// Numbas version: exam_results_page_options
{"name": "Surds: Simplifying Expressions 5b - Rationalising the Denominator", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"name": "Surds: Simplifying Expressions 5b - Rationalising the Denominator", "tags": [], "metadata": {"description": "<p>Rewriting fractions involving surds by rationalising the denominator.</p>", "licence": "Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International"}, "statement": "<p>Rationalise the denominator in the following expression:</p>\n<p>\\[\\simplify[unitFactor]{({a}+{sgn}*sqrt({b}))/sqrt({b})}\\]</p>", "advice": "<p>To rationalise the denominator of a fraction which has the form $\\frac{a\\pm\\sqrt{b}}{\\sqrt{b}}$, we must multiply the numerator and denominator by $\\sqrt{b}$.</p>\n<p>Therefore,</p>\n<p>{advice}</p>", "rulesets": {}, "extensions": [], "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true}, "constants": [], "variables": {"a": {"name": "a", "group": "Ungrouped variables", "definition": "random(1..9)", "description": "", "templateType": "anything", "can_override": false}, "b": {"name": "b", "group": "Ungrouped variables", "definition": "random(2,3,5,6,7)", "description": "", "templateType": "anything", "can_override": false}, "simplify": {"name": "simplify", "group": "Ungrouped variables", "definition": "\"<p>\\\\[ \\\\begin{split}&nbsp;\\\\simplify{({a}+{sgn}*sqrt({b}))/sqrt({b})} &amp;\\\\,=\\\\simplify{({a}+{sgn}*sqrt({b}))sqrt({b})/(sqrt({b})sqrt({b}))}\\\\\\\\ \\\\\\\\ &amp;\\\\,= \\\\simplify{({a}sqrt({b})+{sgn*b})/{b}} \\\\\\\\\\\\\\\\&amp;\\\\,= \\\\simplify[all]{(({a}sqrt({b})/{simp})+({sgn}*{b})/{simp})/{b/simp}} \\\\end{split} \\\\]</p>\"", "description": "", "templateType": "long string", "can_override": false}, "simplified": {"name": "simplified", "group": "Ungrouped variables", "definition": "\"<p>\\\\[ \\\\begin{split}&nbsp;\\\\simplify{({a}+{sgn}*sqrt({b}))/sqrt({b})} &amp;\\\\,=\\\\simplify{({a}+{sgn}*sqrt({b}))sqrt({b})/(sqrt({b})sqrt({b}))}\\\\\\\\ \\\\\\\\ &amp;\\\\,= \\\\simplify{({a}sqrt({b})+{sgn*b})/{b}} \\\\end{split} \\\\]</p>\"", "description": "", "templateType": "long string", "can_override": false}, "advice": {"name": "advice", "group": "Ungrouped variables", "definition": "if(gcf(a,b)>1,{simplify},{simplified})", "description": "", "templateType": "anything", "can_override": false}, "sgn": {"name": "sgn", "group": "Ungrouped variables", "definition": "random(-1,1)", "description": "", "templateType": "anything", "can_override": false}, "simp": {"name": "simp", "group": "Ungrouped variables", "definition": "gcf(a,b)", "description": "", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["a", "b", "simplify", "simplified", "advice", "sgn", "simp"], "variable_groups": [], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"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, "prompt": "<p><em>You can type sqrt(x) to get $\\sqrt{x}$.</em></p>", "answer": "({a/simp}*sqrt({b})+{sgn*b/simp})/{b/simp}", "answerSimplification": "all,simplifyFractions,cancelTerms", "showPreview": true, "checkingType": "absdiff", "checkingAccuracy": 0.001, "failureRate": 1, "vsetRangePoints": 5, "vsetRange": [0, 1], "checkVariableNames": false, "singleLetterVariables": false, "allowUnknownFunctions": true, "implicitFunctionComposition": false, "caseSensitive": false, "mustmatchpattern": {"pattern": "($n+`+-$n`?*sqrt($n))/$n`? `| `+-$n+`+-$n`?*sqrt($n)/$n`?", "partialCredit": 0, "message": "", "nameToCompare": ""}, "valuegenerators": []}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always", "contributors": [{"name": "Ben McGovern", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/4872/"}]}]}], "contributors": [{"name": "Ben McGovern", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/4872/"}]}