// Numbas version: finer_feedback_settings
{"name": "Sine and Cosine rules", "extensions": ["geogebra", "weh", "quantities"], "custom_part_types": [{"source": {"pk": 24, "author": {"name": "William Haynes", "pk": 2530}, "edit_page": "/part_type/24/edit"}, "name": "Angle quantity", "short_name": "angle-quantity-from-reference", "description": "<p>Angle&nbsp;as a quantity in degrees.</p>", "help_url": "", "input_widget": "string", "input_options": {"correctAnswer": "plain_string(settings['correct_quantity'])", "hint": {"static": true, "value": ""}, "allowEmpty": {"static": true, "value": false}}, "can_be_gap": true, "can_be_step": true, "marking_script": "mark:\nswitch( \nright and good_units and right_sign and angle_in_range, add_credit(1.0,'Correct.'),\nright and good_units and not right_sign, add_credit(settings['C2'],'Wrong sign.'),\nright and right_sign and not good_units, add_credit(settings['C2'],'Correct angle, but missing degree symbol.'),\nright and good_units and right_sign and not angle_in_range,add_credit(settings['C1'],'Angle is out of range.'),\nclose and good_units, add_credit(settings['C1'],'Close.'),\nclose and not good_units, add_credit(settings['C3'],'Answer is close, but missing degree symbol.'),\nincorrect('Wrong answer.')\n)\n\ninterpreted_answer:\nqty(student_scalar, student_units)\n\ncorrect_scalar:\nscalar(correct_quantity)\n  \n\ncorrect_quantity:\nsettings['correct_quantity']\n\ncorrect_units:\nunits(correct_quantity)\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:\njoin(\nsplit(studentAnswer[len(match_student_number[0])..len(studentAnswer)]\n,\"\u00b0\"),\" deg\")\n\n\n\ngood_units:\ntry(\nkind(quantity(1, student_units))= kind(correct_quantity),\nmsg,\nfeedback(msg);false)\n\nstudent_quantity:\nswitch(not good_units, \nstudent_scalar * correct_units, \nnot right_sign,\n-quantity(student_scalar, student_units),\nquantity(student_scalar,student_units)\n)\n\nright_sign:\nsign(student_scalar) = sign(correct_quantity)\n\nangle_in_range:\nif(settings['restrict_angle'], abs(student_scalar) <= 90, true)\n\nright:\nwithinTolerance(abs(student_scalar), abs(correct_scalar), settings['right'])\n\nclose:\nwithinTolerance(student_scalar, correct_scalar, settings['close'])", "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( \nright and good_units and right_sign and angle_in_range, add_credit(1.0,'Correct.'),\nright and good_units and not right_sign, add_credit(settings['C2'],'Wrong sign.'),\nright and right_sign and not good_units, add_credit(settings['C2'],'Correct angle, but missing degree symbol.'),\nright and good_units and right_sign and not angle_in_range,add_credit(settings['C1'],'Angle is out of range.'),\nclose and good_units, add_credit(settings['C1'],'Close.'),\nclose and not good_units, add_credit(settings['C3'],'Answer is close, but missing degree symbol.'),\nincorrect('Wrong answer.')\n)"}, {"name": "interpreted_answer", "description": "A value representing the student's answer to this part.", "definition": "qty(student_scalar, student_units)"}, {"name": "correct_scalar", "description": "", "definition": "scalar(correct_quantity)\n  "}, {"name": "correct_quantity", "description": "", "definition": "settings['correct_quantity']"}, {"name": "correct_units", "description": "", "definition": "units(correct_quantity)"}, {"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": "", "definition": "join(\nsplit(studentAnswer[len(match_student_number[0])..len(studentAnswer)]\n,\"\u00b0\"),\" deg\")\n\n"}, {"name": "good_units", "description": "", "definition": "try(\nkind(quantity(1, student_units))= kind(correct_quantity),\nmsg,\nfeedback(msg);false)"}, {"name": "student_quantity", "description": "", "definition": "switch(not good_units, \nstudent_scalar * correct_units, \nnot right_sign,\n-quantity(student_scalar, student_units),\nquantity(student_scalar,student_units)\n)"}, {"name": "right_sign", "description": "", "definition": "sign(student_scalar) = sign(correct_quantity)"}, {"name": "angle_in_range", "description": "", "definition": "if(settings['restrict_angle'], abs(student_scalar) <= 90, true)"}, {"name": "right", "description": "<p>Will check for correct sign elswhere.</p>", "definition": "withinTolerance(abs(student_scalar), abs(correct_scalar), settings['right'])"}, {"name": "close", "description": "<p>Must have correct sign to be close.</p>", "definition": "withinTolerance(student_scalar, correct_scalar, settings['close'])\n"}], "settings": [{"name": "correct_quantity", "label": "Correct Angle as quantity ", "help_url": "", "hint": "", "input_type": "code", "default_value": "qty(45,'deg')", "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 &plusmn; this amount from the correct value.", "input_type": "code", "default_value": "0.1", "evaluate": true}, {"name": "restrict_angle", "label": "Less than 90\u00b0", "help_url": "", "hint": "When checked, angle must be between -90&deg; and +90&deg;.", "input_type": "checkbox", "default_value": true}, {"name": "C1", "label": "Close with units.", "help_url": "", "hint": "Partial Credit for close value with appropriate units.", "input_type": "percent", "default_value": "75"}, {"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 &plusmn; this amount from the correct value.", "input_type": "code", "default_value": "0.5", "evaluate": true}, {"name": "C2", "label": "No units or wrong sign", "help_url": "", "hint": "Partial credit for forgetting units or using wrong sign.", "input_type": "percent", "default_value": "50"}, {"name": "C3", "label": "Close, no units.", "help_url": "", "hint": "Partial Credit for close value without units.", "input_type": "percent", "default_value": "25"}], "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": "Sine and Cosine rules", "advice": "<ol>\n<li>Use the <a href=\"https://www.khanacademy.org/math/basic-geo/basic-geometry-pythagorean-theorem/pythagorean-theorem-distance/a/distance-formula\">distance formula</a> to find the lengths of the three sides.</li>\n<li>Use the <a href=\"https://www.khanacademy.org/math/geometry/hs-geo-trig/hs-geo-solving-general-triangles/a/laws-of-sines-and-cosines-review\">Law of Cosines</a> to find one of the angles.</li>\n<li>Use the <a href=\"https://www.mathsisfun.com/algebra/trig-sine-law.html\">Law of Sines</a> to find the other two angles. &nbsp;Beware of the <a href=\"https://www.geogebra.org/m/CvtkyRM5\">ambiguous case</a>. &nbsp;Check your answers against the diagram.</li>\n</ol>", "variable_groups": [{"variables": ["A", "B", "C", "units"], "name": "Inputs"}, {"variables": ["AB", "BC", "CA", "alpha", "beta", "gamma", "sum"], "name": "results"}], "ungrouped_variables": [], "functions": {}, "extensions": ["geogebra", "quantities", "weh"], "variablesTest": {"condition": "(alpha > 15) and  (beta > 15) and (gamma > 15) and (alpha <> 90) and  (beta <> 90) and (gamma <>90)", "maxRuns": "200"}, "type": "question", "statement": "<p>Determine the lengths of the three sides and the measures of the three angles for the case when <em>A</em> = ({A[0]},{A[1]}), <em>B</em> = ({B[0]},{B[1]}), <em>C</em> = ({C[0]},{C[1]}). &nbsp;Length units are {units}.</p>\n<p>Give numeric answers to&nbsp;engineering accuracy&nbsp;and measure angles in degrees.&nbsp;</p>\n<p>{geogebra_applet('HCFekBp8',[['A',A],['B',B],['C',C]])}</p>\n<p></p>\n<div data-jme-visible=\"false\">\n<p>AB: {AB} &nbsp;BC: {BC} CA: {CA}</p>\n<p>alpha: {alpha} beta: {beta} gamma: {gamma}</p>\n</div>", "preamble": {"js": "\n\n\n\u00a0", "css": ""}, "tags": ["mechanics, statics, trigonometry, law of sines, law of cosines"], "parts": [{"customName": "", "customMarkingAlgorithm": "", "sortAnswers": false, "scripts": {}, "prompt": "<p>The lengths of the three sides are:</p>\n<ul>\n<li><em>AB</em> =&nbsp;[[0]]</li>\n<li><em>BC</em> =&nbsp;[[1]]</li>\n<li><em>CA</em> =&nbsp;[[2]]&nbsp;</li>\n</ul>", "extendBaseMarkingAlgorithm": true, "showCorrectAnswer": true, "variableReplacementStrategy": "originalfirst", "type": "gapfill", "showFeedbackIcon": true, "marks": 0, "unitTests": [], "useCustomName": false, "gaps": [{"customName": "", "customMarkingAlgorithm": "", "scripts": {}, "settings": {"right": "0.1", "C2": "50", "C3": "25", "C1": "75", "correctAnswer": "quantity(AB,units)", "close": "1.0"}, "extendBaseMarkingAlgorithm": true, "showCorrectAnswer": true, "variableReplacementStrategy": "originalfirst", "type": "engineering-answer", "showFeedbackIcon": true, "marks": "4", "unitTests": [], "useCustomName": false, "variableReplacements": []}, {"customName": "", "customMarkingAlgorithm": "", "scripts": {}, "settings": {"right": "0.1", "C2": "50", "C3": "25", "C1": "75", "correctAnswer": "quantity(BC,units)", "close": "1.0"}, "extendBaseMarkingAlgorithm": true, "showCorrectAnswer": true, "variableReplacementStrategy": "originalfirst", "type": "engineering-answer", "showFeedbackIcon": true, "marks": "4", "unitTests": [], "useCustomName": false, "variableReplacements": []}, {"customName": "", "customMarkingAlgorithm": "", "scripts": {}, "settings": {"right": "0.1", "C2": "50", "C3": "25", "C1": "75", "correctAnswer": "quantity(CA,units)", "close": "1.0"}, "extendBaseMarkingAlgorithm": true, "showCorrectAnswer": true, "variableReplacementStrategy": "originalfirst", "type": "engineering-answer", "showFeedbackIcon": true, "marks": "4", "unitTests": [], "useCustomName": false, "variableReplacements": []}], "variableReplacements": []}, {"customName": "", "customMarkingAlgorithm": "", "sortAnswers": false, "scripts": {}, "prompt": "<p>The&nbsp;three angles&nbsp;are:</p>\n<ul>\n<li><em>$\\alpha$</em>&nbsp;=&nbsp;[[0]]</li>\n<li><em>$\\beta$</em>&nbsp;=&nbsp;[[1]]</li>\n<li><em>$\\gamma$</em>&nbsp;=&nbsp;[[2]]</li>\n</ul>", "extendBaseMarkingAlgorithm": true, "showCorrectAnswer": true, "variableReplacementStrategy": "originalfirst", "type": "gapfill", "showFeedbackIcon": true, "marks": 0, "unitTests": [], "useCustomName": false, "gaps": [{"customName": "", "customMarkingAlgorithm": "", "scripts": {}, "settings": {"right": "0.2", "C2": "50", "C3": "25", "correct_quantity": "qty(alpha,'deg')", "C1": "75", "restrict_angle": false, "close": "1.0"}, "extendBaseMarkingAlgorithm": true, "showCorrectAnswer": true, "variableReplacementStrategy": "originalfirst", "type": "angle-quantity-from-reference", "showFeedbackIcon": true, "marks": "4", "unitTests": [], "useCustomName": false, "variableReplacements": []}, {"customName": "", "customMarkingAlgorithm": "", "scripts": {}, "settings": {"right": "0.2", "C2": "50", "C3": "25", "correct_quantity": "qty(beta,'deg')", "C1": "75", "restrict_angle": false, "close": "1.0"}, "extendBaseMarkingAlgorithm": true, "showCorrectAnswer": true, "variableReplacementStrategy": "originalfirst", "type": "angle-quantity-from-reference", "showFeedbackIcon": true, "marks": "4", "unitTests": [], "useCustomName": false, "variableReplacements": []}, {"customName": "", "customMarkingAlgorithm": "", "scripts": {}, "settings": {"right": "0.2", "C2": "50", "C3": "25", "correct_quantity": "qty(gamma,'deg')", "C1": "75", "restrict_angle": false, "close": "1.0"}, "extendBaseMarkingAlgorithm": true, "showCorrectAnswer": true, "variableReplacementStrategy": "originalfirst", "type": "angle-quantity-from-reference", "showFeedbackIcon": true, "marks": "4", "unitTests": [], "useCustomName": false, "variableReplacements": []}], "variableReplacements": []}], "rulesets": {}, "metadata": {"description": "<p>Solve a random oblique triangle for sides and angles.</p>", "licence": "Creative Commons Attribution-NonCommercial 4.0 International"}, "variables": {"AB": {"templateType": "anything", "description": "", "definition": "length(A-B)", "group": "results", "name": "AB"}, "gamma": {"templateType": "anything", "description": "", "definition": "degrees(angle((A-C,B-C)))", "group": "results", "name": "gamma"}, "sum": {"templateType": "anything", "description": "", "definition": "alpha+beta+gamma", "group": "results", "name": "sum"}, "alpha": {"templateType": "anything", "description": "", "definition": "degrees(angle((B-A,C-A)))", "group": "results", "name": "alpha"}, "B": {"templateType": "anything", "description": "", "definition": "vector(random(-8..8),random(-6..6))", "group": "Inputs", "name": "B"}, "A": {"templateType": "anything", "description": "", "definition": "vector(random(-8..8),random(-6..6))", "group": "Inputs", "name": "A"}, "C": {"templateType": "anything", "description": "", "definition": "vector(random(-8..8),random(-6..6))", "group": "Inputs", "name": "C"}, "units": {"templateType": "anything", "description": "", "definition": "random('m','ft','in','cm')", "group": "Inputs", "name": "units"}, "CA": {"templateType": "anything", "description": "", "definition": "length(C-A)", "group": "results", "name": "CA"}, "beta": {"templateType": "anything", "description": "", "definition": "degrees(angle((C-B,A-B)))", "group": "results", "name": "beta"}, "BC": {"templateType": "anything", "description": "", "definition": "length(B-C)", "group": "results", "name": "BC"}}, "contributors": [{"name": "Xiaodan Leng", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2146/"}, {"name": "William Haynes", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2530/"}]}]}], "contributors": [{"name": "Xiaodan Leng", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2146/"}, {"name": "William Haynes", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2530/"}]}