// Numbas version: finer_feedback_settings
{"name": "Geradengleichungen", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"name": "Geradengleichungen", "tags": [], "metadata": {"description": "<p>Find the equation of a straight line which has a given gradient $m$ and passes through the given point $(a,b)$.</p>\n<p>Original: https://numbas.mathcentre.ac.uk/question/11698/equation-of-a-straight-line/ by Newcastle University Mathematics and Statistics,</p>\n<p>translated to German, added Parts b), c), d), e)</p>", "licence": "Creative Commons Attribution 4.0 International"}, "statement": "<p>Verschiedene Fragen zu Geradengleichungen.</p>", "advice": "<p><strong>a)</strong></p>\n<p>Die Geradengleichung hat die Form $y=mx+b$.</p>\n<p>Dabei ist $m$ die Steigung. Wir k&ouml;nnen $b$ (den \"$y$-Achenabschnitt\") ausrechnen, indem wir ausnutzen, dass der Punkt mit Koordinaten $x=\\var{a}$ und $y=\\var{b}$ auf der Geraden liegt, dass also diese Werte f&uuml;r $x$ und $y$ die Geradengleichung erf&uuml;llen m&uuml;ssen.</p>\n<p>Wir erhalten (hier wird $\\times$ statt $\\cdot$ f&uuml;r die Multiplikation geschrieben):<br/>\\[ \\begin{eqnarray} \\var{b}&amp;=&amp;\\simplify[std]{({b-d}/{a-c}){a}+b} \\Rightarrow\\\\ b&amp;=&amp;\\simplify[std]{{b}-({b-d}/{a-c}){a}={(b*c-a*d)}/{(c-a)}} \\end{eqnarray} \\]</p>\n<p>Die Geradengleichung ist mithin<br/>\\[y = \\simplify[std]{({b-d}/{a-c})x+{b*c-a*d}/{c-a}}\\]</p>\n<p></p>\n<p>b)</p>\n<p>Die Geradengleichung hat die Form $y=mx+b$. Dass $P_1$ und $P_2$ beide auf der Geraden liegen, bedeutet, dass</p>\n<p>\\[\\begin{align} \\var{bp1x} m + b &amp; = \\var{bp1y}\\\\ \\var{bp2x} m + b &amp; = \\var{bp2y}\\end{align}\\]</p>\n<p>Wenn wir die beiden Gleichungen voneinander abziehen und nach $m$ aufl&ouml;sen, erhalten wir</p>\n<p>\\[ m = \\frac{\\simplify[basic]{{bp2y}-{bp1y}}}{\\simplify[basic]{{bp2x}-{bp1x}}} = \\simplify{({bp2y}-{bp1y})/({bp2x}-{bp1x})}. \\]</p>\n<p>Dies k&ouml;nnen wir in die erste Gleichung einsetzen, um $b$ auszurechnen. Das Ergebnis ist</p>\n<p>\\[ y = \\simplify[std]{{bm}*x+{bb}}.\\]</p>\n<p></p>\n<p><strong>c)</strong></p>\n<p>F&uuml;r die gesuchten Koordinaten $x$ und $y$ m&uuml;ssen beide Geradengleichungen erf&uuml;llt sein, es gilt also</p>\n<p>\\[\\simplify[std]{{cm1} x + {cb1}} = y = \\simplify[std]{{cm2} x + {cb2}}.\\]</p>\n<p>Diese Gleichung k&ouml;nnen wir nach $x$ aufl&ouml;sen und erhalten</p>\n<p>\\[ x = \\simplify[std]{{(cb1-cb2)/(cm2-cm1)}}\\quad\\text{und}\\quad y = \\simplify[std]{{(cb1-cb2)/(cm2-cm1)*cm1+cb1}}.\\]</p>\n<p></p>\n<p><strong>d)</strong></p>\n<p>Zuerst stellen wir wie in Teil b) die Geradengleichungen f&uuml;r $g$ und $h$ auf:</p>\n<p>\\[ g\\colon y = \\simplify[std]{{dmg} x + {dbg}},\\]</p>\n<p>\\[ h\\colon y = \\simplify[std]{{dmh} x + {dbh}}.\\]</p>\n<p>Dann k&ouml;nnen wir mit demselben Vorgehen wie in Teil c) den Schnittpunkt dieser beiden Geraden berechnen. Das Ergebnis ist der Punkt</p>\n<p>\\[\\left(\\simplify[std]{{dx}}, \\simplify[std]{{dy}}\\right).\\]</p>\n<p></p>\n<p>e)</p>\n<p>Die Geradengleichung f&uuml;r die Gerade durch $P_1$ und $P_2$ ist</p>\n<p>\\[ y = \\simplify[std]{{em}x+{eb}}. \\]</p>\n<p>F&uuml;r die Koordinaten des Schnittpunkts gilt also $y = \\simplify[std]{{em}x+{eb}}$ und $x=\\var{ea}$, der Schnittpunkt ist folglich $(\\var{ea}, \\simplify[std]{{em*ea+eb}})$.</p>\n<p><em>Bemerkung:</em> Die Gerade, die durch die Gleichung $x=\\var{ea}$ ist eine senkrechte Gerade. Diese Gerade ist nicht der Funktionsgraph einer linearen Funktion, und die Gerade l&auml;sst sich daher nicht durch eine Gleichung der Form $y=mx+b$ beschreiben.</p>", "rulesets": {"std": ["all", "!collectNumbers", "!noLeadingMinus", "fractionNumbers", "!collectLikeFractions"]}, "extensions": [], "variables": {"s1": {"name": "s1", "group": "Ungrouped variables", "definition": "random(-1,1)", "description": "", "templateType": "anything"}, "b": {"name": "b", "group": "Ungrouped variables", "definition": "if(b1=d,b1+random(1..3),b1)", "description": "", "templateType": "anything"}, "c": {"name": "c", "group": "Ungrouped variables", "definition": "a+Random(1..4)*s1", "description": "", "templateType": "anything"}, "f": {"name": "f", "group": "Ungrouped variables", "definition": "(b-d)/(a-c)", "description": "", "templateType": "anything"}, "b1": {"name": "b1", "group": "Ungrouped variables", "definition": "random(-9..9)", "description": "", "templateType": "anything"}, "d": {"name": "d", "group": "Ungrouped variables", "definition": "random(-9..9)", "description": "", "templateType": "anything"}, "g": {"name": "g", "group": "Ungrouped variables", "definition": "(b*c-a*d)/(c-a)", "description": "", "templateType": "anything"}, "a": {"name": "a", "group": "Ungrouped variables", "definition": "random(1,-1)*random(1..4)", "description": "", "templateType": "anything"}, "bp1x": {"name": "bp1x", "group": "Part b)", "definition": "random(-3..3)", "description": "", "templateType": "anything"}, "bp1y": {"name": "bp1y", "group": "Part b)", "definition": "random(-3..3)", "description": "", "templateType": "anything"}, "bp2x": {"name": "bp2x", "group": "Part b)", "definition": "random(-3..3 except bp1x)", "description": "", "templateType": "anything"}, "bp2y": {"name": "bp2y", "group": "Part b)", "definition": "random(-3..3)", "description": "", "templateType": "anything"}, "cm1": {"name": "cm1", "group": "Part c)", "definition": "random(-4..4)", "description": "", "templateType": "anything"}, "cb1": {"name": "cb1", "group": "Part c)", "definition": "random(-2..4)", "description": "", "templateType": "anything"}, "cm2": {"name": "cm2", "group": "Part c)", "definition": "random(-5..3 except cm1)", "description": "", "templateType": "anything"}, "cb2": {"name": "cb2", "group": "Part c)", "definition": "random(-3..5)", "description": "", "templateType": "anything"}, "bm": {"name": "bm", "group": "Part b)", "definition": "({bp2y}-{bp1y})/({bp2x}-{bp1x})", "description": "", "templateType": "anything"}, "bb": {"name": "bb", "group": "Part b)", "definition": "(bp1y-(bp2y-bp1y)/(bp2x-bp1x)*bp1x)", "description": "", "templateType": "anything"}, "dp1x": {"name": "dp1x", "group": "Part d)", "definition": "random(-5..5)", "description": "", "templateType": "anything"}, "dp1y": {"name": "dp1y", "group": "Part d)", "definition": "random(-5..5)", "description": "", "templateType": "anything"}, "dp2x": {"name": "dp2x", "group": "Part d)", "definition": "random(-5..5 except dp1x)", "description": "", "templateType": "anything"}, "dp2y": {"name": "dp2y", "group": "Part d)", "definition": "random(-5..5)", "description": "", "templateType": "anything"}, "dmg": {"name": "dmg", "group": "Part d)", "definition": "(dp2y-dp1y)/(dp2x-dp1x)", "description": "", "templateType": "anything"}, "dp3x": {"name": "dp3x", "group": "Part d)", "definition": "random(-5..5)", "description": "", "templateType": "anything"}, "dp3y": {"name": "dp3y", "group": "Part d)", "definition": "random(-5..5)", "description": "", "templateType": "anything"}, "dp4x": {"name": "dp4x", "group": "Part d)", "definition": "random(-5..5 except dp3x)", "description": "", "templateType": "anything"}, "dp4y": {"name": "dp4y", "group": "Part d)", "definition": "random(5..5)", "description": "", "templateType": "anything"}, "dmh": {"name": "dmh", "group": "Part d)", "definition": "(dp4y-dp3y)/(dp4x-dp3x)", "description": "", "templateType": "anything"}, "dbg": {"name": "dbg", "group": "Part d)", "definition": "dp1y - dmg*dp1x", "description": "", "templateType": "anything"}, "dbh": {"name": "dbh", "group": "Part d)", "definition": "dp3y - dmh*dp3x", "description": "", "templateType": "anything"}, "dx": {"name": "dx", "group": "Part d)", "definition": "(dbh-dbg)/(dmg-dmh)", "description": "", "templateType": "anything"}, "dy": {"name": "dy", "group": "Part d)", "definition": "dmg*dx+dbg", "description": "", "templateType": "anything"}, "ea": {"name": "ea", "group": "Part e)", "definition": "random(-4..4)", "description": "", "templateType": "anything"}, "em": {"name": "em", "group": "Part e)", "definition": "(ep2y-ep1y)/(ep2x-ep1x)", "description": "", "templateType": "anything"}, "ep1x": {"name": "ep1x", "group": "Part e)", "definition": "random(-5..5)", "description": "", "templateType": "anything"}, "ep1y": {"name": "ep1y", "group": "Part e)", "definition": "random(-5..5)", "description": "", "templateType": "anything"}, "ep2x": {"name": "ep2x", "group": "Part e)", "definition": "random(-5..5 except ep1x)", "description": "", "templateType": "anything"}, "ep2y": {"name": "ep2y", "group": "Part e)", "definition": "random(-5..5)", "description": "", "templateType": "anything"}, "eb": {"name": "eb", "group": "Part e)", "definition": "ep1y-em*ep1x", "description": "", "templateType": "anything"}}, "variablesTest": {"condition": "!(dmg=dmh)", "maxRuns": 100}, "ungrouped_variables": ["a", "c", "b", "d", "g", "f", "s1", "b1"], "variable_groups": [{"name": "Part b)", "variables": ["bp1x", "bp1y", "bp2x", "bp2y", "bm", "bb"]}, {"name": "Part c)", "variables": ["cm1", "cb1", "cm2", "cb2"]}, {"name": "Part d)", "variables": ["dp1x", "dp1y", "dp2x", "dp2y", "dmg", "dp3x", "dp3y", "dp4x", "dp4y", "dmh", "dbg", "dbh", "dx", "dy"]}, {"name": "Part e)", "variables": ["ea", "em", "ep1x", "ep1y", "ep2x", "ep2y", "eb"]}], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "gapfill", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>Geben Sie die Gleichung der Geraden mit</p>\n<ul>\n<li>Steigung $\\displaystyle \\simplify{{b-d}/{a-c}}$,</li>\n</ul>\n<p>&nbsp;</p>\n<ul>\n<li>die durch den Punkt $(\\var{a},\\var{b})$ geht, an.</li>\n</ul>\n<p>&nbsp;</p>\n<p>Geben Sie Ihre Antwort in der Form $y=mx+b$ f&uuml;r geeignete Werte von $m$ und $b$ an.</p>\n<p>Geben Sie $m$ und $b$ als Bruchzahlen oder als ganze Zahlen an.</p>\n<p>F&uuml;r einen Hinweis klicken Sie <em>Zeige Tipps</em> (es wird 1 Punkt abgezogen).</p>\n<p></p>\n<p>$y=\\;\\phantom{{}}$[[0]]</p>", "stepsPenalty": 1, "steps": [{"type": "information", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>Die Geradengleichung hat die Form $y=mx+b$.</p>\n<p>Dabei ist $m$ die Steigung. Sie k&ouml;nnen $b$ (den \"$y$-Achenabschnitt\") ausrechnen, indem Sie ausnutzen, dass der Punkt mit Koordinaten $x=\\var{a}$ und $y=\\var{b}$ auf der Geraden liegt, dass also diese Werte f&uuml;r $x$ und $y$ die Geradengleichung erf&uuml;llen m&uuml;ssen.</p>"}], "gaps": [{"type": "jme", "useCustomName": false, "customName": "", "marks": 2, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "answer": "({b-d}/{a-c})x+{b*c-a*d}/{c-a}", "answerSimplification": "std", "showPreview": true, "checkingType": "absdiff", "checkingAccuracy": 0.001, "failureRate": 1, "vsetRangePoints": 5, "vsetRange": [0, 1], "checkVariableNames": false, "singleLetterVariables": false, "allowUnknownFunctions": true, "implicitFunctionComposition": false, "notallowed": {"strings": ["."], "showStrings": false, "partialCredit": 0, "message": "Geben Sie die Zahlen als Bruchzahlen (oder ganze Zahlen) an, nicht als Dezimalzahlen."}, "valuegenerators": [{"name": "x", "value": ""}]}], "sortAnswers": false}, {"type": "gapfill", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>Geben Sie die Gleichung der Geraden durch die beiden folgenden Punkte an: $P_1 = (\\var{bp1x}, \\var{bp1y})$, $P_2 = (\\var{bp2x}, \\var{bp2y})$.</p>\n<p>$y=\\;\\phantom{{}}$[[0]]</p>", "gaps": [{"type": "jme", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "answer": "{(bp2y-bp1y)/(bp2x-bp1x)}*x+{bp1y-(bp2y-bp1y)/(bp2x-bp1x)*bp1x}", "answerSimplification": "std", "showPreview": false, "checkingType": "absdiff", "checkingAccuracy": 0.001, "failureRate": 1, "vsetRangePoints": 5, "vsetRange": [0, 1], "checkVariableNames": false, "singleLetterVariables": false, "allowUnknownFunctions": true, "implicitFunctionComposition": false, "notallowed": {"strings": ["."], "showStrings": false, "partialCredit": 0, "message": ""}, "valuegenerators": [{"name": "x", "value": ""}]}], "sortAnswers": false}, {"type": "gapfill", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>Geben Sie den Schnittpunkt $(x,y)$ der folgenden beiden Geraden an:</p>\n<p>$g\\colon y=\\simplify[std]{ {cm1}*x + {cb1}}$, $h\\colon y=\\simplify[std]{ {cm2}*x + {cb2}}$.</p>\n<p>$x=$ [[0]]</p>\n<p>$y=$ [[1]]</p>", "gaps": [{"type": "numberentry", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "{(cb1-cb2)/(cm2-cm1)}", "maxValue": "{(cb1-cb2)/(cm2-cm1)}", "correctAnswerFraction": true, "allowFractions": true, "mustBeReduced": true, "mustBeReducedPC": 0, "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}, {"type": "numberentry", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "{(cb1-cb2)/(cm2-cm1)*cm1+cb1}", "maxValue": "{(cb1-cb2)/(cm2-cm1)*cm1+cb1}", "correctAnswerFraction": true, "allowFractions": true, "mustBeReduced": true, "mustBeReducedPC": 0, "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}], "sortAnswers": false}, {"type": "gapfill", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>Sei $g$ die Gerade durch die Punkt $P_1 = (\\var{dp1x}, \\var{dp1y})$ und $P_2=(\\var{dp2x}, \\var{dp2y})$, und sei $h$ die Gerade durch die Punkte $P_3 = (\\var{dp3x}, \\var{dp3y})$ und $P_4 = (\\var{dp4x}, \\var{dp4y})$. Geben Sie den Schnittpunkt $(x, y)$ von $g$ und $h$ an.</p>\n<p>$x=$ [[0]]</p>\n<p>$y=$ [[1]]</p>", "stepsPenalty": "2", "steps": [{"type": "information", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>Die Geradengleichungen f&uuml;r $g$ und $h$ sind</p>\n<p>\\[ g\\colon y = \\simplify[std]{{dmg} x + {dbg}},\\]</p>\n<p>\\[ h\\colon y = \\simplify[std]{{dmh} x + {dbh}}.\\]</p>"}], "gaps": [{"type": "numberentry", "useCustomName": false, "customName": "", "marks": "2", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "{dx}", "maxValue": "{dx}", "correctAnswerFraction": true, "allowFractions": true, "mustBeReduced": true, "mustBeReducedPC": 0, "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}, {"type": "numberentry", "useCustomName": false, "customName": "", "marks": "2", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "{dy}", "maxValue": "{dy}", "correctAnswerFraction": true, "allowFractions": true, "mustBeReduced": true, "mustBeReducedPC": 0, "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}], "sortAnswers": false}, {"type": "gapfill", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>Geben Sie den Schnittpunkt $(x,y)$ der Geraden $g$ durch die Punkte $P_1 = (\\var{ep1x}, \\var{ep1y})$ und $P_2=(\\var{ep2x}, \\var{ep2y})$ mit der Geraden $x=\\var{ea}$ an.</p>\n<p>$x=$ [[0]]</p>\n<p>$y=$ [[1]]</p>", "stepsPenalty": "1", "steps": [{"type": "information", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>Die Geradengleichung f&uuml;r die Gerade durch $P_1$ und $P_2$ ist</p>\n<p>\\[y = \\simplify[std]{{em}*x+{eb}}.\\]</p>"}], "gaps": [{"type": "numberentry", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "{ea}", "maxValue": "{ea}", "correctAnswerFraction": true, "allowFractions": true, "mustBeReduced": true, "mustBeReducedPC": 0, "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}, {"type": "numberentry", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "{em*ea+eb}", "maxValue": "{em*ea+eb}", "correctAnswerFraction": true, "allowFractions": true, "mustBeReduced": true, "mustBeReducedPC": 0, "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}], "sortAnswers": false}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always", "type": "question", "contributors": [{"name": "Newcastle University Mathematics and Statistics", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/697/"}, {"name": "Ulrich G\u00f6rtz", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/7603/"}]}]}], "contributors": [{"name": "Newcastle University Mathematics and Statistics", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/697/"}, {"name": "Ulrich G\u00f6rtz", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/7603/"}]}