// Numbas version: exam_results_page_options
{"name": "Write a formula based on a word statement and apply it to a given value", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"tags": [], "parts": [{"scripts": {}, "extendBaseMarkingAlgorithm": true, "stepsPenalty": 0, "type": "gapfill", "showCorrectAnswer": true, "prompt": "<p>Write a formula for the number of students, $S$, in terms of the number of professors, $P$.</p>\n<p>[[0]]</p>", "marks": 0, "showFeedbackIcon": true, "variableReplacements": [], "steps": [{"scripts": {}, "extendBaseMarkingAlgorithm": true, "shuffleChoices": false, "minMarks": 0, "type": "1_n_2", "showCorrectAnswer": true, "prompt": "<p>Given the relationship stated above, what would you expect there to be more of: students, or professors?</p>", "marks": 0, "showFeedbackIcon": true, "showCellAnswerState": true, "variableReplacements": [], "choices": ["More students", "More professors"], "distractors": ["", ""], "matrix": ["1", 0], "maxMarks": 0, "variableReplacementStrategy": "originalfirst", "customMarkingAlgorithm": "", "displayColumns": 0, "displayType": "radiogroup", "unitTests": []}, {"scripts": {}, "extendBaseMarkingAlgorithm": true, "type": "information", "showCorrectAnswer": true, "prompt": "<p>Try to write your formula in the form</p>\n<p>\\[ S = \\ldots \\]</p>\n<p>The right-hand side should be in terms of the variable $P$.</p>", "marks": 0, "variableReplacementStrategy": "originalfirst", "showFeedbackIcon": true, "unitTests": [], "variableReplacements": [], "customMarkingAlgorithm": ""}], "sortAnswers": false, "variableReplacementStrategy": "alwaysreplace", "gaps": [{"scripts": {}, "extendBaseMarkingAlgorithm": true, "type": "jme", "showCorrectAnswer": true, "expectedVariableNames": [], "marks": "0", "showFeedbackIcon": true, "variableReplacements": [], "failureRate": 1, "checkingType": "absdiff", "checkVariableNames": false, "vsetRangePoints": 5, "vsetRange": [0, 1], "checkingAccuracy": 0.001, "answer": "{formula}", "variableReplacementStrategy": "originalfirst", "customMarkingAlgorithm": "vrange: 1..100#1\n\n\nvset (The sets of variable values to test against):\n    //some values satisfying the formula\n    repeat(\n        let(p,random(vRange),\n            [\"p\":p, \"s\": 6p]\n        ),\n        settings[\"vsetRangePoints\"]\n    )\n    +\n    //some completely random values, assumed not to satisfy the formula\n    repeat(\n        [\"p\": random(vRange), \"s\": random(vRange)],\n        settings[\"vsetRangePoints\"]\n    )\n\nagree (Do the student's answer and the expected answer agree on each of the sets of variable values?):\n    map(\n        try(\n            resultsEqual(\n                unset(question_definitions,eval(studentexpr,vars)),\n                unset(question_definitions,eval(correctexpr,vars)),\n                settings[\"checkingType\"],\n                settings[\"checkingAccuracy\"]\n            ),\n            message,\n            warn(translate(\"part.jme.answer invalid\",[\"message\":message]));\n            fail(translate(\"part.jme.answer invalid\",[\"message\":message]));\n            false\n        ),\n        vars,\n        vset\n    )", "showPreview": true, "unitTests": []}], "customMarkingAlgorithm": "", "unitTests": []}, {"scripts": {}, "extendBaseMarkingAlgorithm": true, "minValue": "num_students", "type": "numberentry", "showCorrectAnswer": true, "prompt": "<p>There are {num_professors} professors at the University of Qwghlm.</p>\n<p>Use your formula to calculate the number of students.</p>", "marks": 1, "mustBeReduced": false, "showFeedbackIcon": true, "variableReplacements": [{"part": "p0g0", "must_go_first": false, "variable": "formula"}], "mustBeReducedPC": 0, "allowFractions": false, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain", "variableReplacementStrategy": "alwaysreplace", "customMarkingAlgorithm": "formula_satisfied: eval(formula,[\"s\":studentNumber,\"p\":num_professors])\n\nmark (Mark the student's answer):\n    apply(validNumber);\n    if(formula_satisfied,\n      correct(\"Your number satisfies the formula you gave.\"),\n      incorrect(\"Your number does not satisfy the formula you gave.\")\n    )", "maxValue": "num_students", "correctAnswerFraction": false, "unitTests": []}], "preamble": {"js": "", "css": ""}, "functions": {}, "advice": "<h4>a)</h4>\n<p>For every professor, there are {factor} students.</p>\n<p>\\[S = \\simplify[]{{factor} P} \\]</p>\n<h4>b)</h4>\n<p>Substitute $P = \\var{num_professors}$ into the formula:</p>\n<p>\\begin{align}<br/>S &amp;= \\simplify[]{{factor} * P} \\\\<br/>&amp;= \\simplify[]{{factor} * {num_professors}} \\\\<br/>&amp;= \\var{num_students}<br/>\\end{align}</p>", "metadata": {"description": "<p>Given a statement in words of a relationship between two variables, write down a corresponding formula. It's marked correct if values satisfying the relationship satisfy the formula, and values not satisfying the relationship don't.</p>\n<p>Then, given a value for one of the variables, work out the value of the other one. They're substituted into the formula given in the first part and marked correct if it's satisfied.</p>\n<p>Both parts use custom marking algorithms.</p>", "licence": "Creative Commons Attribution 4.0 International"}, "extensions": [], "variablesTest": {"maxRuns": 100, "condition": ""}, "statement": "<p>At the University of Qwghlm, there are {factor} times as many students as professors.</p>", "rulesets": {}, "name": "Write a formula based on a word statement and apply it to a given value", "ungrouped_variables": ["formula", "num_professors", "factor", "num_students"], "variables": {"factor": {"name": "factor", "description": "", "templateType": "anything", "group": "Ungrouped variables", "definition": "random(2..10)"}, "num_professors": {"name": "num_professors", "description": "", "templateType": "anything", "group": "Ungrouped variables", "definition": "random(5*factor..300#(5*factor))"}, "num_students": {"name": "num_students", "description": "", "templateType": "anything", "group": "Ungrouped variables", "definition": "factor*num_professors"}, "formula": {"name": "formula", "description": "", "templateType": "anything", "group": "Ungrouped variables", "definition": "expression(\"S={factor}P\")"}}, "variable_groups": [], "type": "question", "contributors": [{"name": "Christian Lawson-Perfect", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/7/"}]}]}], "contributors": [{"name": "Christian Lawson-Perfect", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/7/"}]}