// Numbas version: exam_results_page_options
{"name": "Katy's copy of Vector addition by applying the parallelogram rule", "extensions": ["geogebra", "weh", "quantities"], "custom_part_types": [{"source": {"pk": 12, "author": {"name": "William Haynes", "pk": 2530}, "edit_page": "/part_type/12/edit"}, "name": "Angle quantity 2020", "short_name": "angle", "description": "<p>Adjusts all angles to 0 &lt; $\\theta$ &lt; 360.</p>\n<p>Accepts '&deg;' and 'deg' as units.</p>\n<p>Penalizes if not close enough or no units.</p>\n<p>90&deg; = -270&deg; = 450&deg;</p>", "help_url": "", "input_widget": "string", "input_options": {"correctAnswer": "plain_string(settings['expected_answer']) ", "hint": {"static": true, "value": ""}, "allowEmpty": {"static": true, "value": false}}, "can_be_gap": true, "can_be_step": true, "marking_script": "original_student_scalar:\nmatchnumber(studentAnswer,['plain','en'])[1]\n\nstudent_scalar:\nmod(original_student_scalar,360)\n\n\nstudent_unit:\nstudentAnswer[len(matchnumber(studentAnswer,['plain','en'])[0])..len(studentAnswer)]\n\ninterpreted_unit:\nif(trim(student_unit)='\u00b0','deg',student_unit)\n\ninterpreted_answer:\nqty(mod(student_scalar,360),'deg')\n\nclose:\nwithintolerance(student_scalar, correct_scalar,decimal(settings['close_tol']))\n\ncorrect_scalar:\nmod(scalar(settings['expected_answer']),360)\n\nright:\nwithintolerance(student_scalar, correct_scalar, decimal(settings['right_tol']))\n\ngood_unit:\nsame(qty(1,interpreted_unit),qty(1,'deg'))\n\nmark:\nassert(close,incorrect('Incorrect.');end());\nif(right,correct('Correct angle.'), set_credit(1 - settings['close_penalty'],'Angle is close.'));\nassert(good_unit,sub_credit(settings['unit_penalty'], 'Missing or incorrect units.'))", "marking_notes": [{"name": "original_student_scalar", "description": "<p>Retuns the scalar part of students answer (which is a quantity) as a number.</p>", "definition": "matchnumber(studentAnswer,['plain','en'])[1]"}, {"name": "student_scalar", "description": "<p>Normalize angle with mod 360</p>", "definition": "mod(original_student_scalar,360)\n"}, {"name": "student_unit", "description": "<p>matchnumber(studentAnswer,['plain','en'])[0] is a string \"12.34\"</p>", "definition": "studentAnswer[len(matchnumber(studentAnswer,['plain','en'])[0])..len(studentAnswer)]"}, {"name": "interpreted_unit", "description": "<p>Allows student to use degree symbol or 'deg' for units.</p>", "definition": "if(trim(student_unit)='\u00b0','deg',student_unit)"}, {"name": "interpreted_answer", "description": "A value representing the student's answer to this part.", "definition": "qty(mod(student_scalar,360),'deg')"}, {"name": "close", "description": "", "definition": "withintolerance(student_scalar, correct_scalar,decimal(settings['close_tol']))"}, {"name": "correct_scalar", "description": "<p>Normalize expected_answer with mod 360</p>", "definition": "mod(scalar(settings['expected_answer']),360)"}, {"name": "right", "description": "", "definition": "withintolerance(student_scalar, correct_scalar, decimal(settings['right_tol']))"}, {"name": "good_unit", "description": "", "definition": "same(qty(1,interpreted_unit),qty(1,'deg'))"}, {"name": "mark", "description": "This is the main marking note. It should award credit and provide feedback based on the student's answer.", "definition": "assert(close,incorrect('Incorrect.');end());\nif(right,correct('Correct angle.'), set_credit(1 - settings['close_penalty'],'Angle is close.'));\nassert(good_unit,sub_credit(settings['unit_penalty'], 'Missing or incorrect units.'))"}], "settings": [{"name": "expected_answer", "label": "Expected Answer", "help_url": "", "hint": "Expected angle as a quantity.", "input_type": "code", "default_value": "qty(30,'deg')", "evaluate": true}, {"name": "unit_penalty", "label": "Unit penalty", "help_url": "", "hint": "Penalty for not including degree sign or 'deg'.", "input_type": "percent", "default_value": "20"}, {"name": "close_penalty", "label": "Close Penalty", "help_url": "", "hint": "Penalty for close answer.", "input_type": "percent", "default_value": "20"}, {"name": "close_tol", "label": "Close", "help_url": "", "hint": "Angle must be $\\pm$ this many degrees to be marked close. &nbsp;&nbsp;", "input_type": "code", "default_value": "0.5", "evaluate": false}, {"name": "right_tol", "label": "Right ", "help_url": "", "hint": "Angle must be $\\pm$ this many degrees to be marked correct. &nbsp;", "input_type": "code", "default_value": "0.1", "evaluate": false}], "public_availability": "restricted", "published": false, "extensions": ["quantities"]}, {"source": {"pk": 14, "author": {"name": "William Haynes", "pk": 2530}, "edit_page": "/part_type/14/edit"}, "name": "Three Significant Digits", "short_name": "three-significant-digits", "description": "<p>Requires answer to three significant digits for full credit. &nbsp;Gives 3/4&nbsp;credit if answer is accurate to 2sf. and 1/4 credit if 1sf</p>", "help_url": "", "input_widget": "number", "input_options": {"correctAnswer": "settings['correct_answer']", "hint": {"static": true, "value": ""}, "allowedNotationStyles": {"static": true, "value": ["plain", "en"]}, "allowFractions": {"static": true, "value": true}}, "can_be_gap": true, "can_be_step": true, "marking_script": "interpreted_answer:\nstudentAnswer\n\ncorrect_answer:\ninput_options[\"correctAnswer\"]\n\nright_sign:\nsign(studentAnswer) = sign(correct_answer)\n\nmark:\nif(right_value & right_sign, correct('Right.'),\n   if(close & right_sign, set_credit(0.5, 'Close.'),\n      if(right_value, set_credit(0.5, 'Right value, wrong sign.'),\n         incorrect('Wrong.'))))\n\nright_value:\nresultsequal(abs(studentAnswer), abs(correct_answer), 'sigfig', 3)\n\nclose:\nresultsequal(abs(studentAnswer), abs(correct_answer), 'sigfig', 2)", "marking_notes": [{"name": "interpreted_answer", "definition": "studentAnswer", "description": "A value representing the student's answer to this part."}, {"name": "correct_answer", "definition": "input_options[\"correctAnswer\"]", "description": ""}, {"name": "right_sign", "definition": "sign(studentAnswer) = sign(correct_answer)", "description": ""}, {"name": "mark", "definition": "if(right_value & right_sign, correct('Right.'),\n   if(close & right_sign, set_credit(0.5, 'Close.'),\n      if(right_value, set_credit(0.5, 'Right value, wrong sign.'),\n         incorrect('Wrong.'))))", "description": "This is the main marking note. It should award credit and provide feedback based on the student's answer."}, {"name": "right_value", "definition": "resultsequal(abs(studentAnswer), abs(correct_answer), 'sigfig', 3)", "description": ""}, {"name": "close", "definition": "resultsequal(abs(studentAnswer), abs(correct_answer), 'sigfig', 2)", "description": ""}], "settings": [{"name": "correct_answer", "input_type": "code", "label": "Correct Answer", "default_value": "309", "help_url": "", "evaluate": true, "hint": ""}], "public_availability": "restricted", "published": false, "extensions": []}], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"metadata": {"licence": "Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International", "description": "<p>Find the sum of two 2-dimensional vectors, graphically and exactly using the parallelogram rule.</p>"}, "functions": {"direction": {"definition": "return Math.atan2(v[1],v[0])\n", "parameters": [["v", "vector"]], "type": "number", "language": "javascript"}}, "ungrouped_variables": [], "parts": [{"marks": 0, "unitTests": [], "variableReplacements": [], "gaps": [{"marks": "2", "unitTests": [], "scripts": {"mark": {"script": "var ans= numbasGGBApplet0.getValue(\"\u03b8_a\")*180/Math.PI;\nthis.resolved_input_options.correctAnswer= Numbas.math.siground(ans,3);    \n", "order": "before"}}, "type": "angle", "showCorrectAnswer": true, "extendBaseMarkingAlgorithm": true, "settings": {"tolerance": "1", "expected_answer": "0"}, "variableReplacementStrategy": "originalfirst", "customMarkingAlgorithm": "", "variableReplacements": [], "showFeedbackIcon": true}, {"marks": 1, "unitTests": [], "scripts": {"mark": {"script": "var ans= numbasGGBApplet0.getValue(\"\u03b8_b\")*180/Math.PI;\nthis.resolved_input_options.correctAnswer= Numbas.math.siground(ans,3);    \n", "order": "before"}}, "type": "angle", "showCorrectAnswer": true, "extendBaseMarkingAlgorithm": true, "settings": {"tolerance": "1", "expected_answer": "2"}, "variableReplacementStrategy": "originalfirst", "customMarkingAlgorithm": "", "variableReplacements": [], "showFeedbackIcon": true}, {"marks": "2", "unitTests": [], "scripts": {"mark": {"script": "var ans= numbasGGBApplet0.getValue(\"\u03b8_r\")*180/Math.PI;\nthis.resolved_input_options.correctAnswer= Numbas.math.siground(ans,3);    \n", "order": "before"}}, "type": "angle", "showCorrectAnswer": true, "extendBaseMarkingAlgorithm": true, "settings": {"tolerance": "1", "expected_answer": "0"}, "variableReplacementStrategy": "originalfirst", "customMarkingAlgorithm": "", "variableReplacements": [], "showFeedbackIcon": true}, {"marks": "2", "unitTests": [], "scripts": {}, "type": "three-significant-digits", "showCorrectAnswer": true, "extendBaseMarkingAlgorithm": true, "settings": {"correct_answer": "abs(R)"}, "variableReplacementStrategy": "originalfirst", "customMarkingAlgorithm": "", "variableReplacements": [], "showFeedbackIcon": true}, {"marks": "3", "unitTests": [], "scripts": {"mark": {"script": "var ans= numbasGGBApplet0.getValue(\"\u03b8_r\")*180/Math.PI;\nthis.resolved_input_options.correctAnswer= Numbas.math.siground(ans,3);    \n", "order": "before"}}, "type": "angle", "showCorrectAnswer": true, "extendBaseMarkingAlgorithm": true, "settings": {"tolerance": "1", "expected_answer": "degrees(direction(R))"}, "variableReplacementStrategy": "originalfirst", "customMarkingAlgorithm": "", "variableReplacements": [], "showFeedbackIcon": true}], "variableReplacementStrategy": "originalfirst", "customMarkingAlgorithm": "", "prompt": "<p><strong>Trigonometric (Exact) Solution</strong></p>\n<p></p>\n<p>Use law of cosines/sines&nbsp;to&nbsp;find the following values, exactly. Give all answers to three significant digits.</p>\n<p>$\\theta_A$ =&nbsp;[[0]]&nbsp;</p>\n<p>$\\theta_B$ =&nbsp;[[1]]</p>\n<p>$\\theta_R$ =&nbsp;[[2]]</p>\n<p>$|\\textbf{R}|$ =&nbsp;[[3]]</p>\n<p>$\\theta_x$ =&nbsp;[[4]]</p>", "scripts": {}, "type": "gapfill", "showCorrectAnswer": true, "sortAnswers": false, "extendBaseMarkingAlgorithm": true, "showFeedbackIcon": true}], "variable_groups": [{"variables": ["FB", "dirB", "Ax", "Ay", "units"], "name": "Inputs"}, {"variables": ["A", "dirA", "B", "R"], "name": "Results"}], "variables": {"B": {"definition": "FB vector(cos(radians(dirB)),sin(radians(dirB)))\n", "templateType": "anything", "name": "B", "description": "<p style=\"padding-left: 30px;\">Force B</p>", "group": "Results"}, "dirA": {"definition": "degrees(atan2(Ay,Ax))", "templateType": "anything", "name": "dirA", "description": "<p>Direction of force A, based on Ax and Ay.</p>", "group": "Results"}, "units": {"definition": "random(['lb','N','kN','kip'])", "templateType": "anything", "name": "units", "description": "", "group": "Inputs"}, "FB": {"definition": "random(5..100#5)", "templateType": "anything", "name": "FB", "description": "<p>Magnitude of force B, &nbsp;Magnitude of A is twice this value.</p>", "group": "Inputs"}, "Ay": {"definition": "random(-4..4 except 0)", "templateType": "anything", "name": "Ay", "description": "", "group": "Inputs"}, "dirB": {"definition": "(random(0..360#15 except 0..360#45))", "templateType": "anything", "name": "dirB", "description": "", "group": "Inputs"}, "A": {"definition": "2 FB vector(cos(radians(dirA)),sin(radians(dirA)))", "templateType": "anything", "name": "A", "description": "<p>Force A</p>", "group": "Results"}, "R": {"definition": "A + B", "templateType": "anything", "name": "R", "description": "", "group": "Results"}, "Ax": {"definition": "random(-4..4 except 0)", "templateType": "anything", "name": "Ax", "description": "", "group": "Inputs"}}, "name": "Katy's copy of Vector addition by applying the parallelogram rule", "rulesets": {}, "preamble": {"js": "Numbas.extensions.weh.scope.ggbApplet.then((diagram) => doThings(diagram));\n\nvar doThings = function(applet){\n  applet.setVisible('show',false);\n};\n\n\n\n", "css": ""}, "tags": [], "statement": "<p>Vector Addition: $\\textbf{R}$ = <span style=\"color: red;\">$\\textbf{A}$</span> + <span style=\"color: blue;\">$\\textbf{B}$</span></p>\n<p style=\"font-face: serif;\">Find the magnitude and direction&nbsp;of resultant&nbsp;$\\textbf{R}$ when <span style=\"color: red;\">$A$</span> = {2 FB} {units} and <span style=\"color: blue;\">$B$</span> = {FB} {units},</p>\n<p style=\"padding-left: 30px;\">by using triginometry.</p>\n<p id=\"weh\">{geogebra_applet('udgn8s84',[['A_x',Ax],['A_y',Ay],['&theta;_B',radians(dirB)]])}</p>", "advice": "<p>Procedure:</p>\n<ol>\n<li>Draw a neat diagram and label the unknown side and angles.</li>\n<li>Determine the angle opposite the&nbsp;unknown force $\\textbf{R}$.</li>\n<li>Use law of cosines&nbsp;to determine the magnitude $|\\textbf{R}|$</li>\n<li>Use either the law of sines or cosines to determine the other two angles.</li>\n<li>Use the angles you have found to determine the direction of force&nbsp;$\\textbf{R}$ from the <em>x</em>-axis.</li>\n</ol>", "extensions": ["geogebra", "weh"], "variablesTest": {"condition": "dirA <> dirB", "maxRuns": "200"}, "type": "question", "contributors": [{"name": "Katy Dobson", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/854/"}, {"name": "William Haynes", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2530/"}]}]}], "contributors": [{"name": "Katy Dobson", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/854/"}, {"name": "William Haynes", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2530/"}]}