// Numbas version: exam_results_page_options
{"name": "\\(y\\) is proportional to \\(x^2\\)", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"functions": {}, "ungrouped_variables": ["k", "x1", "y1", "x2", "y2", "x3", "y3"], "name": "\\(y\\) is proportional to \\(x^2\\)", "tags": [], "variables": {"y2": {"definition": "k*x2^2", "templateType": "anything", "group": "Ungrouped variables", "description": "", "name": "y2"}, "k": {"definition": "random(2..6)", "templateType": "anything", "group": "Ungrouped variables", "description": "", "name": "k"}, "x2": {"definition": "random(3..10 except x1)", "templateType": "anything", "group": "Ungrouped variables", "description": "", "name": "x2"}, "y1": {"definition": "k*x1^2", "templateType": "anything", "group": "Ungrouped variables", "description": "", "name": "y1"}, "x3": {"definition": "random(10..30 except [x1,x2])", "templateType": "anything", "group": "Ungrouped variables", "description": "", "name": "x3"}, "y3": {"definition": "k*x3^2", "templateType": "anything", "group": "Ungrouped variables", "description": "", "name": "y3"}, "x1": {"definition": "random(3..10)", "templateType": "anything", "group": "Ungrouped variables", "description": "", "name": "x1"}}, "rulesets": {}, "parts": [{"prompt": "<p>Find a formula for \\(y\\) in terms of \\(x\\).</p>\n<p>\\(y = \\)&nbsp;[[0]]</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "gaps": [{"vsetrangepoints": 5, "expectedvariablenames": [], "checkingaccuracy": 0.001, "vsetrange": [0, 1], "showpreview": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "scripts": {}, "answer": "{k}*x^2", "marks": 1, "checkvariablenames": false, "checkingtype": "absdiff", "type": "jme"}], "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "gapfill"}, {"prompt": "<p>Find the value of \\(y\\) when \\(x=\\var{x2}\\).</p>", "allowFractions": false, "variableReplacements": [], "maxValue": "y2", "minValue": "y2", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry"}, {"prompt": "<p>Find the value of \\(x\\) when \\(y = \\var{y3}\\).</p>", "allowFractions": false, "variableReplacements": [], "maxValue": "x3", "minValue": "x3", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry"}], "extensions": [], "statement": "<p>You are told that \\(y\\) is proportional to \\(x^2\\) and that when \\(y=\\var{y1}\\), \\(x=\\var{x1}\\).</p>", "variable_groups": [], "variablesTest": {"maxRuns": 100, "condition": ""}, "preamble": {"css": "", "js": ""}, "advice": "<p>Since \\(y\\) is proportional to \\(x^2\\), we can write&nbsp;the following equation:</p>\n<p>\\[ y = kx^2 \\]</p>\n<p>Where \\(k\\) is a number we need to work out.</p>\n<p>We're told that when \\(y=\\var{y1}\\), \\(x=\\var{x1}\\). That is,</p>\n<p>\\[ \\simplify[]{ {y1} = k*({x1}^2)} = k \\times \\var{x1^2} \\]</p>\n<p>So</p>\n<p>\\[ k = \\simplify[]{ {y1} / {x1^2} } = \\var{k} \\]</p>\n<p>We can now write down the formula for \\(y\\) in terms of \\(x\\):</p>\n<p>\\[ y = \\var{k}x^2 \\]</p>", "metadata": {"description": "<p>Work out \\(k\\) when \\( y = kx^2\\).</p>", "licence": null}, "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/"}]}