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[Stack-cvs] stack-dev/sample_questions/diagnostictests FormulaSheet.tex, 1.1, 1.2 DiagnosticTests.xml, 1.1, 1.2 ReadMe.txt, 1.1, 1.2
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From: Simon H. <sim...@us...> - 2010-09-30 16:56:33
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Update of /cvsroot/stack/stack-dev/sample_questions/diagnostictests In directory sfp-cvsdas-3.v30.ch3.sourceforge.com:/tmp/cvs-serv28438/sample_questions/diagnostictests Added Files: FormulaSheet.tex DiagnosticTests.xml ReadMe.txt Log Message: Merging 2.2 branch (with some additional fixes to ensure seamless updating for version lines) --- NEW FILE: DiagnosticTests.xml --- <?xml version="1.0" encoding="UTF-8"?> <mathQuiz version="2.0" xmlns:dc="http://purl.org/dc/elements/1.1/" xmlns:dcterms="http://purl.org/dc/terms/" xmlns:lom="http://www.imsglobal.org/xsd/imsmd_v1p2"><assessmentItem version="2.0" xmlns:dc="http://purl.org/dc/elements/1.1/" xmlns:dcterms="http://purl.org/dc/terms/" xmlns:lom="http://www.imsglobal.org/xsd/imsmd_v1p2"><questionCasValues><questionStem type="CasText"><castext>In a railway journey of \(90km\) an increase of \(5\) kilometers per hour in the speed decreases the time taken by \(15\) minutes. <p>Write a system of equations (one equation per line) to represent this situation using \(v\) as the speed of the train and \(t\) as the time. <br /> #asys# <IEfeedback>asys</IEfeedback> <PRTfeedback>1</PRTfeedback> <p>Eliminate \(t\) from your equations, writing a single equation only in \(v\) which represents this situation. <br /> #veqn# <IEfeedback>veqn</IEfeedback> <PRTfeedback>2</PRTfeedback> <p>What is the velocity? #ansv# <IEfeedback>ansv</IEfeedback> <PRTfeedback>3</PRTfeedback> <p>How confident are you (as a %)? #con1# <IEfeedback>con1</IEfeedback></p></castext><forbidFloats>false</forbidFloats><simplify>true</simplify></questionStem><questionVariables type="RawKeyVal"><rawKeyVals>ta = [v*t=90 , (v+5)*(t-15/60)=90]; tsys = maplist(stack_eqnprepare,ta); tsys1 = maplist(stack_eqnprepare,[v*t=90 , (v+5)*(t-15)=90])</rawKeyVals><forbidFloats>false</forbidFloats><simplify>true</simplify></questionVariables><workedSolution type="CasText"><castext>Let \(v\) be the speed of the train, \(d\) the distance travelled and \(t\) time. If \(t\) is the time (in hours) then \(15\) minutes is \(\frac{1}{4}\) hour. [...1545 lines suppressed...] </castext><forbidFloats>false</forbidFloats><simplify>true</simplify></questionStem><questionVariables type="RawKeyVal"><rawKeyVals>a = rand(9)+1; mag_b = rand(9)+1; sign_b = 2*rand(2)-1; b = mag_b*sign_b; c = 2*rand(2)-1; mag_d = rand(8)+2; sign_d = 2*rand(2)-1; d = mag_d*sign_d; numerat = a*x+b; den1 = x+c; den2 = x+d; den2_squared = den2^2; Aden2_squared = A * den2_squared; Bden1_den2 = B * den1 * den2; Cden1 = C * den1; den = den1 * den2_squared; f = numerat/den; c_minus_d = c-d; mc = -c; md = -d; Aval = (b-a*c)/c_minus_d^2; Cval = (b-a*d)/c_minus_d; Bval = (b - Aval*d^2 - c*Cval)/(c*d); answer = partfrac(f,x)</rawKeyVals><forbidFloats>false</forbidFloats><simplify>true</simplify></questionVariables><workedSolution type="CasText"><castext>The basic partial fraction information is:<hint>alg_partial_fractions</hint> So, given \[ @f@=\frac{A}{@den1@} + \frac{B}{@den2@} + \frac{C}{@den2_squared@},\] then multiplying through by the denominator @den@ we have that \[ @numerat@ = @Aden2_squared@ + @Bden1_den2@+@Cden1@. \] Setting \(x = @mc@\) we see that \(A = @Aval@\) and letting \(x = @md@\) we find that \(C = @Cval@\). Putting \(x = 0\) we can also see that \(B = @Bval@\). Therefore \[ @f@=@answer@.\]</castext><forbidFloats>false</forbidFloats><simplify>true</simplify></workedSolution><questionNote type="CasText"><castext>\[ @f@=@answer@.\]</castext><forbidFloats>false</forbidFloats><simplify>true</simplify></questionNote></questionCasValues><questionparts><questionpart><name>ans1</name><inputType type="Meta"><selection>Algebraic Input</selection><default>Algebraic Input</default><values/></inputType><boxsize>20</boxsize><teachersAns type="CasString"><casString>answer</casString><forbidFloats>false</forbidFloats><simplify>true</simplify></teachersAns><studentAnsKey>ans1</studentAnsKey><syntax 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type="Meta"><selection></selection><default></default><values/></syntax><stackoption><name>formalSyntax</name><type>list</type><default>true</default><values><value>true</value><value>false</value></values><casKey></casKey><casType></casType><selected>true</selected></stackoption><stackoption><name>forbidFloats</name><type>list</type><default>true</default><values><value>true</value><value>false</value></values><casKey>OPT_NoFloats</casKey><casType>ex</casType><selected>true</selected></stackoption><stackoption><name>insertStars</name><type>list</type><default>false</default><values><value>true</value><value>false</value></values><casKey></casKey><casType></casType><selected>false</selected></stackoption><stackoption><name>sameType</name><type>list</type><default>true</default><values><value>true</value><value>false</value></values><casKey></casKey><casType></casType><selected>true</selected></stackoption><stackoption><name>lowestTerms</name><type>list</type><default>true</default><values><value>true</value><value>false</value></values><casKey>OPT_LowestTerms</casKey><casType>ex</casType><selected>true</selected></stackoption><inputTypesParameters/></questionpart></questionparts><PotentialResponseTrees><PotentialResponseTree><prtname>PotResTree_Result</prtname><questionValue>1</questionValue><autoSimplify>true</autoSimplify><feedbackVariables></feedbackVariables><description type="Meta"><selection></selection><default></default><values/></description><PotentialResponses><PR id="0"><answerTest>PartFrac</answerTest><teachersAns>answer</teachersAns><studentAns>ans1</studentAns><testoptions>x</testoptions><quietAnsTest></quietAnsTest><true><rawModMark>=</rawModMark><rawMark>1</rawMark><feedback></feedback><ansnote>ALG-RPF-TRUE</ansnote><nextPR>-1</nextPR></true><false><rawModMark>=</rawModMark><rawMark>0</rawMark><feedback></feedback><ansnote>ALG-RPF-FALSE</ansnote><nextPR>1</nextPR></false><teacherNote></teacherNote></PR><PR id="1"><answerTest>AlgEquiv</answerTest><teachersAns>answer</teachersAns><studentAns>ans1</studentAns><testoptions></testoptions><quietAnsTest></quietAnsTest><true><rawModMark>=</rawModMark><rawMark>0</rawMark><feedback></feedback><ansnote>ALG-RPF-1-FALSE</ansnote><nextPR>2</nextPR></true><false><rawModMark>=</rawModMark><rawMark>0</rawMark><feedback></feedback><ansnote>ALG-RPF-2-FALSE</ansnote><nextPR>-1</nextPR></false><teacherNote></teacherNote></PR><PR id="2"><answerTest>Equal_Com_Ass</answerTest><teachersAns>f</teachersAns><studentAns>ans1</studentAns><testoptions></testoptions><quietAnsTest></quietAnsTest><true><rawModMark>=</rawModMark><rawMark>0</rawMark><feedback><p>This seems to be the same expression that you started with.</p></feedback><ansnote>NO-CHANGE</ansnote><nextPR>-1</nextPR></true><false><rawModMark>=</rawModMark><rawMark>0</rawMark><feedback><p>Although your expression is algebraically equal to the correct answer, it is not in partial fractions 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type="Meta"><selection>http://130.88.73.28/stack-1-0/</selection><default>http://matsrv6.bham.ac.uk/stem</default><values/></dc:publisher><dc:format stackname="questionFormat" type="Meta"><selection>text/xml; charset="utf-8"</selection><default>text/xml; charset="utf-8"</default><values><value key="0">application</value><value key="1">audio</value><value key="2">image</value><value key="3">message</value><value key="4">model</value><value key="5">text</value><value key="6">video</value><value key="7">multipart</value></values></dc:format><lom:context stackname="questionLearningContext" type="Meta"><selection>unspecified</selection><default>unspecified</default><values><value key="PrimaryEducation">Primary Education</value><value key="SecondaryEducation">Secondary Education</value><value key="HigherEducation">Higher Education</value><value key="UniversityFirstCycle">University First Cycle</value><value key="UniversitySecondCycle">University Second Cycle</value><value 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A2</default><values/></lom:keyword></MetaData><ItemOptions><stackoption><name>Display</name><type>list</type><default>LaTeX</default><values><value>LaTeX</value><value>MathML</value></values><casKey>OPT_OUTPUT</casKey><casType>string</casType><selected>LaTeX</selected></stackoption><stackoption><name>MultiplicationSign</name><type>list</type><default>dot</default><values><value>(none)</value><value>dot</value><value>cross</value></values><casKey>make_multsgn</casKey><casType>fun</casType><selected>dot</selected></stackoption><stackoption><name>ComplexNo</name><type>list</type><default>i</default><values><value>i</value><value>j</value><value>symi</value><value>symj</value></values><casKey>make_complexJ</casKey><casType>fun</casType><selected>i</selected></stackoption><stackoption><name>Floats</name><type>list</type><default>true</default><values><value>true</value><value>false</value></values><casKey>OPT_NoFloats</casKey><casType>ex</casType><selected>true</selected></stackoption><stackoption><name>SqrtSign</name><type>list</type><default>true</default><values><value>true</value><value>false</value></values><casKey>sqrtdispflag</casKey><casType>ex</casType><selected>true</selected></stackoption><stackoption><name>Simplify</name><type>list</type><default>true</default><values><value>true</value><value>false</value></values><casKey>simp</casKey><casType>ex</casType><selected>true</selected></stackoption><stackoption><name>MarkModMethod</name><type>list</type><default>Penalty</default><values><value>Penalty</value><value>First Answer</value><value>Last Answer</value></values><casKey></casKey><casType></casType><selected>Penalty</selected></stackoption><stackoption><name>AssumePos</name><type>list</type><default>false</default><values><value>true</value><value>false</value></values><casKey>assume_pos</casKey><casType>ex</casType><selected>false</selected></stackoption><stackoption><name>TeacherEmail</name><type>string</type><default>s.h...@bh...</default><casKey></casKey><casType></casType><selected>Nie...@ma...</selected></stackoption><stackoption><name>Feedback</name><type>list</type><default>TGS</default><values><value>TGS</value><value>TG</value><value>GS</value><value>T</value><value>G</value><value>S</value><value>none</value></values><casKey></casKey><casType></casType><selected>G</selected></stackoption><stackoption><name>FeedbackGenericCorrect</name><type>html</type><default><span class='correct'>Correct answer, well done.</span></default><casKey></casKey><casType></casType><selected><span class='correct'>Correct answer, well done.</span></selected></stackoption><stackoption><name>FeedbackGenericIncorrect</name><type>html</type><default><span class='incorrect'>Incorrect answer.</span></default><casKey></casKey><casType></casType><selected><span class='incorrect'>Incorrect answer.</span></selected></stackoption><stackoption><name>FeedbackGenericPCorrect</name><type>html</type><default><span class='partially'>Your answer is partially correct.</span></default><casKey></casKey><casType></casType><selected><span class='partially'>You may have made a common error.</span></selected></stackoption><stackoption><name>OptWorkedSol</name><type>list</type><default>true</default><values><value>true</value><value>false</value></values><casKey></casKey><casType></casType><selected>false</selected></stackoption></ItemOptions><ItemTests><test><col><key>IE_ans1</key><value>answer</value></col><col><key>PRT_PotResTree_Result</key><value>ALG-RPF-TRUE</value></col><col><key>IE_con1</key><value></value></col></test><test><col><key>IE_ans1</key><value>7*x</value></col><col><key>PRT_PotResTree_Result</key><value>ALG-RPF-2-FALSE</value></col><col><key>IE_con1</key><value></value></col></test><test><col><key>IE_ans1</key><value>f</value></col><col><key>PRT_PotResTree_Result</key><value>NO-CHANGE</value></col><col><key>IE_con1</key><value></value></col></test></ItemTests></assessmentItem></mathQuiz> --- NEW FILE: FormulaSheet.tex --- \documentclass{article} \usepackage{amsmath,amssymb,latexsym,a4wide,times} \usepackage{epsfig} \usepackage{graphicx} \parindent=0pt \parskip=2mm \columnsep=1cm \newcommand{\R}{{\mathbb R}} \newcommand{\N}{{\mathbb N}} \newcommand{\Z}{{\mathbb Z}} \newcommand{\Q}{{\mathbb Q}} \newcommand{\C}{{\mathbb C}} \renewcommand{\d}{\mathrm{d}} \pagestyle{empty} \begin{document} \begin{center} {\Large\bf Facts and formulae} \end{center} Indices: \[ a^ma^n = a^{m+n},\quad \frac{a^m}{a^n} = a^{m-n},\quad (a^m)^n = a^{mn}\] \[ a^0 = 1,\quad a^{-m} = \frac{1}{a^m},\quad a^{\frac{1}{n}} = \sqrt[n]{a},\quad a^{\frac{m}{n}} = \left(\sqrt[n]{a}\right)^m.\] Logarithms: for any $b>0$, $b \neq 1$: $\log_b(a) = c$, means $a = b^c$. \[\log_b(a) + \log_b(b) = \log_b(ab),\quad \log_b(a) - \log_b(b) = \log_b\left(\frac{a}{b}\right),\quad n\log_b(a) = \log_b\left(a^n\right)\] \[\log_b(1) = 0,\quad \log_b(b) = 1,\quad \log_a(x) = \frac{\log_b(x)}{\log_b(a)}\] Natural logarithms use base $e\approx 2.718$, and are denoted $\log_e$ or alternatively $\ln$. Standard Trigonometric Values \[ \sin(45^\circ)={1\over \sqrt{2}}, \qquad \cos(45^\circ) = {1\over \sqrt{2}},\qquad \tan( 45^\circ)=1 \] \[ \sin (30^\circ)={1\over 2}, \qquad \cos (30^\circ)={\sqrt{3}\over 2},\qquad \tan (30^\circ)={1\over \sqrt{3}}\] \[ \sin (60^\circ)={\sqrt{3}\over 2}, \qquad \cos (60^\circ)={1\over 2},\qquad \tan (60^\circ)={ \sqrt{3}} \] Standard Trigonometric Identities \[\sin(a\pm b)\ = \ \sin(a)\cos(b)\ \pm\ \cos(a)\sin(b)\] \[\cos(a\ \pm\ b)\ = \ \cos(a)\cos(b)\ \mp \sin(a)\sin(b)\] \[\tan (a\ \pm\ b)\ = \ {\tan (a)\ \pm\ \tan (b)\over1\ \mp\ \tan (a)\tan (b)}\] \[2\sin(a)\cos(b)\ = \ \sin(a+b)\ +\ \sin(a-b)\] \[2\cos(a)\cos(b)\ = \ \cos(a-b)\ +\ \cos(a+b)\] \[2\sin(a)\sin(b) \ = \ \cos(a-b)\ -\ \cos(a+b)\] \[\sin^2(a)+\cos^2(a)\ = \ 1\] \[1+{\rm cot}^2(a)\ = \ {\rm cosec}^2(a),\quad \tan^2(a) +1 \ = \ \sec^2(a)\] \[\cos(2a)\ = \ \cos^2(a)-\sin^2(a)\ = \ 2\cos^2(a)-1\ = \ 1-2\sin^2(a)\] \[\sin(2a)\ = \ 2\sin(a)\cos(a)\] \[\sin^2(a) \ = \ {1-\cos (2a)\over 2}, \qquad \cos^2(a)\ = \ {1+\cos(2a)\over 2}\] Hyperbolic Functions \[\cosh(x) = \frac{e^x+e^{-x}}{2}, \qquad \sinh(x)=\frac{e^x-e^{-x}}{2}\] \[\tanh(x) = \frac{\sinh(x)}{\cosh(x)} = \frac{{e^x-e^{-x}}}{e^x+e^{-x}}\] \[{\rm sech}(x) ={1\over \cosh(x)}={2\over {\rm e}^x+{\rm e}^{-x}}, \qquad {\rm cosech}(x)= {1\over \sinh(x)}={2\over {\rm e}^x-{\rm e}^{-x}}\] \[{\rm coth}(x) ={\cosh(x)\over \sinh(x)} = {1\over {\rm tanh}(x)} ={{\rm e}^x+{\rm e}^{-x}\over {\rm e}^x-{\rm e}^{-x}}\] Hyperbolic Identities \[{\rm e}^x=\cosh(x)+\sinh(x), \quad {\rm e}^{-x}=\cosh(x)-\sinh(x)\] \[\cosh^2(x) -\sinh^2(x) = 1$$ $$1-{\rm tanh}^2(x)={\rm sech}^2(x)\] \[{\rm coth}^2(x)-1={\rm cosech}^2(x)$$ $$\sinh(x\pm y)=\sinh(x)\ \cosh(y)\ \pm\ \cosh(x)\ \sinh(y)\] \[\cosh(x\pm y)=\cosh(x)\ \cosh(y)\ \pm\ \sinh(x)\ \sinh(y)\] \[\sinh(2x)=2\,\sinh(x)\cosh(x)\] \[\cosh(2x)=\cosh^2(x)+\sinh^2(x)\] \[\cosh^2(x)={\cosh(2x)+1\over 2}\] \[\sinh^2(x)={\cosh(2x)-1\over 2}\] Inverse Hyperbolic Functions \[\cosh^{-1}(x)=\ln\left(x+\sqrt{x^2-1}\right) \quad \mbox{ for } x\geq 1\] \[ \sinh^{-1}(x)=\ln\left(x+\sqrt{x^2+1}\right)\] \[\tanh^{-1}(x) = \frac{1}{2}\ln\left({1+x\over 1-x}\right) \quad \mbox{ for } -1< x < 1\] Calculus rules The Product Rule: \[\frac{\mathrm{d}}{\mathrm{d}{x}} \big(f(x)g(x)\big) = f(x) \cdot \frac{\mathrm{d} g(x)}{\mathrm{d}{x}} + g(x)\cdot \frac{\mathrm{d} f(x)}{\mathrm{d}{x}}.\] The Quotient Rule: \[\frac{d}{dx}\left(\frac{f(x)}{g(x)}\right)=\frac{g(x)\cdot\frac{df(x)}{dx}\ \ - \ \ f(x)\cdot \frac{dg(x)}{dx}}{g(x)^2}. \] The Chain Rule \[\frac{df(g(x))}{dx} = \frac{dg(x)}{dx}\cdot\frac{df(u)}{du}.\] Integration by Substitution: \[\int f(u){{\rm d}u\over {\rm d}x}{\rm d}x=\int f(u){\rm d}u \quad\hbox{and}\quad \int_a^bf(u){{\rm d}u\over {\rm d}x}\,{\rm d}x = \int_{u(a)}^{u(b)}f(u){\rm d}u.\] Integration by Parts: \[\int_a^b u{{\rm d}v\over {\rm d}x}{\rm d}x=\left[uv\right]_a^b- \int_a^b{{\rm d}u\over {\rm d}x}v\,{\rm d}x.\] \begin{center} \begin{tabular}{ll} $f(x)$ & $f'(x)$\\ $k$, constant & $0$ \\ $x^n$, any constant $n$ & $nx^{n-1}$\\ $e^x$ & $e^x$\\ $\ln(x)=\log_{\rm e}(x)$ & $\frac{1}{x}$ \\ $\sin(x)$ & $\cos(x)$ \\ $\cos(x)$ & $-\sin(x)$ \\ $\tan(x) = \frac{\sin(x)}{\cos(x)}$ & $\sec^2(x)$ \\ $\mbox{cosec}(x)=\frac{1}{\sin(x)}$ & $-\mbox{cosec}(x)\cot(x)$ \\ $\sec(x)=\frac{1}{\cos(x)}$ & $\sec(x)\tan(x)$ \\ $\cot(x)=\frac{\cos(x)}{\sin(x)}$ & $-\mbox{cosec}^2(x)$ \\ $\cosh(x)$ & $\sinh(x)$ \\ $\sinh(x)$ & $\cosh(x)$ \\ $\tanh(x)$ & $\mbox{sech}^2(x)$ \\ $\mbox{sech}(x)$ & $-\mbox{sech}sech(x)\tanh(x)$ \\ $\mbox{cosech}(x)$ & $-\mbox{cosech}(x)\coth(x)$ \\ $coth(x)$ & $-\mbox{cosech}^2(x)$ \\ \end{tabular} \end{center} \[\frac{d}{dx}\left(\sin^{-1}(x)\right) = \frac{1}{\sqrt{1-x^2}},\quad \frac{d}{dx}\left(\cos^{-1}(x)\right) = \frac{-1}{\sqrt{1-x^2}},\quad \frac{d}{dx}\left(\tan^{-1}(x)\right) = \frac{1}{1+x^2} \] \[\frac{d}{dx}\left(\cosh^{-1}(x)\right) = \frac{1}{\sqrt{x^2-1}},\quad \frac{d}{dx}\left(\sinh^{-1}(x)\right) = \frac{1}{\sqrt{x^2+1}},\quad \frac{d}{dx}\left(\tanh^{-1}(x)\right) = \frac{1}{1-x^2}\] \begin{center} \begin{tabular}{lll} $f(x)$ & $\int f(x)\ dx$\\ $e^x$ & $e^x+c$ & \\ $\cos(x)$ & $\sin(x)+c$ & \\ $\sin(x)$ & $-\cos(x)+c$ & \\ $\tan(x)$ & $\ln(\sec(x))+c$ & $-\frac{\pi}{2} < x < \frac{\pi}{2}$\\ $\sec x$ & $\ln (\sec(x)+\tan(x))+c$ & $-{\pi\over 2}< x < {\pi\over 2}$\\ cosec$\, x$ & $\ln ($cosec$(x)-\cot(x))+c$ & $0 < x < \pi$\\ cot$\,x$ & $\ln(\sin(x))+c$ & $0< x< \pi$ \\ $\cosh(x)$ & $\sinh(x)+c$ & \\ $\sinh(x)$ & $\cosh(x) + c$ & \\ $\tanh(x)$ & $\ln(\cosh(x))+c$ & \\ coth$(x)$ & $\ln(\sinh(x))+c $ & $x>0$\\ ${1\over x^2+a^2}$ & ${1\over a}\tan^{-1}{x\over a}+c$ & $a>0$\\ [2pt] ${1\over x^2-a^2}$ & ${1\over 2a}\ln{x-a\over x+a}+c$ & $|x|>a>0$\\ [2pt] ${1\over a^2-x^2}$ & ${1\over 2a}\ln{a+x\over a-x}+c$ & $|x|<a$\\ [3pt] ${1\over \sqrt{x^2+a^2}}$ & $\sinh^{-1}\left(\frac{x}{a}\right) + c$ & $a>0$ \\ ${1\over \sqrt{x^2-a^2}}$ & $\cosh^{-1}\left(\frac{x}{a}\right) + c$ & $x\geq a > 0$ \\ ${1\over \sqrt{x^2+k}}$ & $\ln (x+\sqrt{x^2+k})+c$ & \\ ${1\over \sqrt{a^2-x^2}}$ & $\sin^{-1}\left(\frac{x}{a}\right)+c$ & $-a\leq x\leq a$ \end{tabular} \end{center} \vfill {\scriptsize C J Sangwin, \verb$C.J...@bh...$, \today. This formula sheet is released under Creative Commons Attribution-Share Alike.\\ \includegraphics[width=1.5cm]{88x31.png}} \end{document} --- NEW FILE: ReadMe.txt --- Stimulating Techniques in Entry-level Mathematics with the STACK CAA system In April 2010 the National HE STEM Programme (http://www.stemprogramme.com) funded a mini-project stimulating Techniques in Entry-level Mathematics (STEM) with the STACK computer aided assessment (CAA) system}. The aims of this project are to take existing diagnostic tests in core mathematics and develop similar automatic tests for the STACK computer aided assessment system. The outcome of these tests will be a user profile which links outcomes to existing online learning materials. See http://web.mat.bham.ac.uk/C.J.Sangwin/projects/2010STEM/ The questions in this folder are the results of this project. These questions files are released under Creative Commons Attribution-Share Alike. http://creativecommons.org/licenses/by-sa/2.0/uk/ |
