// Numbas version: finer_feedback_settings
{"name": "Adaptive marking: quadratic equation", "extensions": ["stats"], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"name": "Adaptive marking: quadratic equation", "variable_groups": [{"name": "Quadratic equation", "variables": ["roots", "a", "b", "xs", "ys"]}], "parts": [{"unitTests": [], "marks": 0, "sortAnswers": true, "variableReplacements": [], "showCorrectAnswer": true, "prompt": "<p>A quadratic function&nbsp;$f(x)$ goes through the points $(\\var{xs[0]},\\var{ys[0]})$,&nbsp;$(\\var{xs[1]},\\var{ys[1]})$ and&nbsp;$(\\var{xs[2]},\\var{ys[2]})$.</p>\n<p>Find the two roots of $f$.</p>\n<p>First root:&nbsp;[[0]]</p>\n<p>Second root:&nbsp;[[1]]</p>", "gaps": [{"maxValue": "a", "notationStyles": ["plain", "en", "si-en"], "unitTests": [], "variableReplacements": [], "scripts": {}, "marks": "1", "correctAnswerStyle": "plain", "correctAnswerFraction": false, "showCorrectAnswer": true, "mustBeReducedPC": 0, "type": "numberentry", "mustBeReduced": false, "allowFractions": false, "customMarkingAlgorithm": "", "minValue": "a", "extendBaseMarkingAlgorithm": true, "showFeedbackIcon": true, "variableReplacementStrategy": "originalfirst"}, {"maxValue": "b", "notationStyles": ["plain", "en", "si-en"], "unitTests": [], "variableReplacements": [], "scripts": {}, "marks": "1", "correctAnswerStyle": "plain", "correctAnswerFraction": false, "showCorrectAnswer": true, "mustBeReducedPC": 0, "type": "numberentry", "mustBeReduced": false, "allowFractions": false, "customMarkingAlgorithm": "", "minValue": "b", "extendBaseMarkingAlgorithm": true, "showFeedbackIcon": true, "variableReplacementStrategy": "originalfirst"}], "type": "gapfill", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "showFeedbackIcon": true, "variableReplacementStrategy": "originalfirst"}, {"unitTests": [], "marks": 0, "sortAnswers": false, "variableReplacements": [], "showCorrectAnswer": true, "prompt": "<p>Write&nbsp;a quadratic function $g(x)$ whose roots are the values you entered above, with $x^2$ coefficient $1$.</p>\n<p>$g(x) =&nbsp;$&nbsp;[[0]]</p>", "gaps": [{"vsetRange": [0, 1], "unitTests": [], "variableReplacements": [{"part": "p0g0", "variable": "a", "must_go_first": false}, {"part": "p0g1", "variable": "b", "must_go_first": false}], "marks": 1, "checkVariableNames": false, "showPreview": true, "answer": "(x-{a})(x-{b})", "showCorrectAnswer": true, "vsetRangePoints": 5, "expectedVariableNames": [], "failureRate": 1, "checkingAccuracy": 0.001, "type": "jme", "scripts": {}, "checkingType": "absdiff", "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "showFeedbackIcon": true, "variableReplacementStrategy": "originalfirst"}], "type": "gapfill", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "showFeedbackIcon": true, "variableReplacementStrategy": "originalfirst"}, {"maxValue": "mean(roots)", "notationStyles": ["plain", "en", "si-en"], "unitTests": [], "correctAnswerFraction": false, "scripts": {}, "marks": 1, "correctAnswerStyle": "plain", "variableReplacements": [{"part": "p0", "variable": "roots", "must_go_first": false}], "showCorrectAnswer": true, "prompt": "<p>What is the midpoint of the two roots of $f$?</p>", "mustBeReducedPC": 0, "type": "numberentry", "mustBeReduced": false, "allowFractions": false, "customMarkingAlgorithm": "", "minValue": "mean(roots)", "extendBaseMarkingAlgorithm": true, "showFeedbackIcon": true, "variableReplacementStrategy": "originalfirst"}], "statement": "<p>(This question doesn't make a lot of pedagogic sense, it just shows off how adaptive marking works)</p>", "ungrouped_variables": [], "tags": [], "extensions": ["stats"], "variablesTest": {"maxRuns": 100, "condition": ""}, "functions": {}, "preamble": {"js": "", "css": ""}, "metadata": {"description": "<p data-bind=\"html: 'hi'\">Give the student three points lying on a quadratic, and ask them to find the roots.</p>\n<p data-bind=\"html: 'hi'\">Then ask them to find the equation of the quadratic, using their roots. Error in calculating the roots is carried forward.</p>\n<p data-bind=\"html: 'hi'\">Finally, ask them to find the midpoint of the roots (just for fun). Error is carried forward again.</p>", "licence": "Creative Commons Attribution 4.0 International"}, "type": "question", "advice": "", "variables": {"roots": {"name": "roots", "description": "", "templateType": "anything", "definition": "sort(shuffle(list(-5..5))[0..2])", "group": "Quadratic equation"}, "b": {"name": "b", "description": "<p>Greatest root of the quadratic</p>", "templateType": "anything", "definition": "roots[1]", "group": "Quadratic equation"}, "xs": {"name": "xs", "description": "<p>Three given x coordinates</p>", "templateType": "anything", "definition": "shuffle(-5..5 except [a,b])[0..3]", "group": "Quadratic equation"}, "a": {"name": "a", "description": "<p>Least root of the quadratic equation</p>", "templateType": "anything", "definition": "roots[0]", "group": "Quadratic equation"}, "ys": {"name": "ys", "description": "<p>y coordinates corresponding to the given x coordinates</p>", "templateType": "anything", "definition": "map((x-a)*(x-b),x,xs)", "group": "Quadratic equation"}}, "rulesets": {}, "contributors": [{"name": "Bill Foster", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/6/"}, {"name": "Christian Lawson-Perfect", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/7/"}]}]}], "contributors": [{"name": "Bill Foster", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/6/"}, {"name": "Christian Lawson-Perfect", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/7/"}]}