en test
", "licence": "None specified"}, "duration": 0, "percentPass": "0", "showQuestionGroupNames": false, "shuffleQuestionGroups": false, "showstudentname": true, "question_groups": [{"name": "Group", "pickingStrategy": "all-ordered", "pickQuestions": 1, "questionNames": ["", "", ""], "variable_overrides": [[], [], []], "questions": [{"name": "Mathias's copy of Trigonometric form of a Fourier series Evaluate ak & bk", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Frank Doheny", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/789/"}, {"name": "Mathias Sandulescu", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/3503/"}], "tags": [], "metadata": {"description": "Calculating particular harmonic components of a Fourier series expansion.
", "licence": "Creative Commons Attribution 4.0 International"}, "statement": "Given the function:
\n\\(f(t)=\\left[ \\begin{array}{cc}\\,\\,\\var{a}&\\,\\,-\\var{L}<t<-\\simplify{{L}/2}\\\\\\,\\,\\var{b}&\\,\\,-\\simplify{{L}/2}<t<\\simplify{{L}/2}\\\\\\,\\,\\var{c}&\\,\\,\\simplify{{L}/2}<t<\\var{L}\\end{array}\\right] \\,\\,\\,\\,f(t+\\simplify{2*{L}})=f(t)\\)
", "advice": "\\(f(t)=\\left[ \\begin{array}{cc}\\,\\,\\var{a}&\\,\\,-\\var{L}<t<-\\simplify{{L}/2}\\\\\\,\\,\\var{b}&\\,\\,-\\simplify{{L}/2}<t<\\simplify{{L}/2}\\\\\\,\\,\\var{c}&\\,\\,\\simplify{{L}/2}<t<\\var{L}\\end{array}\\right] \\,\\,\\,\\,f(t+\\simplify{2*{L}})=f(t)\\)
\n\nWe derived the formulae for a trigonometric Fourier series of a periodic function having period \\(2L\\)
\n\\(2L=\\simplify{2*{L}}\\implies L=\\var{L}\\)
\nWe can either evaluate \\(a_0=\\frac{1}{L}\\int_{-L}^{L}f(t)dt\\) or use the shortcut:
\n\\(\\frac{a_0}{2}=\\) the average value of the wave over one complete cycle \\(=\\frac{Area}{Base}\\)
\n\\(\\frac{a_0}{2}=\\frac{\\var{a}*\\simplify{{L}/2}+\\var{b}*\\var{L}+\\var{c}*\\simplify{{L}/2}}{\\simplify{2*{L}}}=\\simplify{({a}+2*{b}+{c})/4}\\)
\n\nThe formula for the Fourier coefficient \\(a_k\\) is given by: \\(a_k=\\frac{1}{L}\\int_{-L}^{L}f(t)cos\\left(\\frac{{k}\\pi}{L}t\\right)dt\\)
\n\n\\(a_k=\\frac{1}{\\var{L}}\\left(\\int_{-\\var{L}}^{-\\frac{\\var{L}}{2}}\\var{a}cos\\left(\\frac{{k}\\pi}{\\var{L}}t\\right)dt+\\int_{-\\frac{\\var{L}}{2}}^{\\frac{\\var{L}}{2}}\\var{b}cos\\left(\\frac{{k}\\pi}{\\var{L}}t\\right)dt+\\int_{\\frac{\\var{L}}{2}}^{\\var{L}}\\var{c}cos\\left(\\frac{{k}\\pi}{\\var{L}}t\\right)dt\\right)\\)
\n\\(a_k=\\frac{1}{\\var{L}}\\left(\\frac{\\var{a}*\\var{L}}{{k}\\pi}sin\\left(\\frac{{k}\\pi}{\\var{L}}t\\right)|_{-\\var{L}}^{-\\frac{\\var{L}}{2}}+\\frac{\\var{b}*\\var{L}}{{k}\\pi}sin\\left(\\frac{{k}\\pi}{\\var{L}}t\\right)|_{-\\frac{\\var{L}}{2}}^{\\frac{\\var{L}}{2}}+\\frac{\\var{c}*\\var{L}}{{k}\\pi}sin\\left(\\frac{{k}\\pi}{\\var{L}}t\\right)|_{\\frac{\\var{L}}{2}}^{\\var{L}}\\right)\\)
\n\\(a_k=\\frac{\\var{a}}{{k}\\pi}sin(-\\frac{{k}\\pi}{2})-\\frac{\\var{a}}{{k}\\pi}sin(-{k}\\pi)+\\frac{\\var{b}}{{k}\\pi}sin(\\frac{{k}\\pi}{2})-\\frac{\\var{b}}{{k}\\pi}sin(-\\frac{{k}\\pi}{2})+\\frac{\\var{c}}{{k}\\pi}sin({k}\\pi)-\\frac{\\var{c}}{{k}\\pi}sin(\\frac{{k}\\pi}{2})\\)
\n\\(a_k=-\\frac{\\var{a}}{{k}\\pi}sin(\\frac{{k}\\pi}{2})+\\frac{\\var{b}}{{k}\\pi}sin(\\frac{{k}\\pi}{2})+\\frac{\\var{b}}{{k}\\pi}sin(\\frac{{k}\\pi}{2})-\\frac{\\var{c}}{{k}\\pi}sin(\\frac{{k}\\pi}{2})\\)
\n\\(a_k=\\frac{\\simplify{-{a}+2{b}-{c}}}{{k}\\pi}sin(\\frac{{k}\\pi}{2})\\)
\n\\(a_\\var{k}=\\simplify{(-{a}+2{b}-{c})/({k}*pi)sin({k}*pi/2)}\\)
\nThe formula for the Fourier coefficient \\(b_k\\) is given by: \\(b_k=\\frac{1}{L}\\int_{-L}^{L}f(t)sin\\left(\\frac{{k}\\pi}{L}t\\right)dt\\)
\n\\(b_k=\\frac{1}{\\var{L}}\\left(\\int_{-\\var{L}}^{-\\frac{\\var{L}}{2}}\\var{a}sin\\left(\\frac{{k}\\pi}{\\var{L}}t\\right)dt+\\int_{-\\frac{\\var{L}}{2}}^{\\frac{\\var{L}}{2}}\\var{b}sin\\left(\\frac{{k}\\pi}{\\var{L}}t\\right)dt+\\int_{\\frac{\\var{L}}{2}}^{\\var{L}}\\var{c}sin\\left(\\frac{{k}\\pi}{\\var{L}}t\\right)dt\\right)\\)
\n\\(b_k=\\frac{1}{\\var{L}}\\left(-\\frac{\\var{a}*\\var{L}}{{k}\\pi}cos\\left(\\frac{{k}\\pi}{\\var{L}}t\\right)|_{-\\var{L}}^{-\\frac{\\var{L}}{2}}-\\frac{\\var{b}*\\var{L}}{{k}\\pi}cos\\left(\\frac{{k}\\pi}{\\var{L}}t\\right)|_{-\\frac{\\var{L}}{2}}^{\\frac{\\var{L}}{2}}-\\frac{\\var{c}*\\var{L}}{{k}\\pi}cos\\left(\\frac{{k}\\pi}{\\var{L}}t\\right)|_{\\frac{\\var{L}}{2}}^{\\var{L}}\\right)\\)
\n\\(b_k=-\\frac{\\var{a}}{{k}\\pi}cos(-\\frac{{k}\\pi}{2})+\\frac{\\var{a}}{{k}\\pi}cos(-{k}\\pi)-\\frac{\\var{b}}{{k}\\pi}cos(\\frac{{k}\\pi}{2})+\\frac{\\var{b}}{{k}\\pi}cos(-\\frac{{k}\\pi}{2})-\\frac{\\var{c}}{{k}\\pi}cos({k}\\pi)+\\frac{\\var{c}}{{k}\\pi}cos(\\frac{{k}\\pi}{2})\\)
\n\\(cos(-\\theta)=cos(\\theta)\\)
\n\\(b_k=-\\frac{\\var{a}}{{k}\\pi}cos(\\frac{{k}\\pi}{2})+\\frac{\\var{a}}{{k}\\pi}cos({k}\\pi)-\\frac{\\var{b}}{{k}\\pi}cos(\\frac{{k}\\pi}{2})+\\frac{\\var{b}}{{k}\\pi}cos(\\frac{{k}\\pi}{2})-\\frac{\\var{c}}{{k}\\pi}cos({k}\\pi)+\\frac{\\var{c}}{{k}\\pi}cos(\\frac{{k}\\pi}{2})\\)
\n\\(b_k=\\frac{\\var{c}-\\var{a}}{{k}\\pi}cos(\\frac{{k}\\pi}{2})+\\frac{\\var{a}-\\var{c}}{{k}\\pi}cos({k}\\pi)\\)
\n\\(b_\\var{k}=\\simplify{({c}-{a})/({k}*pi)cos({k}*pi/2)}+\\simplify{(-{c}+{a})/({k}*pi)cos({k}*pi)}\\)
\n\nRecall the amplitude of the \\(\\var{k}\\)th harmonic component is given by \\(\\sqrt{(a_\\var{k})^2+(b_\\var{k})^2}\\)
", "rulesets": {}, "variables": {"k": {"name": "k", "group": "Ungrouped variables", "definition": "random(5 .. 19#2)", "description": "", "templateType": "randrange"}, "c": {"name": "c", "group": "Ungrouped variables", "definition": "random(6 .. 11#1)", "description": "", "templateType": "randrange"}, "L": {"name": "L", "group": "Ungrouped variables", "definition": "random(2 .. 11#1)", "description": "", "templateType": "randrange"}, "b": {"name": "b", "group": "Ungrouped variables", "definition": "random(12 .. 24#1)", "description": "", "templateType": "randrange"}, "a": {"name": "a", "group": "Ungrouped variables", "definition": "random(1 .. 5#2)", "description": "", "templateType": "randrange"}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["a", "L", "k", "b", "c"], "variable_groups": [], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "gapfill", "useCustomName": false, "customName": "", "marks": 0, "showCorrectAnswer": true, "showFeedbackIcon": true, "scripts": {}, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "adaptiveMarkingPenalty": 0, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "prompt": "Calculate the value of the first term of the Fourier series \\(\\frac{a_{0}}{2}\\).
\n\\(\\frac{a_{0}}{2}\\) = [[0]]
", "gaps": [{"type": "numberentry", "useCustomName": false, "customName": "", "marks": 1, "showCorrectAnswer": true, "showFeedbackIcon": true, "scripts": {}, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "adaptiveMarkingPenalty": 0, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "minValue": "({a}/2+{b}+{c}/2)/2", "maxValue": "({a}/2+{b}+{c}/2)/2", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "precisionType": "dp", "precision": "3", "precisionPartialCredit": 0, "precisionMessage": "You have not given your answer to the correct precision.", "strictPrecision": false, "showPrecisionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}], "sortAnswers": false}, {"type": "gapfill", "useCustomName": false, "customName": "", "marks": 0, "showCorrectAnswer": true, "showFeedbackIcon": true, "scripts": {}, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "adaptiveMarkingPenalty": 0, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "prompt": "Determine an expression for the trigonometric Fourier coefficient \\( a_{k}\\) and hence calculate the value for the value for \\(a_{\\var{k}}\\).
\n\\( a_{\\var{k}}\\) = [[0]]
", "gaps": [{"type": "numberentry", "useCustomName": false, "customName": "", "marks": "1", "showCorrectAnswer": true, "showFeedbackIcon": true, "scripts": {}, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "adaptiveMarkingPenalty": 0, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "minValue": "(-{a}+2*{b}-{c})*sin({k}*pi/2)/(k}*pi)", "maxValue": "(-{a}+2*{b}-{c})*sin({k}*pi/2)/(k}*pi)", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "precisionType": "dp", "precision": "3", "precisionPartialCredit": 0, "precisionMessage": "You have not given your answer to the correct precision.", "strictPrecision": false, "showPrecisionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}], "sortAnswers": false}, {"type": "gapfill", "useCustomName": false, "customName": "", "marks": 0, "showCorrectAnswer": true, "showFeedbackIcon": true, "scripts": {}, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "adaptiveMarkingPenalty": 0, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "prompt": "Determine an expression for the trigonometric Fourier coefficient \\( b_{k}\\) and hence calculate the value for the value for \\(b_{\\var{k}}\\), correct to three decimal places.
\n\\( b_{\\var{k}}\\) = [[0]]
", "gaps": [{"type": "numberentry", "useCustomName": false, "customName": "", "marks": "1", "showCorrectAnswer": true, "showFeedbackIcon": true, "scripts": {}, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "adaptiveMarkingPenalty": 0, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "minValue": "({c}-{a})cos({k}*pi/2)/({k}*pi)+({a}-{c})cos({k}*pi)/({k}*pi)", "maxValue": "({c}-{a})cos({k}*pi/2)/({k}*pi)+({a}-{c})cos({k}*pi)/({k}*pi)", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "precisionType": "dp", "precision": "3", "precisionPartialCredit": 0, "precisionMessage": "You have not given your answer to the correct precision.", "strictPrecision": false, "showPrecisionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}], "sortAnswers": false}, {"type": "gapfill", "useCustomName": false, "customName": "", "marks": 0, "showCorrectAnswer": true, "showFeedbackIcon": true, "scripts": {}, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "adaptiveMarkingPenalty": 0, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "prompt": "Calculate the amplitude of the \\(\\var{k}\\)th harmonic component, correct to two decimal places.
\nAmplitude = [[0]]
", "gaps": [{"type": "numberentry", "useCustomName": false, "customName": "", "marks": 1, "showCorrectAnswer": true, "showFeedbackIcon": true, "scripts": {}, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "adaptiveMarkingPenalty": 0, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "minValue": "sqrt(((-{a}+2*{b}-{c})*sin({k}*pi/2)/(k}*pi))^2+(({c}-{a})cos({k}*pi/2)/({k}*pi)+({a}-{c})cos({k}*pi)/({k}*pi))^2)", "maxValue": "sqrt(((-{a}+2*{b}-{c})*sin({k}*pi/2)/(k}*pi))^2+(({c}-{a})cos({k}*pi/2)/({k}*pi)+({a}-{c})cos({k}*pi)/({k}*pi))^2)", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "precisionType": "dp", "precision": "3", "precisionPartialCredit": 0, "precisionMessage": "You have not given your answer to the correct precision.", "strictPrecision": false, "showPrecisionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}], "sortAnswers": false}]}, {"name": "4.307", "extensions": ["quantities"], "custom_part_types": [{"source": {"pk": 7, "author": {"name": "Christian Lawson-Perfect", "pk": 7}, "edit_page": "/part_type/7/edit"}, "name": "Quantity with units", "short_name": "quantity", "description": "The student enters a quantity with units.
", "help_url": "https://github.com/numbas/numbas-extension-quantities", "input_widget": "string", "input_options": {"correctAnswer": "plain_string(settings[\"correctAnswer\"])", "hint": {"static": false, "value": "switch(\n settings[\"hint\"]=\"remind units\",\n \"Include units in your answer.\",\n settings[\"hint\"]=\"show units\",\n \"Give your answer in \"+units_string(settings[\"correctAnswer\"])\n ,\n \"\"\n)"}, "allowEmpty": {"static": true, "value": false}}, "can_be_gap": true, "can_be_step": true, "marking_script": "mark:\napply(valid_number);\napply(student_quantity);\napply(has_units);\napply(compatible);\ntry(\n correctif(close_enough),\n x,\n apply(student_quantity)\n);\napply(same_units)\n\ninterpreted_answer:\nstudent_quantity\n\nallowed_notation_styles:\n[\"plain\",\"en\"]\n\nmatch_student_number:\nmatchnumber(studentAnswer,allowed_notation_styles)\n\nstudent_number:\nmatch_student_number[1]\n\nraw_student_units:\ntry(\n quantity(studentAnswer[len(match_student_number[0])..len(studentAnswer)]),\n message,\n warn(\"Your answer is not a valid quantity.\");\n fail(\"Your answer is not a valid quantity.\")\n)\n\nstudent_units:\nif(compatible(raw_student_units,correct_units) or settings[\"incompatible_units_action\"]<>\"convert\",\n raw_student_units,\n correct_units\n)\n\nstudent_quantity:\napply(student_units);\ntry(\n student_number * student_units,\n message,\n warn(\"Your answer is not a valid quantity.\");\n fail(\"Your answer is not a valid quantity.\")\n)\n\ncorrect_quantity:\nsettings[\"correctAnswer\"]\n\ncompatible:\nif(compatible(raw_student_units,correct_quantity),\n true\n,\n let(message,\"Your answer does not have the correct dimensions.\",\n if(settings[\"incompatible_units_action\"]=\"prevent\",\n warn(message);\n fail(message)\n ,\n if(settings[\"incompatible_units_action\"]=\"convert\",\n incorrect(\"Your answer does not have the correct dimensions. It will be marked as if the correct dimensions were used, and then a penalty will be applied.\")\n ,\n incorrect(\"Your answer does not have the correct dimensions.\");\n end()\n )\n );\n false\n )\n)\n\ncorrect_units:\nunits(correct_quantity)\n\nsame_units:\nassert(raw_student_units=correct_units,\n let(\n message,if(settings[\"hint\"]=\"show units\",\"You did not give your answer in \"+units_string(correct_units)+\".\", \"Your answer is not in the expected units.\"),\n switch(\n settings[\"different_units_action\"]=\"prevent\",\n warn(message);\n fail(message)\n ,\n settings[\"different_units_action\"]=\"incorrect\",\n incorrect(message); \n warn(message);\n end()\n ,\n settings[\"different_units_action\"]=\"warn\",\n warn(message);\n multiply_credit(1-settings[\"different_units_penalty\"],message)\n ,\n settings[\"different_units_penalty\"]<1,\n multiply_credit(1-settings[\"different_units_penalty\"],message)\n ,\n false\n )\n );\n false\n)\n\nhas_units:\nassert(not unitless(student_quantity),\n assert(settings[\"allow_unitless\"],\n warn(\"You must include the units in your answer.\");\n fail(\"You did not include units in your answer.\")\n )\n)\n\ncan_compare:\ncompatible or settings[\"incompatible_units_action\"]=\"convert\"\n\nclose_enough:\nif(can_compare,\n student_quantity>=correct_quantity - wiggle \n and \n student_quantity<=correct_quantity + wiggle \n,\n false\n)\n\nwiggle:\nunits(correct_quantity)*abs(eval(settings[\"wiggle\"]))\n\nvalid_number:\nif(isNaN(student_number),\n warn(translate(\"part.numberentry.answer invalid\"));\n fail(translate(\"part.numberentry.answer invalid\"))\n,\n true\n )", "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": "apply(valid_number);\napply(student_quantity);\napply(has_units);\napply(compatible);\ntry(\n correctif(close_enough),\n x,\n apply(student_quantity)\n);\napply(same_units)"}, {"name": "interpreted_answer", "description": "A value representing the student's answer to this part.", "definition": "student_quantity"}, {"name": "allowed_notation_styles", "description": "", "definition": "[\"plain\",\"en\"]"}, {"name": "match_student_number", "description": "", "definition": "matchnumber(studentAnswer,allowed_notation_styles)"}, {"name": "student_number", "description": "The scalar part of the student's quantity
", "definition": "match_student_number[1]"}, {"name": "raw_student_units", "description": "The units of the student's quantity, before converting.
", "definition": "try(\n quantity(studentAnswer[len(match_student_number[0])..len(studentAnswer)]),\n message,\n warn(\"Your answer is not a valid quantity.\");\n fail(\"Your answer is not a valid quantity.\")\n)"}, {"name": "student_units", "description": "The units of the student's quantity.
\nIf the student used units incompatible with the units in the expected answer, and the \"what to do if incompatible units used\" option is set to \"mark as if correct units used\", the student's units are ignored and the expected units are used instead.
", "definition": "if(compatible(raw_student_units,correct_units) or settings[\"incompatible_units_action\"]<>\"convert\",\n raw_student_units,\n correct_units\n)"}, {"name": "student_quantity", "description": "The student's answer, interpreted as a quantity.
\nMarking fails if the student does not enter a valid quantity.
", "definition": "apply(student_units);\ntry(\n student_number * student_units,\n message,\n warn(\"Your answer is not a valid quantity.\");\n fail(\"Your answer is not a valid quantity.\")\n)"}, {"name": "correct_quantity", "description": "", "definition": "settings[\"correctAnswer\"]"}, {"name": "compatible", "description": "Are the units of the student's quantity compatible with the units of the expected quantity?
", "definition": "if(compatible(raw_student_units,correct_quantity),\n true\n,\n let(message,\"Your answer does not have the correct dimensions.\",\n if(settings[\"incompatible_units_action\"]=\"prevent\",\n warn(message);\n fail(message)\n ,\n if(settings[\"incompatible_units_action\"]=\"convert\",\n incorrect(\"Your answer does not have the correct dimensions. It will be marked as if the correct dimensions were used, and then a penalty will be applied.\")\n ,\n incorrect(\"Your answer does not have the correct dimensions.\");\n end()\n )\n );\n false\n )\n)"}, {"name": "correct_units", "description": "", "definition": "units(correct_quantity)"}, {"name": "same_units", "description": "/Are the student's quantity and the expected quantity in exactly the same units?
", "definition": "assert(raw_student_units=correct_units,\n let(\n message,if(settings[\"hint\"]=\"show units\",\"You did not give your answer in \"+units_string(correct_units)+\".\", \"Your answer is not in the expected units.\"),\n switch(\n settings[\"different_units_action\"]=\"prevent\",\n warn(message);\n fail(message)\n ,\n settings[\"different_units_action\"]=\"incorrect\",\n incorrect(message); \n warn(message);\n end()\n ,\n settings[\"different_units_action\"]=\"warn\",\n warn(message);\n multiply_credit(1-settings[\"different_units_penalty\"],message)\n ,\n settings[\"different_units_penalty\"]<1,\n multiply_credit(1-settings[\"different_units_penalty\"],message)\n ,\n false\n )\n );\n false\n)"}, {"name": "has_units", "description": "", "definition": "assert(not unitless(student_quantity),\n assert(settings[\"allow_unitless\"],\n warn(\"You must include the units in your answer.\");\n fail(\"You did not include units in your answer.\")\n )\n)"}, {"name": "can_compare", "description": "Can the student's answer be compared with the correct answer? True if compatible units used, or \"mark as if correct units used\" selected.
", "definition": "compatible or settings[\"incompatible_units_action\"]=\"convert\""}, {"name": "close_enough", "description": "Is the student's quantity within the allowed tolerance of the expected answer?
", "definition": "if(can_compare,\n student_quantity>=correct_quantity - wiggle \n and \n student_quantity<=correct_quantity + wiggle \n,\n false\n)"}, {"name": "wiggle", "description": "", "definition": "units(correct_quantity)*abs(eval(settings[\"wiggle\"]))"}, {"name": "valid_number", "description": "Is the scalar part of the student's answer a valid number?
", "definition": "if(isNaN(student_number),\n warn(translate(\"part.numberentry.answer invalid\"));\n fail(translate(\"part.numberentry.answer invalid\"))\n,\n true\n )\n"}], "settings": [{"name": "correctAnswer", "label": "Correct answer", "help_url": "", "hint": "The expected quantity.", "input_type": "code", "default_value": "", "evaluate": true}, {"name": "hint", "label": "Input hint", "help_url": "", "hint": "", "input_type": "dropdown", "default_value": "remind units", "choices": [{"value": "none", "label": "None"}, {"value": "remind units", "label": "Remind to include units"}, {"value": "show units", "label": "Show required units"}]}, {"name": "allow_unitless", "label": "Allow unitless answer?", "help_url": "", "hint": "If not ticked, the student is prevented from submitting an answer without specifying units.", "input_type": "checkbox", "default_value": true}, {"name": "incompatible_units_action", "label": "What to do if incompatible units used", "help_url": "", "hint": "If the student's answer is given in units incompatible with the correct answer's units:Et legeme på {m} ligger først i ro . Så blir det i {t} på virket av kraftsummen {f0}.
\nSkriv svarene med 2 desimaler og enhet.
", "advice": "", "rulesets": {}, "variables": {"t": {"name": "t", "group": "Ungrouped variables", "definition": "quantity(random(1..10),\"s\")", "description": "", "templateType": "anything"}, "f0": {"name": "f0", "group": "Ungrouped variables", "definition": "quantity(random(1..5),\"N\")", "description": "", "templateType": "anything"}, "v": {"name": "v", "group": "Unnamed group", "definition": "as_si(precround((f0)/m*t ,2))", "description": "", "templateType": "anything"}, "w0": {"name": "w0", "group": "Unnamed group", "definition": "as_si(precround(s*f0 ,2))", "description": "", "templateType": "anything"}, "s": {"name": "s", "group": "Ungrouped variables", "definition": "as_si(precround(1/2*f0/m*t*t,2))", "description": "", "templateType": "anything"}, "m": {"name": "m", "group": "Ungrouped variables", "definition": "quantity(random(1..20),\"kg\")", "description": "", "templateType": "anything"}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["f0", "m", "s", "t"], "variable_groups": [{"name": "Unnamed group", "variables": ["v", "w0"]}], "functions": {}, "preamble": {"js": "", "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": "Hva blir sluttfarten på legemet? [[0]]
", "gaps": [{"type": "quantity", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "settings": {"correctAnswer": "v", "hint": "remind units", "allow_unitless": true, "incompatible_units_action": "incorrect", "different_units_action": "warn", "different_units_penalty": "100", "wiggle": "0.02"}}], "sortAnswers": false}, {"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": "Kor langt har legemet forflyttet seg ? [[0]]
\n", "gaps": [{"type": "quantity", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "settings": {"correctAnswer": "s", "hint": "remind units", "allow_unitless": true, "incompatible_units_action": "incorrect", "different_units_action": "incorrect", "different_units_penalty": "100", "wiggle": "0.05"}}], "sortAnswers": false}, {"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": "Hvor stor arbeid blir utført på legemet? [[0]]
\n", "gaps": [{"type": "quantity", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "settings": {"correctAnswer": "w0", "hint": "remind units", "allow_unitless": true, "incompatible_units_action": "incorrect", "different_units_action": "incorrect", "different_units_penalty": "100", "wiggle": "0.5"}}], "sortAnswers": false}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always"}, {"name": "3.316", "extensions": ["quantities"], "custom_part_types": [{"source": {"pk": 7, "author": {"name": "Christian Lawson-Perfect", "pk": 7}, "edit_page": "/part_type/7/edit"}, "name": "Quantity with units", "short_name": "quantity", "description": "The student enters a quantity with units.
", "help_url": "https://github.com/numbas/numbas-extension-quantities", "input_widget": "string", "input_options": {"correctAnswer": "plain_string(settings[\"correctAnswer\"])", "hint": {"static": false, "value": "switch(\n settings[\"hint\"]=\"remind units\",\n \"Include units in your answer.\",\n settings[\"hint\"]=\"show units\",\n \"Give your answer in \"+units_string(settings[\"correctAnswer\"])\n ,\n \"\"\n)"}, "allowEmpty": {"static": true, "value": false}}, "can_be_gap": true, "can_be_step": true, "marking_script": "mark:\napply(valid_number);\napply(student_quantity);\napply(has_units);\napply(compatible);\ntry(\n correctif(close_enough),\n x,\n apply(student_quantity)\n);\napply(same_units)\n\ninterpreted_answer:\nstudent_quantity\n\nallowed_notation_styles:\n[\"plain\",\"en\"]\n\nmatch_student_number:\nmatchnumber(studentAnswer,allowed_notation_styles)\n\nstudent_number:\nmatch_student_number[1]\n\nraw_student_units:\ntry(\n quantity(studentAnswer[len(match_student_number[0])..len(studentAnswer)]),\n message,\n warn(\"Your answer is not a valid quantity.\");\n fail(\"Your answer is not a valid quantity.\")\n)\n\nstudent_units:\nif(compatible(raw_student_units,correct_units) or settings[\"incompatible_units_action\"]<>\"convert\",\n raw_student_units,\n correct_units\n)\n\nstudent_quantity:\napply(student_units);\ntry(\n student_number * student_units,\n message,\n warn(\"Your answer is not a valid quantity.\");\n fail(\"Your answer is not a valid quantity.\")\n)\n\ncorrect_quantity:\nsettings[\"correctAnswer\"]\n\ncompatible:\nif(compatible(raw_student_units,correct_quantity),\n true\n,\n let(message,\"Your answer does not have the correct dimensions.\",\n if(settings[\"incompatible_units_action\"]=\"prevent\",\n warn(message);\n fail(message)\n ,\n if(settings[\"incompatible_units_action\"]=\"convert\",\n incorrect(\"Your answer does not have the correct dimensions. It will be marked as if the correct dimensions were used, and then a penalty will be applied.\")\n ,\n incorrect(\"Your answer does not have the correct dimensions.\");\n end()\n )\n );\n false\n )\n)\n\ncorrect_units:\nunits(correct_quantity)\n\nsame_units:\nassert(raw_student_units=correct_units,\n let(\n message,if(settings[\"hint\"]=\"show units\",\"You did not give your answer in \"+units_string(correct_units)+\".\", \"Your answer is not in the expected units.\"),\n switch(\n settings[\"different_units_action\"]=\"prevent\",\n warn(message);\n fail(message)\n ,\n settings[\"different_units_action\"]=\"incorrect\",\n incorrect(message); \n warn(message);\n end()\n ,\n settings[\"different_units_action\"]=\"warn\",\n warn(message);\n multiply_credit(1-settings[\"different_units_penalty\"],message)\n ,\n settings[\"different_units_penalty\"]<1,\n multiply_credit(1-settings[\"different_units_penalty\"],message)\n ,\n false\n )\n );\n false\n)\n\nhas_units:\nassert(not unitless(student_quantity),\n assert(settings[\"allow_unitless\"],\n warn(\"You must include the units in your answer.\");\n fail(\"You did not include units in your answer.\")\n )\n)\n\ncan_compare:\ncompatible or settings[\"incompatible_units_action\"]=\"convert\"\n\nclose_enough:\nif(can_compare,\n student_quantity>=correct_quantity - wiggle \n and \n student_quantity<=correct_quantity + wiggle \n,\n false\n)\n\nwiggle:\nunits(correct_quantity)*abs(eval(settings[\"wiggle\"]))\n\nvalid_number:\nif(isNaN(student_number),\n warn(translate(\"part.numberentry.answer invalid\"));\n fail(translate(\"part.numberentry.answer invalid\"))\n,\n true\n )", "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": "apply(valid_number);\napply(student_quantity);\napply(has_units);\napply(compatible);\ntry(\n correctif(close_enough),\n x,\n apply(student_quantity)\n);\napply(same_units)"}, {"name": "interpreted_answer", "description": "A value representing the student's answer to this part.", "definition": "student_quantity"}, {"name": "allowed_notation_styles", "description": "", "definition": "[\"plain\",\"en\"]"}, {"name": "match_student_number", "description": "", "definition": "matchnumber(studentAnswer,allowed_notation_styles)"}, {"name": "student_number", "description": "The scalar part of the student's quantity
", "definition": "match_student_number[1]"}, {"name": "raw_student_units", "description": "The units of the student's quantity, before converting.
", "definition": "try(\n quantity(studentAnswer[len(match_student_number[0])..len(studentAnswer)]),\n message,\n warn(\"Your answer is not a valid quantity.\");\n fail(\"Your answer is not a valid quantity.\")\n)"}, {"name": "student_units", "description": "The units of the student's quantity.
\nIf the student used units incompatible with the units in the expected answer, and the \"what to do if incompatible units used\" option is set to \"mark as if correct units used\", the student's units are ignored and the expected units are used instead.
", "definition": "if(compatible(raw_student_units,correct_units) or settings[\"incompatible_units_action\"]<>\"convert\",\n raw_student_units,\n correct_units\n)"}, {"name": "student_quantity", "description": "The student's answer, interpreted as a quantity.
\nMarking fails if the student does not enter a valid quantity.
", "definition": "apply(student_units);\ntry(\n student_number * student_units,\n message,\n warn(\"Your answer is not a valid quantity.\");\n fail(\"Your answer is not a valid quantity.\")\n)"}, {"name": "correct_quantity", "description": "", "definition": "settings[\"correctAnswer\"]"}, {"name": "compatible", "description": "Are the units of the student's quantity compatible with the units of the expected quantity?
", "definition": "if(compatible(raw_student_units,correct_quantity),\n true\n,\n let(message,\"Your answer does not have the correct dimensions.\",\n if(settings[\"incompatible_units_action\"]=\"prevent\",\n warn(message);\n fail(message)\n ,\n if(settings[\"incompatible_units_action\"]=\"convert\",\n incorrect(\"Your answer does not have the correct dimensions. It will be marked as if the correct dimensions were used, and then a penalty will be applied.\")\n ,\n incorrect(\"Your answer does not have the correct dimensions.\");\n end()\n )\n );\n false\n )\n)"}, {"name": "correct_units", "description": "", "definition": "units(correct_quantity)"}, {"name": "same_units", "description": "/Are the student's quantity and the expected quantity in exactly the same units?
", "definition": "assert(raw_student_units=correct_units,\n let(\n message,if(settings[\"hint\"]=\"show units\",\"You did not give your answer in \"+units_string(correct_units)+\".\", \"Your answer is not in the expected units.\"),\n switch(\n settings[\"different_units_action\"]=\"prevent\",\n warn(message);\n fail(message)\n ,\n settings[\"different_units_action\"]=\"incorrect\",\n incorrect(message); \n warn(message);\n end()\n ,\n settings[\"different_units_action\"]=\"warn\",\n warn(message);\n multiply_credit(1-settings[\"different_units_penalty\"],message)\n ,\n settings[\"different_units_penalty\"]<1,\n multiply_credit(1-settings[\"different_units_penalty\"],message)\n ,\n false\n )\n );\n false\n)"}, {"name": "has_units", "description": "", "definition": "assert(not unitless(student_quantity),\n assert(settings[\"allow_unitless\"],\n warn(\"You must include the units in your answer.\");\n fail(\"You did not include units in your answer.\")\n )\n)"}, {"name": "can_compare", "description": "Can the student's answer be compared with the correct answer? True if compatible units used, or \"mark as if correct units used\" selected.
", "definition": "compatible or settings[\"incompatible_units_action\"]=\"convert\""}, {"name": "close_enough", "description": "Is the student's quantity within the allowed tolerance of the expected answer?
", "definition": "if(can_compare,\n student_quantity>=correct_quantity - wiggle \n and \n student_quantity<=correct_quantity + wiggle \n,\n false\n)"}, {"name": "wiggle", "description": "", "definition": "units(correct_quantity)*abs(eval(settings[\"wiggle\"]))"}, {"name": "valid_number", "description": "Is the scalar part of the student's answer a valid number?
", "definition": "if(isNaN(student_number),\n warn(translate(\"part.numberentry.answer invalid\"));\n fail(translate(\"part.numberentry.answer invalid\"))\n,\n true\n )\n"}], "settings": [{"name": "correctAnswer", "label": "Correct answer", "help_url": "", "hint": "The expected quantity.", "input_type": "code", "default_value": "", "evaluate": true}, {"name": "hint", "label": "Input hint", "help_url": "", "hint": "", "input_type": "dropdown", "default_value": "remind units", "choices": [{"value": "none", "label": "None"}, {"value": "remind units", "label": "Remind to include units"}, {"value": "show units", "label": "Show required units"}]}, {"name": "allow_unitless", "label": "Allow unitless answer?", "help_url": "", "hint": "If not ticked, the student is prevented from submitting an answer without specifying units.", "input_type": "checkbox", "default_value": true}, {"name": "incompatible_units_action", "label": "What to do if incompatible units used", "help_url": "", "hint": "If the student's answer is given in units incompatible with the correct answer's units:Krefter er målt i newton, N. To krefter er målt med verdiene {n0} ± {u0} og {n1} ± {u1}.
\nBeregn den absolutte og relative usikkerheten for
", "advice": "", "rulesets": {}, "variables": {"n0": {"name": "n0", "group": "Ungrouped variables", "definition": "precround(quantity(random(15.0..25.0#0.2),\"N\"),2)", "description": "", "templateType": "anything"}, "sumabs": {"name": "sumabs", "group": "Unnamed group", "definition": "u0+u1", "description": "", "templateType": "anything"}, "sumrel": {"name": "sumrel", "group": "Unnamed group", "definition": "precround(sumabs/sum,2)", "description": "", "templateType": "anything"}, "difrel": {"name": "difrel", "group": "Unnamed group", "definition": "precround(sumabs/dif,2)", "description": "sumabs / dif
", "templateType": "anything"}, "n1": {"name": "n1", "group": "Ungrouped variables", "definition": "precround(quantity(random(15.0..25.0#0.2),\"N\"),2)", "description": "", "templateType": "anything"}, "u1": {"name": "u1", "group": "Ungrouped variables", "definition": "quantity(random(1..5),\"N\")", "description": "", "templateType": "anything"}, "sum": {"name": "sum", "group": "Unnamed group", "definition": "n0+n1", "description": "", "templateType": "anything"}, "dif": {"name": "dif", "group": "Unnamed group", "definition": "abs(n0-n1)", "description": "", "templateType": "anything"}, "u0": {"name": "u0", "group": "Ungrouped variables", "definition": "quantity(random(1..5),\"N\")", "description": "", "templateType": "anything"}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["n0", "n1", "u0", "u1"], "variable_groups": [{"name": "Unnamed group", "variables": ["sumabs", "sumrel", "sum", "dif", "difrel"]}], "functions": {}, "preamble": {"js": "", "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": "summen av kreftene
\n[[0]] og [[1]]
", "gaps": [{"type": "quantity", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": false, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "settings": {"correctAnswer": "sumabs", "hint": "remind units", "allow_unitless": true, "incompatible_units_action": "incorrect", "different_units_action": "convert", "different_units_penalty": "100", "wiggle": "10^-12"}}, {"type": "quantity", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": false, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "settings": {"correctAnswer": "sumrel", "hint": "none", "allow_unitless": true, "incompatible_units_action": "incorrect", "different_units_action": "convert", "different_units_penalty": "100", "wiggle": "10^-12"}}], "sortAnswers": false}, {"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": "differansen av kreftene
\n[[0]] og [[1]]
", "gaps": [{"type": "quantity", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "settings": {"correctAnswer": "sumabs", "hint": "remind units", "allow_unitless": true, "incompatible_units_action": "incorrect", "different_units_action": "convert", "different_units_penalty": "100", "wiggle": "10^-12"}}, {"type": "quantity", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "settings": {"correctAnswer": "difrel", "hint": "none", "allow_unitless": true, "incompatible_units_action": "incorrect", "different_units_action": "convert", "different_units_penalty": "100", "wiggle": "10^-12"}}], "sortAnswers": false}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always"}]}], "allowPrinting": true, "navigation": {"allowregen": true, "reverse": true, "browse": true, "allowsteps": true, "showfrontpage": true, "showresultspage": "oncompletion", "navigatemode": "sequence", "onleave": {"action": "none", "message": ""}, "preventleave": true, "startpassword": ""}, "timing": {"allowPause": true, "timeout": {"action": "none", "message": ""}, "timedwarning": {"action": "none", "message": ""}}, "feedback": {"showactualmark": true, "showtotalmark": true, "showanswerstate": true, "allowrevealanswer": true, "advicethreshold": 0, "intro": "", "reviewshowscore": true, "reviewshowfeedback": true, "reviewshowexpectedanswer": true, "reviewshowadvice": true, "feedbackmessages": []}, "diagnostic": {"knowledge_graph": {"topics": [], "learning_objectives": []}, "script": "diagnosys", "customScript": ""}, "contributors": [{"name": "Mathias Sandulescu", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/3503/"}], "extensions": ["quantities"], "custom_part_types": [{"source": {"pk": 7, "author": {"name": "Christian Lawson-Perfect", "pk": 7}, "edit_page": "/part_type/7/edit"}, "name": "Quantity with units", "short_name": "quantity", "description": "The student enters a quantity with units.
", "help_url": "https://github.com/numbas/numbas-extension-quantities", "input_widget": "string", "input_options": {"correctAnswer": "plain_string(settings[\"correctAnswer\"])", "hint": {"static": false, "value": "switch(\n settings[\"hint\"]=\"remind units\",\n \"Include units in your answer.\",\n settings[\"hint\"]=\"show units\",\n \"Give your answer in \"+units_string(settings[\"correctAnswer\"])\n ,\n \"\"\n)"}, "allowEmpty": {"static": true, "value": false}}, "can_be_gap": true, "can_be_step": true, "marking_script": "mark:\napply(valid_number);\napply(student_quantity);\napply(has_units);\napply(compatible);\ntry(\n correctif(close_enough),\n x,\n apply(student_quantity)\n);\napply(same_units)\n\ninterpreted_answer:\nstudent_quantity\n\nallowed_notation_styles:\n[\"plain\",\"en\"]\n\nmatch_student_number:\nmatchnumber(studentAnswer,allowed_notation_styles)\n\nstudent_number:\nmatch_student_number[1]\n\nraw_student_units:\ntry(\n quantity(studentAnswer[len(match_student_number[0])..len(studentAnswer)]),\n message,\n warn(\"Your answer is not a valid quantity.\");\n fail(\"Your answer is not a valid quantity.\")\n)\n\nstudent_units:\nif(compatible(raw_student_units,correct_units) or settings[\"incompatible_units_action\"]<>\"convert\",\n raw_student_units,\n correct_units\n)\n\nstudent_quantity:\napply(student_units);\ntry(\n student_number * student_units,\n message,\n warn(\"Your answer is not a valid quantity.\");\n fail(\"Your answer is not a valid quantity.\")\n)\n\ncorrect_quantity:\nsettings[\"correctAnswer\"]\n\ncompatible:\nif(compatible(raw_student_units,correct_quantity),\n true\n,\n let(message,\"Your answer does not have the correct dimensions.\",\n if(settings[\"incompatible_units_action\"]=\"prevent\",\n warn(message);\n fail(message)\n ,\n if(settings[\"incompatible_units_action\"]=\"convert\",\n incorrect(\"Your answer does not have the correct dimensions. It will be marked as if the correct dimensions were used, and then a penalty will be applied.\")\n ,\n incorrect(\"Your answer does not have the correct dimensions.\");\n end()\n )\n );\n false\n )\n)\n\ncorrect_units:\nunits(correct_quantity)\n\nsame_units:\nassert(raw_student_units=correct_units,\n let(\n message,if(settings[\"hint\"]=\"show units\",\"You did not give your answer in \"+units_string(correct_units)+\".\", \"Your answer is not in the expected units.\"),\n switch(\n settings[\"different_units_action\"]=\"prevent\",\n warn(message);\n fail(message)\n ,\n settings[\"different_units_action\"]=\"incorrect\",\n incorrect(message); \n warn(message);\n end()\n ,\n settings[\"different_units_action\"]=\"warn\",\n warn(message);\n multiply_credit(1-settings[\"different_units_penalty\"],message)\n ,\n settings[\"different_units_penalty\"]<1,\n multiply_credit(1-settings[\"different_units_penalty\"],message)\n ,\n false\n )\n );\n false\n)\n\nhas_units:\nassert(not unitless(student_quantity),\n assert(settings[\"allow_unitless\"],\n warn(\"You must include the units in your answer.\");\n fail(\"You did not include units in your answer.\")\n )\n)\n\ncan_compare:\ncompatible or settings[\"incompatible_units_action\"]=\"convert\"\n\nclose_enough:\nif(can_compare,\n student_quantity>=correct_quantity - wiggle \n and \n student_quantity<=correct_quantity + wiggle \n,\n false\n)\n\nwiggle:\nunits(correct_quantity)*abs(eval(settings[\"wiggle\"]))\n\nvalid_number:\nif(isNaN(student_number),\n warn(translate(\"part.numberentry.answer invalid\"));\n fail(translate(\"part.numberentry.answer invalid\"))\n,\n true\n )", "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": "apply(valid_number);\napply(student_quantity);\napply(has_units);\napply(compatible);\ntry(\n correctif(close_enough),\n x,\n apply(student_quantity)\n);\napply(same_units)"}, {"name": "interpreted_answer", "description": "A value representing the student's answer to this part.", "definition": "student_quantity"}, {"name": "allowed_notation_styles", "description": "", "definition": "[\"plain\",\"en\"]"}, {"name": "match_student_number", "description": "", "definition": "matchnumber(studentAnswer,allowed_notation_styles)"}, {"name": "student_number", "description": "The scalar part of the student's quantity
", "definition": "match_student_number[1]"}, {"name": "raw_student_units", "description": "The units of the student's quantity, before converting.
", "definition": "try(\n quantity(studentAnswer[len(match_student_number[0])..len(studentAnswer)]),\n message,\n warn(\"Your answer is not a valid quantity.\");\n fail(\"Your answer is not a valid quantity.\")\n)"}, {"name": "student_units", "description": "The units of the student's quantity.
\nIf the student used units incompatible with the units in the expected answer, and the \"what to do if incompatible units used\" option is set to \"mark as if correct units used\", the student's units are ignored and the expected units are used instead.
", "definition": "if(compatible(raw_student_units,correct_units) or settings[\"incompatible_units_action\"]<>\"convert\",\n raw_student_units,\n correct_units\n)"}, {"name": "student_quantity", "description": "The student's answer, interpreted as a quantity.
\nMarking fails if the student does not enter a valid quantity.
", "definition": "apply(student_units);\ntry(\n student_number * student_units,\n message,\n warn(\"Your answer is not a valid quantity.\");\n fail(\"Your answer is not a valid quantity.\")\n)"}, {"name": "correct_quantity", "description": "", "definition": "settings[\"correctAnswer\"]"}, {"name": "compatible", "description": "Are the units of the student's quantity compatible with the units of the expected quantity?
", "definition": "if(compatible(raw_student_units,correct_quantity),\n true\n,\n let(message,\"Your answer does not have the correct dimensions.\",\n if(settings[\"incompatible_units_action\"]=\"prevent\",\n warn(message);\n fail(message)\n ,\n if(settings[\"incompatible_units_action\"]=\"convert\",\n incorrect(\"Your answer does not have the correct dimensions. It will be marked as if the correct dimensions were used, and then a penalty will be applied.\")\n ,\n incorrect(\"Your answer does not have the correct dimensions.\");\n end()\n )\n );\n false\n )\n)"}, {"name": "correct_units", "description": "", "definition": "units(correct_quantity)"}, {"name": "same_units", "description": "/Are the student's quantity and the expected quantity in exactly the same units?
", "definition": "assert(raw_student_units=correct_units,\n let(\n message,if(settings[\"hint\"]=\"show units\",\"You did not give your answer in \"+units_string(correct_units)+\".\", \"Your answer is not in the expected units.\"),\n switch(\n settings[\"different_units_action\"]=\"prevent\",\n warn(message);\n fail(message)\n ,\n settings[\"different_units_action\"]=\"incorrect\",\n incorrect(message); \n warn(message);\n end()\n ,\n settings[\"different_units_action\"]=\"warn\",\n warn(message);\n multiply_credit(1-settings[\"different_units_penalty\"],message)\n ,\n settings[\"different_units_penalty\"]<1,\n multiply_credit(1-settings[\"different_units_penalty\"],message)\n ,\n false\n )\n );\n false\n)"}, {"name": "has_units", "description": "", "definition": "assert(not unitless(student_quantity),\n assert(settings[\"allow_unitless\"],\n warn(\"You must include the units in your answer.\");\n fail(\"You did not include units in your answer.\")\n )\n)"}, {"name": "can_compare", "description": "Can the student's answer be compared with the correct answer? True if compatible units used, or \"mark as if correct units used\" selected.
", "definition": "compatible or settings[\"incompatible_units_action\"]=\"convert\""}, {"name": "close_enough", "description": "Is the student's quantity within the allowed tolerance of the expected answer?
", "definition": "if(can_compare,\n student_quantity>=correct_quantity - wiggle \n and \n student_quantity<=correct_quantity + wiggle \n,\n false\n)"}, {"name": "wiggle", "description": "", "definition": "units(correct_quantity)*abs(eval(settings[\"wiggle\"]))"}, {"name": "valid_number", "description": "Is the scalar part of the student's answer a valid number?
", "definition": "if(isNaN(student_number),\n warn(translate(\"part.numberentry.answer invalid\"));\n fail(translate(\"part.numberentry.answer invalid\"))\n,\n true\n )\n"}], "settings": [{"name": "correctAnswer", "label": "Correct answer", "help_url": "", "hint": "The expected quantity.", "input_type": "code", "default_value": "", "evaluate": true}, {"name": "hint", "label": "Input hint", "help_url": "", "hint": "", "input_type": "dropdown", "default_value": "remind units", "choices": [{"value": "none", "label": "None"}, {"value": "remind units", "label": "Remind to include units"}, {"value": "show units", "label": "Show required units"}]}, {"name": "allow_unitless", "label": "Allow unitless answer?", "help_url": "", "hint": "If not ticked, the student is prevented from submitting an answer without specifying units.", "input_type": "checkbox", "default_value": true}, {"name": "incompatible_units_action", "label": "What to do if incompatible units used", "help_url": "", "hint": "If the student's answer is given in units incompatible with the correct answer's units: