// Numbas version: finer_feedback_settings
{"navigation": {"preventleave": true, "showresultspage": "oncompletion", "allowregen": true, "onleave": {"message": "", "action": "none"}, "reverse": true, "showfrontpage": true, "browse": true}, "showQuestionGroupNames": false, "metadata": {"description": "", "licence": "Creative Commons Attribution 4.0 International", "notes": ""}, "allQuestions": true, "percentPass": 0, "name": "Loughborough workshop demo", "questions": [], "pickQuestions": 0, "timing": {"timedwarning": {"message": "", "action": "none"}, "allowPause": true, "timeout": {"message": "", "action": "none"}}, "feedback": {"allowrevealanswer": true, "showtotalmark": true, "showactualmark": true, "advicethreshold": 0, "showanswerstate": true, "enterreviewmodeimmediately": true, "showexpectedanswerswhen": "inreview", "showpartfeedbackmessageswhen": "always", "showactualmarkwhen": "always", "showtotalmarkwhen": "always", "showanswerstatewhen": "always", "showadvicewhen": "never"}, "question_groups": [{"questions": [{"name": "4.8 equations with logs", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Jennifer Koenig", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/455/"}], "functions": {}, "ungrouped_variables": ["a", "b", "c", "d"], "tags": ["algebra", "logarithms"], "preamble": {"css": "", "js": ""}, "advice": "<p>Take an example, $log(x-3)=3$</p>\n<p>raise both sides so that they are powers to the base 10</p>\n<p>on the left hand side you are doing $10^{log(x-3)}$ leaves you with just x-3.</p>\n<p><span>$10^{log(x-3)}=10^3$</span></p>\n<p>$x-3=10^3$</p>\n<p>$x-3=1000$</p>\n<p>$x=1003$</p>\n<p>-------------</p>\n<p>Another example, $log(x+4)=-2$</p>\n<p><span>$10^{log(x+4)}=10^{-2}$</span></p>\n<p>$x+4=10^{-2}$</p>\n<p>$x+4=0.01$</p>\n<p>$x=-3.99$</p>", "rulesets": {}, "parts": [{"prompt": "<p>Solve for $x$:</p>\n<p>$log(x-\\var{a}) = \\var{b}$</p>\n<p>$x$ =&nbsp;[[0]]</p>", "marks": 0, "gaps": [{"allowFractions": false, "marks": 1, "maxValue": "{a}+10^{b}", "minValue": "{a}+10^{b}", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "type": "numberentry", "showPrecisionHint": false}], "showCorrectAnswer": true, "scripts": {}, "type": "gapfill"}, {"prompt": "<p>Solve for $x$:</p>\n<p>$log(x-\\var{c}) = \\var{d}$</p>\n<p>$x$ =&nbsp;[[0]]</p>", "marks": 0, "gaps": [{"allowFractions": false, "marks": 1, "maxValue": "{c}+10^{d}", "minValue": "{c}+10^{d}", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "type": "numberentry", "showPrecisionHint": false}], "showCorrectAnswer": true, "scripts": {}, "type": "gapfill"}], "statement": "", "variable_groups": [], "variablesTest": {"maxRuns": 100, "condition": ""}, "variables": {"a": {"definition": "random(2..9)", "templateType": "anything", "group": "Ungrouped variables", "name": "a", "description": ""}, "c": {"definition": "10*random(2..9)", "templateType": "anything", "group": "Ungrouped variables", "name": "c", "description": ""}, "b": {"definition": "random(1..4)", "templateType": "anything", "group": "Ungrouped variables", "name": "b", "description": ""}, "d": {"definition": "random(1..4)", "templateType": "anything", "group": "Ungrouped variables", "name": "d", "description": ""}}, "metadata": {"notes": "", "description": "<p>solve for x where logs are involved</p>", "licence": "Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International"}, "type": "question", "showQuestionGroupNames": false, "question_groups": [{"name": "", "pickingStrategy": "all-ordered", "pickQuestions": 0, "questions": []}]}, {"name": "Algebra: Simplifying Expressions (2 unknowns)", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Michael Proudman", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/269/"}], "tags": ["algebra", "algebraic manipulation", "expanding brackets", "simplification", "simplifying an expression"], "variables": {"a": {"name": "a", "definition": "random(-6..6 except 0)", "templateType": "anything", "description": "", "group": "Ungrouped variables"}, "d": {"name": "d", "definition": "random(1..9 except [c,b])", "templateType": "anything", "description": "", "group": "Ungrouped variables"}, "c": {"name": "c", "definition": "random(-6..6 except [0,a])", "templateType": "anything", "description": "", "group": "Ungrouped variables"}, "b": {"name": "b", "definition": "random(1..9 except a)", "templateType": "anything", "description": "", "group": "Ungrouped variables"}}, "parts": [{"extendBaseMarkingAlgorithm": true, "prompt": "\n      <p>Simplify:</p>\n        <p>$\\simplify[std]{({a}x+{b}y)({c}x+{d}y)-({a}x+{d}y)({c}x+{b}y)}=\\;$[[0]]</p>\n        <p>Do not include brackets in your answer.</p>\n        <p>Input $xy$ as $x*y$.</p>\n      ", "scripts": {}, "type": "gapfill", "showCorrectAnswer": true, "unitTests": [], "variableReplacements": [], "gaps": [{"answerSimplification": "std", "checkingType": "absdiff", "checkingAccuracy": 0.001, "showCorrectAnswer": true, "notallowed": {"showStrings": false, "message": "<p>Do not include brackets in your answer.</p>", "strings": ["("], "partialCredit": 0}, "variableReplacements": [], "showFeedbackIcon": true, "maxlength": {"message": "<p>You can simplify the expression further.</p>", "length": 7, "partialCredit": 0}, "adaptiveMarkingPenalty": 0, "answer": "{(a-c)*(d-b)}*x*y", "customName": "", "extendBaseMarkingAlgorithm": true, "scripts": {}, "type": "jme", "variableReplacementStrategy": "originalfirst", "showPreview": true, "failureRate": 1, "checkVariableNames": false, "vsetRange": [0, 1], "useCustomName": false, "valuegenerators": [{"name": "x", "value": ""}, {"name": "y", "value": ""}], "marks": 2, "customMarkingAlgorithm": "", "vsetRangePoints": 5, "unitTests": []}], "variableReplacementStrategy": "originalfirst", "showFeedbackIcon": true, "marks": 0, "customMarkingAlgorithm": "", "adaptiveMarkingPenalty": 0, "sortAnswers": false, "customName": "", "useCustomName": false}], "metadata": {"licence": "None specified", "description": "<p>Simplify $(ax+by)(cx+dy)-(ax+dy)(cx+by)$. Answer is a multiple of $xy$.</p>"}, "variable_groups": [], "statement": "<p>Simplify the following expression.</p>", "rulesets": {"std": ["all", "!collectNumbers", "!noLeadingMinus"]}, "functions": {}, "variablesTest": {"condition": "", "maxRuns": 100}, "preamble": {"css": "", "js": ""}, "advice": "\n  <p>Expanding the brackets we have:</p>\n    <p>\\[\\begin{eqnarray*}\\simplify[std]{({a}x+{b}y)({c}x+{d}y)-({a}x+{d}y)({c}x+{b}y)}&amp;=&amp;(\\simplify[std]{{a*c}x^2+{b*c+a*d}x*y+{b*d}y^2})-(\\simplify[std]{{a*c}x^2+{b*a+c*d}x*y+{b*d}y^2})\\\\&amp;=&amp;\\simplify[std]{{b*c+a*d}x*y-{b*a+c*d}x*y}\\\\&amp;=&amp;\\var{(a-c)*(d-b)}xy\\end{eqnarray*}\\]</p>\n  ", "ungrouped_variables": ["a", "c", "b", "d"], "type": "question"}, {"name": "Anne Berit's copy of Combining algebraic fractions 1 (Video)", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Anne Berit Fuglestad", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/490/"}], "functions": {}, "ungrouped_variables": ["a", "c", "b", "d", "nb", "a1", "a2", "s1"], "tags": ["algebra", "algebraic fractions", "algebraic manipulation", "chain rule", "combining algebraic fractions", "common denominator"], "preamble": {"css": "", "js": ""}, "advice": "\n    <p>The formula for {nb} fractions is :</p>\n    <p>\\[\\simplify[std]{a / b + {s1} * (c / d) = (ad + {s1} * bc) / bd}\\]</p>\n    <p>and for this exercise we have $\\simplify{b=x+{b}}$, $\\simplify{d=x+{d}}$.<br/>Hence we have:<br/>\\[\\simplify[std]{{a} / ({a1}*x + {b}) + ({c} / ({a2}*x + {d})) = ({a} * ({a2}*x + {d}) + {c} * ({a1}*x + {b})) / (({a1}*x + {b}) * ({a2}*x + {d})) = ({a*a2 + c*a1} * x + {a * d + c * b}) / (({a1}*x + {b}) * ({a2}*x + {d}))}\\]</p>\n    ", "rulesets": {"std": ["all", "!collectNumbers", "fractionNumbers", "!noLeadingMinus"]}, "parts": [{"stepsPenalty": 1, "prompt": "<p>Express \\[\\simplify{{a} / ({a1}x + {b}) + ({c} / ({a2}x + {d}))}\\] as a single fraction.</p>\n<p>Input the fraction here: [[0]]</p>\n<p>Input your answer in the form $\\displaystyle \\frac{(ax+b)}{((cx+d)(ex+f))}$ with no other brackets than those shown.</p>\n<p>Click on <em>Show steps</em> if you need help. You will lose one mark if you do so.</p>\n<p>You will also find a video which goes through a similar example.</p>", "marks": 0, "gaps": [{"notallowed": {"message": "<p>Input as a single fraction.</p>", "showStrings": false, "strings": [")-", ")+"], "partialCredit": 0}, "expectedvariablenames": [], "checkingaccuracy": 1e-05, "vsetrange": [10, 11], "showpreview": true, "vsetrangepoints": 5, "showCorrectAnswer": true, "answersimplification": "std", "scripts": {}, "answer": "({a*a2 +  c*a1} * x + {a * d +  c * b})/ (({a1}*x + {b}) * ({a2}*x + {d}))", "marks": 2, "checkvariablenames": false, "checkingtype": "absdiff", "type": "jme"}], "showCorrectAnswer": true, "scripts": {}, "steps": [{"prompt": "<p>The formula for {nb} fractions is:</p>\n<p>\\[\\simplify[std]{a / b + {s1} * (c / d) = (ad + {s1} * bc) / bd}\\]</p>\n<p>and for this exercise we have $\\simplify{b=x+{b}}$, $\\simplify{d=x+{d}}$.</p>\n<p>Note that in your answer you do not need to expand the denominator.</p>\n<p>The following video goes through an example similar to this one.</p>\n<p><iframe width=\"640\" height=\"480\" src=\"https://player.vimeo.com/video/8169833\" frameborder=\"0\"></iframe></p>", "type": "information", "scripts": {}, "showCorrectAnswer": true, "marks": 0}], "type": "gapfill"}], "statement": "\n    <p>Add the following two fractions together and express as a single fraction over a common denominator.</p>\n    <p>&nbsp;</p>\n    \n    ", "variable_groups": [], "variablesTest": {"maxRuns": 100, "condition": ""}, "variables": {"a": {"definition": "random(1..9)", "templateType": "anything", "group": "Ungrouped variables", "name": "a", "description": ""}, "c": {"definition": "random(-9..9 except [0,-a])", "templateType": "anything", "group": "Ungrouped variables", "name": "c", "description": ""}, "b": {"definition": "random(-9..9 except 0)", "templateType": "anything", "group": "Ungrouped variables", "name": "b", "description": ""}, "d": {"definition": "random(-9..9 except [0,round(b*a2/a1)])", "templateType": "anything", "group": "Ungrouped variables", "name": "d", "description": ""}, "nb": {"definition": "if(c<0,'taking away','adding')", "templateType": "anything", "group": "Ungrouped variables", "name": "nb", "description": ""}, "a1": {"definition": "1", "templateType": "anything", "group": "Ungrouped variables", "name": "a1", "description": ""}, "a2": {"definition": "1", "templateType": "anything", "group": "Ungrouped variables", "name": "a2", "description": ""}, "s1": {"definition": "if(c<0,-1,1)", "templateType": "anything", "group": "Ungrouped variables", "name": "s1", "description": ""}}, "metadata": {"notes": "<p><strong>5/08/2012:</strong></p>\n                        <p>Added tags.</p>\n                        <p>Added description.</p>\n                        <p>Changed to two questions, for the numerator and denomimator, rather than one as difficult to trap student input for this example. Still some ambiguity however.</p>\n                        <p><strong>12/08/2012:</strong></p>\n                        <p>Back to one input of a fraction and trapped input in Forbidden Strings.</p>\n                        <p>Used the except feature of ranges to get non-degenerate examples.</p>\n                        <p>Checked calculation.OK.</p>\n                        <p>Improved display in content areas.</p>\n                        <p><strong>02/02/2013:</strong></p>\n                        <p>Modified variable c so that the coefficient of $x$ in the answer is not 0.&nbsp;</p>\n                        <p>Checked input again, OK.</p>", "description": "<p>Express $\\displaystyle \\frac{a}{x + b} \\pm&nbsp; \\frac{c}{x + d}$&nbsp;as an algebraic single fraction over a common denominator.&nbsp;</p>\n<p>Contains a video&nbsp;in <em>Show steps</em>.</p>", "licence": "Creative Commons Attribution 4.0 International"}, "type": "question", "showQuestionGroupNames": false, "question_groups": [{"name": "", "pickingStrategy": "all-ordered", "pickQuestions": 0, "questions": []}]}, {"name": "Solving Quadratic Equations ", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Clare Lundon", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/492/"}], "functions": {}, "ungrouped_variables": ["a", "c", "b", "d", "f", "s3", "s2", "s1", "n4", "n2", "disc", "rdis", "n1", "c1", "n3", "rep", "n5", "d1"], "tags": ["algebra", "Algebra", "Factorisation", "factorisation", "find roots of a quadratic equation", "quadratic formula", "quadratics", "roots of a quadratic equation", "solving a quadratic equation", "solving equations", "Solving equations", "Steps", "steps"], "preamble": {"css": "", "js": ""}, "advice": "<p><strong>Direct Factorisation</strong></p>\n<p>If you can spot a direct factorisation then this is the quickest way to do this question.</p>\n<p>For this example we have the factorisation</p>\n<p>\\[\\simplify{{a*b} * x ^ 2 + ( {-b*c-a * d}) * x + {c * d} = ({a} * x + { -c}) * ({b} * x + { -d})}\\]</p>\n<p>Hence we find the roots:<br/>\\[\\begin{eqnarray} x&amp;=&amp; \\simplify{{n1-n4}/{2*a*b}}\\\\ x&amp;=&amp; \\simplify{{n1+n4}/{2*a*b}} \\end{eqnarray} \\]</p>\n<p><strong>Other Methods.</strong></p>\n<p>There are several methods of finding the roots &ndash; here are the main methods.</p>\n<p><strong>Finding the roots of a quadratic using the standard formula.</strong></p>\n<p>We can use the following formula for finding the roots of a general quadratic equation $ax^2+bx+c=0$</p>\n<p>The two roots are</p>\n<p>\\[ x = \\frac{-b +\\sqrt{b^2-4ac}}{2a}\\mbox{ and } x = \\frac{-b -\\sqrt{b^2-4ac}}{2a}\\]<br/>there are three main types of solutions depending upon the value of the discriminant $\\Delta=b^2-4ac$</p>\n<p>1. $\\Delta \\gt 0$. The roots are real and distinct</p>\n<p>2. $\\Delta=0$. The roots are real and equal. Their common value is $\\displaystyle -\\frac{b}{2a}$</p>\n<p>3. $\\Delta \\lt 0$. There are no real roots. The root are complex and form a complex conjugate pair.</p>\n<p>For this question the discriminant of $\\simplify{{a*b}x^2+{-b*c-a*d}x+{c*d}}$ is $\\Delta = \\simplify[std]{{-n1}^2-4*{a*b*c*d}}=\\var{disc}$</p>\n<p>{rdis}.</p>\n<p>So the {rep} roots are:</p>\n<p>\\[\\begin{eqnarray} x = \\frac{\\var{n1} - \\sqrt{\\var{disc}}}{\\var{n3}} &amp;=&amp; \\frac{\\var{n1} - \\var{n4} }{\\var{n3}} &amp;=&amp; \\simplify{{n1 - n4}/ {n3}}\\\\ x = \\frac{\\var{n1} + \\sqrt{\\var{disc}}}{\\var{n3}} &amp;=&amp; \\frac{\\var{n1} + \\var{n4} }{\\var{n3}} &amp;=&amp; \\simplify{{n1 + n4}/ {n3}} \\end{eqnarray}\\]</p>\n<p><strong>Completing the square.</strong></p>\n<p>First we complete the square for the quadratic expression $\\simplify{{a*b}x^2+{-n1}x+{c*d}}$<br/>\\[\\begin{eqnarray} \\simplify{{a*b}x^2+{-n1}x+{c*d}}&amp;=&amp;\\var{n5}\\left(\\simplify{x^2+({-n1}/{a*b})x+ {c*d}/{a*b}}\\right)\\\\ &amp;=&amp;\\var{n5}\\left(\\left(\\simplify{x+({-n1}/{2*a*b})}\\right)^2+ \\simplify{{c*d}/{a*b}-({-n1}/({2*a*b}))^2}\\right)\\\\ &amp;=&amp;\\var{n5}\\left(\\left(\\simplify{x+({-n1}/{2*a*b})}\\right)^2 -\\simplify{ {n2^2}/{4*(a*b)^2}}\\right) \\end{eqnarray} \\]<br/>So to solve $\\simplify{{a*b}x^2+{-n1}x+{c*d}}=0$ we have to solve:<br/>\\[\\begin{eqnarray} \\left(\\simplify{x+({-n1}/{2*a*b})}\\right)^2&amp;\\phantom{{}}&amp; -\\simplify{ {n2^2}/{4*(a*b)^2}}=0\\Rightarrow\\\\ \\left(\\simplify{x+({-n1}/{2*a*b})}\\right)^2&amp;\\phantom{{}}&amp;=\\simplify{ {n2^2}/{4*(a*b)^2}=({abs(n2)}/{2*a*b})^2} \\end{eqnarray}\\]<br/>So we get the two {rep} solutions:<br/>\\[\\begin{eqnarray} \\simplify{x+({-n1}/{2*a*b})}&amp;=&amp;\\simplify{-{abs(n2)}/{2*a*b}} \\Rightarrow &amp;x&amp; = \\simplify{({-abs(n2)+n1}/{2*a*b})}\\\\ \\simplify{x+({-n1}/{2*a*b})}&amp;=&amp;\\simplify{({abs(n2)}/{2*a*b})} \\Rightarrow &amp;x&amp; = \\simplify{({n1+abs(n2)}/{2*a*b})} \\end{eqnarray}\\]</p>", "rulesets": {"std": ["all", "!collectNumbers", "fractionNumbers", "!noLeadingMinus"]}, "parts": [{"stepsPenalty": 1, "prompt": "<p>Solve for $x$: &nbsp;\\[\\simplify[std]{{a*b} * x ^ 2 + ( {-b*c-a * d}) * x + {c * d}}=0\\]<br/>The least root is $x=\\;$ [[0]]. The greatest root is $x=\\;$ [[1]]</p>\n<p>You can get more information on solving a quadratic by clicking on Show steps. You will lose 1 mark if you do so.</p>\n<p>Enter the least root first. If the roots are equal, enter the root in both input boxes.</p>\n<p>Enter the roots as fractions or integers, not as decimals.</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "steps": [{"prompt": "\n          <p><strong>Finding the roots by factorisation.</strong></p>\n          <p>Finding a factorisation of a quadratic $q(x)=a(x-r)(x-s)$ where $a$ is the coefficient of $x^2$ gives the roots $x=r$, $x=s$ immendiately.</p>\n          <p>If you cannot find a factorisation then there are several other methods you can use.</p>\n          <p><strong>Using the formula for the roots.</strong></p>\n          <p>You can find the roots by using the formula for finding the roots of a general quadratic equation $ax^2+bx+c=0$</p>\n          <p>The two roots are:</p>\n          <p>\\[ x = \\frac{-b +\\sqrt{b^2-4ac}}{2a}\\mbox{ and } x = \\frac{-b -\\sqrt{b^2-4ac}}{2a}\\]<br/>there are three main types of solutions depending upon the value of the discriminant $\\Delta=b^2-4ac$</p>\n          <p>1. $\\Delta \\gt 0$. The roots are real and distinct</p>\n          <p>2. $\\Delta=0$. The roots are real and equal. Their value is $\\displaystyle \\frac{-b}{2a}$</p>\n          <p>3. $\\Delta \\lt 0$. There are no real roots. The root are complex and form a complex conjugate pair.</p>\n          <p>&nbsp;</p>\n          ", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "information"}], "gaps": [{"notallowed": {"message": "<p>Input numbers as fractions or integers not as a decimals.</p>", "showStrings": false, "strings": ["."], "partialCredit": 0}, "vsetrangepoints": 5, "expectedvariablenames": [], "checkingaccuracy": 0.0001, "vsetrange": [0, 1], "showpreview": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "answersimplification": "std", "scripts": {}, "answer": "{n1-n4}/{2*a*b}", "marks": 1, "checkvariablenames": false, "checkingtype": "absdiff", "type": "jme"}, {"notallowed": {"message": "<p>Input numbers as fractions or integers not as a decimals.</p>", "showStrings": false, "strings": ["."], "partialCredit": 0}, "vsetrangepoints": 5, "expectedvariablenames": [], "checkingaccuracy": 0.0001, "vsetrange": [0, 1], "showpreview": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "answersimplification": "std", "scripts": {}, "answer": "{n1+n4}/{2*a*b}", "marks": 1, "checkvariablenames": false, "checkingtype": "absdiff", "type": "jme"}], "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "gapfill"}], "statement": "<p>Find the roots of the following quadratic equation.</p>", "variable_groups": [], "variablesTest": {"maxRuns": 100, "condition": ""}, "variables": {"a": {"definition": "random(2..5)", "templateType": "anything", "group": "Ungrouped variables", "name": "a", "description": ""}, "c": {"definition": "c1*s3", "templateType": "anything", "group": "Ungrouped variables", "name": "c", "description": ""}, "b": {"definition": "random(1..4)", "templateType": "anything", "group": "Ungrouped variables", "name": "b", "description": ""}, "d": {"definition": "if((a*d1)^2=(b*c)^2, max(d1+1,random(1..5))*s3,d1*s3)", "templateType": "anything", "group": "Ungrouped variables", "name": "d", "description": ""}, "f": {"definition": "a*b", "templateType": "anything", "group": "Ungrouped variables", "name": "f", "description": ""}, "s3": {"definition": "random(1,-1)", "templateType": "anything", "group": "Ungrouped variables", "name": "s3", "description": ""}, "s2": {"definition": "random(1,-1)", "templateType": "anything", "group": "Ungrouped variables", "name": "s2", "description": ""}, "s1": {"definition": "random(1,-1)", "templateType": "anything", "group": "Ungrouped variables", "name": "s1", "description": ""}, "n5": {"definition": "a*b", "templateType": "anything", "group": "Ungrouped variables", "name": "n5", "description": ""}, "disc": {"definition": "(b*c+a*d)^2-4*a*b*c*d", "templateType": "anything", "group": "Ungrouped variables", "name": "disc", "description": ""}, "c1": {"definition": "switch(f=1, random(1..6),f=2,random(1,3,5,7,9),f=3,random(1,2,5,7,8),f=4,random(1,3,5,7,9),f=6, random(1,5,7,8),f=9,random(1,2,4,7,8),f=8,random(1,3,5,7,9),f=12,random(1,5,7),random(1,3,5,7))", "templateType": "anything", "group": "Ungrouped variables", "name": "c1", "description": ""}, "rep": {"definition": "switch(disc=0,'repeated', ' ')", "templateType": "anything", "group": "Ungrouped variables", "name": "rep", "description": ""}, "n1": {"definition": "b*c+a*d", "templateType": "anything", "group": "Ungrouped variables", "name": "n1", "description": ""}, "n2": {"definition": "b*c-a*d", "templateType": "anything", "group": "Ungrouped variables", "name": "n2", "description": ""}, "n3": {"definition": "2*a*b", "templateType": "anything", "group": "Ungrouped variables", "name": "n3", "description": ""}, "n4": {"definition": "abs(n2)", "templateType": "anything", "group": "Ungrouped variables", "name": "n4", "description": ""}, "rdis": {"definition": "switch(disc=0,'The discriminant is '+ 0+' and so we get two repeated roots in this case.',disc<0, 'There are no real roots.','The roots exist and are distinct. ')", "templateType": "anything", "group": "Ungrouped variables", "name": "rdis", "description": ""}, "d1": {"definition": "switch(f=1, random(1..6),f=2,random(1,3,5,7,9),f=3,random(1,2,5,7,8),f=4,random(1,3,5,7,9),f=6, random(1,5,7,8),f=9,random(1,2,4,7,8),f=8,random(1,3,5,7,9),f=12,random(1,5,7),random(1,3,5,7))", "templateType": "anything", "group": "Ungrouped variables", "name": "d1", "description": ""}}, "metadata": {"description": "<p>Solve for $x$: $\\displaystyle ax ^ 2 + bx + c=0$.</p>", "licence": "All rights reserved"}, "type": "question", "showQuestionGroupNames": false, "question_groups": [{"name": "", "pickingStrategy": "all-ordered", "pickQuestions": 0, "questions": []}]}], "pickQuestions": 0, "pickingStrategy": "all-ordered", "name": ""}], "shuffleQuestions": false, "duration": 0, "type": "exam", "contributors": [{"name": "Christian Lawson-Perfect", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/7/"}], "extensions": [], "custom_part_types": [], "resources": []}