// Numbas version: exam_results_page_options
{"name": "Trig: Diagonal of a parallelogram", "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": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"name": "Trig: Diagonal of a parallelogram", "tags": ["geometry", "Statics", "statics", "trig"], "metadata": {"description": "<p>Find an interior angle and length of a diagonal of a random parallelogram.</p>", "licence": "Creative Commons Attribution-NonCommercial 4.0 International"}, "statement": "<p>{applet()}</p>\n<p>The lengths of the sides of parallelogram are $\\overline{AB} =\\overline{CD} = \\var{qty(AB,units)}$ and&nbsp;$\\overline{AD} =\\overline{BC} = \\var{qty(AD,units)}$, and the known angles are $\\theta = \\var{theta}^\\circ$ and $\\phi = \\var{phi}^\\circ$.</p>\n<p>Determine $\\angle{ABC}$ and the length of the diagonal $\\overline{AC}$.</p>\n<p></p>", "advice": "<p><b>From geometry:</b></p>\n<p>$\\begin{align} \\angle ABC &amp;= \\theta + (90&deg; - \\phi)\\\\&nbsp;&amp;= &nbsp;\\var{theta}^{\\circ} + (90^{\\circ}&nbsp;- \\var{phi}^\\circ) \\\\&amp;= \\var{ABC}^{\\circ}\\end{align}$</p>\n<p><strong>From the law of cosines:</strong></p>\n<p>$\\begin{align} (\\overline{AC})^2&amp;= (\\overline{AB})^2 + (\\overline{AD})^2 - 2(\\overline{AB})(\\overline{AD})\\cos{\\angle ABC}\\\\&amp;= \\var{AB}^2&nbsp; + \\var{AD}^2 - 2&nbsp;(\\var{AB})&nbsp;(\\var{AD}) \\cos{\\var{ABC}}\\\\&amp;= \\var{qty(siground(AC ^2,4),units+'^2')}\\\\&nbsp;\\\\\\overline{AC} &amp;= \\sqrt{\\var{qty(siground(AC ^2,4),units+'^2')}}\\\\ &amp;= \\var{qty(AC,units)}\\end{align}$</p>", "rulesets": {}, "extensions": ["geogebra", "quantities"], "variables": {"theta": {"name": "theta", "group": "Ungrouped variables", "definition": "random(20..60#5)", "description": "", "templateType": "anything"}, "phi": {"name": "phi", "group": "Ungrouped variables", "definition": "random(30..75#5)\n", "description": "", "templateType": "anything"}, "AB": {"name": "AB", "group": "Ungrouped variables", "definition": "random(4..10)", "description": "", "templateType": "anything"}, "AD": {"name": "AD", "group": "Ungrouped variables", "definition": "random(4..12)", "description": "", "templateType": "anything"}, "B": {"name": "B", "group": "Ungrouped variables", "definition": "vector(cos(radians(90-theta)), sin(radians(90-theta))) AB", "description": "", "templateType": "anything"}, "D": {"name": "D", "group": "Ungrouped variables", "definition": "vector(cos(radians(-phi)), sin(radians(-phi))) AD", "description": "", "templateType": "anything"}, "C": {"name": "C", "group": "Ungrouped variables", "definition": "B+D", "description": "", "templateType": "anything"}, "units": {"name": "units", "group": "Ungrouped variables", "definition": "random(['in','ft','mm','m'])", "description": "", "templateType": "anything"}, "ABC": {"name": "ABC", "group": "Solution", "definition": "theta + 90 - phi", "description": "<p>angle ABC</p>", "templateType": "anything"}, "AC": {"name": "AC", "group": "Solution", "definition": "siground(sqrt(C[0]^2 + C[1]^2),4)", "description": "", "templateType": "anything"}}, "variablesTest": {"condition": "AB <> AD and C[1] > 1 and ABC <> 90", "maxRuns": 100}, "ungrouped_variables": ["theta", "phi", "AB", "AD", "B", "D", "C", "units"], "variable_groups": [{"name": "Solution", "variables": ["ABC", "AC"]}], "functions": {"applet": {"parameters": [], "type": "ggbapplet", "language": "javascript", "definition": "// 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: 'nxg7xva7'\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  function setGGBPoint(name, nname=name) {\n    // moves point in GGB to Numbas value\n    var pt = Numbas.jme.unwrapValue(question.scope.getVariable(nname));\n    app.setFixed(name,false,false);\n    app.setCoords(name, pt[0], pt[1]);\n    app.setFixed(name,true,true);\n  }\n  \n  setGGBPoint(\"B\");\n  setGGBPoint(\"D\");\n  app.setValue(\"show\",false);\n  app.setVisible(\"f\",false); // diagonal\n  //app.setLabelStyle('\u03b8',2);\n  //app.setLabelStyle('\u03a6',2);\n  //app.setVisible(\"MP\",true);\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   app.setVisible(\"f\",true);\n  app.setValue(\"show\",true);\n  app.setVisible(\"show\",true);\n  app.setLabelVisible(\"show\",false);\n  \n  }\n  catch(err){}  \n})\n\n", "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>$\\angle ABC = $&nbsp; &nbsp;[[0]] &nbsp; &nbsp;$\\overline{AC} = $&nbsp;[[1]]&nbsp;&nbsp;</p>", "gaps": [{"type": "engineering-answer", "useCustomName": true, "customName": "$\\angle AC$", "marks": "10", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "settings": {"correctAnswer": "qty(ABC,'deg')", "right": "0.2", "close": "1.0", "C1": "75", "C2": "50", "C3": "25"}}, {"type": "engineering-answer", "useCustomName": true, "customName": "AC", "marks": "10", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "settings": {"correctAnswer": "qty(ac,units)", "right": "0.2", "close": "1.0", "C1": "75", "C2": "50", "C3": "25"}}], "sortAnswers": false}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always", "contributors": [{"name": "William Haynes", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2530/"}]}]}], "contributors": [{"name": "William Haynes", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2530/"}]}