// Numbas version: finer_feedback_settings
{"name": "Transpose formula with square root", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"name": "Transpose formula with square root", "tags": [], "metadata": {"description": "<p>Rearrange a formula with a square root to make a variable under the root the subject.</p>", "licence": "Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International"}, "statement": "<p>Transpose the formula \\(v=\\sqrt{\\simplify{x+{a}*y}}\\)&nbsp; to make \\(\\var{selected_variable}\\) the subject.</p>", "advice": "<p><span data-jme-visible=\"sel_variable=0\">$\\begin{align}v&amp;=\\sqrt{\\simplify{x+{a}*y}}\\\\ v^2 &amp;= \\simplify{x+{a}*y}\\qquad\\text{square both sides}\\\\ \\simplify{v^2-{a}y} &amp;=x\\qquad\\text{move }\\var{a}y\\text{ to the other side}\\\\x&amp;= \\simplify{v^2-{a}y} \\end{align}$</span></p>\n<p><span data-jme-visible=\"sel_variable=1\">$\\begin{align}v&amp;=\\sqrt{\\simplify{x+{a}*y}}\\\\ v^2 &amp;= \\simplify{x+{a}*y}\\qquad\\text{square both sides}\\\\&nbsp; \\simplify{v^2-x} &amp;=\\var{a}y \\qquad\\text{move }x\\text{ to the other side}\\\\ \\simplify{(v^2-x)/{a}} &amp;= y\\qquad\\text{divide by }\\var{a}\\\\y&amp;=\\simplify{(v^2-x)/{a}} \\end{align}$</span></p>", "rulesets": {}, "extensions": [], "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true}, "constants": [], "variables": {"a": {"name": "a", "group": "Ungrouped variables", "definition": "random(1..9)*random(1,-1)", "description": "", "templateType": "anything", "can_override": false}, "variables": {"name": "variables", "group": "Ungrouped variables", "definition": "[latex(\"x\"),latex(\"y\")]", "description": "", "templateType": "anything", "can_override": false}, "sel_variable": {"name": "sel_variable", "group": "Ungrouped variables", "definition": "random(0,1)", "description": "", "templateType": "anything", "can_override": false}, "selected_variable": {"name": "selected_variable", "group": "Ungrouped variables", "definition": "variables[sel_variable]", "description": "", "templateType": "anything", "can_override": false}, "answer": {"name": "answer", "group": "Ungrouped variables", "definition": "if(sel_variable=0, substitute([\"a\":a],expression(\"v^2-a*y\")), substitute([\"a\":a],expression(\"1/a*(v^2-x)\")))", "description": "", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["a", "variables", "sel_variable", "selected_variable", "answer"], "variable_groups": [], "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": "<p>\\(\\var{selected_variable}=\\)[[0]]</p>", "gaps": [{"type": "jme", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "answer": "{answer}", "showPreview": true, "checkingType": "absdiff", "checkingAccuracy": 0.001, "failureRate": 1, "vsetRangePoints": 5, "vsetRange": [0, 1], "checkVariableNames": false, "singleLetterVariables": false, "allowUnknownFunctions": true, "implicitFunctionComposition": false, "caseSensitive": false, "valuegenerators": []}], "sortAnswers": false}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always", "type": "question", "contributors": [{"name": "Don Shearman", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/680/"}, {"name": "Merryn Horrocks", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/4052/"}]}]}], "contributors": [{"name": "Don Shearman", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/680/"}, {"name": "Merryn Horrocks", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/4052/"}]}