// Numbas version: exam_results_page_options
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"mustBeReduced": false, "variableReplacements": [], "allowFractions": false, "maxValue": "a2/a3", "marks": 1, "minValue": "a2/a3", "scripts": {}, "correctAnswerStyle": "plain", "correctAnswerFraction": false}]}, {"prompt": "<p></p>\n<p>$\\frac{\\var{b1}}{\\sqrt{\\var{b2}}}=$<fraction><numerator>[[0]]$\\sqrt{}$[[1]]</numerator><denominator>[[2]]</denominator></fraction></p>", "showFeedbackIcon": true, "variableReplacements": [], "type": "gapfill", "variableReplacementStrategy": "originalfirst", "marks": 0, "showCorrectAnswer": true, "scripts": {}, "gaps": [{"mustBeReducedPC": 0, "showCorrectAnswer": true, "type": "numberentry", "variableReplacementStrategy": "originalfirst", "showFeedbackIcon": true, "notationStyles": ["plain", "en", "si-en"], "mustBeReduced": false, "variableReplacements": [], "allowFractions": false, "maxValue": "b1/b3", "marks": 1, "minValue": "b1/b3", "scripts": {}, "correctAnswerStyle": "plain", "correctAnswerFraction": false}, {"mustBeReducedPC": 0, 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"originalfirst", "showFeedbackIcon": true, "notationStyles": ["plain", "en", "si-en"], "mustBeReduced": false, "variableReplacements": [], "allowFractions": false, "maxValue": "c2", "marks": 1, "minValue": "c2", "scripts": {}, "correctAnswerStyle": "plain", "correctAnswerFraction": false}]}, {"prompt": "<p>$\\frac{\\var{d4}\\sqrt{\\var{d1}}}{\\sqrt{\\var{d2}}}=$<fraction><numerator>[[0]]$\\sqrt{}$[[1]]</numerator><denominator>[[2]]</denominator></fraction></p>", "showFeedbackIcon": true, "variableReplacements": [], "type": "gapfill", "variableReplacementStrategy": "originalfirst", "marks": 0, "showCorrectAnswer": true, "scripts": {}, "gaps": [{"mustBeReducedPC": 0, "showCorrectAnswer": true, "type": "numberentry", "variableReplacementStrategy": "originalfirst", "showFeedbackIcon": true, "notationStyles": ["plain", "en", "si-en"], "mustBeReduced": false, "variableReplacements": [], "allowFractions": false, "maxValue": "d4/d3", "marks": 1, "minValue": "d4/d3", "scripts": {}, 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"numberentry", "variableReplacementStrategy": "originalfirst", "showFeedbackIcon": true, "notationStyles": ["plain", "en", "si-en"], "mustBeReduced": false, "variableReplacements": [], "allowFractions": false, "maxValue": "(f7)^0.5", "marks": 1, "minValue": "(f7)^0.5", "scripts": {}, "correctAnswerStyle": "plain", "correctAnswerFraction": false}, {"mustBeReducedPC": 0, "showCorrectAnswer": true, "type": "numberentry", "variableReplacementStrategy": "originalfirst", "showFeedbackIcon": true, "notationStyles": ["plain", "en", "si-en"], "mustBeReduced": false, "variableReplacements": [], "allowFractions": false, "maxValue": "(f4*f3)", "marks": 1, "minValue": "(f4*f3)", "scripts": {}, "correctAnswerStyle": "plain", "correctAnswerFraction": false}, {"mustBeReducedPC": 0, "showCorrectAnswer": true, "type": "numberentry", "variableReplacementStrategy": "originalfirst", "showFeedbackIcon": true, "notationStyles": ["plain", "en", "si-en"], "mustBeReduced": false, "variableReplacements": [], "allowFractions": false, "maxValue": "f3", "marks": 1, "minValue": "f3", "scripts": {}, "correctAnswerStyle": "plain", "correctAnswerFraction": false}]}], "statement": "<p>Express each of the following in the form $\\frac{a\\sqrt{b}}{c}$ where a, b and c are integers,&nbsp;where a and c have no common factors</p>", "name": "Katherine's copy of Surds 2", "functions": {}, "variable_groups": [], "advice": "<p>The best approach here is to first rationalise the denominator. We do this by multiplying both top and bottom by an approriate value.</p>\n<p>For example to rationalise the denominator for an expression like $\\frac{a}{\\sqrt{b}}$, we multiply numerator and denominator by $\\sqrt{b}$ to get $\\frac{a\\sqrt{b}}{b}$</p>\n<p>Similarly to rationalise the denominator for an expression like $\\frac{a+\\sqrt{b}}{c+\\sqrt{d}}$, we multiply numerator and denominator by $c-\\sqrt{d}$ to get $\\frac{(a+\\sqrt{b})(c-\\sqrt{d})}{c^2-d}$</p>\n<p>Dont forget that:</p>\n<p>$\\sqrt{a \\times b} = \\sqrt{a} \\times \\sqrt{b}$</p>\n<p>$\\sqrt{\\frac{a}{b}} = \\frac{\\sqrt{a}}{\\sqrt{b}}$</p>\n<p>$(a+\\sqrt{b})(a-\\sqrt{b})=a^2-b$</p>\n<p>Remember to check that your answer is in its simplest form.</p>", "variablesTest": {"condition": "gcd({c1},{c2})=1", "maxRuns": 100}, "variables": {"f5": {"description": "", "name": "f5", "templateType": "anything", "definition": "f3*f1*f1", "group": "Ungrouped variables"}, "f8": {"description": "", "name": "f8", "templateType": "anything", "definition": "f4*f7", "group": "Ungrouped variables"}, "d4": {"description": "", "name": "d4", "templateType": "anything", "definition": "random([4,6,10,12,14,20,22,26] except [2*d1])", "group": "Ungrouped variables"}, "e4": {"description": "", "name": "e4", "templateType": "anything", "definition": "random([2,3,5,7] except [e2])", "group": "Ungrouped variables"}, "f1": {"description": "", "name": "f1", "templateType": "anything", "definition": "random(2..5)", "group": "Ungrouped variables"}, "b1": {"description": "", "name": "b1", "templateType": "anything", "definition": "random(2..19)", "group": "Ungrouped variables"}, "a3": {"description": "", "name": "a3", "templateType": "anything", "definition": "gcd(a1,a2)", "group": "Ungrouped variables"}, "d3": {"description": "", "name": "d3", "templateType": "anything", "definition": "gcd(d4,d2)", "group": "Ungrouped variables"}, "f2": {"description": "", "name": "f2", "templateType": "anything", "definition": "random(2..5 except f1)", "group": "Ungrouped variables"}, "b2": {"description": "", "name": "b2", "templateType": "anything", "definition": "random(2,3,5,6,7,10,11,13,14,15,17,19,21,23,22,26,29)", "group": "Ungrouped variables"}, "c1": {"description": "", "name": "c1", "templateType": "anything", "definition": "random(2,3,5,7,11,13,17,19,23,29)", "group": "Ungrouped variables"}, "a1": {"description": "", "name": "a1", "templateType": "anything", "definition": "random(2..19)", "group": "Ungrouped variables"}, "f4": {"description": "", "name": "f4", "templateType": "anything", "definition": "random([2,3,5,7] except f1 except f2 except f3)", "group": "Ungrouped variables"}, "e3": {"description": "", "name": "e3", "templateType": "anything", "definition": "random(2..9)", "group": "Ungrouped variables"}, "f7": {"description": "", "name": "f7", "templateType": "anything", "definition": "random([4,9,16] except f3)", "group": "Ungrouped variables"}, "b3": {"description": "", "name": "b3", "templateType": "anything", "definition": "gcd(b2,b1)", "group": "Ungrouped variables"}, "c2": {"description": "", "name": "c2", "templateType": "anything", "definition": "random([2,3,5,7,11,13,17,19,23,29] except [c1])", "group": "Ungrouped variables"}, "a2": {"description": "", "name": "a2", "templateType": "anything", "definition": "random(2,3,5,6,7,10,11,13,14,15,17,19,21,23,22,26,29)", "group": "Ungrouped variables"}, "f3": {"description": "", "name": "f3", "templateType": "anything", "definition": "random([2,3,5,7,11,13] except f2 except f1)", "group": "Ungrouped variables"}, "e1": {"description": "", "name": "e1", "templateType": "anything", "definition": "random(2..9)", "group": "Ungrouped variables"}, "d1": {"description": "", "name": "d1", "templateType": "anything", "definition": "random([2,3,5,7,11,13,17,19,23,29] except [c1])", "group": "Ungrouped variables"}, "f6": {"description": "", "name": "f6", "templateType": "anything", "definition": "f8*f2*f2", "group": "Ungrouped variables"}, "d2": {"description": "", "name": "d2", "templateType": "anything", "definition": "d4/2", "group": "Ungrouped variables"}, "e2": {"description": "", "name": "e2", "templateType": "anything", "definition": "random([2,3,5,7])", "group": "Ungrouped variables"}, "e5": {"description": "", "name": "e5", "templateType": "anything", "definition": "gcd(e1,e3*e4)", "group": "Ungrouped variables"}}, "preamble": {"css": "fraction {\n  display: inline-block;\n  vertical-align: middle;\n}\nfraction > numerator, fraction > denominator {\n  float: left;\n  width: 100%;\n  text-align: center;\n  line-height: 2.5em;\n}\nfraction > numerator {\n  border-bottom: 1px solid;\n  padding-bottom: 5px;\n}\nfraction > denominator {\n  padding-top: 5px;\n}\nfraction input {\n    line-height: 1em;\n}\n\nfraction .part {\n    margin: 0;\n}\n\n.table-responsive, .fractiontable {\n  display:inline-block;\n}\n.fractiontable {\n  padding: 0; \n  border: 0;\n}\n\n.fractiontable  .tddenom \n{\n text-align: center;\n}\n\n.fractiontable .tdnum \n{\n  border-bottom: 1px solid black; \n  text-align: center;\n}\n\n\n.fractiontable tr {\n    height: 3em;\n}", "js": "document.createElement('fraction');\ndocument.createElement('numerator');\ndocument.createElement('denominator');"}, "type": "question", "contributors": [{"name": "Katherine Tomlinson", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/1652/"}]}]}], "contributors": [{"name": "Katherine Tomlinson", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/1652/"}]}