// Numbas version: exam_results_page_options
{"name": "Vector addition: parallelogram rule", "extensions": ["geogebra", "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": 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": "Vector addition: parallelogram rule", "tags": ["mechanics, statics, parallelogram rule, vector addition"], "metadata": {"description": "<p>Find the sum of two 2-dimensional vectors, graphically and exactly using the parallelogram rule.</p>", "licence": "Creative Commons Attribution-NonCommercial 4.0 International"}, "statement": "<p>Find the magnitude and direction&nbsp;of resultant &nbsp;$\\mathbf{R}$ when $\\mathbf{A}&nbsp;= \\var{qty(2 FB, units)}$ and $\\mathbf{B}&nbsp;= \\var{qty(FB,units)}$,</p>\n<p>{geogebra_applet('udgn8s84',['A_x':&nbsp;Ax&nbsp;,&nbsp;'A_y':&nbsp;Ay,&nbsp;'&theta;_B':&nbsp;dirB + '&deg;' ])}</p>\n<p></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>", "rulesets": {}, "extensions": ["geogebra", "quantities"], "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true}, "constants": [], "variables": {"thetaR": {"name": "thetaR", "group": "Ungrouped variables", "definition": "loc(R,A,B)", "description": "", "templateType": "anything", "can_override": false}, "A": {"name": "A", "group": "Results", "definition": "2 FB vector(cos(radians(dirA)),sin(radians(dirA)))", "description": "<p>Force A</p>", "templateType": "anything", "can_override": false}, "R": {"name": "R", "group": "Results", "definition": "A + B", "description": "", "templateType": "anything", "can_override": false}, "thetaA": {"name": "thetaA", "group": "Ungrouped variables", "definition": "loc(A,B,R)", "description": "", "templateType": "anything", "can_override": false}, "FB": {"name": "FB", "group": "Inputs", "definition": "random(5..100#5)", "description": "<p>Magnitude of force B, &nbsp;Magnitude of A is twice this value.</p>", "templateType": "anything", "can_override": false}, "Ay": {"name": "Ay", "group": "Inputs", "definition": "random(-4..4 except 0)", "description": "", "templateType": "anything", "can_override": false}, "thetaB": {"name": "thetaB", "group": "Ungrouped variables", "definition": "loc(B,A,R)", "description": "", "templateType": "anything", "can_override": false}, "dirA": {"name": "dirA", "group": "Results", "definition": "degrees(atan2(Ay,Ax))", "description": "<p>Direction of force A, based on Ax and Ay.</p>", "templateType": "anything", "can_override": false}, "Ax": {"name": "Ax", "group": "Inputs", "definition": "random(-4..4 except 0)", "description": "", "templateType": "anything", "can_override": false}, "units": {"name": "units", "group": "Inputs", "definition": "random(['lb','N','kN'])", "description": "", "templateType": "anything", "can_override": false}, "dirB": {"name": "dirB", "group": "Inputs", "definition": "(random(0..360#15 except 0..360#45))", "description": "", "templateType": "anything", "can_override": false}, "B": {"name": "B", "group": "Results", "definition": "FB vector(cos(radians(dirB)),sin(radians(dirB)))\n", "description": "<p style=\"padding-left: 30px;\">Force B</p>", "templateType": "anything", "can_override": false}, "dirR": {"name": "dirR", "group": "Results", "definition": "degrees(atan2(R[1],r[0]))", "description": "", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "abs(dirA- dirB) > 25 and abs(dirA-dirB) < 160 ", "maxRuns": "200"}, "ungrouped_variables": ["thetaA", "thetaB", "thetaR"], "variable_groups": [{"name": "Inputs", "variables": ["FB", "dirB", "Ax", "Ay", "units"]}, {"name": "Results", "variables": ["dirA", "A", "B", "R", "dirR"]}], "functions": {"direction": {"parameters": [["v", "vector"]], "type": "number", "language": "javascript", "definition": "return Math.atan2(v[1],v[0])\n"}, "loc": {"parameters": [["A", "vector"], ["B", "vector"], ["C", "vector"]], "type": "number", "language": "jme", "definition": "degrees(arccos((abs(A)^2-abs(B)^2-abs(C)^2)/(-2 * abs(B) * abs(C))))"}}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "gapfill", "useCustomName": true, "customName": "Graphical Solution", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "\n    ", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<ol>\n<li>Use a ruler and protractor, a CAD program, or Geogebra, to carefully draw a neat, labeled, accurately scaled diagram representing the vector addition &nbsp;$\\mathbf{R} = \\mathbf{A}+\\mathbf{B}$ using the parallelogram rule.</li>\n<li>Based on your scaled diagram, &nbsp;estimate the magnitude of resultant and its direction of measured from positive x- axis:</li>\n</ol>\n<p>$|\\mathbf{R}|$ =&nbsp;[[0]]&nbsp;$\\qquad \\theta_x$ &nbsp;= &nbsp;[[1]]</p>", "gaps": [{"type": "engineering-answer", "useCustomName": true, "customName": "$\\theta_x$", "marks": "5", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "settings": {"correctAnswer": "qty(abs(R),units)", "right": "0.2", "close": "1.0", "C1": "75", "C2": "50", "C3": "25"}}, {"type": "angle", "useCustomName": true, "customName": "$|R|$", "marks": "5", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "settings": {"expected_answer": "qty(dirR,'deg')", "unit_penalty": "20", "close_penalty": "20", "close_tol": "0.5", "right_tol": "0.1"}}], "sortAnswers": false}, {"type": "gapfill", "useCustomName": true, "customName": "Trigonometric (Exact) Solution", "marks": 0, "scripts": {"mark": {"script": "//numbasGGBApplet0.setVisible('show',true);\n//numbasGGBApplet0.setValue('show',true);", "order": "after"}}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<ol>\n<li>Label the three angles inside the triangle $\\theta_A$, $\\theta_B$, and $\\theta_R$ where the subscript is the name of the side opposite.</li>\n<li>Use law of cosines/sines&nbsp;to&nbsp;find the following values, exactly.</li>\n</ol>\n<p>$\\theta_A =$&nbsp;[[0]]&nbsp; $\\qquad \\theta_B = $[[1]]&nbsp;$\\qquad \\theta_R =$&nbsp;[[2]]&nbsp; $\\qquad |\\mathbf{R}| =$&nbsp;[[3]]&nbsp;</p>\n<p></p>", "gaps": [{"type": "angle", "useCustomName": true, "customName": "$\\theta_A$", "marks": "5", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "settings": {"expected_answer": "qty(thetaA,'deg')", "unit_penalty": "20", "close_penalty": "20", "close_tol": "0.5", "right_tol": "0.1"}}, {"type": "angle", "useCustomName": true, "customName": "$\\theta_B$", "marks": "5", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "settings": {"expected_answer": "qty(thetaB,'deg')", "unit_penalty": "20", "close_penalty": "20", "close_tol": "0.5", "right_tol": "0.1"}}, {"type": "angle", "useCustomName": true, "customName": "$\\theta_C$", "marks": "5", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "settings": {"expected_answer": "qty(thetaR,'deg')", "unit_penalty": "20", "close_penalty": "20", "close_tol": "0.5", "right_tol": "0.1"}}, {"type": "engineering-answer", "useCustomName": true, "customName": "$|R|$", "marks": "5", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "settings": {"correctAnswer": "qty(abs(R),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/"}]}