// Numbas version: exam_results_page_options
{"name": "\u00dcbungen (Lektion 5)", "metadata": {"description": "<p>Grichische Antike 1</p>", "licence": "Creative Commons Attribution 4.0 International"}, "duration": 0, "percentPass": 0, "showQuestionGroupNames": false, "showstudentname": true, "question_groups": [{"name": "Group", "pickingStrategy": "all-ordered", "pickQuestions": 1, "questionNames": ["", "", ""], "questions": [{"name": "Achilles und die Schildkr\u00f6te", "extensions": [], "custom_part_types": [], "resources": [["question-resources/achilles-tortoise.svg", "/srv/numbas/media/question-resources/achilles-tortoise.svg"]], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Andreas Vohns", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/3622/"}], "tags": [], "metadata": {"description": "<p>Eine ganz olle Kamelle ; )</p>", "licence": "Creative Commons Attribution 4.0 International"}, "statement": "<p>Angenommen ein&nbsp;gesunder Achilles l&auml;uft {factor}-mal so schnell wie die Schildkr&ouml;te, der wir einen Vorsprung von {distance} Ellen geben.</p>\n<p style=\"text-align: center;\"><img src=\"resources/question-resources/achilles-tortoise.svg\"/></p>\n<p>Die Schildkr&ouml;te&nbsp;lege zudem eine Elle in {speed} Sekunden zur&uuml;ck.</p>", "advice": "<p>Wir ermitteln zun&auml;chst die <strong>Entfernung</strong> &uuml;ber die (unendliche) geometrische Reihe:</p>\n<p>$\\var{distance}\\cdot\\displaystyle\\sum_{k=0}^\\infty\\frac{1}{\\var{factor}}^k=\\frac{\\var{distance}}{1-\\frac{1}{\\var{factor}}}=\\var[fractionNumbers]{meet}=\\var[fractionNumbers,mixedFractions]{meet}\\approx\\var{meeta}$</p>\n<p>Die <strong>Zeit</strong> l&auml;sst sich nun entweder dadurch ermitteln, dass man diese Entfernung durch die Geschwindigkeit von Achilles ($\\frac{\\var{factor}}{\\var{speed}}$ Ellen pro Sekunde) dividiert:</p>\n<p>$\\var[fractionNumbers]{meet}:\\frac{\\var{factor}}{\\var{speed}}=\\var[fractionNumbers]{meet}\\cdot\\frac{\\var{speed}}{\\var{factor}}=\\var[fractionNumbers]{meet*speed/factor}=\\var[fractionNumbers,mixedFractions]{meet*speed/factor}\\approx=\\var{timea}$</p>\n<p>oder erneut &uuml;ber eine geometrische Reihe:</p>\n<p>$\\var[fractionNumbers]{distance/speed}\\cdot\\displaystyle\\sum_{k=0}^\\infty\\frac{1}{\\var{factor}}^k=\\frac{\\var[fractionNumbers]{distance/speed}}{1-\\frac{1}{\\var{factor}}}=\\var[fractionNumbers]{time}=\\var[fractionNumbers,mixedFractions]{time}\\approx\\var{timea}$</p>", "rulesets": {}, "variables": {"factor": {"name": "factor", "group": "Ungrouped variables", "definition": "random(2..6)*10", "description": "", "templateType": "anything"}, "distance": {"name": "distance", "group": "Ungrouped variables", "definition": "factor*10", "description": "", "templateType": "anything"}, "meet": {"name": "meet", "group": "Ungrouped variables", "definition": "distance/(1-1/factor)", "description": "", "templateType": "anything"}, "speed": {"name": "speed", "group": "Ungrouped variables", "definition": "10-random(3..7)", "description": "", "templateType": "anything"}, "time": {"name": "time", "group": "Ungrouped variables", "definition": "meet/((1/speed)*factor)", "description": "", "templateType": "anything"}, "meeta": {"name": "meeta", "group": "Ungrouped variables", "definition": "precround(meet,2)", "description": "", "templateType": "anything"}, "timea": {"name": "timea", "group": "Ungrouped variables", "definition": "precround(time,2)", "description": "", "templateType": "anything"}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["factor", "distance", "meet", "speed", "time", "meeta", "timea"], "variable_groups": [], "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>Achilles wird dann die Schildkr&ouml;te nach&nbsp;[[1]] Sekunden <br/>und einer Entfernung von&nbsp;[[0]] Ellen eingeholt haben.</p>\n<p><em>Beistrich (,) als Dezimaltrennzeichen verwenden!</em></p>", "gaps": [{"type": "numberentry", "useCustomName": true, "customName": "meeting", "marks": "2.5", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": false, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "{meeta}-0.005", "maxValue": "{meeta}+0.005", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "precisionType": "dp", "precision": "2", "precisionPartialCredit": 0, "precisionMessage": "You have not given your answer to the correct precision.", "strictPrecision": false, "showPrecisionHint": true, "notationStyles": ["eu", "plain-eu"], "correctAnswerStyle": "plain-eu"}, {"type": "numberentry", "useCustomName": true, "customName": "timer", "marks": "1.5", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": false, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "{timea}-0.005", "maxValue": "{timea}+0.005", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "precisionType": "dp", "precision": "2", "precisionPartialCredit": 0, "precisionMessage": "You have not given your answer to the correct precision.", "strictPrecision": false, "showPrecisionHint": true, "notationStyles": ["eu", "plain-eu"], "correctAnswerStyle": "plain-eu"}], "sortAnswers": false}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always"}, {"name": "Proportionen", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Andreas Vohns", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/3622/"}], "tags": [], "metadata": {"description": "<p>Zu Euklid Buch 5, Definition 5</p>", "licence": "Creative Commons Attribution 4.0 International"}, "statement": "<p>Gegeben sie die folgende Proportion:</p>\n<p style=\"text-align: center;\">$x:\\var{a}=\\var{b}:x$</p>\n<p><span style=\"margin: 0px auto; border: 2px dotted #000000; position: absolute; z-index: 2147483647; visibility: hidden; left: 1060px; width: 0px; top: 69px; height: 0px;\"></span><span style=\"z-index: 2147483647; position: absolute; visibility: hidden; left: 1045px; width: 50px; top: 54px; height: 20px; font-size: 10px; color: black;\"></span></p>", "advice": "<p>a) Aus&nbsp;$x:\\var{a}=\\var{b}:x$ folgt unmittelbar $x^2=\\var{square}$ und daraus&nbsp;$\\frac{\\sqrt{\\var{square}}}{\\var{a}}=\\frac{\\var{b}}{\\sqrt{\\var{square}}}\\approx\\var{ratio_approx}$ .</p>\n<p>b) Es ist&nbsp;$m\\cdot x=\\var{m}\\cdot\\sqrt{\\var{square}}\\approx\\var{m*root_approx}$,&nbsp;</p>\n<p>(i) soll $n\\cdot\\var{a}$ gr&ouml;&szlig;er als diese Zahl sein, so muss $n\\cdot \\var{a}&gt;\\var{m*root_approx}\\Leftrightarrow n&gt;\\var{m*root_approx/a}$ sein,</p>\n<p>(ii) soll $n\\cdot\\var{a}$&nbsp;kleiner&nbsp;als diese Zahl sein, so muss $n\\cdot\\var{a}&lt;\\var{m*root_approx}\\Leftrightarrow n&lt;\\var{m*root_approx/a}$ sein,</p>\n<p>die gesuchten nat&uuml;rlichen Zahlen sind daher $\\var{n_min}$ und $\\var{n_max}$.</p>", "rulesets": {}, "variables": {"a": {"name": "a", "group": "Ungrouped variables", "definition": "random(1..3)*2", "description": "", "templateType": "anything"}, "b": {"name": "b", "group": "Ungrouped variables", "definition": "(2*random(3..5)+1)", "description": "", "templateType": "anything"}, "square": {"name": "square", "group": "Ungrouped variables", "definition": "a*b", "description": "", "templateType": "anything"}, "root": {"name": "root", "group": "Ungrouped variables", "definition": "sqrt(square)", "description": "", "templateType": "anything"}, "ratio": {"name": "ratio", "group": "Ungrouped variables", "definition": "root/a", "description": "", "templateType": "anything"}, "root_approx": {"name": "root_approx", "group": "Ungrouped variables", "definition": "precround(root,3)", "description": "", "templateType": "anything"}, "ratio_approx": {"name": "ratio_approx", "group": "Ungrouped variables", "definition": "precround(ratio,3)", "description": "", "templateType": "anything"}, "m": {"name": "m", "group": "Ungrouped variables", "definition": "precround(1/ratio,1)*10", "description": "", "templateType": "anything"}, "n_max": {"name": "n_max", "group": "Ungrouped variables", "definition": "floor(m*ratio)", "description": "", "templateType": "anything"}, "n_min": {"name": "n_min", "group": "Ungrouped variables", "definition": "ceil(m*ratio)", "description": "", "templateType": "anything"}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["a", "b", "square", "root", "ratio", "root_approx", "ratio_approx", "m", "n_max", "n_min"], "variable_groups": [], "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>Ermitteln Sie durch algebraische Umformung:</p>\n<p>i) Den Wert von $x^2=$[[0]]</p>\n<p>ii) Den Wert der Proportion als Dezimalzahl:&nbsp;$\\frac{x}{\\var{a}}=\\frac{\\var{b}}{x}=$&nbsp;[[1]]</p>\n<p><em>Dezimaltrennzeichen ist der Beistrich (,).</em></p>", "gaps": [{"type": "numberentry", "useCustomName": true, "customName": "x2", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "{square}", "maxValue": "{square}", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "precisionType": "dp", "precision": 0, "precisionPartialCredit": 0, "precisionMessage": "You have not given your answer to the correct precision.", "strictPrecision": false, "showPrecisionHint": false, "notationStyles": ["eu", "plain-eu"], "correctAnswerStyle": "plain-eu"}, {"type": "numberentry", "useCustomName": true, "customName": "prop", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "{ratio_approx}-0.001", "maxValue": "{ratio_approx}+0.001", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "precisionType": "dp", "precision": "3", "precisionPartialCredit": 0, "precisionMessage": "You have not given your answer to the correct precision.", "strictPrecision": false, "showPrecisionHint": true, "notationStyles": ["eu", "plain-eu"], "correctAnswerStyle": "plain-eu"}], "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>Laut Eudoxos (gem&auml;&szlig; Elementen des Euklid, Buch V, Definition 5) muss es dann Zahlen $m,n\\in\\mathbb{N}$ geben, so dass</p>\n<p style=\"text-align: center;\">$(1)\\qquad m\\cdot x&lt;n\\cdot\\var{a}\\quad\\wedge\\quad m\\cdot\\var{b}&lt;n\\cdot x$</p>\n<p>bzw.</p>\n<p style=\"text-align: center;\">$(2)\\qquad m\\cdot x&gt;n\\cdot\\var{a}\\quad\\wedge\\quad m\\cdot\\var{b}&gt;n\\cdot x$</p>\n<p>gilt.&nbsp;</p>\n<p>Wir setzen nun $m=\\var{m}$.</p>\n<p>i) Ermitteln Sie die&nbsp;kleinste Zahl $n$, so dass der Fall $(1)$ eintritt: $\\quad n=$[[1]]</p>\n<p>ii) Ermitteln Sie die&nbsp;gr&ouml;&szlig;te Zahl $n$,&nbsp;so dass der Fall $(2)$ eintritt: $\\ \\,\\quad n=$[[0]]</p>\n<p><span style=\"margin: 0px auto; border: 2px dotted #000000; position: absolute; z-index: 2147483647; visibility: hidden; left: 638px; width: 0px; top: 133px; height: 0px;\"></span><span style=\"z-index: 2147483647; position: absolute; visibility: hidden; left: 623px; width: 50px; top: 118px; height: 20px; font-size: 10px; color: black;\"></span></p>", "gaps": [{"type": "numberentry", "useCustomName": true, "customName": "n1", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "{n_max}", "maxValue": "{n_max}", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "precisionType": "dp", "precision": 0, "precisionPartialCredit": 0, "precisionMessage": "You have not given your answer to the correct precision.", "strictPrecision": false, "showPrecisionHint": false, "notationStyles": ["eu", "plain-eu"], "correctAnswerStyle": "plain-eu"}, {"type": "numberentry", "useCustomName": true, "customName": "n2", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "{n_min}", "maxValue": "{n_min}", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "precisionType": "dp", "precision": 0, "precisionPartialCredit": 0, "precisionMessage": "You have not given your answer to the correct precision.", "strictPrecision": false, "showPrecisionHint": false, "notationStyles": ["eu", "plain-eu"], "correctAnswerStyle": "plain-eu"}], "sortAnswers": false}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always"}, {"name": "Winkeldreiteilung", "extensions": ["geogebra"], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Andreas Vohns", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/3622/"}], "tags": [], "metadata": {"description": "<p>Archimedische Winkeldreiteilung</p>", "licence": "Creative Commons Attribution 4.0 International"}, "statement": "<p>Gegeben ist der blaue Winkel $\\measuredangle EAB$ (bitte etwas Geduld beim Laden des Applets haben):</p>\n<p style=\"text-align: center;\">{app}</p>\n<p><span style=\"margin: 0px auto; border: 2px dotted #000000; position: absolute; z-index: 2147483647; visibility: hidden; left: 52px; width: 0px; top: 39px; height: 0px;\"></span><span style=\"z-index: 2147483647; position: absolute; visibility: hidden; left: 37px; width: 50px; top: 24px; height: 20px; font-size: 10px; color: black;\"></span></p>", "advice": "<p>L&ouml;sung:&nbsp;</p>\n<p>{app2}</p>\n<p>(Genaues Arbeiten ist erforderlich)</p>\n<p></p>", "rulesets": {}, "variables": {"defs": {"name": "defs", "group": "Ungrouped variables", "definition": "[['E',pe],['za',angle*pi/180]]", "description": "", "templateType": "anything"}, "pe": {"name": "pe", "group": "Ungrouped variables", "definition": "vector(radius,0)", "description": "", "templateType": "anything"}, "angle": {"name": "angle", "group": "Ungrouped variables", "definition": "3*random(15..25)", 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"angle", "app", "target_position", "radius", "app2", "defs2"], "variable_groups": [], "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>Ermitteln Sie gem&auml;&szlig; der Konstruktion des Archimedes den gedrittelten Winkel. Sie k&ouml;nnen den Punkt $D$ dazu verschrieben und mit Hilfe des Schiebereglers die auf dem Lineal abgetragene L&auml;nge $|\\overline{DC}|$ variieren.</p>\n<p>[[0]]</p>", "gaps": [{"type": "extension", "useCustomName": false, "customName": "", "marks": 1, "scripts": {"constructor": {"script": "this.marks=3", "order": "after"}}, "customMarkingAlgorithm": "g_pos (The position of the object A, as a vector):\n  value(app,\"G\")\n\nc_pos (The position of the object A, as a vector):\n  value(app,\"C\")\n\nzb:\n  value(app,\"zbv\")\n\nza:\n  value(app,\"zav\")\n\nmark:\n  if(value(app,\"L\")=radius,add_credit(1/6,\"Markierung am Lineal korrekt.\"),negative_feedback(\"Markierung am Lineal falsch.\"));  \n  if(precround(g_pos,1)=precround(c_pos,1),add_credit(2/6,\"Punkt C korrekt platziert.\"),negative_feedback(\"Punkt C ungenau/nicht richtig platiert.\"));\n  if(abs(precround(zb*3,1)-precround(za,1))<0.15,add_credit(3/6,\"Winkel korrekt ermittelt.\"),negative_feedback(\"Winkel ungenau/nicht korrekt ermittelt.\"))\n  \ninterpreted_answer:\n  zb", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null}], "sortAnswers": false}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always"}]}], "allowPrinting": true, "navigation": {"allowregen": false, "reverse": true, "browse": true, "allowsteps": true, "showfrontpage": false, "showresultspage": "oncompletion", "navigatemode": "menu", "onleave": {"action": "none", "message": ""}, "preventleave": true, "startpassword": ""}, "timing": {"allowPause": true, "timeout": {"action": "none", "message": ""}, "timedwarning": {"action": "none", "message": ""}}, "feedback": {"showactualmark": true, "showtotalmark": true, "showanswerstate": true, "allowrevealanswer": true, "advicethreshold": 0, "intro": "", "reviewshowscore": true, "reviewshowfeedback": true, "reviewshowexpectedanswer": true, "reviewshowadvice": true, "feedbackmessages": []}, "contributors": [{"name": "Andreas Vohns", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/3622/"}], "extensions": ["geogebra"], "custom_part_types": [], "resources": [["question-resources/achilles-tortoise.svg", "/srv/numbas/media/question-resources/achilles-tortoise.svg"]]}