// Numbas version: exam_results_page_options
{"name": "Copy of Q2 Adding and subtracting surds", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"name": "Copy of Q2 Adding and subtracting surds", "tags": [], "metadata": {"description": "<p>Adding and subtracting surds. Parts b) and c) involve simplification of surds.</p>", "licence": "Creative Commons Attribution 4.0 International"}, "statement": "<p>To include a square root sign in your answer use <code>sqrt()</code>. For example, to write $\\sqrt{3}$, type <code>sqrt(3)</code> into the answer box. If you are entering a number multiplied by the square root of some other number, for example $3\\sqrt{5}$, type <code>3sqrt(5)</code> into the answer box.</p>", "advice": "<h4></h4>\n<h4></h4>\n<p></p>\n<p><strong>a)</strong></p>\n<p>Simplify&nbsp; $\\simplify[!cancelTerms]{{d}sqrt({a}) - sqrt({a})+{n}sqrt({a})}$.</p>\n<p>The surds are all like surds, so we can collect like surds.</p>\n<p>$\\simplify[!cancelTerms]{{d}sqrt({a}) - sqrt({a})+{n}sqrt({a})={d-1+n}sqrt({a})}$.</p>\n<p></p>\n<p><strong>b)</strong></p>\n<p>$\\simplify[!cancelTerms]{{d}sqrt({a})&nbsp;+ sqrt({v^2*a})-sqrt({b^2*a})}$</p>\n<p>Look for factors of the surds which are square numbers&nbsp;&nbsp;( $4, 9, 16, 25, 36, 49, 64, 81, 100,&nbsp; ... $).</p>\n<p>In this question the second term has a square factor&nbsp; $\\var{v^2}$&nbsp; and the third term has a square factor&nbsp;&nbsp;$\\var{b^2}$.</p>\n<p>\\[<br/>\\begin{align}<br/>\\simplify[!cancelTerms]{{d}sqrt({a})&nbsp;+ sqrt({v^2*a})-sqrt({b^2*a})} &amp;= \\var{d}\\sqrt{\\var{a}}&nbsp;+&nbsp;(\\sqrt{\\simplify{{v}^2}} \\times \\sqrt{\\var{a}})-(\\sqrt{\\simplify{{b}^2}} \\times \\sqrt{\\var{a}}) \\\\<br/>&amp;= \\var{d}\\sqrt{\\var{a}} +\\var{v}\\sqrt{\\var{a}}-\\var{b}\\sqrt{\\var{a}} \\\\<br/>&amp;= \\simplify{({d}+{v}-{b})sqrt({a})} \\text{.}<br/>\\end{align}<br/>\\]</p>\n<p><strong>c)</strong></p>\n<p>\\[<br/>\\begin{align}<br/>\\simplify{{d}sqrt({a}) - {b}sqrt({v}^2{a})+{n}sqrt({b}^2*{a})} &amp;= \\var{d}\\sqrt{\\var{a}} - \\var{b}(\\sqrt{\\simplify{{v}^2}} \\times \\sqrt{\\var{a}})+\\var{n}(\\sqrt{\\simplify{{b}^2}} \\times \\sqrt{\\var{a}}) \\\\<br/>&amp;= \\var{d}\\sqrt{\\var{a}} -\\var{b}(\\simplify{{v}*sqrt({a})})+\\var{n}(\\simplify{{b}*sqrt({a})}) \\\\<br/> &amp;= \\simplify{{d}sqrt({a})}-\\simplify{{b}*{v}sqrt({a})}+\\simplify{{n}*{b}sqrt({a})} \\\\<br/> &amp;= \\simplify{({d}-{b}*{v}+{n}*{b})sqrt({a})} \\text{.}<br/>\\end{align}<br/>\\]</p>\n<h4></h4>", "rulesets": {}, "extensions": [], "variables": {"n": {"name": "n", "group": "Ungrouped variables", "definition": "random(3..10 #1)", "description": "", "templateType": "anything"}, "v": {"name": "v", "group": "Ungrouped variables", "definition": "random(2,3,5)", "description": "", "templateType": "anything"}, "d": {"name": "d", "group": "Ungrouped variables", "definition": "random(2..7 except 4)", "description": "", "templateType": "anything"}, "b": {"name": "b", "group": "Ungrouped variables", "definition": "random(2..5 #1 except v except sqrt(m^2*d) except 3)", "description": "", "templateType": "anything"}, "a": {"name": "a", "group": "Ungrouped variables", "definition": "random(2..11 #1 except 4 except 6 except 8 except 9 except 10 except v)  ", "description": "", "templateType": "anything"}, "m": {"name": "m", "group": "Ungrouped variables", "definition": "random(2..5 #1 except n^2)", "description": "", "templateType": "anything"}}, "variablesTest": {"condition": "n^2 > a", "maxRuns": 100}, "ungrouped_variables": ["d", "n", "b", "a", "v", "m"], "variable_groups": [], "functions": {}, "preamble": {"js": "", "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}\n"}, "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>Simplify $\\simplify[!cancelTerms]{{d}sqrt({a}) - sqrt({a})+{n}sqrt({a})}$.</p>\n<p>$\\simplify[!cancelTerms]{{d}sqrt({a}) - sqrt({a})+{n}sqrt({a})}$ =&nbsp;[[0]].</p>\n<p></p>", "gaps": [{"type": "jme", "useCustomName": false, "customName": "", "marks": "2", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "answer": "{(d-1+n)}sqrt({a})", "showPreview": true, "checkingType": "absdiff", "checkingAccuracy": 0.001, "failureRate": 1, "vsetRangePoints": 5, "vsetRange": [0, 1], "checkVariableNames": false, "singleLetterVariables": false, "allowUnknownFunctions": true, "implicitFunctionComposition": false, "mustmatchpattern": {"pattern": "(`+- $n;b `where (abs(b)<>1 and b<>0))`? *`+-sqrt($n;a) `where filter(x<2, x, factorise(a))=factorise(a) `| m_exactly(0)", "partialCredit": 0, "message": "You haven't fully simplified.", "nameToCompare": ""}, "valuegenerators": []}], "sortAnswers": false}, {"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>Simplify $\\simplify[!cancelTerms]{{d}sqrt({a})&nbsp;+ sqrt({v^2*a})-sqrt({b^2*a})}$.</p>\n<p>$\\simplify[!cancelTerms]{{d}sqrt({a})&nbsp;+ sqrt({v^2*a})-sqrt({b^2*a})}$=&nbsp;[[0]].</p>\n<p></p>", "gaps": [{"type": "jme", "useCustomName": false, "customName": "", "marks": "2", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "answer": "{(d+v-b)}sqrt({a})", "showPreview": true, "checkingType": "absdiff", "checkingAccuracy": 0.001, "failureRate": 1, "vsetRangePoints": 5, "vsetRange": [0, 1], "checkVariableNames": false, "singleLetterVariables": false, "allowUnknownFunctions": true, "implicitFunctionComposition": false, "mustmatchpattern": {"pattern": "(`+- $n;b `where (abs(b)<>1 and b<>0))`? *`+-sqrt($n;a) `where filter(x<2, x, factorise(a))=factorise(a) `| m_exactly(0)", "partialCredit": 0, "message": "You haven't fully simplified.", "nameToCompare": ""}, "valuegenerators": []}], "sortAnswers": false}, {"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>Simplify $\\simplify{{d}sqrt({a}) - {b}sqrt({v}^2*{a})+{n}sqrt({b}^2*{a})}$.</p>\n<p>$\\simplify{{d}sqrt({a}) - {b}sqrt({v}^2*{a})+{n}sqrt({b}^2*{a})} =$ [[0]].</p>\n<p></p>", "gaps": [{"type": "jme", "useCustomName": false, "customName": "", "marks": "2", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "answer": "{(d-b*v+n*b)}sqrt({a})", "showPreview": true, "checkingType": "absdiff", "checkingAccuracy": 0.001, "failureRate": 1, "vsetRangePoints": 5, "vsetRange": [0, 1], "checkVariableNames": false, "singleLetterVariables": false, "allowUnknownFunctions": true, "implicitFunctionComposition": false, "mustmatchpattern": {"pattern": "(`+- $n;b `where (abs(b)<>1 and b<>0))`? *`+-sqrt($n;a) `where filter(x<2, x, factorise(a))=factorise(a) `| m_exactly(0)", "partialCredit": 0, "message": "You haven't fully simplified.", "nameToCompare": ""}, "valuegenerators": []}], "sortAnswers": false}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always", "contributors": [{"name": "Christian Lawson-Perfect", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/7/"}, {"name": "Elliott Fletcher", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/1591/"}, {"name": "Jim Pettigrew", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2037/"}, {"name": "Adelle Colbourn", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2083/"}]}]}], "contributors": [{"name": "Christian Lawson-Perfect", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/7/"}, {"name": "Elliott Fletcher", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/1591/"}, {"name": "Jim Pettigrew", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2037/"}, {"name": "Adelle Colbourn", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2083/"}]}