// Numbas version: exam_results_page_options
{"name": "Centroid of a composite area: rectangles and triangles", "extensions": ["geogebra", "quantities"], "custom_part_types": [{"source": {"pk": 19, "author": {"name": "William Haynes", "pk": 2530}, "edit_page": "/part_type/19/edit"}, "name": "Engineering Accuracy with units", "short_name": "engineering-answer", "description": "<p>A value with units marked right if within an adjustable % error of the correct value. &nbsp;Marked close if within a wider margin of error.</p>", "help_url": "", "input_widget": "string", "input_options": {"correctAnswer": "siground(settings['correctAnswer'],4)", "hint": {"static": true, "value": ""}, "allowEmpty": {"static": true, "value": true}}, "can_be_gap": true, "can_be_step": true, "marking_script": "mark:\nswitch( \n  right and good_units and right_sign, add_credit(1.0,'Correct.'),\n  right and good_units and not right_sign, add_credit(settings['C2'],'Wrong sign.'),\n  right and right_sign and not good_units, add_credit(settings['C2'],'Correct value, but wrong or missing units.'),\n  close and good_units, add_credit(settings['C1'],'Close.'),\n  close and not good_units, add_credit(settings['C3'],'Answer is close, but wrong or missing units.'),\n  incorrect('Wrong answer.')\n)\n\n\ninterpreted_answer:\nqty(student_scalar, student_units)\n\n\n\ncorrect_quantity:\nsettings[\"correctAnswer\"]\n\n\n\ncorrect_units:\nunits(correct_quantity)\n\n\nallowed_notation_styles:\n[\"plain\",\"en\"]\n\nmatch_student_number:\nmatchnumber(studentAnswer,allowed_notation_styles)\n\nstudent_scalar:\nmatch_student_number[1]\n\nstudent_units:\nreplace_regex('ohms','ohm',\n  replace_regex('\u00b0', ' deg',\n    replace_regex('-', ' ' ,\n      studentAnswer[len(match_student_number[0])..len(studentAnswer)])),\"i\")\n\ngood_units:\ntry(\ncompatible(quantity(1, student_units),correct_units),\nmsg,\nfeedback(msg);false)\n\n\nstudent_quantity:\nswitch(not good_units, \n       student_scalar * correct_units, \n       not right_sign,\n       -quantity(student_scalar, student_units),\n       quantity(student_scalar,student_units)\n)\n  \n\n\npercent_error:\ntry(\nscalar(abs((correct_quantity - student_quantity)/correct_quantity))*100  \n,msg,\nif(student_quantity=correct_quantity,0,100))\n   \n\nright:\npercent_error <= settings['right']\n\n\nclose:\nright_sign and percent_error <= settings['close']\n\nright_sign:\nsign(student_scalar) = sign(correct_quantity)", "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": "switch( \n  right and good_units and right_sign, add_credit(1.0,'Correct.'),\n  right and good_units and not right_sign, add_credit(settings['C2'],'Wrong sign.'),\n  right and right_sign and not good_units, add_credit(settings['C2'],'Correct value, but wrong or missing units.'),\n  close and good_units, add_credit(settings['C1'],'Close.'),\n  close and not good_units, add_credit(settings['C3'],'Answer is close, but wrong or missing units.'),\n  incorrect('Wrong answer.')\n)\n"}, {"name": "interpreted_answer", "description": "A value representing the student's answer to this part.", "definition": "qty(student_scalar, student_units)\n\n"}, {"name": "correct_quantity", "description": "", "definition": "settings[\"correctAnswer\"]\n\n"}, {"name": "correct_units", "description": "", "definition": "units(correct_quantity)\n"}, {"name": "allowed_notation_styles", "description": "", "definition": "[\"plain\",\"en\"]"}, {"name": "match_student_number", "description": "", "definition": "matchnumber(studentAnswer,allowed_notation_styles)"}, {"name": "student_scalar", "description": "", "definition": "match_student_number[1]"}, {"name": "student_units", "description": "<p>Modify&nbsp;the&nbsp;unit portion of&nbsp;the student's answer by</p>\n<p>1. replacing \"ohms\" with \"ohm\" &nbsp;case insensitive</p>\n<p>2.&nbsp;replacing '-'&nbsp;with ' '&nbsp;</p>\n<p>3. replacing '&deg;' with ' deg'&nbsp;</p>\n<p>to allow answers like 10 ft-lb and 30&deg;</p>", "definition": "replace_regex('ohms','ohm',\n  replace_regex('\u00b0', ' deg',\n    replace_regex('-', ' ' ,\n      studentAnswer[len(match_student_number[0])..len(studentAnswer)])),\"i\")"}, {"name": "good_units", "description": "", "definition": "try(\ncompatible(quantity(1, student_units),correct_units),\nmsg,\nfeedback(msg);false)\n"}, {"name": "student_quantity", "description": "<p>This fixes the student answer for two common errors. &nbsp;</p>\n<p>If student_units are wrong&nbsp;&nbsp;- replace with correct units</p>\n<p>If student_scalar has the wrong sign - replace with right sign</p>\n<p>If student makes both errors, only one gets fixed.</p>", "definition": "switch(not good_units, \n       student_scalar * correct_units, \n       not right_sign,\n       -quantity(student_scalar, student_units),\n       quantity(student_scalar,student_units)\n)\n  \n"}, {"name": "percent_error", "description": "", "definition": "try(\nscalar(abs((correct_quantity - student_quantity)/correct_quantity))*100  \n,msg,\nif(student_quantity=correct_quantity,0,100))\n   "}, {"name": "right", "description": "", "definition": "percent_error <= settings['right']\n"}, {"name": "close", "description": "<p>Only marked close if the student actually has the right sign.</p>", "definition": "right_sign and percent_error <= settings['close']"}, {"name": "right_sign", "description": "", "definition": "sign(student_scalar) = sign(correct_quantity) "}], "settings": [{"name": "correctAnswer", "label": "Correct Quantity.", "help_url": "", "hint": "The correct answer given as a JME quantity.", "input_type": "code", "default_value": "", "evaluate": true}, {"name": "right", "label": "% Accuracy for right.", "help_url": "", "hint": "Question will be considered correct if the scalar part of the student's answer is within this % of correct value.", "input_type": "code", "default_value": "0.2", "evaluate": true}, {"name": "close", "label": "% Accuracy for close.", "help_url": "", "hint": "Question will be considered close if the scalar part of the student's answer is within this % of correct value.", "input_type": "code", "default_value": "1.0", "evaluate": true}, {"name": "C1", "label": "Close with units.", "help_url": "", "hint": "Partial Credit for close value with appropriate units. &nbsp;if correct answer is 100 N and close is &plusmn;1%,<br />99 &nbsp;N is accepted.", "input_type": "percent", "default_value": "75"}, {"name": "C2", "label": "No units or wrong sign", "help_url": "", "hint": "Partial credit for forgetting units or using wrong sign.<br />If the correct answer is 100 N, both 100 and -100 N are accepted.", "input_type": "percent", "default_value": "50"}, {"name": "C3", "label": "Close, no units.", "help_url": "", "hint": "Partial Credit for close value but forgotten units.<br />This value would be close&nbsp;if the expected units were provided. &nbsp;If the correct answer is 100 N, and close is &plusmn;1%,<br />99 is accepted.", "input_type": "percent", "default_value": "25"}], "public_availability": "always", "published": true, "extensions": ["quantities"]}], "resources": [["question-resources/centroid-t-r.ggb", "/srv/numbas/media/question-resources/centroid-t-r.ggb"]], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"name": "Centroid of a composite area: rectangles and triangles", "tags": ["centroids", "first moment of area", "mechanics", "Mechanics", "statics", "Statics"], "metadata": {"description": "<p>Find the centroid of a shape made up of a rectangle and two triangles.</p>", "licence": "Creative Commons Attribution-NonCommercial 4.0 International"}, "statement": "<p>{applet()}</p>\n<p>Determine the coordinates of the centroid of the polygon shown. &nbsp;Grid units are [{units}].</p>\n<p>Consider the polygon to be made up of a ({b0} $\\times$&nbsp;{h0}) rectangle {sign1} a ({b1} $\\times$&nbsp;{h1}) triangle {sign2} a ({b2} $\\times$&nbsp;{h2}) triangle.</p>", "advice": "<div>\n<table border=\"1px\" style=\"float: left;\">\n<tbody>\n<tr>\n<td>Part</td>\n<td>$A_i$</td>\n<td>$\\bar{x}_i$</td>\n<td>$\\bar{y}_i$</td>\n<td>$A_i\\bar{x}_i$</td>\n<td>$A_i\\bar{y}_i$</td>\n</tr>\n<tr>\n<td>Rectangle</td>\n<td>{A0}</td>\n<td>{bar(C0[0])}</td>\n<td>{bar(C0[1])}</td>\n<td>{Q(a0, c0[0])}</td>\n<td>{Q(a0, c0[1])}</td>\n</tr>\n<tr>\n<td>Triangle 1</td>\n<td>{A1}</td>\n<td>{bar(C1[0])}</td>\n<td>{bar(C1[1])}</td>\n<td>{Q(a1, c1[0])}</td>\n<td>{Q(a1, c1[1])}</td>\n</tr>\n<tr>\n<td>Triangle 2</td>\n<td>{A2}</td>\n<td>{bar(C2[0])}</td>\n<td>{bar(C2[1])}</td>\n<td>{Q(a2, c2[0])}</td>\n<td>{Q(a2, c2[1])}</td>\n</tr>\n<tr>\n<td>$\\Sigma$</td>\n<td>{AT}</td>\n<td></td>\n<td></td>\n<td>{display(xbar AT)}</td>\n<td>{display(ybar AT)}</td>\n</tr>\n</tbody>\n</table>\n</div>\n<div>\n<p>$\\qquad\\bar{x} = \\dfrac{\\Sigma A_i\\bar{x}_i}{\\Sigma A_i} = &nbsp;\\var{display(xbar)}$</p>\n<p>$\\qquad \\bar{y} = &nbsp;\\dfrac{\\Sigma A_i\\bar{y}_i}{\\Sigma A_i} &nbsp;=\\var{display(ybar)}$</p>\n</div>", "rulesets": {}, "extensions": ["geogebra", "quantities"], "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true}, "constants": [], "variables": {"A": {"name": "A", "group": "Ungrouped variables", "definition": "vector(0,random(2..12))", "description": "", "templateType": "anything", "can_override": false}, "C2": {"name": "C2", "group": "geometry", "definition": "vector(A[0],B[1])+(vector(B[0],A[1])-vector(A[0],B[1]))/3  ", "description": "", "templateType": "anything", "can_override": false}, "A0": {"name": "A0", "group": "geometry", "definition": "b0 h0", "description": "", "templateType": "anything", "can_override": false}, "A2": {"name": "A2", "group": "geometry", "definition": "b2 h2/2 if(sign2='+',1,-1)", "description": "", "templateType": "anything", "can_override": false}, "b0": {"name": "b0", "group": "geometry", "definition": "qty(B[0\n  ],units)", "description": "", "templateType": "anything", "can_override": false}, "C": {"name": "C", "group": "Ungrouped variables", "definition": "vector(random(2..12),0)", "description": "", "templateType": "anything", "can_override": false}, "b2": {"name": "b2", "group": "geometry", "definition": "b0", "description": "", "templateType": "anything", "can_override": false}, "C1": {"name": "C1", "group": "geometry", "definition": "vector(B[0],C[1])+(vector(C[0],B[1])-vector(B[0],C[1]))/3  ", "description": "", "templateType": "anything", "can_override": false}, "A1": {"name": "A1", "group": "geometry", "definition": "b1 h1 /2 if(sign1='+',1,-1)", "description": "", "templateType": "anything", "can_override": false}, "ybar": {"name": "ybar", "group": "Unnamed group", "definition": "(a0 c0[1] + a1 c1[1] + a2 c2[1])/AT qty(1,units)", "description": "", "templateType": "anything", "can_override": false}, "h1": {"name": "h1", "group": "geometry", "definition": "h0", "description": "", "templateType": "anything", "can_override": false}, "B": {"name": "B", "group": "Ungrouped variables", "definition": "vector(random(2..12),random(2..12))", "description": "", "templateType": "anything", "can_override": false}, "h0": {"name": "h0", "group": "geometry", "definition": "qty(B[1],units)", "description": "", "templateType": "anything", "can_override": false}, "sign2": {"name": "sign2", "group": "geometry", "definition": "if(b[1]<a[1],'+','\u2013')", "description": "", "templateType": "anything", "can_override": false}, "C0": {"name": "C0", "group": "geometry", "definition": "(B/2)", "description": "", "templateType": "anything", "can_override": false}, "AT": {"name": "AT", "group": "geometry", "definition": "A0+A1+A2", "description": "", "templateType": "anything", "can_override": false}, "h2": {"name": "h2", "group": "geometry", "definition": "qty(abs(b[1]-A[1]),units)", "description": "", "templateType": "anything", "can_override": false}, "xbar": {"name": "xbar", "group": "Unnamed group", "definition": "(a0 c0[0] + a1 c1[0] + a2 c2[0])/AT qty(1,units)", "description": "", "templateType": "anything", "can_override": false}, "b1": {"name": "b1", "group": "geometry", "definition": "qty(abs(b[0]-c[0]),units)", "description": "", "templateType": "anything", "can_override": false}, "units": {"name": "units", "group": "Ungrouped variables", "definition": "random('in','cm','ft','m')", "description": "", "templateType": "anything", "can_override": false}, "sign1": {"name": "sign1", "group": "geometry", "definition": "if(b[0]<c[0],'+','\u2013')", "description": "", "templateType": "anything", "can_override": false}, "debug": {"name": "debug", "group": "Ungrouped variables", "definition": "false", "description": "", "templateType": "anything", "can_override": false}, "D": {"name": "D", "group": "Ungrouped variables", "definition": "vector(0,0)", "description": "", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "B[1]<>A[1] and B[0]<>C[0]", "maxRuns": "100"}, "ungrouped_variables": ["A", "B", "C", "D", "units", "debug"], "variable_groups": [{"name": "geometry", "variables": ["b0", "h0", "b2", "h1", "b1", "h2", "sign1", "sign2", "A0", "A1", "A2", "AT", "C0", "C2", "C1"]}, {"name": "Unnamed group", "variables": ["xbar", "ybar"]}], "functions": {"Q": {"parameters": [["area", "quantity"], ["distance", "number"]], "type": "quantity", "language": "jme", "definition": "display(area*distance*qty(1,units))"}, "display": {"parameters": [["q", "quantity"]], "type": "quantity", "language": "jme", "definition": "string(siground(q,4))"}, "bar": {"parameters": [["coord", "number"]], "type": "quantity", "language": "jme", "definition": "display(quantity(coord,units))"}, "applet": {"parameters": [], "type": "ggbapplet", "language": "javascript", "definition": "\n// Create the worksheet. \n// This function returns an object with a container `element` and a `promise` resolving to a GeoGebra applet.\nvar params = {\n  material_id: 'ftkm8mfx',\n  //alternate method, load from file.\n  //filename: \"resources/question-resources/centroid-t-r.ggb\",\n  //width:400,\n  //height:300\n  // was geogebra_applet('ftkm8mfx',[['A',A],['B',B],['C',C]])\n}\n\nvar result = Numbas.extensions.geogebra.createGeogebraApplet(params);\n\n// Once the applet has loaded, run some commands to manipulate the worksheet.\nresult.promise.then(function(d) {\n  var app = d.app;\n  question.applet = d;\n  \n  \nfunction setGGBPoint(name) {\n    // moves point in GGB to location of Numbas Vector Variable\n    var pt = question.scope.evaluate(name).value\n    app.setFixed(name,false,false);\n    app.setCoords(name, pt[0], pt[1]);\n    app.setFixed(name,true,true);\n  }\n\n  setGGBPoint(\"A\");\n  setGGBPoint(\"B\");\n  setGGBPoint(\"C\");\n  setGGBPoint(\"D\");\n  app.setVisible(\"Centroid\",false);\n  \n});\n\n// This function returns the result of `createGeogebraApplet` as an object \n// with the JME data type 'ggbapplet', which can be substituted into the question's content.\nreturn new Numbas.jme.types.ggbapplet(result);"}}, "preamble": {"js": "question.signals.on('adviceDisplayed',function() {\n   try{\n    var app = question.applet.app;\n \n  app.setVisible(\"Centroid\",true);\n  \n  }\n  catch(err){}  \n})\n\n\n\n", "css": "table.centroid{margin-left:0;}\n\ntable.centroid td {\n  width:6em; \n  vertical-align:center; \n  text-align:center;}\ntable.centroid *.underline {border-bottom: 2px solid black;}\n\n"}, "parts": [{"type": "gapfill", "useCustomName": true, "customName": "Info Table", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<table style=\"float: left; width: 625px;\" class=\"centroid\">\n<tbody>\n<tr class=\"underline\">\n<th style=\"width: 120px;\">Part</th>\n<td style=\"width: 120px; text-align: center;\">$A_i$</td>\n<td style=\"width: 120px; text-align: center;\">$\\bar{x}_i$</td>\n<td style=\"width: 120px; text-align: center;\">$\\bar{y}_i$</td>\n<td style=\"width: 120px; text-align: center;\">$A_i\\bar{x}_i$</td>\n<td style=\"width: 120px; text-align: center;\">$A_i\\bar{y}_i$</td>\n</tr>\n<tr>\n<th>Rectangle</th>\n<td>[[0]]</td>\n<td>[[4]]</td>\n<td>[[7]]</td>\n<td>[[10]]</td>\n<td>[[13]]</td>\n</tr>\n<tr>\n<th>Triangle 1</th>\n<td>[[1]]</td>\n<td>[[5]]</td>\n<td>[[8]]</td>\n<td>[[11]]</td>\n<td>[[14]]</td>\n</tr>\n<tr style=\"border-bottom: 2px;\">\n<th>Triangle 2</th>\n<td class=\"underline\">[[2]]</td>\n<td>[[6]]</td>\n<td>[[9]]</td>\n<td class=\"underline\">[[12]]</td>\n<td class=\"underline\">[[15]]</td>\n</tr>\n<tr>\n<th>$\\Sigma$</th>\n<td>[[3]]</td>\n<td></td>\n<td></td>\n<td>[[16]]</td>\n<td>\n<p>[[17]]</p>\n</td>\n</tr>\n</tbody>\n</table>", "gaps": [{"type": "engineering-answer", "useCustomName": true, "customName": "A_0", "marks": "0", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": false, "showFeedbackIcon": false, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "settings": {"correctAnswer": "A0", "right": "0.2", "close": "1.0", "C1": "75", "C2": "50", "C3": "25"}}, {"type": "engineering-answer", "useCustomName": true, "customName": "A_1", "marks": "0", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": false, "showFeedbackIcon": false, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "settings": {"correctAnswer": "A1", "right": "0.2", "close": "1.0", "C1": "75", "C2": "50", "C3": "25"}}, {"type": "engineering-answer", "useCustomName": true, "customName": "A_2", "marks": "0", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": false, "showFeedbackIcon": false, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "settings": {"correctAnswer": "A2", "right": "0.2", "close": "1.0", "C1": "75", "C2": "50", "C3": "25"}}, {"type": "engineering-answer", "useCustomName": true, "customName": "$A$", "marks": "5", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": false, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "settings": {"correctAnswer": "AT", "right": "0.2", "close": "1.0", "C1": "75", "C2": "50", "C3": "25"}}, {"type": "engineering-answer", "useCustomName": true, "customName": "x_0", "marks": "0", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": false, "showFeedbackIcon": false, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "settings": {"correctAnswer": "qty(c0[0],units)", "right": "0.2", "close": "1.0", "C1": "75", "C2": "50", "C3": "25"}}, {"type": "engineering-answer", "useCustomName": true, "customName": "x_1", "marks": "0", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": false, "showFeedbackIcon": false, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "settings": {"correctAnswer": "qty(c1[0],units)", "right": "0.2", "close": "1.0", "C1": "75", "C2": "50", "C3": "25"}}, {"type": "engineering-answer", "useCustomName": true, "customName": "x_2", "marks": "0", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": false, "showFeedbackIcon": false, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "settings": {"correctAnswer": "qty(c2[0],units)", "right": "0.2", "close": "1.0", "C1": "75", "C2": "50", "C3": "25"}}, {"type": "engineering-answer", "useCustomName": true, "customName": "y_0", "marks": "0", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": false, "showFeedbackIcon": false, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "settings": {"correctAnswer": "qty(c0[1],units)", "right": "0.2", "close": "1.0", "C1": "75", "C2": "50", "C3": "25"}}, {"type": "engineering-answer", "useCustomName": true, "customName": "y_1", "marks": "0", 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