>
<idnumber/>
<stackversion>
<text/>
</stackversion>
<questionvariables>
<text>a:ev((rand([1,3,5,7,9])*rand([1,-1])),simp);
b:ev((rand([2,4,6,8,10])*rand([1,-1])),simp);
c:ev(rand(5)+2,simp);
ta:ev((a*c)/(b*c),simp);</text>
</questionvariables>
<specificfeedback format="html">
<text><![CDATA[<p>[[feedback:prt1]]</p>]]></text>
</specificfeedback>
<questionnote format="moodle_auto_format">
<text>\[\frac{@ev(a*c,simp)@}{@ev(b*c,simp)@} = {@ta@}.\]</text>
</questionnote>
<questiondescription format="moodle_auto_format">
<text/>
</questiondescription>
<questionsimplify>0</questionsimplify>
<assumepositive>0</assumepositive>
<assumereal>0</assumereal>
<scientificnotation>*10</scientificnotation>
<multiplicationsign>dot</multiplicationsign>
<sqrtsign>1</sqrtsign>
<complexno>i</complexno>
<inversetrig>cos-1</inversetrig>
<logicsymbol>lang</logicsymbol>
<matrixparens>[</matrixparens>
<isbroken>0</isbroken>
<prescribedmetadata/>
<metadata>
{"author":[{"firstName":"Tony","lastName":"Barnard","institution":"","year":"1999"}],"language":["en"],"isPartOf":"STACK Library - Algebra Refresher","license":"cc-sa-4.0","additional":{"UoE":{"Notes":"This is automatically generated metadata."}},"freeform":{}}
</metadata>
<variantsselectionseed/>
<input>
<name>ans</name>
<type>algebraic</type>
<tans>ta</tans>
<boxsize>15</boxsize>
<strictsyntax>1</strictsyntax>
<insertstars>0</insertstars>
<syntaxhint/>
<syntaxattribute>0</syntaxattribute>
<forbidwords/>
<allowwords/>
<forbidfloat>1</forbidfloat>
<requirelowestterms>0</requirelowestterms>
<checkanswertype>1</checkanswertype>
<mustverify>1</mustverify>
<showvalidation>1</showvalidation>
<options/>
</input>
<prt>
<name>prt1</name>
<value>1.0000000</value>
<autosimplify>0</autosimplify>
<feedbackstyle>1</feedbackstyle>
<feedbackvariables>
<text/>
</feedbackvariables>
<node>
<name>0</name>
<answertest>AlgEquiv</answertest><sans>ans</sans><tans>ta</tans>
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<truescoremode>=</truescoremode><truescore>0</truescore>
<truepenalty/><truenextnode>1</truenextnode><trueanswernote>1-0-T</trueanswernote>
<truefeedback format="html"><text/></truefeedback>
<falsescoremode>=</falsescoremode><falsescore>0</falsescore>
<falsepenalty/><falsenextnode>-1</falsenextnode><falseanswernote>1-0-F</falseanswernote>
<falsefeedback format="html"><text><![CDATA[<p>The fraction must have the same value as the original fraction.</p>]]></text></falsefeedback>
</node>
<node>
<name>1</name>
<answertest>LowestTerms</answertest><sans>ans</sans><tans>ta</tans>
<testoptions/><quiet>0</quiet>
<truescoremode>=</truescoremode><truescore>1</truescore>
<truepenalty/><truenextnode>-1</truenextnode><trueanswernote>1-1-T</trueanswernote>
<truefeedback format="html"><text/></truefeedback>
<falsescoremode>=</falsescoremode><falsescore>0</falsescore>
<falsepenalty/><falsenextnode>-1</falsenextnode><falseanswernote>1-1-F</falseanswernote>
<falsefeedback format="html"><text><![CDATA[<p>The value is correct; now cancel common factors.</p>]]></text></falsefeedback>
</node>
</prt>
<deployedseed>554625703</deployedseed>
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<qtest>
<testcase>1</testcase>
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<name>ans</name>
<value>ta</value>
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<expectedscore>1.0000000</expectedscore>
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<expectedanswernote>1-0-T | 1-1-T</expectedanswernote>
</expected>
</qtest>
<qtest>
<testcase>2</testcase>
<description/>
<testinput>
<name>ans</name>
<value>(ev(a*c,simp))/(ev(b*c,simp))</value>
</testinput>
<expected>
<name>prt1</name>
<expectedscore>0.0000000</expectedscore>
<expectedpenalty>0.1000000</expectedpenalty>
<expectedanswernote>1-0-T | 1-1-F</expectedanswernote>
</expected>
</qtest>
<qtest>
<testcase>3</testcase><description>Wrong value in lowest terms</description>
<testinput><name>ans</name><value>123/127</value></testinput>
<expected><name>prt1</name><expectedscore>0</expectedscore><expectedpenalty>0.1</expectedpenalty><expectedanswernote>1-0-F</expectedanswernote></expected>
</qtest>
</question>
</quiz>
AlgMap-4.1
Algebra Refresher / 04 Multiplication and division of fractions · 1 answer field · 2 author tests.
Write the following expression as a single fraction in it's simplest form:
\[{\frac{3}{13}}\cdot{3}.\]
Show source
```{.stack-question}
#| file: questions/corpus/AlgMap-4-1.xml
#| question: AlgMap-4.1
#| label: corpus-algmap-4-1
#| review: true
```Show STACK source
<?xml version="1.0" encoding="UTF-8"?>
<quiz>
<question type="stack">
<name>
<text>AlgMap-4.1</text>
</name>
<questiontext format="html">
<text><![CDATA[<p>Write the following expression as a single fraction in it's simplest form: <br /> \[{@ev(a/b,simp)@}\cdot{@ev(c,simp)@}.\] <br /> [[input:ans]] [[validation:ans]]</p>]]></text>
</questiontext>
<generalfeedback format="html">
<text><![CDATA[<p>Note that: \[{\frac{a}{b}} \cdot {c}=\frac{{a} \cdot {c}}{b}.\] Therefore in this example: \[{@ev(a/b,simp)@}\cdot{@c@}=\frac{@ev(a*c,simp)@}{@b@}.\] Don't forget to simplify your fraction as well by removing common factors from the numerator and denominator. So: \[{@ev((a*c)/b,simp)@}.\]</p>]]></text>
</generalfeedback>
<defaultgrade>1</defaultgrade>
<penalty>0.1</penalty>
<hidden>0</hidden>
<idnumber/>
<stackversion>
<text/>
</stackversion>
<questionvariables>
<text>a:ev(rand(12)+1,simp);
b:ev(a+rand(12)+1,simp);
c:ev(rand(11)+2,simp);
ta:ev((a/b)*c,simp);</text>
</questionvariables>
<specificfeedback format="html">
<text><![CDATA[<p>[[feedback:prt1]]</p>]]></text>
</specificfeedback>
<questionnote format="moodle_auto_format">
<text>\[{@ev(a/b,simp)@}\cdot{@ev(c,simp)@} = {@ta@}. \]</text>
</questionnote>
<questiondescription format="moodle_auto_format">
<text/>
</questiondescription>
<questionsimplify>0</questionsimplify>
<assumepositive>0</assumepositive>
<assumereal>0</assumereal>
<scientificnotation>*10</scientificnotation>
<multiplicationsign>dot</multiplicationsign>
<sqrtsign>1</sqrtsign>
<complexno>i</complexno>
<inversetrig>cos-1</inversetrig>
<logicsymbol>lang</logicsymbol>
<matrixparens>[</matrixparens>
<isbroken>0</isbroken>
<prescribedmetadata/>
<metadata>
{"author":[{"firstName":"Tony","lastName":"Barnard","institution":"","year":"1999"}],"language":["en"],"isPartOf":"STACK Library - Algebra Refresher","license":"cc-sa-4.0","additional":{"UoE":{"Notes":"This is automatically generated metadata."}},"freeform":{}}
</metadata>
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</input>
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</feedbackvariables>
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<name>0</name>
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<answertest>EqualComAss</answertest>
<sans>ans</sans>
<tans>ta</tans>
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<quiet>0</quiet>
<truescoremode>=</truescoremode>
<truescore>1.0000000</truescore>
<truepenalty/>
<truenextnode>-1</truenextnode>
<trueanswernote>1-0-T </trueanswernote>
<truefeedback format="html">
<text/>
</truefeedback>
<falsescoremode>=</falsescoremode>
<falsescore>0.0000000</falsescore>
<falsepenalty/>
<falsenextnode>1</falsenextnode>
<falseanswernote>1-0-F </falseanswernote>
<falsefeedback format="html">
<text/>
</falsefeedback>
</node>
<node>
<name>1</name>
<description/>
<answertest>AlgEquiv</answertest>
<sans>ans</sans>
<tans>ta</tans>
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<truescore>0.0000000</truescore>
<truepenalty/>
<truenextnode>-1</truenextnode>
<trueanswernote>1-1-T </trueanswernote>
<truefeedback format="html">
<text><![CDATA[<p>Your answer is algebraically equivalent to \(\frac{@a@}{@b@}*{@c@}\) but isn't fully simplified.</p>]]></text>
</truefeedback>
<falsescoremode>=</falsescoremode>
<falsescore>0.0000000</falsescore>
<falsepenalty/>
<falsenextnode>-1</falsenextnode>
<falseanswernote>1-1-F </falseanswernote>
<falsefeedback format="html">
<text/>
</falsefeedback>
</node>
</prt>
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<value>ta</value>
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<expectedscore>1.0000000</expectedscore>
<expectedpenalty>0.0000000</expectedpenalty>
<expectedanswernote>1-0-T</expectedanswernote>
</expected>
</qtest>
<qtest>
<testcase>2</testcase>
<description/>
<testinput>
<name>ans</name>
<value>(a/b)*c</value>
</testinput>
<expected>
<name>prt1</name>
<expectedscore>0.0000000</expectedscore>
<expectedpenalty>0.1000000</expectedpenalty>
<expectedanswernote>1-1-T </expectedanswernote>
</expected>
</qtest>
</question>
</quiz>
AlgMap-4.13
Algebra Refresher / 04 Multiplication and division of fractions · 1 answer field · 4 author tests.
Express \(3x + 1 + \frac{3}{x + 1}\) as a single fraction \[ {3}x+{1}+\frac{3}{x+1} \]
Show source
```{.stack-question}
#| file: questions/corpus/AlgMap-4-13.xml
#| question: AlgMap-4.13
#| label: corpus-algmap-4-13
#| review: true
```Show STACK source
<?xml version="1.0" encoding="UTF-8"?>
<quiz>
<question type="stack">
<name>
<text>AlgMap-4.13</text>
</name>
<questiontext format="html">
<text><![CDATA[<p>Express {@p@} as a single fraction \[ {@A@}x+{@B@}+\frac{@C@}{x+1} \] [[input:ans]] [[validation:ans]]</p>]]></text>
</questiontext>
<generalfeedback format="html">
<text><![CDATA[<p>First write each term over a common denominator \[ {@(A*x+B)*D/D+C/D = ((A*x+B)*D+C)/D@}\] Then expand out brackets on the top and collect like terms to get \[ {@ev(expand((A*x+B)*D+C),simp)/D@}.\] </p>]]></text>
</generalfeedback>
<defaultgrade>1</defaultgrade>
<penalty>0.1</penalty>
<hidden>0</hidden>
<idnumber/>
<stackversion>
<text/>
</stackversion>
<questionvariables>
<text>A:ev(rand(4)+2,simp);
B:ev(rand(4)+1,simp);
C:ev(rand(4)+1,simp);
D:x+1;
p:A*x+B+C/D;
ta:ev(factor(expand((A*x+B)*D+C)),simp)/D;</text>
</questionvariables>
<specificfeedback format="html">
<text><![CDATA[<p>[[feedback:prt1]]</p>]]></text>
</specificfeedback>
<questionnote format="moodle_auto_format">
<text>{@p = ta@}.</text>
</questionnote>
<questiondescription format="moodle_auto_format">
<text/>
</questiondescription>
<questionsimplify>0</questionsimplify>
<assumepositive>0</assumepositive>
<assumereal>0</assumereal>
<scientificnotation>*10</scientificnotation>
<multiplicationsign>none</multiplicationsign>
<sqrtsign>1</sqrtsign>
<complexno>i</complexno>
<inversetrig>cos-1</inversetrig>
<logicsymbol>lang</logicsymbol>
<matrixparens>[</matrixparens>
<isbroken>0</isbroken>
<prescribedmetadata/>
<metadata>
{"author":[{"firstName":"Tony","lastName":"Barnard","institution":"","year":"1999"}],"language":["en"],"isPartOf":"STACK Library - Algebra Refresher","license":"cc-sa-4.0","additional":{"UoE":{"Notes":"This is automatically generated metadata."}},"freeform":{}}
</metadata>
<variantsselectionseed/>
<input>
<name>ans</name>
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<tans>((A*x+B)*(x+1)+C)/x+1</tans>
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<description/>
<testinput>
<name>ans</name>
<value>p</value>
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<name>prt1</name>
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<expectedanswernote>1-0-F </expectedanswernote>
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<testcase>3</testcase>
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<testinput>
<name>ans</name>
<value>p+1</value>
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<name>prt1</name>
<expectedscore>0.0000000</expectedscore>
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<expectedanswernote>1-0-F </expectedanswernote>
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<testcase>4</testcase>
<description/>
<testinput>
<name>ans</name>
<value>ev(expand((A*x+B)*D+C),simp)/D</value>
</testinput>
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<expectedscore>1.0000000</expectedscore>
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AlgMap-6.4
Algebra Refresher / 06 Simplifying algebraic expressions · 1 answer field · 3 author tests.
Corrected teaching copy: The worked explanation now states c^a · c^b = c^(a+b); the original incorrectly used addition. The original XML is preserved unchanged; this card and its source panels use the corrected copy linked below.
Simplify the algebraic expression: \[{c^{a} \cdot c^{b}}.\] Be sure to leave your answer in the form \(x^y\).
Show source
```{.stack-question}
#| file: questions/corrected/AlgMap-6-4.xml
#| question: AlgMap-6.4 (corrected teaching copy)
#| label: corpus-algmap-6-4
#| review: true
```Show STACK source
<?xml version="1.0" encoding="UTF-8"?>
<!-- Teaching correction by CTM, 2026-10-16. Derived from the pinned STACK
corpus/AlgMap-6-4.xml export; CC BY-SA 4.0. Original authors and source:
../corpus/manifest.json. The original export is preserved unchanged. -->
<quiz>
<question type="stack">
<name>
<text>AlgMap-6.4 (corrected teaching copy)</text>
</name>
<questiontext format="html">
<text><![CDATA[<p>Simplify the algebraic expression: \[{@p@}.\] Be sure to leave your answer in the form \(x^y\). <br /> <br /> [[input:ans]] [[validation:ans]]</p>]]></text>
</questiontext>
<generalfeedback format="html">
<text><![CDATA[<p>Here we can use the rules of indices, \(c^a\cdot c^b=c^{a+b}\), which apply to algebraic expressions as well as numeric values.</p>]]></text>
</generalfeedback>
<defaultgrade>1</defaultgrade>
<penalty>0.1</penalty>
<hidden>0</hidden>
<idnumber/>
<stackversion>
<text/>
</stackversion>
<questionvariables>
<text>p:(c^a)*(c^b);
ta:c^(a+b);</text>
</questionvariables>
<specificfeedback format="html">
<text><![CDATA[<p>[[feedback:prt1]]</p>]]></text>
</specificfeedback>
<questionnote format="moodle_auto_format">
<text>\[{@c@}^{@a@}\cdot {@c@}^{@b@} = {@ta@} .\]</text>
</questionnote>
<questiondescription format="moodle_auto_format">
<text/>
</questiondescription>
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<scientificnotation>*10</scientificnotation>
<multiplicationsign>dot</multiplicationsign>
<sqrtsign>1</sqrtsign>
<complexno>i</complexno>
<inversetrig>cos-1</inversetrig>
<logicsymbol>lang</logicsymbol>
<matrixparens>[</matrixparens>
<isbroken>0</isbroken>
<prescribedmetadata/>
<metadata>
{"author":[{"firstName":"Tony","lastName":"Barnard","institution":"","year":"1999"}],"language":["en"],"isPartOf":"STACK Library - Algebra Refresher","license":"cc-sa-4.0","additional":{"UoE":{"Notes":"This is automatically generated metadata."}},"freeform":{}}
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<truepenalty/>
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<trueanswernote>1-0-T </trueanswernote>
<truefeedback format="html">
<text/>
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<falsepenalty/>
<falsenextnode>1</falsenextnode>
<falseanswernote>1-0-F </falseanswernote>
<falsefeedback format="html">
<text/>
</falsefeedback>
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<node>
<name>1</name>
<description/>
<answertest>AlgEquiv</answertest>
<sans>ans</sans>
<tans>ta</tans>
<testoptions/>
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<truescore>0.0000000</truescore>
<truepenalty/>
<truenextnode>-1</truenextnode>
<trueanswernote>1-1-T </trueanswernote>
<truefeedback format="html">
<text><![CDATA[<p>Your answer is equivalent to the correct answer but you haven't fully simplified.</p>]]></text>
</truefeedback>
<falsescoremode>=</falsescoremode>
<falsescore>0.0000000</falsescore>
<falsepenalty/>
<falsenextnode>-1</falsenextnode>
<falseanswernote>1-1-F </falseanswernote>
<falsefeedback format="html">
<text/>
</falsefeedback>
</node>
</prt>
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<description/>
<testinput>
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<description/>
<testinput>
<name>ans</name>
<value>p</value>
</testinput>
<expected>
<name>prt1</name>
<expectedscore>0.0000000</expectedscore>
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<expectedanswernote>1-1-T </expectedanswernote>
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<qtest>
<testcase>3</testcase>
<description/>
<testinput>
<name>ans</name>
<value>c^(a*b)</value>
</testinput>
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<name>prt1</name>
<expectedscore>0.0000000</expectedscore>
<expectedpenalty>0.1000000</expectedpenalty>
<expectedanswernote>1-1-F </expectedanswernote>
</expected>
</qtest>
</question>
</quiz>
AlgMap-6.7
Algebra Refresher / 06 Simplifying algebraic expressions · 1 answer field · 2 author tests.
Write the follwing expression, \(\left( {6}\cdot {y} \right)^{2}\), without brackets.
Show source
```{.stack-question}
#| file: questions/corpus/AlgMap-6-7.xml
#| question: AlgMap-6.7
#| label: corpus-algmap-6-7
#| review: true
```Show STACK source
<?xml version="1.0" encoding="UTF-8"?>
<quiz>
<question type="stack">
<name>
<text>AlgMap-6.7</text>
</name>
<questiontext format="html">
<text><![CDATA[<p>Write the follwing expression, \(\left( {@a@}\cdot {@v@} \right)^{@b@}\), without brackets. <br /> <br /> [[input:ans]] [[validation:ans]]</p>]]></text>
</questiontext>
<generalfeedback format="html">
<text><![CDATA[<p>Remember that \[\left( {a}\cdot{b} \right)^n = {a^n}\cdot{b^n}. \] Therefore in this example: \[\left({@a@}\cdot {@v@} \right)^{@b@} = \left({@a@}^{@b@} \right)\cdot \left({@v@}^{@b@} \right) = {@a^b@}\cdot{@v^b@}. \]</p>]]></text>
</generalfeedback>
<defaultgrade>1</defaultgrade>
<penalty>0.1</penalty>
<hidden>0</hidden>
<idnumber/>
<stackversion>
<text/>
</stackversion>
<questionvariables>
<text>v:rand([x,y,z,t]);
a:rand(7)+2;
b:rand([2,3]);
ta:expand((a*v)^b);</text>
</questionvariables>
<specificfeedback format="html">
<text><![CDATA[<p>[[feedback:prt1]]</p>]]></text>
</specificfeedback>
<questionnote format="moodle_auto_format">
<text>\[\left( {@a@}\cdot {@v@} \right)^{@b@} = {@ta@}.\]</text>
</questionnote>
<questiondescription format="moodle_auto_format">
<text/>
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<scientificnotation>*10</scientificnotation>
<multiplicationsign>dot</multiplicationsign>
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<complexno>i</complexno>
<inversetrig>cos-1</inversetrig>
<logicsymbol>lang</logicsymbol>
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<isbroken>0</isbroken>
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<metadata>
{"author":[{"firstName":"Tony","lastName":"Barnard","institution":"","year":"1999"}],"language":["en"],"isPartOf":"STACK Library - Algebra Refresher","license":"cc-sa-4.0","additional":{"UoE":{"Notes":"This is automatically generated metadata."}},"freeform":{}}
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<text/>
</falsefeedback>
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<node>
<name>1</name>
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<answertest>AlgEquiv</answertest>
<sans>ans</sans>
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<trueanswernote>1-1-T </trueanswernote>
<truefeedback format="html">
<text><![CDATA[<p>Don't forget when you are removing brackets from these types of expression to raise the constant to the power as well as the variable!</p>]]></text>
</truefeedback>
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<text/>
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<testcase>2</testcase>
<description/>
<testinput>
<name>ans</name>
<value>a*v^b</value>
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<expected>
<name>prt1</name>
<expectedscore>0.0000000</expectedscore>
<expectedpenalty>0.1000000</expectedpenalty>
<expectedanswernote>1-1-T </expectedanswernote>
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</qtest>
</question>
</quiz>
AlgMap-7.1
Algebra Refresher / 07 Removing brackets · 1 answer field · 2 author tests.
Expand the following:
\(\left( x-{3} \right) \left(x+{3} \right)\) =Show source
```{.stack-question}
#| file: questions/corpus/AlgMap-7-1.xml
#| question: AlgMap-7.1
#| label: corpus-algmap-7-1
#| review: true
```Show STACK source
<?xml version="1.0" encoding="UTF-8"?>
<quiz>
<!-- question: 954 -->
<question type="stack">
<name>
<text>AlgMap-7.1</text>
</name>
<questiontext format="html">
<text><![CDATA[<p>Expand the following:</p>
\(\left( x-{@a@} \right) \left(x+{@a@} \right)\) = [[input:ans1]] [[validation:ans1]]]]></text>
</questiontext>
<generalfeedback format="html">
<text><![CDATA[<p>
The difference of two squares comes up very often in mathematics:
\[\left( x-y \right) \left(x+y \right) = x^2-y^2. \]
In this example:
\[ \left( x-{@a@} \right) \left( x+{@a@} \right) = x^2-{@a^2@}. \]
</p>]]></text>
</generalfeedback>
<defaultgrade>1</defaultgrade>
<penalty>0.1</penalty>
<hidden>0</hidden>
<idnumber></idnumber>
<stackversion>
<text>2026010500</text>
</stackversion>
<questionvariables>
<text>a:rand(10)+1;
ta1:x^2-a^2;</text>
</questionvariables>
<specificfeedback format="html">
<text><![CDATA[<p>[[feedback:prt1]]</p>]]></text>
</specificfeedback>
<questionnote format="moodle_auto_format">
<text>\[\left( x-{@a@} \right) \left( x+{@a@} \right) = {@ta1@}.\]</text>
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<text></text>
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<inversetrig>cos-1</inversetrig>
<logicsymbol>lang</logicsymbol>
<matrixparens>[</matrixparens>
<isbroken>0</isbroken>
<prescribedmetadata/>
<metadata>
{"author":[{"firstName":"Tony","lastName":"Barnard","institution":"","year":"1999"}],"language":["en"],"isPartOf":"STACK Library - Algebra Refresher","license":"cc-sa-4.0","additional":{"UoE":{"Notes":"This is automatically generated metadata."}},"freeform":{}}
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<expectedscore>1.0000000</expectedscore>
<expectedpenalty>0.0000000</expectedpenalty>
<expectedanswernote>1-0-T</expectedanswernote>
</expected>
</qtest>
<qtest>
<testcase>2</testcase>
<description></description>
<testinput>
<name>ans1</name>
<value>(x-a)*(x+a)</value>
</testinput>
<expected>
<name>prt1</name>
<expectedscore>0.0000000</expectedscore>
<expectedpenalty>0.1000000</expectedpenalty>
<expectedanswernote>1-0-F</expectedanswernote>
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</question>
</quiz>
AlgMap-8.5
Algebra Refresher / 08 Algebraic fractions · 1 answer field · 4 author tests.
Simplify the following algebraic fraction: \[ \frac{- a + b}{a - b}. \]
Show source
```{.stack-question}
#| file: questions/corpus/AlgMap-8-5.xml
#| question: AlgMap-8.5
#| label: corpus-algmap-8-5
#| review: true
```Show STACK source
<?xml version="1.0" encoding="UTF-8"?>
<quiz>
<question type="stack">
<name>
<text>AlgMap-8.5</text>
</name>
<questiontext format="html">
<text><![CDATA[<p>Simplify the following algebraic fraction: \[ \frac{@b-a@}{@a-b@}. \] <br /> [[input:ans]] [[validation:ans]]</p>]]></text>
</questiontext>
<generalfeedback format="html">
<text><![CDATA[<p>The first step should be to take a factor of \({-1}\) from the numerator of the fraction so that: \[ \frac{@b-a@}{@a-b@} = \frac{-(a-b)}{@a-b@}. \] Now, it is clear that the factor \((a-b)\) can be cancelled from the numerator and the denominator of the fraction leaving {@ta@}.</p>]]></text>
</generalfeedback>
<defaultgrade>1</defaultgrade>
<penalty>0.1</penalty>
<hidden>0</hidden>
<idnumber/>
<stackversion>
<text/>
</stackversion>
<questionvariables>
<text>ta:-1;</text>
</questionvariables>
<specificfeedback format="html">
<text><![CDATA[<p>[[feedback:prt1]]</p>]]></text>
</specificfeedback>
<questionnote format="moodle_auto_format">
<text>\[ \frac{@b-a@}{@a-b@} = {@ta@}. \]</text>
</questionnote>
<questiondescription format="moodle_auto_format">
<text/>
</questiondescription>
<questionsimplify>1</questionsimplify>
<assumepositive>0</assumepositive>
<assumereal>0</assumereal>
<scientificnotation>*10</scientificnotation>
<multiplicationsign>dot</multiplicationsign>
<sqrtsign>1</sqrtsign>
<complexno>i</complexno>
<inversetrig>cos-1</inversetrig>
<logicsymbol>lang</logicsymbol>
<matrixparens>[</matrixparens>
<isbroken>0</isbroken>
<prescribedmetadata/>
<metadata>
{"author":[{"firstName":"Tony","lastName":"Barnard","institution":"","year":"1999"}],"language":["en"],"isPartOf":"STACK Library - Algebra Refresher","license":"cc-sa-4.0","additional":{"UoE":{"Notes":"This is automatically generated metadata."}},"freeform":{}}
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<input>
<name>ans</name>
<type>algebraic</type>
<tans>ta</tans>
<boxsize>15</boxsize>
<strictsyntax>1</strictsyntax>
<insertstars>0</insertstars>
<syntaxhint/>
<syntaxattribute>0</syntaxattribute>
<forbidwords/>
<allowwords/>
<forbidfloat>1</forbidfloat>
<requirelowestterms>0</requirelowestterms>
<checkanswertype>1</checkanswertype>
<mustverify>1</mustverify>
<showvalidation>1</showvalidation>
<options/>
</input>
<prt>
<name>prt1</name>
<value>1.0000000</value>
<autosimplify>0</autosimplify>
<feedbackstyle>1</feedbackstyle>
<feedbackvariables>
<text/>
</feedbackvariables>
<node>
<name>0</name>
<description/>
<answertest>EqualComAss</answertest>
<sans>ans</sans>
<tans>ta</tans>
<testoptions/>
<quiet>0</quiet>
<truescoremode>=</truescoremode>
<truescore>1.0000000</truescore>
<truepenalty/>
<truenextnode>-1</truenextnode>
<trueanswernote>1-0-T </trueanswernote>
<truefeedback format="html">
<text/>
</truefeedback>
<falsescoremode>=</falsescoremode>
<falsescore>0.0000000</falsescore>
<falsepenalty/>
<falsenextnode>1</falsenextnode>
<falseanswernote>1-0-F </falseanswernote>
<falsefeedback format="html">
<text/>
</falsefeedback>
</node>
<node>
<name>1</name>
<description/>
<answertest>AlgEquiv</answertest>
<sans>ans</sans>
<tans>ta</tans>
<testoptions/>
<quiet>0</quiet>
<truescoremode>=</truescoremode>
<truescore>0.0000000</truescore>
<truepenalty/>
<truenextnode>-1</truenextnode>
<trueanswernote>1-1-T </trueanswernote>
<truefeedback format="html">
<text><![CDATA[<p>Your answer is algebraically equivalent to the correct answer but you haven't simplified fully.</p>]]></text>
</truefeedback>
<falsescoremode>=</falsescoremode>
<falsescore>0.0000000</falsescore>
<falsepenalty/>
<falsenextnode>2</falsenextnode>
<falseanswernote>1-1-F </falseanswernote>
<falsefeedback format="html">
<text/>
</falsefeedback>
</node>
<node>
<name>2</name>
<description/>
<answertest>AlgEquiv</answertest>
<sans>ans</sans>
<tans>1</tans>
<testoptions/>
<quiet>0</quiet>
<truescoremode>=</truescoremode>
<truescore>0.0000000</truescore>
<truepenalty/>
<truenextnode>-1</truenextnode>
<trueanswernote>1-2-T </trueanswernote>
<truefeedback format="html">
<text><![CDATA[<p>You seemed to have dropped a minus sign! Your answer should be negative.</p>]]></text>
</truefeedback>
<falsescoremode>=</falsescoremode>
<falsescore>0.0000000</falsescore>
<falsepenalty/>
<falsenextnode>3</falsenextnode>
<falseanswernote>1-2-F </falseanswernote>
<falsefeedback format="html">
<text/>
</falsefeedback>
</node>
<node>
<name>3</name>
<description/>
<answertest>AlgEquiv</answertest>
<sans>ans</sans>
<tans>0</tans>
<testoptions/>
<quiet>0</quiet>
<truescoremode>=</truescoremode>
<truescore>0.0000000</truescore>
<truepenalty/>
<truenextnode>-1</truenextnode>
<trueanswernote>1-3-T </trueanswernote>
<truefeedback format="html">
<text><![CDATA[<p>Remember that \(\frac{x}{x} = 1\) and not equal to zero.</p>]]></text>
</truefeedback>
<falsescoremode>=</falsescoremode>
<falsescore>0.0000000</falsescore>
<falsepenalty/>
<falsenextnode>-1</falsenextnode>
<falseanswernote>1-3-F </falseanswernote>
<falsefeedback format="html">
<text/>
</falsefeedback>
</node>
</prt>
<qtest>
<testcase>1</testcase>
<description/>
<testinput>
<name>ans</name>
<value>ta</value>
</testinput>
<expected>
<name>prt1</name>
<expectedscore>1.0000000</expectedscore>
<expectedpenalty>0.0000000</expectedpenalty>
<expectedanswernote>1-0-T</expectedanswernote>
</expected>
</qtest>
<qtest>
<testcase>2</testcase>
<description/>
<testinput>
<name>ans</name>
<value>(b-a)/(a-b)</value>
</testinput>
<expected>
<name>prt1</name>
<expectedscore>0.0000000</expectedscore>
<expectedpenalty>0.1000000</expectedpenalty>
<expectedanswernote>1-1-T </expectedanswernote>
</expected>
</qtest>
<qtest>
<testcase>3</testcase>
<description/>
<testinput>
<name>ans</name>
<value>1</value>
</testinput>
<expected>
<name>prt1</name>
<expectedscore>0.0000000</expectedscore>
<expectedpenalty>0.1000000</expectedpenalty>
<expectedanswernote>1-2-T </expectedanswernote>
</expected>
</qtest>
<qtest>
<testcase>4</testcase>
<description/>
<testinput>
<name>ans</name>
<value>0</value>
</testinput>
<expected>
<name>prt1</name>
<expectedscore>0.0000000</expectedscore>
<expectedpenalty>0.1000000</expectedpenalty>
<expectedanswernote>1-3-T </expectedanswernote>
</expected>
</qtest>
</question>
</quiz>
AlgMap-9.1
Algebra Refresher / 09 Linear equations · 1 answer field · 1 author test.
Solve the following equation for \(y\):
\[ {5 y + 2} = {5}. \]
\({y}\) =
\({y}\) =
Show source
```{.stack-question}
#| file: questions/corpus/AlgMap-9-1.xml
#| question: AlgMap-9.1
#| label: corpus-algmap-9-1
#| review: true
```Show STACK source
<?xml version="1.0" encoding="UTF-8"?>
<quiz>
<question type="stack">
<name>
<text>AlgMap-9.1</text>
</name>
<questiontext format="html">
<text><![CDATA[Solve the following equation for {@v@}:
\[ {@cf1*v+k1@} = {@k2@}. \] <br>
\({@v@}\) = [[input:ans]] [[validation:ans]]]]></text>
</questiontext>
<generalfeedback format="html">
<text><![CDATA[The objective is to get the equation into the form \({@v@} = p\) where \(p\) is a rational number. To obtain \({@v@}\) on one side of the equation it may be necessary to under-take several operations which must be performed on both sides of the equation. In this example: <br>
\[ {@cf1*v+k1@} = {@k2@}. \]
We first move all the constants to one side (\({@-k1@}\)):
\[ {@cf1*v@} = {@k2-k1@}. \]
Then divide by the coefficient of \({@v@}\) (\({@cf1@}\)):
\[ {@v@} = {@ta@}. \]
And so we now have obtained a value for {@v@}.]]></text>
</generalfeedback>
<defaultgrade>1</defaultgrade>
<penalty>0.1</penalty>
<hidden>0</hidden>
<idnumber/>
<stackversion>
<text/>
</stackversion>
<questionvariables>
<text>v:rand([x,y,z,t]);
cf1:rand(6)+1;
k1:rand(10)+1;
k2:rand(10)+1;
ta:(k2-k1)/cf1;</text>
</questionvariables>
<specificfeedback format="html">
<text><![CDATA[<p>[[feedback:prt1]]</p>]]></text>
</specificfeedback>
<questionnote format="moodle_auto_format">
<text>\[ {@cf1*v+k1@} = {@k2@} \Rightarrow {@v@} = {@ta@}. \]</text>
</questionnote>
<questiondescription format="moodle_auto_format">
<text/>
</questiondescription>
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<scientificnotation>*10</scientificnotation>
<multiplicationsign>none</multiplicationsign>
<sqrtsign>1</sqrtsign>
<complexno>i</complexno>
<inversetrig>cos-1</inversetrig>
<logicsymbol>lang</logicsymbol>
<matrixparens>[</matrixparens>
<isbroken>0</isbroken>
<prescribedmetadata/>
<metadata>
{"author":[{"firstName":"Tony","lastName":"Barnard","institution":"","year":"1999"}],"language":["en"],"isPartOf":"STACK Library - Algebra Refresher","license":"cc-sa-4.0","additional":{"UoE":{"Notes":"This is automatically generated metadata."}},"freeform":{}}
</metadata>
<variantsselectionseed/>
<input>
<name>ans</name>
<type>algebraic</type>
<tans>ta</tans>
<boxsize>15</boxsize>
<strictsyntax>1</strictsyntax>
<insertstars>0</insertstars>
<syntaxhint/>
<syntaxattribute>0</syntaxattribute>
<forbidwords/>
<allowwords/>
<forbidfloat>1</forbidfloat>
<requirelowestterms>1</requirelowestterms>
<checkanswertype>1</checkanswertype>
<mustverify>1</mustverify>
<showvalidation>1</showvalidation>
<options/>
</input>
<prt>
<name>prt1</name>
<value>1.0000000</value>
<autosimplify>1</autosimplify>
<feedbackstyle>1</feedbackstyle>
<feedbackvariables>
<text/>
</feedbackvariables>
<node>
<name>0</name>
<description/>
<answertest>AlgEquiv</answertest>
<sans>ans</sans>
<tans>ta</tans>
<testoptions/>
<quiet>0</quiet>
<truescoremode>=</truescoremode>
<truescore>1.0000000</truescore>
<truepenalty/>
<truenextnode>-1</truenextnode>
<trueanswernote>1-0-T </trueanswernote>
<truefeedback format="html">
<text/>
</truefeedback>
<falsescoremode>=</falsescoremode>
<falsescore>0.0000000</falsescore>
<falsepenalty/>
<falsenextnode>-1</falsenextnode>
<falseanswernote>1-0-F </falseanswernote>
<falsefeedback format="html">
<text/>
</falsefeedback>
</node>
</prt>
<deployedseed>253453649</deployedseed>
<deployedseed>332413405</deployedseed>
<deployedseed>343041774</deployedseed>
<deployedseed>223289048</deployedseed>
<deployedseed>754301387</deployedseed>
<deployedseed>1781387469</deployedseed>
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<deployedseed>544014872</deployedseed>
<deployedseed>246266401</deployedseed>
<deployedseed>854303989</deployedseed>
<qtest>
<testcase>1</testcase>
<description/>
<testinput>
<name>ans</name>
<value>ta</value>
</testinput>
<expected>
<name>prt1</name>
<expectedscore>1.0000000</expectedscore>
<expectedpenalty>0.0000000</expectedpenalty>
<expectedanswernote>1-0-T</expectedanswernote>
</expected>
</qtest>
</question>
</quiz>
AlgMap-9.6
Algebra Refresher / 09 Linear equations · 1 answer field · 1 author test.
Solve the following equation for \(y\):
\[ {\frac{18}{5} - \frac{y}{5}} = {\frac{y}{5} + \frac{1}{10}}.\]
\({y}\) =
\({y}\) =
Show source
```{.stack-question}
#| file: questions/corpus/AlgMap-9-6.xml
#| question: AlgMap-9.6
#| label: corpus-algmap-9-6
#| review: true
```Show STACK source
<?xml version="1.0" encoding="UTF-8"?>
<quiz>
<question type="stack">
<name>
<text>AlgMap-9.6</text>
</name>
<questiontext format="html">
<text><![CDATA[Solve the following equation for {@v@}:
\[ {@(3-v)/5+3@} = {@(2*v+1)/10@}.\] <br>
\({@v@}\) = [[input:ans]] [[validation:ans]]]]></text>
</questiontext>
<generalfeedback format="html">
<text>The objective is to get the equation into the form \({@v@} = p\) where \(p\) is a rational number. When fractions are involved it is often best to multiply both sides of the equation by a certain value so that the fractions are removed. In this example:
\[ {@(3-v)/5+3@} = {@(2*v+1)/10@}.\]
Multiply through by \(10\):
\[ {@2*(3-v)+30@} = {@2*v+1@}. \]
Remove Brackets:
\[ {@6-2*v+30@} = {@2*v+1@}. \]
Gather like terms \({@+(2*v-1)@}\):
\[ {@35@} = {@4*v@}. \]
Finally divide by coefficient of \({@v@}\) (\(4\)):
\[ {@v@} = {@35/4@}. \]</text>
</generalfeedback>
<defaultgrade>1</defaultgrade>
<penalty>0.1</penalty>
<hidden>0</hidden>
<idnumber/>
<stackversion>
<text/>
</stackversion>
<questionvariables>
<text>v:rand([x,y,z,t]);
ta:35/4;</text>
</questionvariables>
<specificfeedback format="html">
<text><![CDATA[<p>[[feedback:prt1]]</p>]]></text>
</specificfeedback>
<questionnote format="moodle_auto_format">
<text>\[ {@(3-v)/5+3@} = {@(2*v+1)/10@} \Rightarrow {@v@} = {@ta@}. \]</text>
</questionnote>
<questiondescription format="moodle_auto_format">
<text/>
</questiondescription>
<questionsimplify>1</questionsimplify>
<assumepositive>0</assumepositive>
<assumereal>0</assumereal>
<scientificnotation>*10</scientificnotation>
<multiplicationsign>none</multiplicationsign>
<sqrtsign>1</sqrtsign>
<complexno>i</complexno>
<inversetrig>cos-1</inversetrig>
<logicsymbol>lang</logicsymbol>
<matrixparens>[</matrixparens>
<isbroken>0</isbroken>
<prescribedmetadata/>
<metadata>
{"author":[{"firstName":"Tony","lastName":"Barnard","institution":"","year":"1999"}],"language":["en"],"isPartOf":"STACK Library - Algebra Refresher","license":"cc-sa-4.0","additional":{"UoE":{"Notes":"This is automatically generated metadata."}},"freeform":{}}
</metadata>
<variantsselectionseed/>
<input>
<name>ans</name>
<type>algebraic</type>
<tans>ta</tans>
<boxsize>15</boxsize>
<strictsyntax>1</strictsyntax>
<insertstars>0</insertstars>
<syntaxhint/>
<syntaxattribute>0</syntaxattribute>
<forbidwords/>
<allowwords/>
<forbidfloat>1</forbidfloat>
<requirelowestterms>1</requirelowestterms>
<checkanswertype>1</checkanswertype>
<mustverify>1</mustverify>
<showvalidation>1</showvalidation>
<options/>
</input>
<prt>
<name>prt1</name>
<value>1.0000000</value>
<autosimplify>1</autosimplify>
<feedbackstyle>1</feedbackstyle>
<feedbackvariables>
<text/>
</feedbackvariables>
<node>
<name>0</name>
<description/>
<answertest>AlgEquiv</answertest>
<sans>ans</sans>
<tans>ta</tans>
<testoptions/>
<quiet>0</quiet>
<truescoremode>=</truescoremode>
<truescore>1.0000000</truescore>
<truepenalty/>
<truenextnode>-1</truenextnode>
<trueanswernote>1-0-T </trueanswernote>
<truefeedback format="html">
<text/>
</truefeedback>
<falsescoremode>=</falsescoremode>
<falsescore>0.0000000</falsescore>
<falsepenalty/>
<falsenextnode>-1</falsenextnode>
<falseanswernote>1-0-F </falseanswernote>
<falsefeedback format="html">
<text/>
</falsefeedback>
</node>
</prt>
<deployedseed>1775658430</deployedseed>
<deployedseed>1085854555</deployedseed>
<deployedseed>995216167</deployedseed>
<deployedseed>730877766</deployedseed>
<qtest>
<testcase>1</testcase>
<description/>
<testinput>
<name>ans</name>
<value>ta</value>
</testinput>
<expected>
<name>prt1</name>
<expectedscore>1.0000000</expectedscore>
<expectedpenalty>0.0000000</expectedpenalty>
<expectedanswernote>1-0-T</expectedanswernote>
</expected>
</qtest>
</question>
</quiz>
AlgMap-10.1
Algebra Refresher / 10 Expressions single term common factors · 1 answer field · 2 author tests.
Factorise the following: \[{6 - 18 y}.\]
Show source
```{.stack-question}
#| file: questions/corpus/AlgMap-10-1.xml
#| question: AlgMap-10.1
#| label: corpus-algmap-10-1
#| review: true
```Show STACK source
<?xml version="1.0" encoding="UTF-8"?>
<quiz>
<question type="stack">
<name>
<text>AlgMap-10.1</text>
</name>
<questiontext format="html">
<text><![CDATA[Factorise the following: \[{@k1-cf1*v@}.\]
<br>
[[input:ans]] [[validation:ans]]]]></text>
</questiontext>
<generalfeedback format="html">
<text>Simply remove all common factors from the expression. In this example:
\[ {@k1-cf1*v@} = {@ta@}. \]</text>
</generalfeedback>
<defaultgrade>1</defaultgrade>
<penalty>0.1</penalty>
<hidden>0</hidden>
<idnumber/>
<stackversion>
<text/>
</stackversion>
<questionvariables>
<text>v:rand([x,y,z,t]);
fac:rand(6)+2;
k1:(rand(6)+1)*fac;
cf1:(rand(6)+1)*fac;
ta:factor(k1-cf1*v);</text>
</questionvariables>
<specificfeedback format="html">
<text><![CDATA[<p>[[feedback:prt1]]</p>]]></text>
</specificfeedback>
<questionnote format="moodle_auto_format">
<text>\[ {@k1-cf1*v@} = {@ta@}. \]</text>
</questionnote>
<questiondescription format="moodle_auto_format">
<text/>
</questiondescription>
<questionsimplify>1</questionsimplify>
<assumepositive>0</assumepositive>
<assumereal>0</assumereal>
<scientificnotation>*10</scientificnotation>
<multiplicationsign>none</multiplicationsign>
<sqrtsign>1</sqrtsign>
<complexno>i</complexno>
<inversetrig>cos-1</inversetrig>
<logicsymbol>lang</logicsymbol>
<matrixparens>[</matrixparens>
<isbroken>0</isbroken>
<prescribedmetadata/>
<metadata>
{"author":[{"firstName":"Tony","lastName":"Barnard","institution":"","year":"1999"}],"language":["en"],"isPartOf":"STACK Library - Algebra Refresher","license":"cc-sa-4.0","additional":{"UoE":{"Notes":"This is automatically generated metadata."}},"freeform":{}}
</metadata>
<variantsselectionseed/>
<input>
<name>ans</name>
<type>algebraic</type>
<tans>ta</tans>
<boxsize>15</boxsize>
<strictsyntax>1</strictsyntax>
<insertstars>0</insertstars>
<syntaxhint/>
<syntaxattribute>0</syntaxattribute>
<forbidwords/>
<allowwords/>
<forbidfloat>1</forbidfloat>
<requirelowestterms>1</requirelowestterms>
<checkanswertype>1</checkanswertype>
<mustverify>1</mustverify>
<showvalidation>1</showvalidation>
<options/>
</input>
<prt>
<name>prt1</name>
<value>1.0000000</value>
<autosimplify>1</autosimplify>
<feedbackstyle>1</feedbackstyle>
<feedbackvariables>
<text/>
</feedbackvariables>
<node>
<name>0</name>
<description/>
<answertest>FacForm</answertest>
<sans>ans</sans>
<tans>ta</tans>
<testoptions>v</testoptions>
<quiet>0</quiet>
<truescoremode>=</truescoremode>
<truescore>1.0000000</truescore>
<truepenalty/>
<truenextnode>-1</truenextnode>
<trueanswernote>1-0-T </trueanswernote>
<truefeedback format="html">
<text/>
</truefeedback>
<falsescoremode>=</falsescoremode>
<falsescore>0.0000000</falsescore>
<falsepenalty/>
<falsenextnode>-1</falsenextnode>
<falseanswernote>1-0-F </falseanswernote>
<falsefeedback format="html">
<text/>
</falsefeedback>
</node>
</prt>
<deployedseed>1910622122</deployedseed>
<deployedseed>1142759260</deployedseed>
<deployedseed>91955274</deployedseed>
<deployedseed>114660474</deployedseed>
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<deployedseed>1789902044</deployedseed>
<deployedseed>516754182</deployedseed>
<deployedseed>173380566</deployedseed>
<qtest>
<testcase>1</testcase>
<description/>
<testinput>
<name>ans</name>
<value>ta</value>
</testinput>
<expected>
<name>prt1</name>
<expectedscore>1.0000000</expectedscore>
<expectedpenalty>0.0000000</expectedpenalty>
<expectedanswernote>1-0-T</expectedanswernote>
</expected>
</qtest>
<qtest>
<testcase>2</testcase>
<description/>
<testinput>
<name>ans</name>
<value>k1-cf1*v</value>
</testinput>
<expected>
<name>prt1</name>
<expectedscore>0.0000000</expectedscore>
<expectedpenalty>0.1000000</expectedpenalty>
<expectedanswernote>1-0-F </expectedanswernote>
</expected>
</qtest>
</question>
</quiz>
AlgMap-11.1
Algebra Refresher / 11 Rearranging algebraic formulae · 2 answer fields · 1 author test.
The equation \( c = ab \) can be described as the subject, \(c\), in terms of \(a\) and \(b\). It is also possible to obtain equivalent expressions of the from:
\(a\) in terms of \(b\) and \(c\).
\(b\) in terms of \(a\) and \(c\).
Identify these expressions:
\(a\) =
\(b\) =
\(a\) in terms of \(b\) and \(c\).
\(b\) in terms of \(a\) and \(c\).
Identify these expressions:
\(a\) =
\(b\) =
Show source
```{.stack-question}
#| file: questions/corpus/AlgMap-11-1.xml
#| question: AlgMap-11.1
#| label: corpus-algmap-11-1
#| review: true
```Show STACK source
<?xml version="1.0" encoding="UTF-8"?>
<quiz>
<question type="stack">
<name>
<text>AlgMap-11.1</text>
</name>
<questiontext format="html">
<text><![CDATA[The equation \( c = ab \) can be described as the subject, \(c\), in terms of \(a\) and \(b\). It is also possible to obtain equivalent expressions of the from: <br>
<br>
\(a\) in terms of \(b\) and \(c\). <br>
\(b\) in terms of \(a\) and \(c\). <br>
<br>
Identify these expressions: <br>
<br>
\(a\) = [[input:ans1]]
[[validation:ans1]] <br>
[[feedback:prt1]]
<br>
\(b\) = [[input:ans2]]
[[validation:ans2]]
[[feedback:prt2]]]]></text>
</questiontext>
<generalfeedback format="html">
<text>To rearrange the equation \(c = ab\) to make \(a\) the subject divide both sides of the equation by \(b\) to give:
\[ a = \frac{c}{b}. \]
To make \(b\) the subject just divide by \(a\):
\[ b = \frac{c}{a}. \]</text>
</generalfeedback>
<defaultgrade>1</defaultgrade>
<penalty>0.1</penalty>
<hidden>0</hidden>
<idnumber/>
<stackversion>
<text/>
</stackversion>
<questionvariables>
<text>ta1:c/b;
ta2:c/a;</text>
</questionvariables>
<specificfeedback format="html">
<text/>
</specificfeedback>
<questionnote format="moodle_auto_format">
<text>\[ c = ab \Rightarrow {@ta1@} \mbox{and}\ {@ta2@} \]</text>
</questionnote>
<questiondescription format="moodle_auto_format">
<text/>
</questiondescription>
<questionsimplify>1</questionsimplify>
<assumepositive>0</assumepositive>
<assumereal>0</assumereal>
<scientificnotation>*10</scientificnotation>
<multiplicationsign>dot</multiplicationsign>
<sqrtsign>1</sqrtsign>
<complexno>i</complexno>
<inversetrig>cos-1</inversetrig>
<logicsymbol>lang</logicsymbol>
<matrixparens>[</matrixparens>
<isbroken>0</isbroken>
<prescribedmetadata/>
<metadata>
{"author":[{"firstName":"Tony","lastName":"Barnard","institution":"","year":"1999"}],"language":["en"],"isPartOf":"STACK Library - Algebra Refresher","license":"cc-sa-4.0","additional":{"UoE":{"Notes":"This is automatically generated metadata."}},"freeform":{}}
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AlgMap-11.8
Algebra Refresher / 11 Rearranging algebraic formulae · 1 answer field · 2 author tests.
Rearrange the following:
\[a={b \sqrt{x}}.\]
Make \(x\) the subject of the formula.
\(x\) =
\(x\) =
Show source
```{.stack-question}
#| file: questions/corpus/AlgMap-11-8.xml
#| question: AlgMap-11.8
#| label: corpus-algmap-11-8
#| review: true
```Show STACK source
<?xml version="1.0" encoding="UTF-8"?>
<quiz>
<question type="stack">
<name>
<text>AlgMap-11.8</text>
</name>
<questiontext format="html">
<text><![CDATA[Rearrange the following:
\[a={@b*sqrt(x)@}.\]
Make \(x\) the subject of the formula. <br>
<br>
\(x\) = [[input:ans]] [[validation:ans]]]]></text>
</questiontext>
<generalfeedback format="html">
<text>To rearrange formulae perform operations to both sides of the formula to obtain an equation with \(x\) as the subject.
\[ a={@b*sqrt(x)@}. \]
To remove the surd, square both sides of the equation:
\[ {@a^2@} = {@b^2*x@}. \]
Divide by \({@b^2@}\):
\[ {@a^2/b^2@} = {@x@}. \]
Now you have an equation for \(x\).</text>
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</questionvariables>
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<text><![CDATA[<p>[[feedback:prt1]]</p>]]></text>
</specificfeedback>
<questionnote format="moodle_auto_format">
<text>\[a={@b*sqrt(x)@} \Rightarrow x = {@ta@}. \]</text>
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AlgMap-13.1
Algebra Refresher / 13 Factorising algebraic expressions · 1 answer field · 2 author tests.
Factorise the following:
\[ {3 y^{2} - 32 y + 64}. \]
Show source
```{.stack-question}
#| file: questions/corpus/AlgMap-13-1-.xml
#| question: AlgMap-13.1
#| label: corpus-algmap-13-1
#| review: true
```Show STACK source
<?xml version="1.0" encoding="UTF-8"?>
<quiz>
<question type="stack">
<name>
<text>AlgMap-13.1</text>
</name>
<questiontext format="html">
<text><![CDATA[Factorise the following:
\[ {@expand((cf1*v+a)*(cf2*v+b))@}. \] <br>
[[input:ans]] [[validation:ans]]]]></text>
</questiontext>
<generalfeedback format="html">
<text>As can be seen by multiplying out a general, factorised quadratic:
\[ (cx+a)(dx+b) = cdx^2+(da+cb)x+ab, \]
\(a\) and \(b\) are factors of the constant term, and \(c\) and \(d\) are factors of the \(x^2\) coefficient so there are only a finite number of (integer) cases that are possible. With practice it should be simple enough to find \(a\), \(b\), \(c\) and \(d\).
In this example:
\[ {@expand((cf1*v+a)*(cf2*v+b))@}. \]
Equating with the general quadratic above gives:
\[{cd = {@cf1*cf2@}}.\]
\[{da+cb = {@cf2*a+cf1*b@}}.\]
\[{ab = {@a*b@}}.\]
The correct values are: \(a = {@a@}\), and \(b = {@b@}\), \(c = {@cf1@}\) and, \(d = {@cf2@}\). By substituting these back into the general quadratic, and factorising constants out, we obtain the factored form: \[{@ta@}.\]</text>
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cf1:rand(4)+1;
cf2:(rand(4)+1)*rand([1,-1]);
a:(rand(9)+1)*rand([1,-1]);
b:(rand(9)+1)*rand([1,-1]);
ta:factor((cf1*v+a)*(cf2*v+b));</text>
</questionvariables>
<specificfeedback format="html">
<text><![CDATA[<p>[[feedback:prt1]]</p>]]></text>
</specificfeedback>
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<text>\[ {@expand((cf1*v+a)*(cf2*v+b))@} = {@ta@} \]</text>
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AlgMap-14.1
Algebra Refresher / 14 Algebraic fractions involving factorising · 1 answer field · 3 author tests.
Reduce the following fraction to it's lowest terms:
\[ {\frac{6 y + 12}{12 y}}. \]
Show source
```{.stack-question}
#| file: questions/corpus/AlgMap-14-1.xml
#| question: AlgMap-14.1
#| label: corpus-algmap-14-1
#| review: true
```Show STACK source
<?xml version="1.0" encoding="UTF-8"?>
<quiz>
<question type="stack">
<name>
<text>AlgMap-14.1</text>
</name>
<questiontext format="html">
<text><![CDATA[Reduce the following fraction to it's lowest terms:
\[ {@(cf1*v+k1)/(cf2*v)@}. \]
<br>
[[input:ans]] [[validation:ans]]]]></text>
</questiontext>
<generalfeedback format="html">
<text>By factorisng the numerator we obtain: \[\frac{@factor(cf1*v+k1)@}{@cf2*v@}. \]
Then we can simplify the constants from the numerator and denominator to obtain:
\[ {@ta@}. \]</text>
</generalfeedback>
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<text/>
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f:rand(5)+2;
cf1:(rand(3)+1)*f;
cf2:(rand(3)+1)*f;
k1:(rand(2)+2)*cf1;
ta:factor((cf1*v+k1)/(cf2*v));
ta2:ratsimp((cf1*v+k1)/(cf2*v));</text>
</questionvariables>
<specificfeedback format="html">
<text><![CDATA[<p>[[feedback:prt1]]</p>]]></text>
</specificfeedback>
<questionnote format="moodle_auto_format">
<text>\[ {@(cf1*v+k1)/(cf2*v)@} = {@ta@}. \]</text>
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<answertest>AlgEquiv</answertest>
<sans>gcd(num(ans),denom(ans))</sans>
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<falsefeedback format="html">
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</falsefeedback>
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<value>ta</value>
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<expectedanswernote>1-2-T</expectedanswernote>
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<testcase>2</testcase>
<description/>
<testinput>
<name>ans</name>
<value>ta2</value>
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<expected>
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<expectedanswernote>1-2-T</expectedanswernote>
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<testcase>3</testcase>
<description/>
<testinput>
<name>ans</name>
<value>(cf1*v+k1)/(cf2*v)</value>
</testinput>
<expected>
<name>prt1</name>
<expectedscore>0.0000000</expectedscore>
<expectedpenalty>0.1000000</expectedpenalty>
<expectedanswernote>1-2-F </expectedanswernote>
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</quiz>
Complex_Convert_1
Topics / Complex Numbers · 1 answer field · 2 author tests.
Consider the complex number \[z={- \frac{5 \sqrt{3}}{2} + \frac{5 i}{2}} \] Evaluate the modulus of \(z\) \((r = |z|)\) and the principal value of the argument of \(z\) (\(\theta = \mathrm{Arg}(z)\)). Enter your results in the correct order, i.e. \([r,\theta]\).
\([r,\theta] = \)
Show source
```{.stack-question}
#| file: questions/corpus/Complex_Convert_1.xml
#| question: Complex_Convert_1
#| label: corpus-complex-convert-1
#| review: true
```Show STACK source
<?xml version="1.0" encoding="UTF-8"?>
<quiz>
<question type="stack">
<name>
<text>Complex_Convert_1</text>
</name>
<questiontext format="html">
<text><![CDATA[<p>Consider the complex number \[z={@z1@} \] Evaluate the modulus of \(z\) \((r = |z|)\) and the principal value of the argument of \(z\) (\(\theta = \mathrm{Arg}(z)\)). Enter your results in the correct order, i.e. \([r,\theta]\).</p>
<p> </p>
<p>\([r,\theta] = \) [[input:ans1]] [[validation:ans1]]</p>]]></text>
</questiontext>
<generalfeedback format="html">
<text><![CDATA[<p>\[r=\sqrt{x^2+y^2}\] \[r=\sqrt{\left({@x@}\right)^2+\left({@y@}\right)^2}=\sqrt{{@x*x@}+{@y*y@}}\] \[r=\sqrt{@x*x+y*y@}={@rval@}\] \[tan(\mathrm{arg}(z))=\frac{y}{x}=\frac{@y@}{@x@}={@y/x@}\] \[\mathrm{arg}(z)={@argsol@} + k\cdot\pi\] Considering the appropriate quadrant of the complex plane to fix \(k\), we find that \[\mathrm{arg}(z)={@principaltheta@}\].</p>]]></text>
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<text>argset:[Pi/6,Pi/4,Pi/3];
n1:rand(3)+1;
modsol:rand(5)+1;
argsol:ev(((-1)^rand(2))*(rand(2)*Pi-argset[n1]),simp);
z1:ev(modsol*cos(argsol) + modsol*i*sin(argsol),simp);
x:modsol*cos(argsol);
y:modsol*sin(argsol);
rval:sqrt(x*x+y*y);
principaltheta:%pi - mod (%pi - argsol, 2*%pi);</text>
</questionvariables>
<specificfeedback format="html">
<text><![CDATA[<p>[[feedback:Result]]</p>]]></text>
</specificfeedback>
<questionnote format="moodle_auto_format">
<text>\(z={@z1@}\) gives \([{@modsol@},{@principaltheta@}]\)</text>
</questionnote>
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<text/>
</questiondescription>
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<inversetrig>cos-1</inversetrig>
<logicsymbol>lang</logicsymbol>
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{"author":[{"firstName":"","lastName":"","institution":"Unknown - Legacy question","year":"2025"}],"language":["en"],"isPartOf":"STACK Library","license":"cc-sa-4.0","additional":{"UoE":{"Notes":"This is automatically generated metadata."}},"freeform":{}}
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<value>[modsol,principaltheta]</value>
</testinput>
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<expectedscore>1.0000000</expectedscore>
<expectedpenalty>0.0000000</expectedpenalty>
<expectedanswernote>Result-0-T</expectedanswernote>
</expected>
</qtest>
<qtest>
<testcase>2</testcase>
<description/>
<testinput>
<name>ans1</name>
<value>[x,y]</value>
</testinput>
<expected>
<name>Result</name>
<expectedscore>0.0000000</expectedscore>
<expectedpenalty>0.0000000</expectedpenalty>
<expectedanswernote>Result-0-F</expectedanswernote>
</expected>
</qtest>
</question>
</quiz>
Logs_1
Topics / Logs and Exponentials · 1 answer field · 3 author tests.
Given that \(\ln(a)={4}\) , express: \[\log_{a}(x^{3})\] as a single multiple of a natural logarithm.
\(\log_{a}(x^{3}) = \)
Show source
```{.stack-question}
#| file: questions/corpus/Logs_1.xml
#| question: Logs_1
#| label: corpus-logs-1
#| review: true
```Show STACK source
<?xml version="1.0" encoding="UTF-8"?>
<quiz>
<question type="stack">
<name>
<text>Logs_1</text>
</name>
<questiontext format="html">
<text><![CDATA[<p>Given that \(\ln(a)={@a@}\) , express: \[\log_{a}(x^{@n@})\] as a single multiple of a natural logarithm.</p>
<p>\(\log_{a}(x^{@ n @}) = \) [[input:ans1]] [[validation:ans1]]</p>]]></text>
</questiontext>
<generalfeedback format="html">
<text><![CDATA[<p>Below are the basic rules of logarithms.<br />\[\log_{b}(mn) = \log_{b}(m) +\log_{b}(n)\]<br />\[\log_{b}\left(\frac{m}{n}\right) = \log_{b}(m) -\log_{b}(n)\]<br />\[\log_{b}(m^n) = n\cdot\log_{b}(m)\]</p>
<p>\[\log_{a}(m)=\frac{\log_{b}(m)}{\log_{b}(a)}\]</p>
<p><br />Hence \[\log_{a}(x^{@n@}) = {@n@}\log_{a}(x) = {@n@}\frac{\ln(x)}{\ln(a)}\]</p>
<p>\[ = {@n@}\frac{\ln(x)}{@a@}={@correctanswer@}\]</p>]]></text>
</generalfeedback>
<defaultgrade>1</defaultgrade>
<penalty>0</penalty>
<hidden>0</hidden>
<idnumber/>
<stackversion>
<text/>
</stackversion>
<questionvariables>
<text>a:rand(8)+2;
n:rand(8)+2;
correctanswer:ev(n*ln(x)/a);
wronganswer1:ev(n*a/ln(x));
wronganswer2:n*a*ln(x);</text>
</questionvariables>
<specificfeedback format="html">
<text><![CDATA[<p>[[feedback:Result]]</p>]]></text>
</specificfeedback>
<questionnote format="moodle_auto_format">
<text>When \(\displaystyle \ln(a)={@a@}, \log_{a}(x^{@n@}) ={@correctanswer@}\)</text>
</questionnote>
<questiondescription format="moodle_auto_format">
<text/>
</questiondescription>
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<scientificnotation>*10</scientificnotation>
<multiplicationsign>dot</multiplicationsign>
<sqrtsign>1</sqrtsign>
<complexno>i</complexno>
<inversetrig>cos-1</inversetrig>
<logicsymbol>lang</logicsymbol>
<matrixparens>[</matrixparens>
<isbroken>0</isbroken>
<prescribedmetadata/>
<metadata>
{"author":[{"firstName":"","lastName":"","institution":"Unknown - Legacy question","year":"2025"}],"language":["en"],"isPartOf":"STACK Library","license":"cc-sa-4.0","additional":{"UoE":{"Notes":"This is automatically generated metadata."}},"freeform":{}}
</metadata>
<variantsselectionseed/>
<input>
<name>ans1</name>
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<checkanswertype>1</checkanswertype>
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<showvalidation>1</showvalidation>
<options/>
</input>
<prt>
<name>Result</name>
<value>1.0000000</value>
<autosimplify>1</autosimplify>
<feedbackstyle>1</feedbackstyle>
<feedbackvariables>
<text/>
</feedbackvariables>
<node>
<name>0</name>
<description/>
<answertest>AlgEquiv</answertest>
<sans>ans1</sans>
<tans>correctanswer</tans>
<testoptions/>
<quiet>0</quiet>
<truescoremode>=</truescoremode>
<truescore>1.0000000</truescore>
<truepenalty/>
<truenextnode>-1</truenextnode>
<trueanswernote>Result-0-T</trueanswernote>
<truefeedback format="html">
<text/>
</truefeedback>
<falsescoremode>=</falsescoremode>
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<falseanswernote>Result-0-F</falseanswernote>
<falsefeedback format="html">
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<name>1</name>
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<answertest>AlgEquiv</answertest>
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<truenextnode>-1</truenextnode>
<trueanswernote>Result-1-T</trueanswernote>
<truefeedback format="html">
<text><![CDATA[<p>Check the Log Laws</p>]]></text>
</truefeedback>
<falsescoremode>=</falsescoremode>
<falsescore>0.0000000</falsescore>
<falsepenalty/>
<falsenextnode>2</falsenextnode>
<falseanswernote>Result-1-F</falseanswernote>
<falsefeedback format="html">
<text/>
</falsefeedback>
</node>
<node>
<name>2</name>
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<answertest>AlgEquiv</answertest>
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<testoptions/>
<quiet>0</quiet>
<truescoremode>=</truescoremode>
<truescore>0.0000000</truescore>
<truepenalty/>
<truenextnode>-1</truenextnode>
<trueanswernote>Result-2-T</trueanswernote>
<truefeedback format="html">
<text><![CDATA[<p>Check the Log Laws</p>]]></text>
</truefeedback>
<falsescoremode>=</falsescoremode>
<falsescore>0.0000000</falsescore>
<falsepenalty/>
<falsenextnode>-1</falsenextnode>
<falseanswernote>Result-2-F</falseanswernote>
<falsefeedback format="html">
<text/>
</falsefeedback>
</node>
</prt>
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<testcase>1</testcase>
<description/>
<testinput>
<name>ans1</name>
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</testinput>
<expected>
<name>Result</name>
<expectedscore>1.0000000</expectedscore>
<expectedpenalty>0.0000000</expectedpenalty>
<expectedanswernote>Result-0-T</expectedanswernote>
</expected>
</qtest>
<qtest>
<testcase>2</testcase>
<description/>
<testinput>
<name>ans1</name>
<value>wronganswer1</value>
</testinput>
<expected>
<name>Result</name>
<expectedscore>0.0000000</expectedscore>
<expectedpenalty>0.0000000</expectedpenalty>
<expectedanswernote>Result-1-T</expectedanswernote>
</expected>
</qtest>
<qtest>
<testcase>3</testcase>
<description/>
<testinput>
<name>ans1</name>
<value>wronganswer2</value>
</testinput>
<expected>
<name>Result</name>
<expectedscore>0.0000000</expectedscore>
<expectedpenalty>0.0000000</expectedpenalty>
<expectedanswernote>Result-2-T</expectedanswernote>
</expected>
</qtest>
</question>
</quiz>
LinearAlgebra_elementary_1
Linear algebra / Matrix input · 1 answer field · 2 author tests.
Give the elementary matrix which, when multiplied to the left of a 3 by 3 matrix, will replace row 2 by row 2 + \(3\) times row 3.
\(\textbf{E} = \)
Show source
```{.stack-question}
#| file: questions/corpus/LinearAlgebra_elementary_1.xml
#| question: LinearAlgebra_elementary_1
#| label: corpus-linearalgebra-elementary-1
#| review: true
```Show STACK source
<?xml version="1.0" encoding="UTF-8"?>
<quiz>
<question type="stack">
<name>
<text>LinearAlgebra_elementary_1</text>
</name>
<questiontext format="html">
<text><![CDATA[<p>Give the elementary matrix which, when multiplied to the left of a 3 by 3 matrix, will replace row 2 by row 2 + {@avar@} times row 3.</p>
<p>\(\textbf{E} = \) [[input:ans1]]</p>
<p>[[validation:ans1]]</p>]]></text>
</questiontext>
<generalfeedback format="html">
<text/>
</generalfeedback>
<defaultgrade>1</defaultgrade>
<penalty>0.5</penalty>
<hidden>0</hidden>
<idnumber/>
<stackversion>
<text/>
</stackversion>
<questionvariables>
<text>avar:rand_with_step(2,6,1);
correctanswer:matrix([1,0,0],[0,1,avar],[0,0,1]);
wronganswer1:matrix([1,0,0],[0,1,0],[0,avar,1]);</text>
</questionvariables>
<specificfeedback format="html">
<text><![CDATA[<p>[[feedback:Result]]</p>]]></text>
</specificfeedback>
<questionnote format="moodle_auto_format">
<text>{@correctanswer@}</text>
</questionnote>
<questiondescription format="moodle_auto_format">
<text/>
</questiondescription>
<questionsimplify>1</questionsimplify>
<assumepositive>0</assumepositive>
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<scientificnotation>*10</scientificnotation>
<multiplicationsign>dot</multiplicationsign>
<sqrtsign>1</sqrtsign>
<complexno>i</complexno>
<inversetrig>cos-1</inversetrig>
<logicsymbol>lang</logicsymbol>
<matrixparens>[</matrixparens>
<isbroken>0</isbroken>
<prescribedmetadata/>
<metadata>
{"author":[{"firstName":"","lastName":"","institution":"Unknown - Legacy question","year":"2025"}],"language":["en"],"isPartOf":"STACK Library","license":"cc-sa-4.0","additional":{"UoE":{"Notes":"This is automatically generated metadata."}},"freeform":{}}
</metadata>
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<input>
<name>ans1</name>
<type>matrix</type>
<tans>correctanswer</tans>
<boxsize>20</boxsize>
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<insertstars>0</insertstars>
<syntaxhint/>
<syntaxattribute>0</syntaxattribute>
<forbidwords>determinant, invert</forbidwords>
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<checkanswertype>1</checkanswertype>
<mustverify>1</mustverify>
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<options/>
</input>
<prt>
<name>Result</name>
<value>1.0000000</value>
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<trueanswernote>Result-0-T </trueanswernote>
<truefeedback format="html">
<text/>
</truefeedback>
<falsescoremode>=</falsescoremode>
<falsescore>0.0000000</falsescore>
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<falsenextnode>-1</falsenextnode>
<falseanswernote>Result-0-F </falseanswernote>
<falsefeedback format="html">
<text/>
</falsefeedback>
</node>
</prt>
<deployedseed>948077501</deployedseed>
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<description/>
<testinput>
<name>ans1</name>
<value>correctanswer</value>
</testinput>
<expected>
<name>Result</name>
<expectedscore>1.0000000</expectedscore>
<expectedpenalty>0.0000000</expectedpenalty>
<expectedanswernote>Result-0-T</expectedanswernote>
</expected>
</qtest>
<qtest>
<testcase>2</testcase>
<description/>
<testinput>
<name>ans1</name>
<value>wronganswer1</value>
</testinput>
<expected>
<name>Result</name>
<expectedscore>0.0000000</expectedscore>
<expectedpenalty>0.5000000</expectedpenalty>
<expectedanswernote>Result-0-F</expectedanswernote>
</expected>
</qtest>
</question>
</quiz>
LinearAlgebra_elementary_2
Linear algebra / Matrix input · 1 answer field · 2 author tests.
Give the elementary matrix which, when multiplied to the left of a 3 by 3 matrix, will replace row 1 by row 1 + \(3\) times row 3.
\(\textbf{E} = \)
Show source
```{.stack-question}
#| file: questions/corpus/LinearAlgebra_elementary_2.xml
#| question: LinearAlgebra_elementary_2
#| label: corpus-linearalgebra-elementary-2
#| review: true
```Show STACK source
<?xml version="1.0" encoding="UTF-8"?>
<quiz>
<question type="stack">
<name>
<text>LinearAlgebra_elementary_2</text>
</name>
<questiontext format="html">
<text><![CDATA[<p>Give the elementary matrix which, when multiplied to the left of a 3 by 3 matrix, will replace row 1 by row 1 + {@avar@} times row 3.</p>
<p>\(\textbf{E} = \) [[input:ans1]]</p>
<p>[[validation:ans1]]</p>]]></text>
</questiontext>
<generalfeedback format="html">
<text/>
</generalfeedback>
<defaultgrade>1</defaultgrade>
<penalty>0.5</penalty>
<hidden>0</hidden>
<idnumber/>
<stackversion>
<text/>
</stackversion>
<questionvariables>
<text>avar:rand_with_step(2,6,1);
correctanswer:matrix([1,0,avar],[0,1,0],[0,0,1]);
wronganswer1:matrix([1,0,0],[0,1,0],[0,avar,1]);</text>
</questionvariables>
<specificfeedback format="html">
<text><![CDATA[<p>[[feedback:Result]]</p>]]></text>
</specificfeedback>
<questionnote format="moodle_auto_format">
<text>{@correctanswer@}</text>
</questionnote>
<questiondescription format="moodle_auto_format">
<text/>
</questiondescription>
<questionsimplify>1</questionsimplify>
<assumepositive>0</assumepositive>
<assumereal>0</assumereal>
<scientificnotation>*10</scientificnotation>
<multiplicationsign>dot</multiplicationsign>
<sqrtsign>1</sqrtsign>
<complexno>i</complexno>
<inversetrig>cos-1</inversetrig>
<logicsymbol>lang</logicsymbol>
<matrixparens>[</matrixparens>
<isbroken>0</isbroken>
<prescribedmetadata/>
<metadata>
{"author":[{"firstName":"","lastName":"","institution":"Unknown - Legacy question","year":"2025"}],"language":["en"],"isPartOf":"STACK Library","license":"cc-sa-4.0","additional":{"UoE":{"Notes":"This is automatically generated metadata."}},"freeform":{}}
</metadata>
<variantsselectionseed/>
<input>
<name>ans1</name>
<type>matrix</type>
<tans>correctanswer</tans>
<boxsize>20</boxsize>
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<insertstars>0</insertstars>
<syntaxhint/>
<syntaxattribute>0</syntaxattribute>
<forbidwords>determinant, invert</forbidwords>
<allowwords/>
<forbidfloat>1</forbidfloat>
<requirelowestterms>1</requirelowestterms>
<checkanswertype>1</checkanswertype>
<mustverify>1</mustverify>
<showvalidation>1</showvalidation>
<options/>
</input>
<prt>
<name>Result</name>
<value>1.0000000</value>
<autosimplify>1</autosimplify>
<feedbackstyle>1</feedbackstyle>
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<answertest>AlgEquiv</answertest>
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<truescore>1.0000000</truescore>
<truepenalty/>
<truenextnode>-1</truenextnode>
<trueanswernote>Result-0-T </trueanswernote>
<truefeedback format="html">
<text/>
</truefeedback>
<falsescoremode>=</falsescoremode>
<falsescore>0.0000000</falsescore>
<falsepenalty/>
<falsenextnode>-1</falsenextnode>
<falseanswernote>Result-0-F </falseanswernote>
<falsefeedback format="html">
<text/>
</falsefeedback>
</node>
</prt>
<deployedseed>404337827</deployedseed>
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<description/>
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<value>correctanswer</value>
</testinput>
<expected>
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<expectedscore>1.0000000</expectedscore>
<expectedpenalty>0.0000000</expectedpenalty>
<expectedanswernote>Result-0-T</expectedanswernote>
</expected>
</qtest>
<qtest>
<testcase>2</testcase>
<description/>
<testinput>
<name>ans1</name>
<value>wronganswer1</value>
</testinput>
<expected>
<name>Result</name>
<expectedscore>0.0000000</expectedscore>
<expectedpenalty>0.5000000</expectedpenalty>
<expectedanswernote>Result-0-F</expectedanswernote>
</expected>
</qtest>
</question>
</quiz>
LinearAlgebra_elementary_3
Linear algebra / Matrix input · 1 answer field · 2 author tests.
Give the elementary matrix which, when multiplied to the left of a 3 by 3 matrix, will replace row 2 by row 2 + \(3\) times row 1.
\(\textbf{E} = \)
Show source
```{.stack-question}
#| file: questions/corpus/LinearAlgebra_elementary_3.xml
#| question: LinearAlgebra_elementary_3
#| label: corpus-linearalgebra-elementary-3
#| review: true
```Show STACK source
<?xml version="1.0" encoding="UTF-8"?>
<quiz>
<question type="stack">
<name>
<text>LinearAlgebra_elementary_3</text>
</name>
<questiontext format="html">
<text><![CDATA[<p>Give the elementary matrix which, when multiplied to the left of a 3 by 3 matrix, will replace row 2 by row 2 + {@avar@} times row 1.</p>
<p>\(\textbf{E} = \) [[input:ans1]]</p>
<p>[[validation:ans1]]</p>]]></text>
</questiontext>
<generalfeedback format="html">
<text/>
</generalfeedback>
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LinearAlgebra_elementary_4
Linear algebra / Matrix input · 1 answer field · 2 author tests.
Give the elementary matrix which, when multiplied to the left of a 3 by 3 matrix, will replace row 1 by row 1 - \(3\) times row 2.
\(\textbf{E} = \)
Show source
```{.stack-question}
#| file: questions/corpus/LinearAlgebra_elementary_4.xml
#| question: LinearAlgebra_elementary_4
#| label: corpus-linearalgebra-elementary-4
#| review: true
```Show STACK source
<?xml version="1.0" encoding="UTF-8"?>
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<question type="stack">
<name>
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<questiontext format="html">
<text><![CDATA[<p>Give the elementary matrix which, when multiplied to the left of a 3 by 3 matrix, will replace row 1 by row 1 - {@avar@} times row 2.</p>
<p>\(\textbf{E} = \) [[input:ans1]]</p>
<p>[[validation:ans1]]</p>]]></text>
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For developers
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You can still download and inspect these original questions. Each explanation gives the first issue found while importing or preparing the question; other features may also need adaptation.
AlgMap-3.1
Algebra Refresher / 03 Addition and subtraction of fractions · Cannot import this question. prt[prt1]/node[0]/answertest: unsupported answer test 'EqualComAssRules'.
AlgMap-3.3
Algebra Refresher / 03 Addition and subtraction of fractions · Cannot prepare this variant at seed 73699510. questionvariables[simp]: reassigned variable is unsupported.
AlgMap-5.1
Algebra Refresher / 05 Combinations of arithmetic operations on fractions · Cannot prepare this variant at seed 1965111916. questionvariables[simp]: reassigned variable is unsupported.
AlgMap-7.10
Algebra Refresher / 07 Removing brackets · Cannot prepare this variant at seed 1181131383. questionvariables[ta]: reassigned variable is unsupported.
AlgMap-12.1
Algebra Refresher / 12 Simultaneous linear equations · Cannot prepare this variant at seed 1841615900. questionvariables[sysl]: Unexpected character '.' (U+002E) at position 1.
AlgMap-15.1
Algebra Refresher / 15 Quadratic equations · Cannot prepare this variant at seed 2060820372. instantiation: Unexpected character '?' (U+003F) at position 1.
Limits_1
Topics / Limits · Cannot import this question. prt[Result]/node[0]/truepenalty: branch-specific penalties are unsupported.
Matrices_find det 2*2
Topics / LinearAlgebra / Matrix Calculations · Cannot prepare this variant at seed 1113104891. questionvariables[correctanswer]: Function determinant is not allowed; use determinant*(…) for multiplication.
Inequality_1
Topics / Inequalities · Cannot prepare this variant at seed 1959651692. questionvariables[correctanswer]: Unexpected character '>' (U+003E) at position 1.
Numerical input (min sf)
Features / input type sample questions · Cannot import this question. input[ans1]/options: input-specific options are unsupported.
7.3.26 (Write sim. eqns. with matrices)
Introductory Mathematics / Matrix equations · Cannot prepare this variant at seed 1930245414. questiontext: unsupported HTML attribute 'style' on <ul>.
How this gallery was checked
The reproducible baseline records 23 passed, 1 with test mismatches, and 11 blocked (3 at import, 8 while preparing a variant). It retained 82 authored test cases and replayed 162 seed/case combinations across 24 prepared questions; 2 combinations disagreed. Results for these variants do not establish complete STACK/Maxima agreement.
Sources
These unchanged questions come from the STACK question library at its pinned revision and retain CC BY-SA 4.0. The source manifest links every question to its exact upstream file. The presentation teaching copy records its limited HTML change and licensing; three other corrected teaching copies record their mathematical or grading changes.