// Numbas version: exam_results_page_options
{"name": "Intersezione di due rette nel piano cartesiano (soluzione analitica)", "extensions": ["geogebra"], "custom_part_types": [{"source": {"pk": 1, "author": {"name": "Christian Lawson-Perfect", "pk": 7}, "edit_page": "/part_type/1/edit"}, "name": "Yes/no", "short_name": "yes-no", "description": "<p>The student is shown two radio choices: \"Yes\" and \"No\". One of them is correct.</p>", "help_url": "", "input_widget": "radios", "input_options": {"correctAnswer": "if(eval(settings[\"correct_answer_expr\"]), 0, 1)", "hint": {"static": true, "value": ""}, "choices": {"static": true, "value": ["Yes", "No"]}}, "can_be_gap": true, "can_be_step": true, "marking_script": "mark:\nif(studentanswer=correct_answer,\n  correct(),\n  incorrect()\n)\n\ninterpreted_answer:\nstudentAnswer=0\n\ncorrect_answer:\nif(eval(settings[\"correct_answer_expr\"]),0,1)", "marking_notes": [{"name": "mark", "description": "This is the main marking note. It should award credit and provide feedback based on the student's answer.", "definition": "if(studentanswer=correct_answer,\n  correct(),\n  incorrect()\n)"}, {"name": "interpreted_answer", "description": "A value representing the student's answer to this part.", "definition": "studentAnswer=0"}, {"name": "correct_answer", "description": "", "definition": "if(eval(settings[\"correct_answer_expr\"]),0,1)"}], "settings": [{"name": "correct_answer_expr", "label": "Is the answer \"Yes\"?", "help_url": "", "hint": "An expression which evaluates to <code>true</code> or <code>false</code>.", "input_type": "mathematical_expression", "default_value": "true", "subvars": false}], "public_availability": "always", "published": true, "extensions": []}], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"name": "Intersezione di due rette nel piano cartesiano (soluzione analitica)", "tags": [], "metadata": {"description": "<p style=\"-webkit-user-select: auto;\">Risolvi per $x$ e $y$: &nbsp;\\[ \\begin{eqnarray} a_1x+b_1y&amp;=&amp;c_1\\\\&nbsp; &nbsp;a_2x+b_2y&amp;=&amp;c_2&nbsp;\\end{eqnarray} \\]</p>", "licence": "Creative Commons Attribution 4.0 International"}, "statement": "<p>Determina analiticamente le coordinate del punto di intersezione delle rette&nbsp; $r : \\, \\simplify[std]{{a}x+{b}y-{c}} = 0$ &nbsp;e &nbsp;$s : \\, \\simplify[std]{{a1}x+{b1}y-{c1}} = 0$.</p>\n<p>Inserisci le risposte come frazioni o numeri interi, non come numeri decimali.</p>", "advice": "<p style=\"text-align: justify;\">\\[ \\left\\lbrace \\begin{eqnarray} \\simplify[std]{{a}x+{b}y}&amp;=&amp;\\var{c}&amp;\\mbox{ ........(1)}\\\\ \\simplify[std]{{a1}x+{b1}y}&amp;=&amp;\\var{c1}&amp;\\mbox{ ........(2)} \\end{eqnarray} \\right. \\]<br/>Per risolvere per&nbsp;$x$ moltiplica l'equazione&nbsp;(1) per&nbsp;{this} e l'equazione (2) per&nbsp;{that}</p>\n<p style=\"text-align: justify;\">Ci&ograve; d&agrave;:<br/>\\[ \\left\\lbrace\\begin{eqnarray} \\simplify[std]{{a*this}x+{b*this}y}&amp;=&amp;\\var{this*c}&amp;\\mbox{ ........(3)}\\\\ \\simplify[std]{{a1*that}x+{b1*that}y}&amp;=&amp;\\var{that*c1}&amp;\\mbox{ ........(4)} \\end{eqnarray} \\right.\\] <br/>Ora&nbsp;{aort} (4) {fromorto} (3) per&nbsp;ottenere<br/>\\[\\simplify[std]{({a*this}+{s6*a1*that})x={this*c}+{s6*that*c1}}\\]<br/>Cos&igrave; otteniamo la soluzione per $x$:<br/>\\[x = \\simplify{{c*b1-b*c1}/{b1*a-a1*b}}\\]<br/>La sostituzione in una qualunque delle equazioni&nbsp;(1) e&nbsp;(2) d&agrave;:<br/>\\[y = \\simplify{{c*a1-a*c1}/{b*a1-a*b1}}\\]<br/>Puoi controllare che entrambe le soluzioni sono corrette vedendo che&nbsp;soddisfano entrambe le equazioni&nbsp;(1) e&nbsp;(2) attraverso la sostituzione di questi valori nelle equazioni.</p>", "rulesets": {"std": ["all", "!collectNumbers", "fractionNumbers", "!noLeadingMinus"]}, "extensions": ["geogebra"], 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"Risoluzione analitica", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>Fai i calcoli su un foglio e poi carica una foto utilizzando il bottone qui sotto.</p>\n<p style=\"text-align: justify;\">Contrassegna chiaramente il file in modo che sia attribuibile a te (per esempio chiamandolo il_mio_cognome.jpg)</p>\n<p style=\"text-align: justify;\"><em>N.B. Se compare una finestra di dialogo, clicca su \"Rimani sulla pagina\": si dovrebbe aprire comunque il link in un nuovo pannello.</em></p>\n<p style=\"text-align: center;\"><button class=\"btn btn-success\" onclick=\" window.open('https://www.dropbox.com/request/FjTqCcLa84e1QJolMi1m','_blank')\"> Carica i calcoli</button></p>\n<p>Hai caricato il file?</p>\n<p>[[0]]</p>", "stepsPenalty": "0", "steps": [{"type": "information", "useCustomName": true, "customName": "Sistema", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p style=\"text-align: justify;\">La richiesta &egrave; equivalente a quella di risolvere&nbsp;il seguente sistema lineare nelle variabili $x$ e&nbsp;$y$:</p>\n<p style=\"text-align: justify;\">\\[ \\left\\lbrace \\begin{eqnarray} \\simplify[std]{{a}x+{b}y}&amp;=&amp;\\var{c}\\\\ \\simplify[std]{{a1}x+{b1}y}&amp;=&amp;\\var{c1} \\end{eqnarray} \\right. \\]</p>"}], "gaps": [{"type": "yes-no", "useCustomName": true, "customName": "fileloaded", "marks": "2", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "settings": {"correct_answer_expr": "true"}}], "sortAnswers": true}, {"type": "gapfill", "useCustomName": true, "customName": "Soluzione", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>$x=\\phantom{{}}$[[0]]</p>\n<p>$y=\\phantom{{}}$[[1]]</p>\n<p>Inserisci le tue risposte in forma di numeri interi e frazioni, non numeri decimali.</p>", "gaps": [{"type": "jme", "useCustomName": true, "customName": "x", "marks": "0.5", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "answer": "{c*b1-b*c1}/{b1*a-a1*b}", "answerSimplification": "std", "showPreview": true, "checkingType": "absdiff", "checkingAccuracy": 0.001, "failureRate": 1, "vsetRangePoints": 5, "vsetRange": [0, 1], "checkVariableNames": false, "singleLetterVariables": false, "allowUnknownFunctions": true, "implicitFunctionComposition": false, "caseSensitive": false, "notallowed": {"strings": ["."], "showStrings": false, "partialCredit": 0, "message": "<p>Inserisci una&nbsp;frazione o un numero intero, non un&nbsp;numero decimale.</p>"}, "valuegenerators": []}, {"type": "jme", "useCustomName": true, "customName": "y", "marks": "0.5", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "answer": "{c*a1-a*c1}/{b*a1-a*b1}", "answerSimplification": "std", "showPreview": true, "checkingType": "absdiff", "checkingAccuracy": 0.001, "failureRate": 1, "vsetRangePoints": 5, "vsetRange": [0, 1], "checkVariableNames": false, "singleLetterVariables": false, "allowUnknownFunctions": true, "implicitFunctionComposition": false, "caseSensitive": false, "notallowed": {"strings": ["."], "showStrings": false, "partialCredit": 0, "message": "<p>Inserisci una&nbsp;frazione o un numero intero, non un&nbsp;numero decimale.</p>"}, "valuegenerators": []}], "sortAnswers": false}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always", "contributors": [{"name": "Newcastle University Mathematics and Statistics", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/697/"}, {"name": "Irene Paniccia", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/4869/"}]}]}], "contributors": [{"name": "Newcastle University Mathematics and Statistics", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/697/"}, {"name": "Irene Paniccia", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/4869/"}]}