// Numbas version: finer_feedback_settings
{"name": "Surds 2", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"functions": {}, "ungrouped_variables": ["a1", "a2", "a3", "b1", "b2", "b3", "c1", "c2", "d1", "d2", "d3", "d4", "e1", "e2", "e3", "e4", "e5", "f1", "f2", "f3", "f4", "f5", "f6", "f7", "f8"], "name": "Surds 2", "tags": [], "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');"}, "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>", "rulesets": {}, "parts": [{"prompt": "<p>$\\frac{\\var{a1}}{\\sqrt{\\var{a2}}}=$<fraction><numerator>[[0]]$\\sqrt{}$[[1]]</numerator><denominator>[[2]]</denominator></fraction></p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "gaps": [{"integerPartialCredit": 0, "integerAnswer": true, "allowFractions": false, "variableReplacements": [], "maxValue": "a1/a3", "minValue": "a1/a3", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}, {"allowFractions": false, "variableReplacements": [], "maxValue": "a2", "minValue": "a2", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}, {"allowFractions": false, "variableReplacements": [], "maxValue": "a2/a3", "minValue": "a2/a3", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}], "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "gapfill"}, {"prompt": "<p></p>\n<p>$\\frac{\\var{b1}}{\\sqrt{\\var{b2}}}=$<fraction><numerator>[[0]]$\\sqrt{}$[[1]]</numerator><denominator>[[2]]</denominator></fraction></p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "gaps": [{"allowFractions": false, "variableReplacements": [], "maxValue": "b1/b3", "minValue": "b1/b3", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}, {"allowFractions": false, "variableReplacements": [], "maxValue": "b2", "minValue": "b2", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}, {"allowFractions": false, "variableReplacements": [], "maxValue": "b2/b3", "minValue": "b2/b3", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}], "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "gapfill"}, {"prompt": "<p>$\\frac{\\var{c1}}{\\sqrt{\\var{c2}}}=$<fraction><numerator>[[0]]$\\sqrt{}$[[1]]</numerator><denominator>[[2]]</denominator></fraction></p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "gaps": [{"vsetrangepoints": 5, "expectedvariablenames": [], "checkingaccuracy": 0.001, "vsetrange": [0, 1], "showpreview": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "scripts": {}, "answer": "{c1}", "marks": 1, "checkvariablenames": false, "checkingtype": "absdiff", "type": "jme"}, {"allowFractions": false, "variableReplacements": [], "maxValue": "{c2}", "minValue": "{c2}", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}, {"allowFractions": false, "variableReplacements": [], "maxValue": "c2", "minValue": "c2", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}], "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "gapfill"}, {"prompt": "<p>$\\frac{\\var{d4}\\sqrt{\\var{d1}}}{\\sqrt{\\var{d2}}}=$<fraction><numerator>[[0]]$\\sqrt{}$[[1]]</numerator><denominator>[[2]]</denominator></fraction></p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "gaps": [{"allowFractions": false, "variableReplacements": [], "maxValue": "d4/d3", "minValue": "d4/d3", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}, {"allowFractions": false, "variableReplacements": [], "maxValue": "d1*d2", "minValue": "d1*d2", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}, {"allowFractions": false, "variableReplacements": [], "maxValue": "d2/d3", "minValue": "d2/d3", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}], "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "gapfill"}, {"prompt": "<p>$\\frac{\\var{e1}\\sqrt{\\var{e2}}}{\\var{e3}\\sqrt{\\var{e4}}}=$<fraction><numerator>[[0]]$\\sqrt{}$[[1]]</numerator><denominator>[[2]]</denominator></fraction></p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "gaps": [{"allowFractions": false, "variableReplacements": [], "maxValue": "e1/e5", "minValue": "e1/e5", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}, {"allowFractions": false, "variableReplacements": [], "maxValue": "e2*e4", "minValue": "e2*e4", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}, {"allowFractions": false, "variableReplacements": [], "maxValue": "e3*e4/e5", "minValue": "e3*e4/e5", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}], "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "gapfill"}, {"prompt": "<p>$\\frac{\\var{f1}\\sqrt{\\var{f6}}}{\\var{f2}\\sqrt{\\var{f5}}}=$<fraction><numerator>[[0]]$\\sqrt{}$[[1]]</numerator><denominator>[[2]]</denominator></fraction></p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "gaps": [{"allowFractions": false, "variableReplacements": [], "maxValue": "(f7)^0.5", "minValue": "(f7)^0.5", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}, {"allowFractions": false, "variableReplacements": [], "maxValue": "(f4*f3)", "minValue": "(f4*f3)", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}, {"allowFractions": false, "variableReplacements": [], "maxValue": "f3", "minValue": "f3", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}], "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "gapfill"}], "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>", "variable_groups": [], "variablesTest": {"maxRuns": 100, "condition": "gcd({c1},{c2})=1"}, "variables": {"f1": {"definition": "random(2..5)", "templateType": "anything", "group": "Ungrouped variables", "name": "f1", "description": ""}, "f2": {"definition": "random(2..5 except f1)", "templateType": "anything", "group": "Ungrouped variables", "name": "f2", "description": ""}, "f3": {"definition": "random([2,3,5,7,11,13] except f2 except f1)", "templateType": "anything", "group": "Ungrouped variables", "name": "f3", "description": ""}, "f4": {"definition": "random([2,3,5,7] except f1 except f2 except f3)", "templateType": "anything", "group": "Ungrouped variables", "name": "f4", "description": ""}, "f5": {"definition": "f3*f1*f1", "templateType": "anything", "group": "Ungrouped variables", "name": "f5", "description": ""}, "f6": {"definition": "f8*f2*f2", "templateType": "anything", "group": "Ungrouped variables", "name": "f6", "description": ""}, "f7": {"definition": "random([4,9,16] except f3)", "templateType": "anything", "group": "Ungrouped variables", "name": "f7", "description": ""}, "f8": {"definition": "f4*f7", "templateType": "anything", "group": "Ungrouped variables", "name": "f8", "description": ""}, "b1": {"definition": "random(2..19)", "templateType": "anything", "group": "Ungrouped variables", "name": "b1", "description": ""}, "b2": {"definition": "random(2,3,5,6,7,10,11,13,14,15,17,19,21,23,22,26,29)", "templateType": "anything", "group": "Ungrouped variables", "name": "b2", "description": ""}, "b3": {"definition": "gcd(b2,b1)", "templateType": "anything", "group": "Ungrouped variables", "name": "b3", "description": ""}, "d4": {"definition": "random([4,6,10,12,14,20,22,26] except [2*d1])", "templateType": "anything", "group": "Ungrouped variables", "name": "d4", "description": ""}, "d2": {"definition": "d4/2", "templateType": "anything", "group": "Ungrouped variables", "name": "d2", "description": ""}, "d3": {"definition": "gcd(d4,d2)", "templateType": "anything", "group": "Ungrouped variables", "name": "d3", "description": ""}, "d1": {"definition": "random([2,3,5,7,11,13,17,19,23,29] except [c1])", "templateType": "anything", "group": "Ungrouped variables", "name": "d1", "description": ""}, "a1": {"definition": "random(2..19)", "templateType": "anything", "group": "Ungrouped variables", "name": "a1", "description": ""}, "a3": {"definition": "gcd(a1,a2)", "templateType": "anything", "group": "Ungrouped variables", "name": "a3", "description": ""}, "a2": {"definition": "random(2,3,5,6,7,10,11,13,14,15,17,19,21,23,22,26,29)", "templateType": "anything", "group": "Ungrouped variables", "name": "a2", "description": ""}, "e5": {"definition": "gcd(e1,e3*e4)", "templateType": "anything", "group": "Ungrouped variables", "name": "e5", "description": ""}, "e4": {"definition": "random([2,3,5,7] except [e2])", "templateType": "anything", "group": "Ungrouped variables", "name": "e4", "description": ""}, "c1": {"definition": "random(2,3,5,7,11,13,17,19,23,29)", "templateType": "anything", "group": "Ungrouped variables", "name": "c1", "description": ""}, "e1": {"definition": "random(2..9)", "templateType": "anything", "group": "Ungrouped variables", "name": "e1", "description": ""}, "e3": {"definition": "random(2..9)", "templateType": "anything", "group": "Ungrouped variables", "name": "e3", "description": ""}, "e2": {"definition": "random([2,3,5,7])", "templateType": "anything", "group": "Ungrouped variables", "name": "e2", "description": ""}, "c2": {"definition": "random([2,3,5,7,11,13,17,19,23,29] except [c1])", "templateType": "anything", "group": "Ungrouped variables", "name": "c2", "description": ""}}, "metadata": {"notes": "", "description": "", "licence": "Creative Commons Attribution 4.0 International"}, "type": "question", "showQuestionGroupNames": false, "question_groups": [{"name": "", "pickingStrategy": "all-ordered", "pickQuestions": 0, "questions": []}], "contributors": [{"name": "joshua boddy", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/557/"}]}]}], "contributors": [{"name": "joshua boddy", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/557/"}]}