// Numbas version: finer_feedback_settings
{"name": "21. HCF and LCM", "metadata": {"description": "<p>Practice finding factors, HCF and LCM.</p>", "licence": "Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International"}, "duration": 0, "percentPass": 0, "showQuestionGroupNames": false, "shuffleQuestionGroups": false, "showstudentname": true, "question_groups": [{"name": "Group", "pickingStrategy": "all-ordered", "pickQuestions": 1, "questionNames": ["", "", ""], "variable_overrides": [[], [], []], "questions": [{"name": "21.a Find common factors of two numbers", "extensions": [], "custom_part_types": [{"source": {"pk": 2, "author": {"name": "Christian Lawson-Perfect", "pk": 7}, "edit_page": "/part_type/2/edit"}, "name": "List of numbers", "short_name": "list-of-numbers", "description": "<p>The answer is a comma-separated list of numbers.</p>\n<p>The list is marked correct if each number occurs the same number of times as in the expected answer, and no extra numbers are present.</p>\n<p>You can optionally treat the answer as a set, so the number of occurrences doesn't matter, only whether each number is included or not.</p>", "help_url": "", "input_widget": "string", "input_options": {"correctAnswer": "join(\n  if(settings[\"correctAnswerFractions\"],\n    map(let([a,b],rational_approximation(x), string(a/b)),x,settings[\"correctAnswer\"])\n  ,\n    settings[\"correctAnswer\"]\n  ),\n  settings[\"separator\"] + \" \"\n)", "hint": {"static": false, "value": "if(settings[\"show_input_hint\"],\n  \"Enter a list of numbers separated by <code>{settings['separator']}</code>.\",\n  \"\"\n)"}, "allowEmpty": {"static": true, "value": true}}, "can_be_gap": true, "can_be_step": true, "marking_script": "bits:\nlet(b,filter(x<>\"\",x,split(studentAnswer,settings[\"separator\"])),\n    if(isSet,list(set(b)),b)\n)\n\nexpected_numbers:\nlet(l,settings[\"correctAnswer\"] as \"list\",\n    if(isSet,list(set(l)),l)\n)\n\nvalid_numbers:\nif(all(map(not isnan(x),x,interpreted_answer)),\n    true,\n    let(index,filter(isnan(interpreted_answer[x]),x,0..len(interpreted_answer)-1)[0], wrong, bits[index],\n      warn(wrong+\" is not a valid number\");\n      fail(wrong+\" is not a valid number.\")\n    )\n  )\n\nis_sorted:\nassert(sort(interpreted_answer)=interpreted_answer,\n    multiply_credit(0.5,\"Not in order\")\n  )\n\nincluded:\nmap(\n      let(\n        num_student,len(filter(x=y,y,interpreted_answer)),\n        num_expected,len(filter(x=y,y,expected_numbers)),\n        switch(\n          num_student=num_expected,\n            true,\n          num_student<num_expected,\n            incorrect(\n              if(isSet,\"Your answer does not contain \"+x+\" but should.\",\n                \"Your answer does not contain \"+x+\" enough times.\"\n              )\n            );false\n          ,\n            incorrect(\n              if(isSet,\"Your answer contains \"+x+\" but should not.\",\n                \"Your answer contains \"+x+\" too many times.\"\n              )\n            );false\n        )\n      )\n      ,\n      x,\n      sort(list(set(expected_numbers)))\n  )\n\nall_included:\nall(included)\n\nno_extras:\nif(all(map(x in expected_numbers, x, interpreted_answer)),\n    true\n  ,\n    incorrect(\"Your answer contains \"+extra_numbers[0]+\" but should not.\");\n    false\n  )\n\ninterpreted_answer:\nif(lower(studentAnswer) in [\"empty\",\"\u2205\"],[],\n  map(\n    if(settings[\"allowFractions\"],parsenumber_or_fraction(x,notationStyles), parsenumber(x,notationStyles))\n    ,x\n    ,bits\n  )\n)\n\nmark:\nif(studentanswer=\"\",fail(\"You have not entered an answer\"),false);\napply(valid_numbers);\napply(included);\napply(no_extras);\ncorrectif(all_included and no_extras)\n\nnotationStyles:\n[\"en\"]\n\nisSet:\nsettings[\"isSet\"]\n\nextra_numbers:\nfilter(not (x in expected_numbers),x,interpreted_answer)", "marking_notes": [{"name": "bits", "description": "<p>The separate items in the student's answer</p>", "definition": "let(b,filter(x<>\"\",x,split(studentAnswer,settings[\"separator\"])),\n    if(isSet,list(set(b)),b)\n)"}, {"name": "expected_numbers", "description": "", "definition": "let(l,settings[\"correctAnswer\"] as \"list\",\n    if(isSet,list(set(l)),l)\n)"}, {"name": "valid_numbers", "description": "<p>Is every number in the student's list valid?</p>", "definition": "if(all(map(not isnan(x),x,interpreted_answer)),\n    true,\n    let(index,filter(isnan(interpreted_answer[x]),x,0..len(interpreted_answer)-1)[0], wrong, bits[index],\n      warn(wrong+\" is not a valid number\");\n      fail(wrong+\" is not a valid number.\")\n    )\n  )"}, {"name": "is_sorted", "description": "<p>Are the student's answers in ascending order?</p>", "definition": "assert(sort(interpreted_answer)=interpreted_answer,\n    multiply_credit(0.5,\"Not in order\")\n  )"}, {"name": "included", "description": "<p>Is each number in the expected answer present in the student's list the correct number of times?</p>", "definition": "map(\n      let(\n        num_student,len(filter(x=y,y,interpreted_answer)),\n        num_expected,len(filter(x=y,y,expected_numbers)),\n        switch(\n          num_student=num_expected,\n            true,\n          num_student<num_expected,\n            incorrect(\n              if(isSet,\"Your answer does not contain \"+x+\" but should.\",\n                \"Your answer does not contain \"+x+\" enough times.\"\n              )\n            );false\n          ,\n            incorrect(\n              if(isSet,\"Your answer contains \"+x+\" but should not.\",\n                \"Your answer contains \"+x+\" too many times.\"\n              )\n            );false\n        )\n      )\n      ,\n      x,\n      sort(list(set(expected_numbers)))\n  )"}, {"name": "all_included", "description": "<p>Has every number been included the right number of times?</p>", "definition": "all(included)"}, {"name": "no_extras", "description": "<p>True if the student's list doesn't contain any numbers that aren't in the expected answer.</p>", "definition": "if(all(map(x in expected_numbers, x, interpreted_answer)),\n    true\n  ,\n    incorrect(\"Your answer contains \"+extra_numbers[0]+\" but should not.\");\n    false\n  )"}, {"name": "interpreted_answer", "description": "A value representing the student's answer to this part.", "definition": "if(lower(studentAnswer) in [\"empty\",\"\u2205\"],[],\n  map(\n    if(settings[\"allowFractions\"],parsenumber_or_fraction(x,notationStyles), parsenumber(x,notationStyles))\n    ,x\n    ,bits\n  )\n)"}, {"name": "mark", "description": "This is the main marking note. It should award credit and provide feedback based on the student's answer.", "definition": "if(studentanswer=\"\",fail(\"You have not entered an answer\"),false);\napply(valid_numbers);\napply(included);\napply(no_extras);\ncorrectif(all_included and no_extras)"}, {"name": "notationStyles", "description": "", "definition": "[\"en\"]"}, {"name": "isSet", "description": "<p>Should the answer be considered as a set, so the number of times an element occurs doesn't matter?</p>", "definition": "settings[\"isSet\"]"}, {"name": "extra_numbers", "description": "<p>Numbers included in the student's answer that are not in the expected list.</p>", "definition": "filter(not (x in expected_numbers),x,interpreted_answer)"}], "settings": [{"name": "correctAnswer", "label": "Correct answer", "help_url": "", "hint": "The list of numbers that the student should enter. The order does not matter.", "input_type": "code", "default_value": "", "evaluate": true}, {"name": "allowFractions", "label": "Allow the student to enter fractions?", "help_url": "", "hint": "", "input_type": "checkbox", "default_value": false}, {"name": "correctAnswerFractions", "label": "Display the correct answers as fractions?", "help_url": "", "hint": "", "input_type": "checkbox", "default_value": false}, {"name": "isSet", "label": "Is the answer a set?", "help_url": "", "hint": "If ticked, the number of times an element occurs doesn't matter, only whether it's included at all.", "input_type": "checkbox", "default_value": false}, {"name": "show_input_hint", "label": "Show the input hint?", "help_url": "", "hint": "", "input_type": "checkbox", "default_value": true}, {"name": "separator", "label": "Separator", "help_url": "", "hint": "The substring that should separate items in the student's list", "input_type": "string", "default_value": ",", "subvars": false}], "public_availability": "always", "published": true, "extensions": []}], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Mash Sheffield", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/4679/"}, {"name": "Andrew Neate", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/21832/"}], "tags": [], "metadata": {"description": "<p>Find the common factors of two numbers</p>", "licence": "Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International"}, "statement": "<p>List the common factors of $\\var{x}$ and $\\var{y}$.</p>", "advice": "<p>First work out what the factors of $\\var{x}$ and $\\var{y}$ are. The factors for $\\var{x}$ are:</p>\n<p>\\[\\var{DisplayXFactors}\\]</p>\n<p>and the factors for $\\var{y}$ are:</p>\n<p>\\[\\var{DisplayYFactors}.\\]</p>\n<p>The common factors are thoses which appear in both lists.</p>", "rulesets": {}, "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true, "j": false}, "constants": [], "variables": {"x": {"name": "x", "group": "Ungrouped variables", "definition": "random(2..70)", "description": "", "templateType": "anything", "can_override": false}, "y": {"name": "y", "group": "Ungrouped variables", "definition": "random(2..70)", "description": "", "templateType": "anything", "can_override": false}, "CommonFactors": {"name": "CommonFactors", "group": "Ungrouped variables", "definition": "intersection(set(divisors(x)),set(divisors(y)))", "description": "", "templateType": "anything", "can_override": false}, "test": {"name": "test", "group": "Ungrouped variables", "definition": "foldl((total, x) -> total + x, \"\", [\"a\",\"b\",\"c\"])", "description": "", "templateType": "anything", "can_override": false}, "XFactors": {"name": "XFactors", "group": "Ungrouped variables", "definition": "if(x=1,\"1\",\", \"+string(x)) for: x of:divisors(x)", "description": "", "templateType": "anything", "can_override": false}, "YFactors": {"name": "YFactors", "group": "Ungrouped variables", "definition": "if(x=1,\"1\",\", \"+string(x)) for: x of:divisors(y)", "description": "", "templateType": "anything", "can_override": false}, "DisplayXFactors": {"name": "DisplayXFactors", "group": "Ungrouped variables", "definition": "foldl((total, x) -> total + x, \"\", XFactors)", "description": "", "templateType": "anything", "can_override": false}, "DisplayYFactors": {"name": "DisplayYFactors", "group": "Ungrouped variables", "definition": "foldl((total, x) -> total + x, \"\", YFactors)", "description": "", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "len(CommonFactors)>1 && x<>y && len(CommonFactors)<4", "maxRuns": 100}, "ungrouped_variables": ["x", "y", "CommonFactors", "test", "XFactors", "YFactors", "DisplayXFactors", "DisplayYFactors"], "variable_groups": [], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "list-of-numbers", "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": "CommonFactors", "allowFractions": false, "correctAnswerFractions": false, "isSet": true, "show_input_hint": true, "separator": ","}}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always"}, {"name": "21.b Find HCF of two numbers", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Mash Sheffield", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/4679/"}, {"name": "Andrew Neate", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/21832/"}], "tags": [], "metadata": {"description": "<p>Find the HCF of two numbers using prime factor decomposition.</p>", "licence": "Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International"}, "statement": "<p>By finding prime factors or otherwise, find the highest common factor of $\\var{x}$ and $\\var{y}$.</p>", "advice": "<p>One way to work out the highest common factor is to find all factors of both numbers and pick the largest one. A quicker and more consistent method is the following.</p>\n<p>First write each number as a product of prime powers. In this case we have&nbsp;</p>\n<p>\\[\\var{x}=\\simplify[unitPower]{{DisplayXPrimePowers}}\\]</p>\n<p>\\[\\var{y}=\\simplify[unitPower]{{DisplayYPrimePowers}}.\\]</p>\n<p>The highest common factor is then found by multiplying each prime factor the least number of times it occurs in either $\\var{x}$ or $\\var{y}$. This gives us an answer of $\\text{HCF}(\\var{x},\\var{y})=\\var{HCF}$.</p>\n<p></p>\n<p><a href=\"https://www.sheffield.ac.uk/mash/maths-resources/maths-all#Factors\"><span style=\"font-weight: 400;\">Use this link to find some resources which will help you revise this topic.</span></a></p>", "rulesets": {}, "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true, "j": false}, "constants": [], "variables": {"x": {"name": "x", "group": "Ungrouped variables", "definition": "random(2..70)", "description": "", "templateType": "anything", "can_override": false}, "y": {"name": "y", "group": "Ungrouped variables", "definition": "random(2..70)", "description": "", "templateType": "anything", "can_override": false}, "CommonFactors": {"name": "CommonFactors", "group": "Ungrouped variables", "definition": "intersection(set(divisors(x)),set(divisors(y)))", "description": "", "templateType": "anything", "can_override": false}, "Primes": {"name": "Primes", "group": "Ungrouped variables", "definition": "[2,3,5,7,11,13,17,19,23,29,31,37,41,43,47,53,59,61,67,71,73,79,83,89,97]", "description": "", "templateType": "anything", "can_override": false}, "XPrimePowersList": {"name": "XPrimePowersList", "group": "Ungrouped variables", "definition": "string(d[0])+\"^\"+string(d[1]) for: d of: filter(x[1]>0,x,zip(primes,factorise(x)))", "description": "", "templateType": "anything", "can_override": false}, "DisplayXPrimePowers": {"name": "DisplayXPrimePowers", "group": "Ungrouped variables", "definition": "expression(join(XPrimePowersList,\"*\"))", "description": "", "templateType": "anything", "can_override": false}, "HCF": {"name": "HCF", "group": "Ungrouped variables", "definition": "gcd(x,y)", "description": "", "templateType": "anything", "can_override": false}, "YPrimePowersList": {"name": "YPrimePowersList", "group": "Ungrouped variables", "definition": "string(d[0])+\"^\"+string(d[1]) for: d of: filter(x[1]>0,x,zip(primes,factorise(y)))", "description": "", "templateType": "anything", "can_override": false}, "DisplayYPrimePowers": {"name": "DisplayYPrimePowers", "group": "Ungrouped variables", "definition": "expression(join(YPrimePowersList,\"*\"))", "description": "", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "len(CommonFactors)>1 && x<>y && len(CommonFactors)<4", "maxRuns": 100}, "ungrouped_variables": ["x", "y", "CommonFactors", "Primes", "XPrimePowersList", "DisplayXPrimePowers", "YPrimePowersList", "DisplayYPrimePowers", "HCF"], "variable_groups": [], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "numberentry", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "HCF", "maxValue": "HCF", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always"}, {"name": "21.c LCM of two numbers", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Simon Thomas", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/3148/"}, {"name": "Mash Sheffield", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/4679/"}, {"name": "Andrew Neate", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/21832/"}, {"name": "Will Morgan", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/21933/"}], "tags": [], "metadata": {"description": "<p>Calculating the LCM of two numbers by using prime factorisation.</p>", "licence": "Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International"}, "statement": "<p>By considering the prime factorisation of $\\var{x}$ and $\\var{y}$, or otherwise, find the lowest common multiple (LCM) of $\\var{x}$ and $\\var{y}$.</p>", "advice": "<p>We can write $\\var{x}$ and $\\var{y}$ as a product of prime factors as follows:</p>\n<p>$\\var{x}=\\var{show_factors(x)}$</p>\n<p>$\\var{y}=\\var{show_factors(y)}$.</p>\n<p></p>\n<p>For LCM of $\\var{x}$ and $\\var{y}$ we need to multiply each factor the greatest number of times it occurs in either $\\var{x}$ or $\\var{y}$.</p>\n<p>i.e. LCM$(x,y) = \\var{show_factors(lcm_xy)}=\\var{lcm_xy}$.</p>\n<p></p>\n<p><a href=\"https://www.sheffield.ac.uk/mash/maths-resources/maths-all#Factors\"><span style=\"font-weight: 400;\">Use this link to find some resources which will help you revise this topic.</span></a></p>", "rulesets": {}, "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true, "j": false}, "constants": [], "variables": {"x": {"name": "x", "group": "Ungrouped variables", "definition": "random(2..70)", "description": "", "templateType": "anything", "can_override": false}, "y": {"name": "y", "group": "Ungrouped variables", "definition": "random(2..70)", "description": "", "templateType": "anything", "can_override": false}, "lcm_xy": {"name": "lcm_xy", "group": "Ungrouped variables", "definition": "lcm(x,y)", "description": "", "templateType": "anything", "can_override": false}, "primes": {"name": "primes", "group": "Ungrouped variables", "definition": "[2,3,5,7,11,13,17,19,23,29,31,37,41,43,47,53,59,61,67,71,73,79,83,89,97]", "description": "", "templateType": "anything", "can_override": false}, "XPrimePowersList": {"name": "XPrimePowersList", "group": "Ungrouped variables", "definition": "string(d[0])+\"^\"+string(d[1]) for: d of: filter(x[1]>0,x,zip(primes,factorise(x)))", "description": "", "templateType": "anything", "can_override": false}, "DisplayXPrimePowers": {"name": "DisplayXPrimePowers", "group": "Ungrouped variables", "definition": "expression(join(XPrimePowersList,\"*\"))", "description": "", "templateType": "anything", "can_override": false}, "YPrimePowersList": {"name": "YPrimePowersList", "group": "Ungrouped variables", "definition": "string(d[0])+\"^\"+string(d[1]) for: d of: filter(x[1]>0,x,zip(primes,factorise(y)))", "description": "", "templateType": "anything", "can_override": false}, "DisplayYPrimePowers": {"name": "DisplayYPrimePowers", "group": "Ungrouped variables", "definition": "expression(join(YPrimePowersList,\"*\"))", "description": "", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "", "maxRuns": "500"}, "ungrouped_variables": ["primes", "lcm_xy", "x", "y", "XPrimePowersList", "DisplayXPrimePowers", "YPrimePowersList", "DisplayYPrimePowers"], "variable_groups": [], "functions": {"show_factors": {"parameters": [["n", "number"]], "type": "string", "language": "jme", "definition": "latex(  // mark the output as a string of raw LaTeX\n  join(\n    map(\n      if(a=1,p,p+'^{'+a+'}'), // when the exponent is 1, return p, otherwise return p^{exponent}\n      [p,a],\n      filter(x[1]>0,x,zip(primes,factorise(n)))  // for all the primes p which are factors of n, return p and its exponent\n    ),\n    ' \\\\times ' // join all the prime powers up with \\times symbols\n  )\n)"}}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "numberentry", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "lcm_xy", "maxValue": "lcm_xy", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always"}]}], "allowPrinting": true, "navigation": {"allowregen": true, "reverse": true, "browse": true, "allowsteps": true, "showfrontpage": false, "navigatemode": "sequence", "onleave": {"action": "none", "message": ""}, "preventleave": false, "typeendtoleave": false, "startpassword": "", "autoSubmit": true, "allowAttemptDownload": false, "downloadEncryptionKey": "", "showresultspage": "oncompletion"}, "timing": {"allowPause": false, "timeout": {"action": "none", "message": ""}, "timedwarning": {"action": "none", "message": ""}}, "feedback": {"enterreviewmodeimmediately": true, "showactualmarkwhen": "always", "showtotalmarkwhen": "always", "showanswerstatewhen": "always", "showpartfeedbackmessageswhen": "always", "showexpectedanswerswhen": "inreview", "showadvicewhen": "inreview", "allowrevealanswer": true, "intro": "", "end_message": "", "results_options": {"printquestions": true, "printadvice": true}, "feedbackmessages": [], "reviewshowexpectedanswer": true, "showanswerstate": true, "reviewshowfeedback": true, "showactualmark": true, "showtotalmark": true, "reviewshowscore": true, "reviewshowadvice": true}, "diagnostic": {"knowledge_graph": {"topics": [], "learning_objectives": []}, "script": "diagnosys", "customScript": ""}, "contributors": [{"name": "Mash Sheffield", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/4679/"}, {"name": "Andrew Neate", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/21832/"}], "extensions": [], "custom_part_types": [{"source": {"pk": 2, "author": {"name": "Christian Lawson-Perfect", "pk": 7}, "edit_page": "/part_type/2/edit"}, "name": "List of numbers", "short_name": "list-of-numbers", "description": "<p>The answer is a comma-separated list of numbers.</p>\n<p>The list is marked correct if each number occurs the same number of times as in the expected answer, and no extra numbers are present.</p>\n<p>You can optionally treat the answer as a set, so the number of occurrences doesn't matter, only whether each number is included or not.</p>", "help_url": "", "input_widget": "string", "input_options": {"correctAnswer": "join(\n  if(settings[\"correctAnswerFractions\"],\n    map(let([a,b],rational_approximation(x), string(a/b)),x,settings[\"correctAnswer\"])\n  ,\n    settings[\"correctAnswer\"]\n  ),\n  settings[\"separator\"] + \" \"\n)", "hint": {"static": false, "value": "if(settings[\"show_input_hint\"],\n  \"Enter a list of numbers separated by <code>{settings['separator']}</code>.\",\n  \"\"\n)"}, "allowEmpty": {"static": true, "value": true}}, "can_be_gap": true, "can_be_step": true, "marking_script": "bits:\nlet(b,filter(x<>\"\",x,split(studentAnswer,settings[\"separator\"])),\n    if(isSet,list(set(b)),b)\n)\n\nexpected_numbers:\nlet(l,settings[\"correctAnswer\"] as \"list\",\n    if(isSet,list(set(l)),l)\n)\n\nvalid_numbers:\nif(all(map(not isnan(x),x,interpreted_answer)),\n    true,\n    let(index,filter(isnan(interpreted_answer[x]),x,0..len(interpreted_answer)-1)[0], wrong, bits[index],\n      warn(wrong+\" is not a valid number\");\n      fail(wrong+\" is not a valid number.\")\n    )\n  )\n\nis_sorted:\nassert(sort(interpreted_answer)=interpreted_answer,\n    multiply_credit(0.5,\"Not in order\")\n  )\n\nincluded:\nmap(\n      let(\n        num_student,len(filter(x=y,y,interpreted_answer)),\n        num_expected,len(filter(x=y,y,expected_numbers)),\n        switch(\n          num_student=num_expected,\n            true,\n          num_student<num_expected,\n            incorrect(\n              if(isSet,\"Your answer does not contain \"+x+\" but should.\",\n                \"Your answer does not contain \"+x+\" enough times.\"\n              )\n            );false\n          ,\n            incorrect(\n              if(isSet,\"Your answer contains \"+x+\" but should not.\",\n                \"Your answer contains \"+x+\" too many times.\"\n              )\n            );false\n        )\n      )\n      ,\n      x,\n      sort(list(set(expected_numbers)))\n  )\n\nall_included:\nall(included)\n\nno_extras:\nif(all(map(x in expected_numbers, x, interpreted_answer)),\n    true\n  ,\n    incorrect(\"Your answer contains \"+extra_numbers[0]+\" but should not.\");\n    false\n  )\n\ninterpreted_answer:\nif(lower(studentAnswer) in [\"empty\",\"\u2205\"],[],\n  map(\n    if(settings[\"allowFractions\"],parsenumber_or_fraction(x,notationStyles), parsenumber(x,notationStyles))\n    ,x\n    ,bits\n  )\n)\n\nmark:\nif(studentanswer=\"\",fail(\"You have not entered an answer\"),false);\napply(valid_numbers);\napply(included);\napply(no_extras);\ncorrectif(all_included and no_extras)\n\nnotationStyles:\n[\"en\"]\n\nisSet:\nsettings[\"isSet\"]\n\nextra_numbers:\nfilter(not (x in expected_numbers),x,interpreted_answer)", "marking_notes": [{"name": "bits", "description": "<p>The separate items in the student's answer</p>", "definition": "let(b,filter(x<>\"\",x,split(studentAnswer,settings[\"separator\"])),\n    if(isSet,list(set(b)),b)\n)"}, {"name": "expected_numbers", "description": "", "definition": "let(l,settings[\"correctAnswer\"] as \"list\",\n    if(isSet,list(set(l)),l)\n)"}, {"name": "valid_numbers", "description": "<p>Is every number in the student's list valid?</p>", "definition": "if(all(map(not isnan(x),x,interpreted_answer)),\n    true,\n    let(index,filter(isnan(interpreted_answer[x]),x,0..len(interpreted_answer)-1)[0], wrong, bits[index],\n      warn(wrong+\" is not a valid number\");\n      fail(wrong+\" is not a valid number.\")\n    )\n  )"}, {"name": "is_sorted", "description": "<p>Are the student's answers in ascending order?</p>", "definition": "assert(sort(interpreted_answer)=interpreted_answer,\n    multiply_credit(0.5,\"Not in order\")\n  )"}, {"name": "included", "description": "<p>Is each number in the expected answer present in the student's list the correct number of times?</p>", "definition": "map(\n      let(\n        num_student,len(filter(x=y,y,interpreted_answer)),\n        num_expected,len(filter(x=y,y,expected_numbers)),\n        switch(\n          num_student=num_expected,\n            true,\n          num_student<num_expected,\n            incorrect(\n              if(isSet,\"Your answer does not contain \"+x+\" but should.\",\n                \"Your answer does not contain \"+x+\" enough times.\"\n              )\n            );false\n          ,\n            incorrect(\n              if(isSet,\"Your answer contains \"+x+\" but should not.\",\n                \"Your answer contains \"+x+\" too many times.\"\n              )\n            );false\n        )\n      )\n      ,\n      x,\n      sort(list(set(expected_numbers)))\n  )"}, {"name": "all_included", "description": "<p>Has every number been included the right number of times?</p>", "definition": "all(included)"}, {"name": "no_extras", "description": "<p>True if the student's list doesn't contain any numbers that aren't in the expected answer.</p>", "definition": "if(all(map(x in expected_numbers, x, interpreted_answer)),\n    true\n  ,\n    incorrect(\"Your answer contains \"+extra_numbers[0]+\" but should not.\");\n    false\n  )"}, {"name": "interpreted_answer", "description": "A value representing the student's answer to this part.", "definition": "if(lower(studentAnswer) in [\"empty\",\"\u2205\"],[],\n  map(\n    if(settings[\"allowFractions\"],parsenumber_or_fraction(x,notationStyles), parsenumber(x,notationStyles))\n    ,x\n    ,bits\n  )\n)"}, {"name": "mark", "description": "This is the main marking note. It should award credit and provide feedback based on the student's answer.", "definition": "if(studentanswer=\"\",fail(\"You have not entered an answer\"),false);\napply(valid_numbers);\napply(included);\napply(no_extras);\ncorrectif(all_included and no_extras)"}, {"name": "notationStyles", "description": "", "definition": "[\"en\"]"}, {"name": "isSet", "description": "<p>Should the answer be considered as a set, so the number of times an element occurs doesn't matter?</p>", "definition": "settings[\"isSet\"]"}, {"name": "extra_numbers", "description": "<p>Numbers included in the student's answer that are not in the expected list.</p>", "definition": "filter(not (x in expected_numbers),x,interpreted_answer)"}], "settings": [{"name": "correctAnswer", "label": "Correct answer", "help_url": "", "hint": "The list of numbers that the student should enter. The order does not matter.", "input_type": "code", "default_value": "", "evaluate": true}, {"name": "allowFractions", "label": "Allow the student to enter fractions?", "help_url": "", "hint": "", "input_type": "checkbox", "default_value": false}, {"name": "correctAnswerFractions", "label": "Display the correct answers as fractions?", "help_url": "", "hint": "", "input_type": "checkbox", "default_value": false}, {"name": "isSet", "label": "Is the answer a set?", "help_url": "", "hint": "If ticked, the number of times an element occurs doesn't matter, only whether it's included at all.", "input_type": "checkbox", "default_value": false}, {"name": "show_input_hint", "label": "Show the input hint?", "help_url": "", "hint": "", "input_type": "checkbox", "default_value": true}, {"name": "separator", "label": "Separator", "help_url": "", "hint": "The substring that should separate items in the student's list", "input_type": "string", "default_value": ",", "subvars": false}], "public_availability": "always", "published": true, "extensions": []}], "resources": []}